% This file is part of MetaPost. The MetaPost program is in the public domain.

@* Nota bene.

This is not the official reference library but a version meant for \LUAMETATEX\
in combination with \METAFUN, which is integrated in \CONTEXT. When the original
gets improved I will diff the progression of the original \CWEB\ files and merge
improvements.

I'm pretty sure that the \TEX part of this file doesn't process but I'll look into
that later. The comments are kept as they were but there are occasional remakts
because we changes some bits and pieces. The references to properties, variables,
constants etc, are mostly kept. I due time I'll fix it and see if I can render
the file, but for not it's okay to just read the comments. I admit that I check
things in Visual Studio anyway, which is why there are now |enum| used.

This split is needed because the original library is the one used for \METAPOST\
the program which is used by DEK, and I don't want to mess up his workflow. At
some point I might emulate \METAPOST\ but I might as well decide to remove the
interaction completely from this variant. It al depends on the outcome of
experiments that Alan and I conduct, and as it's done in free time, it will take
while. Don't push us, don't nag, don't complain. The original library is where
the support is concentrated and you can always use that with the \MKIV\ macros.

Todo: check typecasts, the halfword and quarterwords are now integers.
Todo: Move more variables into the scope that they're used.
Todo: Remove some (int) cast that are left overs from quarterword.
Todo: Remove unused variables ... postpone more padding till that is done.
Todo: Support color in group objects

Because we don't want macros to clash with fields in record, setters and getters
are prefixed by |mp_|. In order not clash with typedefs and accessors, in some
cases |mp_get_| and |mp_set_| are used (eventually that might be true for all
these cases). The |mp_free_| functions are complemented by |mp_new_| functions.
In \MPLIB\ 2 |mp_get_| is used instead so keep that in mind when comparing the
sources. I might also pass |mp| to all macros, just for consistency.

To be considered: use the same record for rgb and cmyk (less code eventually).

In order to make extensions a bit easier (and also because of consistency in
enumerations, some _token and _sym and similar specifiers have been made _command
(it was already somewhat inconsistent anyway). When something gets compared to
cur_cmd it makes sense to use _command anyway.

% some (int) can go

(Hans Hagen, 2019+)

@* Comment.

At some point Taco Hoekwater brilliantly converted \MP\ into a library. Since
then usage and integration of \METAPOST\ in \CONTEXT\ went even further than
before. There were some backends added for \SVG\ and \PNG, and several number
systems could be used. This was quite an effort! The \MP\ program became a
wrapper around this library.

The library is also used in \LUATEX\ but there we don't need the backend code at
all. Also, having the traditional \TFM\ generating code (inherited from \MF)
makes not much sense because we now live in an \OPENTYPE\ universum and the hard
coded 256 limitations were even for \TYPEONE\ not okay. The GUST font team use
their own tools around \MP\ anyway.

This variant (below) is therefore a stripped down library. Everything related to
loading fonts is gone, and if a \PS\ backend is needed the functionality has to
go into its own module (as with \SVG\ and \PNG). This means that code removed
here has to go there. One problen then is that the output primitives have to be
brought in too, but in good \CWEB\ practices, that then can be done via change
files (basically extending the data structures and such).

However, a more modern variant could be to just use the library with \LUA,
produce \PDF\ and convert that to any format needed. This is what we do in
\CONTEXT. After a decade of usage I like to change a few interface aspects so
here this happens.

So: this variant is {\em not} the official \MP\ library but one meant for usage
in \LUAMETATEX\ and experiments by Alan Braslau and Hans Hagen for more advanced
graphics, produced by cooperation between \LUA\ and \MP. This strategy permits
experiments without interference with the full blown version. Of course we can
retrofit interesting extensions into its larger version at some point. It's all a
work of love, done in our own time, so don't push our agenda in this.

Stripping is easier than adding and the things I added were not at the level of
the language or processing but the interface to \LUA\ as well as some details of
text processing. Some more of that might happen. For instance, all file \IO\ now
goes via \LUA\ so we assume the callbacks being set.

On my agenda are to delegate printing of messages and errors to the plugin. Also
filenames might be done differently. Messages are already normalized.

As a start the psout.w file was stripped and turned into a mpcommon.w file. This
means that the old \PS\ output code is no longer there. Because that file got
small it eventually got merged in here which (1) permits some reshuffling and (2)
gives room for optimizing the interface to \LUA\ (do we need the indirectness?).

Quite some code has been stripped because we assume that \LUA\ can provide these
features: file io, logging, management, error handling, etc. This saves quite a
bit of code and also detangles a bit the mixed program vs. library code. For now
the \quote {terminal} approach is kept.

In the process I reformatted the source a bit. Sorry. It is no big deal because
it looks like \METAPOST\ is not evolving, but what does evolve is the code here:
scanners and more access, to mention a few. I've added braces so that comments
can go with single statements and there can be no doubt when \WEB\ macros are
used (some braces could go there. More variables will become local (to branches
for instance). Messages are done more directly, etc. etc. One of the reasons for
doing that is that it looks nicer in Visual Studio. There it helps to move some
variables to a more local scope. Of course a side effect is that backporting is
now no longer an option. In some cases redundant braces were removed (when it's
clear in the w file) and some else statements have been added where confusion
takes place because that one doesn't return (so compilers can for instance warn
about uninitialized pointers). I made sure that the resulting code is readable
in visual studio.

Work in progress: prefix with mp_ so that macros don't clash with fields and we
can get rid of _ hackery.

Maybe some day: zpair zpath zdraw ztransform: just add an extra z dimension
to the existing data types which makes it compatible too.

Todo: consider double only
Todo: use documented c
Todo: rework some (more) helpers

Todo: center
Todo: centerofmass
Todo: ceiling x
Todo: x div y
Todo: x mod y
Todo: dir x
Todo: unitvector

(Hans Hagen, 2019+)

@* Introduction.

This is \MP\ by John Hobby, a graphics-language processor based on D. E. Knuth's
\MF.

Much of the original Pascal version of this program was copied with permission
from MF.web Version 1.9. It interprets a language very similar to D.E. Knuth's
METAFONT, but with changes designed to make it more suitable for PostScript
output.

The main purpose of the following program is to explain the algorithms of \MP\ as
clearly as possible. However, the program has been written so that it can be
tuned to run efficiently in a wide variety of operating environments by making
comparatively few changes. Such flexibility is possible because the documentation
that follows is written in the |WEB| language, which is at a higher level than
C.

A large piece of software like \MP\ has inherent complexity that cannot be
reduced below a certain level of difficulty, although each individual part is
fairly simple by itself. The |WEB| language is intended to make the algorithms
as readable as possible, by reflecting the way the individual program pieces fit
together and by providing the cross-references that connect different parts.
Detailed comments about what is going on, and about why things were done in
certain ways, have been liberally sprinkled throughout the program. These
comments explain features of the implementation, but they rarely attempt to
explain the \MP\ language itself, since the reader is supposed to be familiar
with {\em The \METAFONT\ book} as well as the manual @.WEB@> @:METAFONTbook}{\sl
The {\logos METAFONT}book@> {\em A User's Manual for \METAPOST}, Computing
Science Technical Report 162, AT\AM T Bell Laboratories.

@ The present implementation is a preliminary version, but the possibilities for
new features are limited by the desire to remain as nearly compatible with \MF\
as possible.

On the other hand, the |WEB| description can be extended without changing the
core of the program, and it has been designed so that such extensions are not
extremely difficult to make. The |banner| string defined here should be changed
whenever \MP\ undergoes any modifications, so that it will be clear which version
of \MP\ might be the guilty party when a problem arises. @^extensions to \MP@>
@^system dependencies@>

At some point I started adding features to the library (think of stacking) but
the more interesting additions came when Mikael Sundqvist and we side tracked from
extending math at the \TEX\ end to more \METAFUN: intersection lists, arctime
lists, path iteration, a few more helpers, some fixes, a bit more control, access
to previously hidden functionality, appended paths, etc. And there is undoubtly
more to come. As with all \LUATEX\ and \LUAMETATEX\ development, most gets
explained in the history documents in the \CONTEXT\ distribution and articles. It
was around version 3.14 (end May 2022).

@d default_banner "This is MPLIB for LuaMetaTeX, version 3.14"

@<Metapost version header@>=
# define metapost_version "3.14"

@ We used to have three header files: common, mpmp and mplib, but there ws some
(growing) dependency on the one hand and we decided to target just \LUAMETATEX\
on the other. After all, this is a special version. So, we now have one header
file only. The variables from |MP_options| are included inside the |MP_instance|
wholesale. This also permits some further stripping. Actually we can probably
get rid of the intermediate \POSTSCRIPT\ representation or add a little more
abstraction.

@(mp.h@>=
# ifndef MP_H
# define MP_H 1

# include "avl.h"
# include "auxmemory.h"
# include <string.h>
# include <setjmp.h>

@<Metapost version header@>
typedef struct MP_instance *MP;
@<Exported types@>
typedef struct MP_options {
    @<Option variables@>
} MP_options;
@<Exported function headers@>
@<MPlib header stuff@>
@<Declare helpers@>
@<Enumeration types@>
@<Types in the outer block@>
@<Constants in the outer block@>
typedef struct MP_instance {
    @<Option variables@>
    @<Global variables@>
} MP_instance;
@<Internal library declarations@>
@<MPlib internal header stuff@>
@<MPlib export header stuff@>
# endif

@ @c
# include "mpconfig.h"
# include "mp.h"
# include "mpmath.h"
# include "mpmathdouble.h"
# include "mpmathbinary.h"
# include "mpmathdecimal.h"
# include "mpstrings.h"

@h @<Declarations@>
@<Error handling procedures@>

@ Here are the functions that set up the \MP\ instance.

@<Declarations@>=
MP_options *mp_options    (void);
MP          mp_initialize (MP_options * opt);

@ @c
MP_options *mp_options (void)
{
    MP_options *opt = mp_memory_clear_allocate(sizeof(MP_options));
    return opt;
}

@ The whole instance structure is initialized with zeroes, this greatly reduces
the number of statements needed in the |Allocate or initialize variables| block.

@c
static MP mp_do_new (jmp_buf *buf)
{
    MP mp = mp_memory_clear_allocate(sizeof(MP_instance));
    if (mp == NULL) {
        mp_memory_free(buf);
        return NULL;
    } else {
        mp->jump_buf = buf;
        return mp;
    }
}

static void mp_free (MP mp)
{
    @<Dealloc variables@>
    @<Finish non-interactive use@>
    mp_memory_free(mp->jump_buf);
    @<Free table entries@>
    free_math();
    mp_memory_free(mp);
}

static void mp_do_initialize (MP mp)
{
    @<Set initial values of key variables@>
}

@ For the retargetable math library, we need to have a pointer, at least.

@<Global variables@>=
math_data *math;

@ @<Exported types@>=
typedef enum mp_number_type {
    mp_nan_type,
    mp_scaled_type,
    mp_fraction_type,
    mp_angle_type,
    mp_double_type,
    mp_binary_type,
    mp_decimal_type
} mp_number_type;

typedef union mp_number_store {
    void   *num;
    double  dval;
    int     val;
} mp_number_store;

typedef struct mp_number_data {
    mp_number_store data;
    mp_number_type  type;
} mp_number_data;

typedef struct mp_number_data mp_number;

# define is_number(A) ((A).type != mp_nan_type)

@ Switching to also passing pointers for the origins made the \LUAMETATEX\ binary
go down from 3061799 bytes to 2960091 bytes (mid May 2022).

We have a few more helpers for cloning: |negated| and |abs| because these happen
often and it saves some lines of code in already long functions.

@<Types in the outer block@>=
typedef void   (*convert_func)                      (mp_number *r);
typedef void   (*m_log_func)                        (MP mp, mp_number *r, mp_number *a);
typedef void   (*m_exp_func)                        (MP mp, mp_number *r, mp_number *a);
typedef void   (*m_unif_rand_func)                  (MP mp, mp_number *ret, mp_number *x_orig);
typedef void   (*m_norm_rand_func)                  (MP mp, mp_number *ret);
typedef void   (*pyth_add_func)                     (MP mp, mp_number *r, mp_number *a, mp_number *b);
typedef void   (*pyth_sub_func)                     (MP mp, mp_number *r, mp_number *a, mp_number *b);
typedef void   (*power_of_func)                     (MP mp, mp_number *r, mp_number *a, mp_number *b);
typedef void   (*n_arg_func)                        (MP mp, mp_number *r, mp_number *a, mp_number *b);
typedef void   (*velocity_func)                     (MP mp, mp_number *r, mp_number *a, mp_number *b, mp_number *c, mp_number *d, mp_number *e);
typedef int    (*ab_vs_cd_func)                     (mp_number *a, mp_number *b, mp_number *c, mp_number *d);
typedef void   (*crossing_point_func)               (MP mp, mp_number *r, mp_number *a, mp_number *b, mp_number *c);
typedef void   (*number_from_int_func)              (mp_number *A, int B);
typedef void   (*number_from_boolean_func)          (mp_number *A, int B);
typedef void   (*number_from_scaled_func)           (mp_number *A, int B);
typedef void   (*number_from_double_func)           (mp_number *A, double B);
typedef void   (*number_from_addition_func)         (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_half_from_addition_func)    (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_from_subtraction_func)      (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_half_from_subtraction_func) (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_from_div_func)              (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_from_mul_func)              (mp_number *A, mp_number *B, mp_number *C);
typedef void   (*number_from_int_div_func)          (mp_number *A, mp_number *B, int C);
typedef void   (*number_from_int_mul_func)          (mp_number *A, mp_number *B, int C);
typedef void   (*number_from_oftheway_func)         (MP mp, mp_number *A, mp_number *t, mp_number *B, mp_number *C);
typedef void   (*number_negate_func)                (mp_number *A);
typedef void   (*number_add_func)                   (mp_number *A, mp_number *B);
typedef void   (*number_subtract_func)              (mp_number *A, mp_number *B);
typedef void   (*number_modulo_func)                (mp_number *A, mp_number *B);
typedef void   (*number_half_func)                  (mp_number *A);
typedef void   (*number_double_func)                (mp_number *A);
typedef void   (*number_abs_func)                   (mp_number *A);
typedef void   (*number_clone_func)                 (mp_number *A, mp_number *B);
typedef void   (*number_negated_clone_func)         (mp_number *A, mp_number *B);
typedef void   (*number_abs_clone_func)             (mp_number *A, mp_number *B);
typedef void   (*number_swap_func)                  (mp_number *A, mp_number *B);
typedef void   (*number_add_scaled_func)            (mp_number *A, int b);
typedef void   (*number_multiply_int_func)          (mp_number *A, int b);
typedef void   (*number_divide_int_func)            (mp_number *A, int b);
typedef int    (*number_to_int_func)                (mp_number *A);
typedef int    (*number_to_boolean_func)            (mp_number *A);
typedef int    (*number_to_scaled_func)             (mp_number *A);
typedef int    (*number_round_func)                 (mp_number *A);
typedef void   (*number_floor_func)                 (mp_number *A);
typedef double (*number_to_double_func)             (mp_number *A);
typedef int    (*number_odd_func)                   (mp_number *A);
typedef int    (*number_equal_func)                 (mp_number *A, mp_number *B);
typedef int    (*number_less_func)                  (mp_number *A, mp_number *B);
typedef int    (*number_greater_func)               (mp_number *A, mp_number *B);
typedef int    (*number_nonequalabs_func)           (mp_number *A, mp_number *B);
typedef void   (*make_scaled_func)                  (MP mp, mp_number *ret, mp_number *A, mp_number *B);
typedef void   (*make_fraction_func)                (MP mp, mp_number *ret, mp_number *A, mp_number *B);
typedef void   (*take_fraction_func)                (MP mp, mp_number *ret, mp_number *A, mp_number *B);
typedef void   (*take_scaled_func)                  (MP mp, mp_number *ret, mp_number *A, mp_number *B);
typedef void   (*sin_cos_func)                      (MP mp, mp_number *A, mp_number *S, mp_number *C);
typedef void   (*slow_add_func)                     (MP mp, mp_number *A, mp_number *S, mp_number *C);
typedef void   (*sqrt_func)                         (MP mp, mp_number *ret, mp_number *A);
typedef void   (*init_randoms_func)                 (MP mp, int seed);
typedef void   (*allocate_number_func)              (MP mp, mp_number *A, mp_number_type t);
typedef void   (*allocate_number_clone_func)        (MP mp, mp_number *A, mp_number_type t, mp_number *B);
typedef void   (*allocate_number_abs_func)          (MP mp, mp_number *A, mp_number_type t, mp_number *B);
typedef void   (*allocate_number_double_func)       (MP mp, mp_number *A, double B);
typedef void   (*free_number_func)                  (MP mp, mp_number *n);
typedef void   (*fraction_to_round_scaled_func)     (mp_number *n);
typedef void   (*print_func)                        (MP mp, mp_number *A);
typedef char  *(*tostring_func)                     (MP mp, mp_number *A);
typedef void   (*scan_func)                         (MP mp, int A);
typedef void   (*mp_free_func)                      (MP mp);
typedef void   (*set_precision_func)                (MP mp);

/*
    We use a prefix |md_| so that we don't get complaints about recursive macro
    definitions. This is cleaner than redefining the macros.
*/

typedef struct math_data {
    mp_number                         md_precision_default;
    mp_number                         md_precision_max;
    mp_number                         md_precision_min;
    mp_number                         md_epsilon_t;
    mp_number                         md_inf_t;
    mp_number                         md_negative_inf_t;
    mp_number                         md_one_third_inf_t;
    mp_number                         md_zero_t;
    mp_number                         md_unity_t;
    mp_number                         md_two_t;
    mp_number                         md_three_t;
    mp_number                         md_half_unit_t;
    mp_number                         md_three_quarter_unit_t;
    mp_number                         md_fraction_one_t;
    mp_number                         md_fraction_half_t;
    mp_number                         md_fraction_three_t;
    mp_number                         md_fraction_four_t;
    mp_number                         md_one_eighty_deg_t;
    mp_number                         md_negative_one_eighty_deg_t;
    mp_number                         md_three_sixty_deg_t;
    mp_number                         md_one_k;
    mp_number                         md_sqrt_8_e_k;
    mp_number                         md_twelve_ln_2_k;
    mp_number                         md_coef_bound_k;
    mp_number                         md_coef_bound_minus_1;
    mp_number                         md_twelvebits_3;
    mp_number                         md_arc_tol_k;
    mp_number                         md_twentysixbits_sqrt2_t;
    mp_number                         md_twentyeightbits_d_t;
    mp_number                         md_twentysevenbits_sqrt2_d_t;
    mp_number                         md_fraction_threshold_t;
    mp_number                         md_half_fraction_threshold_t;
    mp_number                         md_scaled_threshold_t;
    mp_number                         md_half_scaled_threshold_t;
    mp_number                         md_near_zero_angle_t;
    mp_number                         md_p_over_v_threshold_t;
    mp_number                         md_equation_threshold_t;
    mp_number                         md_warning_limit_t;
    allocate_number_func              md_allocate;
    allocate_number_clone_func        md_allocate_clone;
    allocate_number_abs_func          md_allocate_abs;
    allocate_number_double_func       md_allocate_double;
    free_number_func                  md_free;
    number_from_int_func              md_from_int;
    number_from_boolean_func          md_from_boolean;
    number_from_scaled_func           md_from_scaled;
    number_from_double_func           md_from_double;
    number_from_addition_func         md_from_addition;
    number_half_from_addition_func    md_half_from_addition;
    number_from_subtraction_func      md_from_subtraction;
    number_half_from_subtraction_func md_half_from_subtraction;
    number_from_div_func              md_from_div;
    number_from_mul_func              md_from_mul;
    number_from_int_div_func          md_from_int_div;
    number_from_int_mul_func          md_from_int_mul;
    number_from_oftheway_func         md_from_oftheway;
    number_negate_func                md_negate;
    number_add_func                   md_add;
    number_subtract_func              md_subtract;
    number_half_func                  md_half;
    number_modulo_func                md_modulo;
    number_double_func                md_do_double;
    number_abs_func                   md_abs;
    number_clone_func                 md_clone;
    number_negated_clone_func         md_negated_clone;
    number_abs_clone_func             md_abs_clone;
    number_swap_func                  md_swap;
    number_add_scaled_func            md_add_scaled;
    number_multiply_int_func          md_multiply_int;
    number_divide_int_func            md_divide_int;
    number_to_int_func                md_to_int;
    number_to_boolean_func            md_to_boolean;
    number_to_scaled_func             md_to_scaled;
    number_to_double_func             md_to_double;
    number_odd_func                   md_odd;
    number_equal_func                 md_equal;
    number_less_func                  md_less;
    number_greater_func               md_greater;
    number_nonequalabs_func           md_nonequalabs;
    number_round_func                 md_round_unscaled;
    number_floor_func                 md_floor_scaled;
    make_scaled_func                  md_make_scaled;
    make_fraction_func                md_make_fraction;
    take_fraction_func                md_take_fraction;
    take_scaled_func                  md_take_scaled;
    velocity_func                     md_velocity;
    ab_vs_cd_func                     md_ab_vs_cd;
    crossing_point_func               md_crossing_point;
    n_arg_func                        md_n_arg;
    m_log_func                        md_m_log;
    m_exp_func                        md_m_exp;
    m_unif_rand_func                  md_m_unif_rand;
    m_norm_rand_func                  md_m_norm_rand;
    pyth_add_func                     md_pyth_add;
    pyth_sub_func                     md_pyth_sub;
    power_of_func                     md_power_of;
    fraction_to_round_scaled_func     md_fraction_to_round_scaled;
    convert_func                      md_fraction_to_scaled;
    convert_func                      md_scaled_to_fraction;
    convert_func                      md_scaled_to_angle;
    convert_func                      md_angle_to_scaled;
    init_randoms_func                 md_init_randoms;
    sin_cos_func                      md_sin_cos;
    sqrt_func                         md_sqrt;
    slow_add_func                     md_slow_add;
    print_func                        md_print;
    tostring_func                     md_tostring;
    scan_func                         md_scan_numeric;
    scan_func                         md_scan_fractional;
    mp_free_func                      md_free_math;
    set_precision_func                md_set_precision;
} math_data;

@ This procedure gets things started properly.

@c
MP mp_initialize (MP_options * opt)
{
    MP mp;
    jmp_buf *buf = mp_memory_allocate(sizeof(jmp_buf));
    if (buf == NULL || setjmp(*buf) != 0) {
        return NULL;
    }
    mp = mp_do_new(buf);
    if (mp == NULL) {
        return NULL;
    }
    if (opt->job_name == NULL || ! *(opt->job_name)) {
        return NULL;
    }
    mp->job_name   = mp_strdup(opt->job_name);
    mp->userdata   = opt->userdata;
    mp->extensions = opt->extensions;
    @<Set default function pointers@>

    mp->find_file       = opt->find_file       ? opt->find_file       : mp_find_file      ;
    mp->open_file       = opt->open_file       ? opt->open_file       : mp_open_file      ;
    mp->read_file       = opt->read_file       ? opt->read_file       : mp_read_file      ;
    mp->close_file      = opt->close_file      ? opt->close_file      : mp_close_file     ;
    mp->write_file      = opt->write_file      ? opt->write_file      : mp_write_file     ;
    mp->shipout_backend = opt->shipout_backend ? opt->shipout_backend : mp_shipout_backend;
    mp->run_script      = opt->run_script      ? opt->run_script      : mp_run_script     ;
    mp->run_internal    = opt->run_internal    ? opt->run_internal    : mp_run_internal   ;
    mp->run_logger      = opt->run_logger      ? opt->run_logger      : mp_run_logger     ;
    mp->run_overload    = opt->run_overload    ? opt->run_overload    : mp_run_overload   ;
    mp->run_error       = opt->run_error       ? opt->run_error       : mp_run_error      ;
    mp->run_warning     = opt->run_warning     ? opt->run_warning     : mp_run_warning    ;
    mp->make_text       = opt->make_text       ? opt->make_text       : mp_make_text      ;

    mp->find_file_id    = opt->find_file_id;
    mp->run_script_id   = opt->run_script_id;
    mp->run_internal_id = opt->run_internal_id;
    mp->run_logger_id   = opt->run_logger_id;
    mp->run_overload_id = opt->run_overload_id;
    mp->run_error_id    = opt->run_error_id;
    mp->run_warning_id  = opt->run_warning_id;
    mp->make_text_id    = opt->make_text_id;
    mp->open_file_id    = opt->open_file_id;

    if (opt->banner && *(opt->banner)) {
        mp->banner = mp_strdup(opt->banner);
    } else {
        mp->banner = mp_strdup(default_banner);
    }
    switch (opt->math_mode) {
        case mp_math_scaled_mode:
            mp->math = mp_initialize_scaled_math(mp);
            break;
        case mp_math_decimal_mode:
            mp->math = mp_initialize_decimal_math(mp);
            break;
        case mp_math_binary_mode:
            mp->math = mp_initialize_binary_math(mp);
            break;
        default:
            mp->math = mp_initialize_double_math(mp);
            break;
    }
    @<Allocate or initialize variables@>
    mp_reallocate_paths(mp, 1000);
    /* in case we quit during initialization: */
    mp->history = mp_fatal_error_stop;
    mp_do_initialize(mp);
    /* initialize the tables */
    mp_init_tab(mp);
    switch (opt->math_mode) {
        case mp_math_scaled_mode:
            set_internal_string(mp_number_system_internal, mp_intern(mp, "scaled"));
            break;
        case mp_math_decimal_mode:
            set_internal_string(mp_number_system_internal, mp_intern(mp, "decimal"));
            break;
        case mp_math_binary_mode:
            set_internal_string(mp_number_system_internal, mp_intern(mp, "binary"));
            break;
        default:
            set_internal_string(mp_number_system_internal, mp_intern(mp, "double"));
            break;
    }
    /* call |primitive| for each primitive */
    mp_init_prim(mp);
    mp_fix_date_and_time(mp);
    mp->history = mp_spotless;
    set_precision();
    @<Fix up |job_name|@>
    return mp;
}

@ @<Exported function headers@>=
extern MP_options *mp_options    (void);
extern MP          mp_initialize (MP_options * opt);
extern int         mp_status     (MP mp);
extern int         mp_finished   (MP mp);
extern void       *mp_userdata   (MP mp);

@ @c
int   mp_status   (MP mp) { return mp->history; }
int   mp_finished (MP mp) { return mp->finished; }
void *mp_userdata (MP mp) { return mp->userdata; }

@ The overall \MP\ program begins with the heading just shown, after which comes
a bunch of procedure declarations and function declarations. Finally we will get
to the main program, which begins with the comment |start_here|. If you want to
skip down to the main program now, you can look up |start_here| in the index. But
the author suggests that the best way to understand this program is to follow
pretty much the order of \MP's components as they appear in the \CWEB\
description you are now reading, since the present ordering is intended to
combine the advantages of the \quote {bottom up} and \quote {top down} approaches
to the problem of understanding a somewhat complicated system.

@ The following parameters can be changed at compile time to extend or reduce
\MP's capacity. @^system dependencies@>

@<Constants...@>=
# define bistack_size 1500  /* size of stack for bisection algorithms;  should
                               probably be left at this value */

@ Like the preceding parameters, the following quantities can be changed to
extend or reduce \MP's capacity.

@ @<Glob...@>=
int max_in_open;   /* maximum number of input files and error insertions that can
                      be going on simultaneously */
int param_size;    /* maximum number of simultaneous macro parameters */
int padding_size;  /* so that the next array nicely sits in the cache */

@ @<Option variables@>=
int   halt_on_error;   /* do we quit at the first error? */
void *userdata;        /* this allows the calling application to setup local (e.g. L for Lua) */
char *banner;          /* the banner that is printed to the screen and log */
int   utf8_mode;
int   text_mode;
int   show_mode;

@ @<Dealloc variables@>=
mp_memory_free(mp->banner);

@ @<Allocate or ...@>=
mp->param_size      = 4;
mp->max_in_open     = 0;
mp->halt_on_error   = opt->halt_on_error ? 1 : 0;
mp->utf8_mode       = opt->utf8_mode     ? 1 : 0;
mp->text_mode       = opt->text_mode     ? 1 : 0;
mp->show_mode       = opt->show_mode     ? 1 : 0;

@ Here are some macros for common programming idioms (incr and decr are now
inlined).

@d odd(A) (abs(A) % 2 == 1) /* replaced by proper number_odd calls, tex has: ((x) & 1) */

@* The character set.

@ We assume proper ASCII codes to be used and likely UTF-8 so we dropped the two
way mapping from input to internal and from internal to to output (actually that
mapping was not that robust because some strings bypassed the conversions).

@* Input and output.

The bane of portability is the fact that different operating systems treat input
and output quite differently, perhaps because computer scientists have not given
sufficient attention to this problem. People have felt somehow that input and
output are not part of \quote {real} programming. Well, it is true that some kinds of
programming are more fun than others. With existing input/output conventions
being so diverse and so messy, the only sources of joy in such parts of the code
are the rare occasions when one can find a way to make the program a little less
bad than it might have been. We have two choices, either to attack I/O now and
get it over with, or to postpone I/O until near the end. Neither prospect is very
attractive, so let's get it over with.

The basic operations we need to do are (1)~inputting and outputting of text, to
or from a file or the user's terminal; (2)~inputting and outputting of eight-bit
bytes, to or from a file; (3)~instructing the operating system to initiate \quote
{open} or to terminate \quote {close} input or output from a specified file;
(4)~testing whether the end of an input file has been reached; (5)~display of
bits on the user's screen. The bit-display operation will be discussed in a later
section; we shall deal here only with more traditional kinds of I/O.

@ Finding files happens in a slightly roundabout fashion: the \MP\ instance
object contains a field that holds a function pointer that finds a file, and
returns its name, or NULL. For this, it receives three parameters: the
non-qualified name |fname|, the intended |fopen| operation type |fmode|, and the
type of the file |ftype|.

The file types that are passed on in |ftype| can be used to differentiate file
searches if a library like kpathsea is used, the fopen mode is passed along for
the same reason.

@ @<Exported types@>=
enum mp_filetype {
    mp_filetype_terminal, /* the terminal (input) */
    mp_filetype_program,  /* \MP\ language input */
    mp_filetype_text      /* first text file for readfrom and writeto primitives */
};

typedef char *(*mp_file_finder)     (MP, const char *, const char *, int);
typedef char *(*mp_script_runner)   (MP, const char *m, size_t len, int n);
typedef void  (*mp_internal_runner) (MP, int action, int n, int type, const char *iname);
typedef void  (*mp_log_runner)      (MP, int, const char *s, size_t l);
typedef int   (*mp_overload_runner) (MP, int, const char *, int);
typedef void  (*mp_error_runner)    (MP, const char *, const char *, int);
typedef void  (*mp_warning_runner)  (MP, const char *);
typedef char *(*mp_text_maker)      (MP, const char *, size_t, int);
typedef void *(*mp_file_opener)     (MP, const char *, const char *, int);
typedef char *(*mp_file_reader)     (MP, void *, size_t *);
typedef void  (*mp_file_closer)     (MP, void *);
typedef int   (*mp_file_eoftest)    (MP, void *);
typedef void  (*mp_file_flush)      (MP, void *);
typedef void  (*mp_file_writer)     (MP, void *, const char *);

@ @<Option variables@>=
mp_file_finder     find_file;
mp_script_runner   run_script;
mp_internal_runner run_internal;
mp_log_runner      run_logger;
mp_overload_runner run_overload;
mp_error_runner    run_error;
mp_warning_runner  run_warning;
mp_text_maker      make_text;
mp_file_opener     open_file;
mp_file_closer     close_file;
mp_file_reader     read_file;
mp_file_writer     write_file;

int find_file_id;
int run_script_id;
int run_internal_id;
int run_logger_id;
int run_overload_id;
int run_error_id;
int run_warning_id;
int make_text_id;
int open_file_id;

@ The default function for finding files is |mp_find_file|. It is pretty stupid:
it will only find files in the current directory.

@c
static char *mp_find_file (MP mp, const char *fname, const char *fmode, int ftype)
{
    (void) mp; (void) fname; (void) fmode; (void) ftype;
    mp_fatal_error(mp, "no 'find_file' callback set");
    return NULL;
}

static char *mp_run_script (MP mp, const char *str, size_t len, int n)
{
    (void) mp; (void) str; (void) len; (void) n;
    mp_fatal_error(mp, "no 'run_script' callback set");
    return NULL;
}

void mp_run_internal (MP mp, int action, int n, int type, const char *iname)
{
    (void) mp; (void) action; (void) n; (void) type; (void) iname;
    mp_fatal_error(mp, "no 'run_internal' callback set");
}

@ The logger has to deal with the console and the log file and gets information
about the target.

@c
static void mp_run_logger (MP mp, int target, const char *s, size_t l)
{
    (void) mp; (void) target; (void) s; (void) l;
    mp_fatal_error(mp, "no 'run_logger' callback set");
}


@ The overload catch is responsible for its own reporting and quitting
if needed. The check only happens when the mode is set.

@c
static int mp_run_overload (MP mp, int property, const char *str, int mode)
{
    (void) mp; (void) property; (void) str; (void) mode;
    mp_fatal_error(mp, "no 'run_overload' callback set");
    return 0;
}

static void mp_check_overload (MP mp, mp_sym p)
{
    /* not the fastest check */
    if (number_nonzero(internal_value(mp_overloadmode_internal))) {
        if (mp->run_overload(mp, p->property, (const char *) p->text->str, number_to_int(internal_value(mp_overloadmode_internal)))) {
            p->property = 0;
        } else {
            /* we keep the property */
        }
    } else {
        /* we reset the mode */
        p->property = 0;
    }
}

@ Error and warning handling can be delegated too. Warnings are not really used yet
but they might show up some day.

@c
static void mp_run_error (MP mp, const char *msg, const char *hlp, int interaction)
{
    (void) mp; (void) msg; (void) hlp; (void) interaction;
    mp_fatal_error(mp, "no 'run_error' callback set");
}

static void mp_run_warning (MP mp, const char *msg)
{
    (void) mp; (void) msg;
    mp_fatal_error(mp, "no 'run_warning' callback set");
}

@ The |btex ... etex| handling is still present and depends on a callback and
some cooperation with the backend. In \CONTEXT\ we implements text objects as
paths with properties (pre- and postscripts).

@c
static char *mp_make_text (MP mp, const char *str, size_t len, int mode)
{
    (void) mp; (void) mode; (void) str; (void) len;
    mp_fatal_error(mp, "no 'make_text' callback set");
    return NULL;
}

@ Watch out: at this moment we have |mp_find_file| as well as |open_file| and
both need to be set.

@<Declarations@>=
static char *mp_find_file    (MP mp, const char *fname, const char *fmode, int ftype);
static void *mp_open_file    (MP mp, const char *fname, const char *fmode, int ftype);
static char *mp_read_file    (MP mp, void *f, size_t * size);
static void  mp_close_file   (MP mp, void *f);
static void  mp_write_file   (MP mp, void *f, const char *s);
static char *mp_run_script   (MP mp, const char *str, size_t len, int n);
static void  mp_run_internal (MP mp, int action, int n, int type, const char *iname);
static void  mp_run_logger   (MP mp, int target, const char *s, size_t l);
static int   mp_run_overload (MP mp, int property, const char *, int);
static void  mp_run_error    (MP mp, const char *, const char *, int);
static void  mp_run_warning  (MP mp, const char *);
static char *mp_make_text    (MP mp, const char *str, size_t len, int mode);

@ As with the other callbacks, once they are needed and not set an error is
triggered. It made no sense to keep not used code around.

@c
static void *mp_open_file (MP mp, const char *fname, const char *fmode, int ftype)
{
    (void) mp; (void) fname; (void) fmode; (void) ftype;
    mp_fatal_error(mp, "no 'open_file' callback set");
    return NULL;
}

@ (Almost) all file names pass through |name_of_file|.

@<Glob...@>=
char *name_of_file; /* the name of a system file */

@ If this parameter is true, the terminal and log will report the found file
names for input files instead of the requested ones. It is off by default because
it creates an extra filename lookup.

@ \MP's file-opening procedures return |false| if no file identified by
|name_of_file| could be opened.

The |do_open_file| function takes care of the |print_found_names| parameter. The
file helpers are mandate callbacks. Not setting them triggers an error.

@c
static int mp_do_open_file (MP mp, void **f, int ftype, const char *mode)
{
    /*
        For now we keep the two step find and open approach because we get back
        the full (found) name but all logic is at the \LUA\ end. Maybe some day
        we need the original name.
    */
    char *s = (mp->find_file)(mp, mp->name_of_file, mode, ftype);
    if (s != NULL) {
        mp_memory_free(mp->name_of_file);
        mp->name_of_file = mp_strdup(s);
     // lmt_generic_free(s);
        lmt_memory_free(s);
        *f = (mp->open_file)(mp, mp->name_of_file, mode, ftype);
    } else {
        *f = NULL;
    }
    return (*f ? 1 : 0);
}

static int mp_open_in (MP mp, void **f, int ftype)
{
    return mp_do_open_file(mp, f, ftype, "r");
}

static int mp_open_out (MP mp, void **f, int ftype)
{
    return mp_do_open_file(mp, f, ftype, "w");
}

static char *mp_read_file (MP mp, void *f, size_t *size)
{
    (void) mp; (void) f; (void) size;
    mp_fatal_error(mp, "no 'read_file' callback set");
    return NULL;
}

static void mp_write_file (MP mp, void *f, const char *s)
{
    (void) mp; (void) f; (void) s;
    mp_fatal_error(mp, "no 'read_file' callback set");
}

static void mp_close_file (MP mp, void *f)
{
    (void) mp; (void) f;
    mp_fatal_error(mp, "no 'close_file' callback set");
}

@ Input from text files is read one line at a time, using a routine called
|input_ln|. This function is defined in terms of global variables called
|buffer|, |first|, and |last| that will be described in detail later; for now, it
suffices for us to know that |buffer| is an array of |unsigned char| values, and
that |first| and |last| are indices into this array representing the beginning
and ending of a line of text.

@<Glob...@>=
size_t         buf_size;      /* maximum number of characters simultaneously present in current lines of open files */
unsigned char *buffer;        /* lines of characters being read */
size_t         first;         /* the first unused position in |buffer| */
size_t         last;          /* end of the line just input to |buffer| */
size_t         max_buf_stack; /* largest index used in |buffer| */

@ @<Allocate or initialize ...@>=
mp->buf_size = 200;
mp->buffer   = mp_memory_allocate((size_t) (mp->buf_size + 1) * sizeof(unsigned char));

@ @<Dealloc variables@>=
mp_memory_free(mp->buffer);

@ @c
static void mp_reallocate_buffer (MP mp, size_t l)
{
    if (l > max_halfword) {
        mp_confusion(mp, "buffer size"); /* can't happen (I hope) */
    } else {
        unsigned char *buffer = mp_memory_allocate((size_t) (l + 1) * sizeof(unsigned char));
        memcpy(buffer, mp->buffer, (mp->buf_size + 1));
        mp_memory_free(mp->buffer);
        mp->buffer = buffer;
        mp->buf_size = l;
    }
}

@ The |input_ln| function brings the next line of input from the specified field
into available positions of the buffer array and returns the value |true|, unless
the file has already been entirely read, in which case it returns |false| and
sets |last := first|. In general, the |unsigned char| numbers that represent the
next line of the file are input into |buffer [first]|, |buffer [first + 1]|,
\dots, |buffer [last - 1]|; and the global variable |last| is set equal to
|first| plus the length of the line. Trailing blanks are removed from the line;
thus, either |last = first| (in which case the line was entirely blank) or
|buffer [last - 1] <>" "|. @^inner loop@>

The variable |max_buf_stack|, which is used to keep track of how large the
|buf_size| parameter must be to accommodate the present job, is also kept up to
date by |input_ln|.

@c
static int mp_input_ln (MP mp, void *f)
{
    /* inputs the next line or returns |false| */
    char *s;
    size_t size = 0;
    mp->last = mp->first; /* cf.\ Matthew 19\thinspace:\thinspace30 */
    s = (mp->read_file)(mp, f, &size);
    if (s == NULL) {
        return 0;
    } else if (size > 0) {
        mp->last = mp->first + size;
        if (mp->last >= mp->max_buf_stack) {
            mp->max_buf_stack = mp->last + 1;
            while (mp->max_buf_stack > mp->buf_size) {
                mp_reallocate_buffer(mp, (mp->buf_size + (mp->buf_size >> 2)));
            }
        }
        memcpy((mp->buffer + mp->first), s, size);
    }
 // lmt_generic_free(s);
    lmt_memory_free(s);
    return 1;
}

@ The user's terminal acts essentially like other files of text, except that it
is used both for input and for output. When the terminal is considered an input
file, the file variable is called |term_in|, and when it is considered an output
file the file variable is |term_out|. @^system dependencies@>

@<Glob...@>=
void *term_in;  /* the terminal as an input file */

@ Sometimes it is necessary to synchronize the input/output mixture that happens
on the user's terminal, and three system-dependent procedures are used for this
purpose. The first of these, |update_terminal|, is called when we want to make
sure that everything we have output to the terminal so far has actually left the
computer's internal buffers and been sent. The second, |clear_terminal|, is
called when we wish to cancel any input that the user may have typed ahead (since
we are about to issue an unexpected error message). The third,
|wake_up_terminal|, is supposed to revive the terminal if the user has disabled
it by some instruction to the operating system. The following macros show how
these operations can be specified: @^system dependencies@>

@<MPlib internal header stuff@>=
# define update_terminal()  mp_print_nl_only(mp); /* empty the terminal output buffer */
# define clear_terminal()                         /* clear the terminal input buffer */
# define wake_up_terminal() mp_print_nl_only(mp); /* cancel the user's cancellation of output */

@ The global variable |loc| should be set so that the character to be read next
by \MP\ is in |buffer [loc]|. This character should not be blank, and we should
have |loc < last|.

@d loc mp->cur_input.loc_field /* location of first unread character in |buffer| */

@* Globals for strings.

@ Symbolic token names and diagnostic messages are variable-length strings of
eight-bit characters. Many strings \MP\ uses are simply literals in the compiled
source, like the error messages and the names of the internal parameters. Other
strings are used or defined from the \MP\ input language, and these have to be
interned.

\MP\ uses strings more extensively than \MF\ does, but the necessary operations
can still be handled with a fairly simple data structure. The avl tree |strings|
contains all of the known string structures.

Each structure contains an |unsigned char| pointer containing the eight-bit data,
a |size_t| that holds the length of that data, and an |int| that indicates how
often this string is referenced (this will be explained below). Such strings are
referred to by structure pointers called |mp_string|.

Besides the avl tree, there is a set of three variables called |cur_string|,
|cur_length| and |cur_string_size| that are used for strings while they are being
built.

@<Exported types...@>=
typedef struct mp_lstring {
    unsigned char *str;  /* the string value */
    size_t         len;  /* its length */
    int            refs; /* number of references */
} mp_lstring;

typedef mp_lstring *mp_string; /* for pointers to string values */

@ The string handling functions are in |mpstrings.w|, but strings need a bunch
of globals and those are defined here in the main file.

@<Glob...@>=
avl_tree       strings;         /* string avl tree */
unsigned char *cur_string;      /*  current string buffer */
size_t         cur_length;      /* current index in that buffer */
size_t         cur_string_size; /*  malloced size of |cur_string| */

@ @<Allocate or initialize ...@>=
mp_initialize_strings(mp);

@ @<Dealloc variables@>=
mp_dealloc_strings(mp);

@ The next four variables are for keeping track of string memory usage.

@<Glob...@>=
int pool_in_use;   /* total number of string bytes actually in use */
int max_pl_used;   /* maximum |pool_in_use| so far */
int strs_in_use;   /* total number of strings actually in use */
int max_strs_used; /* maximum |strs_in_use| so far */

@* On-line and off-line printing.

Messages that are sent to a user's terminal and to the transcript-log file are
produced by several |print| procedures. These procedures will direct their
output to a variety of places, based on the setting of the global variable
|selector|, which has the following possible values:

\yskip

\hang |term_and_log|, the normal setting, prints on the terminal and on the
transcript file.

\hang |log_only|, prints only on the transcript file.

\hang |term_only|, prints only on the terminal.

\hang |no_print|, doesn't print at all. This is used only in rare cases before
the transcript file is open.

\hang |pseudo|, puts output into a cyclic buffer that is used by the
|show_context| routine; when we get to that routine we shall discuss the
reasoning behind this curious mode.

\hang |new_string|, appends the output to the current string in the string pool.

\hang |>= first_file| prints on one of the files used for the |write|
@:write_}{|write| primitive@> command.

\yskip

\noindent The symbolic names |term_and_log|, etc., have been assigned numeric
codes that satisfy the convenient relations |no_print + 1 = term_only|, |no_print
+ 2 = log_only|, |term_only + 2 = log_only + 1 = term_and_log|. These relations
are not used when |selector| could be |pseudo|, or |new_string|. We need not
check for unprintable characters when |selector < pseudo|. We no longer use that
magic and just test the constants.

Two additional global variables, |term_offset| and |file_offset| record if
characters have been printed since they were most recently cleared. We use
|term_offset|, and |file_offset|, on the other hand, keep track of how many
characters have appeared so far on the current line that has been output to the
terminal, the transcript file, or piped into \LUA.

@<MPlib internal header stuff@>=
typedef enum mp_selectors {
    mp_new_string_selector,   /* printing is deflected to the string pool */
    mp_no_print_selector,     /* |selector| setting that makes data disappear */
    mp_term_only_selector,    /* printing is destined for the terminal only */
    mp_log_only_selector,     /* printing is destined for the transcript file only */
    mp_term_and_log_selector, /* normal |selector| setting */
    mp_first_file_selector,   /* first write file selector */
} mp_selectors;

typedef enum mp_logging_targets {
    mp_void_logging_target,
    mp_term_logging_target,
    mp_file_logging_target,
    mp_both_logging_target,
    mp_error_logging_target,
} mp_logging_targets;

@ @<Glob...@>=
unsigned int   selector;    /* where to print a message */
unsigned int   term_offset; /* the number of characters on the current terminal line */
unsigned int   file_offset; /* the number of characters on the current file line */

@ @<Initialize the output routines@>=
mp->term_offset = 0;
mp->file_offset = 0;

@ Macro abbreviations for output to the terminal and to the log file are defined
here for convenience. Some systems need special conventions for terminal output,
and it is possible to adhere to those conventions by changing |wterm|,
|wterm_ln|, and |wterm_cr| here. @^system dependencies@>

@<MPlib internal header stuff@>=
# define mp_fputs(b,f) (mp->write_file)(mp, f, b)

# define mp_log_string(target,s)  (mp->run_logger)(mp, target, s, strlen(s))
# define mp_log_mpstr(target,s,l) (mp->run_logger)(mp, target, s, l)
# define mp_log_cr(target)        (mp->run_logger)(mp, target, "\n", 1)
# define mp_log_chr(target,s)     { unsigned char ss[2] = { s, 0 }; (mp->run_logger)(mp, target, (const char *) ss, 1); }
# define mp_log_error(s)          (mp->run_logger)(mp, mp_error_logging_target, s, strlen(s))

@ To end a line of text output, we call |print_ln|. Cases |0..max_write_files|
use an array |wr_file| that will be declared later.

The names of the print functions are more or less in sync with the ones used
in the \LUAMETATEX\ source code.

@<Declarations@>=
static void mp_print_str    (MP mp, const char *s);
static void mp_print_nl     (MP mp, const char *s);
static void mp_print_fmt    (MP mp, const char *s, ...);
static void mp_print_ln     (MP mp);
static void mp_print_chr    (MP mp, unsigned char k);
static void mp_print_mp_str (MP mp, mp_string s);
static void mp_print_nl     (MP mp, const char *s);
static void mp_print_two    (MP mp, mp_number *x, mp_number *y);

@ @<Exported function headers@>=
extern void mp_print_e_str (MP mp, const char *s);
extern void mp_print_e_chr (MP mp, unsigned char k);

@ @c
static void mp_print_ln (MP mp)
{
    switch (mp->selector) {
        case mp_term_and_log_selector:
            mp_log_cr(mp_both_logging_target);
            mp->term_offset = 0;
            mp->file_offset = 0;
            break;
        case mp_log_only_selector:
            mp_log_cr(mp_file_logging_target);
            mp->file_offset = 0;
            break;
        case mp_term_only_selector:
            mp_log_cr(mp_term_logging_target);
            mp->term_offset = 0;
            break;
        case mp_no_print_selector:
        case mp_new_string_selector:
            break;
        default:
            mp_fputs("\n", mp->wr_file[mp->selector - mp_first_file_selector]);
    }
}

@ The |print_char| procedure sends one character to the desired destination. All
printing comes through |print_ln| or |print_char|, hence these routines are the
ones that limit lines to at most |max_print_line| characters. But we must make an
exception for the \POSTSCRIPT\ output file since it is not safe to cut up lines
arbitrarily in \POSTSCRIPT. Anyway, we don't have a backend other than \LUA\ so
we just flush all without checking, so the nicely cleaned up offset code is
now gone too (just a boolean) so we lost |max_print_line|, |error_line| etc.

@c
static void mp_print_chr (MP mp, unsigned char s)
{
    switch (mp->selector) {
        case mp_term_and_log_selector:
            mp_log_chr(mp_both_logging_target, s);
            mp->term_offset = 1;
            mp->file_offset = 1;
            break;
        case mp_log_only_selector:
            mp_log_chr(mp_file_logging_target, s);
            mp->file_offset = 1;
            break;
        case mp_term_only_selector:
            mp_log_chr(mp_term_logging_target, s);
            mp->term_offset = 1;
            break;
        case mp_no_print_selector:
            break;
        case mp_new_string_selector:
            mp_str_room(mp, 1);
            mp_append_char(mp, s);
            break;
        default:
            {
                unsigned char ss[2] = { s, 0 };
                mp_fputs((char *) ss, mp->wr_file[mp->selector - mp_first_file_selector]);
            }
    }
}

void mp_print_e_chr (MP mp, unsigned char s)
{
    mp_print_chr(mp, s);
}

static void mp_do_print (MP mp, const char *s, size_t len)
{
    if (len == 0) {
        return;
    } else if (mp->selector == mp_new_string_selector) {
        mp_str_room(mp, (int) len);
        memcpy((mp->cur_string + mp->cur_length), s, len);
        mp->cur_length += len;
    } else {
        switch (mp->selector) {
            case mp_term_and_log_selector:
                mp_log_mpstr(mp_both_logging_target, s, (int) len);
                mp->term_offset = 1;
                mp->file_offset = 1;
                break;
            case mp_log_only_selector:
                mp_log_mpstr(mp_file_logging_target, s, (int) len);
                mp->file_offset = 1;
                break;
            case mp_term_only_selector:
                mp_log_mpstr(mp_term_logging_target, s, (int) len);
                mp->term_offset = 1;
                break;
            case mp_no_print_selector:
                break;
            case mp_new_string_selector:
                mp_str_room(mp, (int) len);
                mp_append_str(mp, s);
                break;
            default:
                mp_fputs(s, mp->wr_file[mp->selector - mp_first_file_selector]);
                break;
        }
    }
}

static void mp_print_str (MP mp, const char *s)
{
    mp_do_print(mp, s, strlen(s));
}

void mp_print_e_str (MP mp, const char *s)
{
    mp_print_str(mp,s);
}

static void mp_print_fmt (MP mp, const char *s, ...)
{
    va_list ap;
    char pval[256];
    va_start(ap, s);
    vsnprintf(pval, 256, s, ap);
    mp_do_print(mp, pval, strlen(pval));
    va_end(ap);
}

static void mp_print_mp_str (MP mp, mp_string s)
{
    mp_do_print(mp, (const char *) s->str, s->len);
}

@ Here is the very first thing that \MP\ prints: a headline that identifies the
version number and base name.

@<Initialize the output...@>=
mp_log_string(mp_term_logging_target, mp->banner);
mp_log_string(mp_term_logging_target, ", running in ");
mp_log_string(mp_term_logging_target, mp_str(mp, internal_string(mp_number_system_internal)));
mp_log_string(mp_term_logging_target, " mode.");
mp_print_ln(mp);
update_terminal();

@ @<Declarations@>=
static void mp_print_nl_only (MP mp);

@ The procedure |print_nl| is like |print|, but it makes sure that the string
appears at the beginning of a new line.

@c
static void mp_print_nl_only (MP mp)
{
    switch (mp->selector) {
        case mp_term_and_log_selector:
            if (mp->file_offset > 0) {
                mp_log_cr(mp_file_logging_target);
                mp->file_offset = 0;
            }
            if (mp->term_offset > 0) {
                mp_log_cr(mp_term_logging_target);
                mp->term_offset = 0;
            }
            break;
        case mp_log_only_selector:
            if (mp->file_offset > 0) {
                mp_log_cr(mp_file_logging_target);
                mp->file_offset = 0;
            }
            break;
        case mp_term_only_selector:
            if (mp->term_offset > 0) {
                mp_log_cr(mp_term_logging_target);
                mp->term_offset = 0;
            }
            break;
        case mp_no_print_selector:
        case mp_new_string_selector:
            break;
    }
}

static void mp_print_nl (MP mp, const char *s)
{
    mp_print_nl_only(mp);
    mp_print_str(mp, s);
}

@ The following procedure, which prints out the decimal representation of a given
integer |n|, assumes that all integers fit nicely into a |int|. @^system
dependencies@>

@c
static void mp_print_int (MP mp, int n)
{
    char s[12];
    mp_snprintf(s, 12, "%d", (int) n);
    mp_print_str(mp, s);
}

@ @<Declarations@>=
static void mp_print_int (MP mp, int n);

@* Reporting errors.

@ The global variable |interaction| has four settings, representing increasing
amounts of user interaction:

@<Exported types@>=
enum mp_interaction_mode {
    mp_unspecified_mode, /* extra value for command-line switch */
    mp_batch_mode,       /* omits all stops and omits terminal output */
    mp_nonstop_mode,     /* omits all stops */
    mp_scroll_mode,      /* omits error stops */
    mp_error_stop_mode,  /* stops at every opportunity to interact */
    mp_silent_mode       /* stops at every opportunity to interact but not always*/
};

@ @<Option variables@>=
int interaction;    /* current level of interaction */
int extensions;

@ Set it here so it can be overwritten by the commandline

@<Allocate or initialize ...@>=
mp->interaction = opt->interaction;
if (mp->interaction == mp_unspecified_mode || mp->interaction > mp_silent_mode) {
    mp->interaction = mp_error_stop_mode;
}
if (mp->interaction < mp_unspecified_mode) {
    mp->interaction = mp_batch_mode;
}

@ \MP\ is careful not to call |error| when the print |selector| setting might be
unusual. The only possible values of |selector| at the time of error messages are

\yskip

\hang|no_print| (when |interaction=mp_batch_mode| and |log_file| not yet open);

\hang|term_only| (when |interaction>mp_batch_mode| and |log_file| not yet open);

\hang|log_only| (when |interaction=mp_batch_mode| and |log_file| is open);

\hang|term_and_log| (when |interaction>mp_batch_mode| and |log_file| is open).

@ The global variable |history| records the worst level of error that has been
detected. It has four possible values: |spotless|, |warning_issued|,
|error_message_issued|, and |fatal_error_stop|.

Another global variable, |error_count|, is increased by one when an |error|
occurs without an interactive dialog, and it is reset to zero at the end of every
statement. If |error_count| reaches 100, \MP\ decides that there is no point in
continuing further.

@<Exported types@>=
enum mp_history_state {
    mp_spotless,             /* |history| value when nothing has been amiss yet */
    mp_warning_issued,       /* |history| value when |begin_diagnostic| has been called */
    mp_error_message_issued, /* |history| value when |error| has been called */
    mp_fatal_error_stop,     /* |history| value when termination was premature */
    mp_system_error_stop     /* |history| value when termination was due to disaster */
};

@ @<Glob...@>=
int history;     /* has the source input been clean so far? */
int error_count; /* the number of scrolled errors since the last statement ended */

@ The value of |history| is initially |fatal_error_stop|, but it will be changed
to |spotless| if \MP\ survives the initialization process.

@ Since errors can be detected almost anywhere in \MP, we want to declare the
error procedures near the beginning of the program. But the error procedures in
turn use some other procedures, which need to be declared |forward| before we get
to |error| itself.

It is possible for |error| to be called recursively if some error arises when
|get_next| is being used to delete a token, and/or if some fatal error occurs
while \MP\ is trying to fix a non-fatal one. But such recursion @^recursion@> is
never more than two levels deep.

@<Declarations@>=
static void mp_get_next           (MP mp);
static void mp_begin_file_reading (MP mp);

@ @<Exported function ...@>=
extern void mp_show_context (MP mp);

@ @<Internal ...@>=
void mp_normalize_selector (MP mp);

@ @<Glob...@>=
int       use_err_help; /* should the |err_help| string be shown? */
int       padding_help; /* well ... why not.  */
mp_string err_help;     /* a string set up by |errhelp| */

@ @<Allocate or ...@>=
mp->use_err_help = 0;

@ The |jump_out| procedure just cuts across all active procedure levels and goes
to |end_of_MP|. This is the only nonlocal |goto| statement in the whole program.
It is used when there is no recovery from a particular error.

The program uses a |jump_buf| to handle this, this is initialized at three spots:
the start of |mp_new|, the start of |mp_initialize|, and the start of |mp_run|.
Those are the only library entry points. @^system dependencies@>

@<Glob...@>=
jmp_buf *jump_buf;

@ If the array of internals is still |NULL| when |jump_out| is called, a crash
occured during initialization, and it is not safe to run the normal cleanup
routine.

@<Error hand...@>=
void mp_jump_out (MP mp)
{
    if (mp->internal != NULL && mp->history < mp_system_error_stop) {
        mp_close_files_and_terminate(mp);
    }
    longjmp(*(mp->jump_buf), 1);
}

@ @<Internal ...@>=
void mp_jump_out (MP mp);

@ @<Error hand...@>=
void mp_warn (MP mp, const char *msg)
{
    int selector = mp->selector;
    mp_normalize_selector(mp);
    mp_print_nl(mp, "Warning: ");
    mp_print_str(mp, msg);
    mp_print_ln(mp);
    mp->selector = selector;
}

@ Here now is the general |error| routine.

Individual lines of help are recorded in the array |help_line|, which contains
entries in positions |0 .. (help_ptr - 1)|. They should be printed in reverse
order, i.e., with |help_line [0]| appearing last.

@c
void mp_error (MP mp, const char *msg, const char *hlp)
{
    int selector = mp->selector;
    mp_normalize_selector(mp);
    mp->run_error(mp, msg, hlp, mp->interaction);
    if (mp->history < mp_error_message_issued) {
        mp->history = mp_error_message_issued;
    }
    if (mp->halt_on_error) {
        mp->history = mp_fatal_error_stop;
        mp_jump_out(mp);
    }
    ++mp->error_count;
    if (mp->error_count == 100) {
        mp_print_nl(mp, "(That makes 100 errors; please try again.)");
        @.That makes 100 errors...@>
        mp->history = mp_fatal_error_stop;
        mp_jump_out(mp);
    }
    mp->selector = selector;
}

@ @<Exported function ...@>=
extern void mp_error (MP mp, const char *msg, const char *hlp);
extern void mp_warn  (MP mp, const char *msg);

@ In anomalous cases, the print selector might be in an unknown state; the
following subroutine is called to fix things just enough to keep running a bit
longer.

@c
void mp_normalize_selector (MP mp)
{
    mp->selector = mp->interaction == mp_batch_mode ? mp_log_only_selector : mp_term_and_log_selector;
}

@ The following procedure prints \MP's last words before dying.

@<Error hand...@>=
void mp_fatal_error (MP mp, const char *s)
{
    /* prints |s|, and that's it */
    mp_normalize_selector(mp);
    if (mp->interaction == mp_error_stop_mode) {
        /* no more interaction */
        mp->interaction = mp_scroll_mode;
    }
    mp_error(mp, "Emergency stop", s);
    mp->history = mp_fatal_error_stop;
    /* irrecoverable error */
    mp_jump_out(mp);
@.Emergency stop@>
}

@ @<Exported function ...@>=
extern void mp_fatal_error (MP mp, const char *s);

@ The program might sometime run completely amok, at which point there is no
choice but to stop. If no previous error has been detected, that's bad news; a
message is printed that is really intended for the \MP\ maintenance person
instead of the user (unless the user has been particularly diabolical). The index
entries for \quote {this can't happen} may help to pinpoint the problem. @^dry
rot@>

@<Internal library ...@>=
void mp_confusion (MP mp, const char *s);

@ Consistency check violated; |s| tells where.

@<Error hand...@>=
void mp_confusion (MP mp, const char *s)
{
    char msg[256];
    const char *hlp = NULL;
    mp_normalize_selector(mp);
    if (mp->history < mp_error_message_issued) {
        mp_snprintf(msg, 256, "This can't happen (%s)", s);
        hlp =
            "I'm broken. Please show this to someone who can fix can fix it and try\n"
            "again";
        @.This can't happen@>
    } else {
        hlp =
            "One of your faux pas seems to have wounded me deeply ... in fact, I'm barely\n"
            "conscious. Please fix it and try again.";
        mp_snprintf(msg, 256, "I can't go on meeting you like this");
        @.I can't go on...@>
    }
    if (mp->interaction == mp_error_stop_mode) {
        /* no more interaction */
        mp->interaction = mp_scroll_mode;
    }
    mp_error(mp, msg, hlp);
    mp->history=mp_fatal_error_stop;
    /* irrecoverable error */
    mp_jump_out(mp);
}

@ A couple of state variables:

@<Global...@>=
int run_state; /* are we processing input ? */
int finished;  /* set true by |close_files_and_terminate| */

@ @<Allocate or ...@>=
mp->finished = 0;

@* Arithmetic with scaled numbers.

The principal computations performed by \MP\ are done entirely in terms of
integers less than $2^{31}$ in magnitude; thus, the arithmetic specified in this
program can be carried out in exactly the same way on a wide variety of
computers, including some small ones. @^small computers@>

But C does not rigidly define the |/| operation in the case of negative
dividends; for example, the result of |(-2 * n - 1) / 2| is |- ( n + 1)| on some
computers and |-n| on others (is this true ?). There are two principal types of
arithmetic: \quotation {translation-preserving,} in which the identity |(a + q *
b) / b = (a / b) + q| is valid; and \quotation {negation-preserving,} in which
|(-a) / b = -(a/b)|. This leads to two \MP s, which can produce different
results, although the differences should be negligible when the language is being
used properly. The \TEX\ processor has been defined carefully so that both
varieties of arithmetic will produce identical output, but it would be too
inefficient to constrain \MP\ in a similar way.

@d inf_t          mp->math->md_inf_t
@d negative_inf_t mp->math->md_negative_inf_t

@ A single computation might use several subroutine calls, and it is desirable to
avoid producing multiple error messages in case of arithmetic overflow. So the
routines below set the global variable |arith_error| to |true| instead of
reporting errors directly to the user. @^overflow in arithmetic@>

@<Glob...@>=
int arith_error;

@ @<Allocate or ...@>=
mp->arith_error = 0;

@ At crucial points the program will say |check_arith|, to test if an arithmetic
error has been detected.

@d check_arith()
    if (mp->arith_error) {
        mp_clear_arith(mp);
    }

@c
static void mp_clear_arith (MP mp) {
    mp_error(
        mp,
        "Arithmetic overflow",
        "Uh, oh. A little while ago one of the quantities that I was computing got too\n"
        "large, so I'm afraid your answers will be somewhat askew. You'll probably have to\n"
        "adopt different tactics next time. But I shall try to carry on anyway."
    );
    @.Arithmetic overflow@>
    mp->arith_error = 0;
}

@ The definitions of these are set up by the math initialization. Here
|arc_tol_k| is the criterium to quit when change in arc length
estimate reaches it.

@d arc_tol_k                 mp->math->md_arc_tol_k
@d coef_bound_k              mp->math->md_coef_bound_k
@d coef_bound_minus_1        mp->math->md_coef_bound_minus_1
@d sqrt_8_e_k                mp->math->md_sqrt_8_e_k
@d twelve_ln_2_k             mp->math->md_twelve_ln_2_k
@d twelvebits_3              mp->math->md_twelvebits_3
@d one_k                     mp->math->md_one_k
@d epsilon_t                 mp->math->md_epsilon_t
@d unity_t                   mp->math->md_unity_t
@d zero_t                    mp->math->md_zero_t
@d two_t                     mp->math->md_two_t
@d three_t                   mp->math->md_three_t
@d half_unit_t               mp->math->md_half_unit_t
@d three_quarter_unit_t      mp->math->md_three_quarter_unit_t
@d twentysixbits_sqrt2_t     mp->math->md_twentysixbits_sqrt2_t
@d twentyeightbits_d_t       mp->math->md_twentyeightbits_d_t
@d twentysevenbits_sqrt2_d_t mp->math->md_twentysevenbits_sqrt2_d_t
@d warning_limit_t           mp->math->md_warning_limit_t
@d precision_default         mp->math->md_precision_default
@d precision_min             mp->math->md_precision_min
@d precision_max             mp->math->md_precision_max

@ In fact, the two sorts of scaling discussed above aren't quite sufficient; \MP\
has yet another, used internally to keep track of angles.

@ We often want to print two scaled quantities in parentheses, separated by a
comma.

@c
static void mp_print_two (MP mp, mp_number *x, mp_number *y)
{
    mp_print_chr(mp, '(');
    print_number(*x);
    mp_print_chr(mp, ',');
    print_number(*y);
    mp_print_chr(mp, ')');
}

@d fraction_one_t            mp->math->md_fraction_one_t
@d fraction_half_t           mp->math->md_fraction_half_t
@d fraction_three_t          mp->math->md_fraction_three_t
@d fraction_four_t           mp->math->md_fraction_four_t
@d one_eighty_deg_t          mp->math->md_one_eighty_deg_t
@d negative_one_eighty_deg_t mp->math->md_negative_one_eighty_deg_t
@d three_sixty_deg_t         mp->math->md_three_sixty_deg_t

@ And now let's complete our collection of numeric utility routines by
considering random number generation. \MP\ generates pseudo-random numbers with
the additive scheme recommended in Section 3.6 of {\em The Art of Computer
Programming}; however, the results are random fractions between 0 and
|fraction_one-1|, inclusive.

There's an auxiliary array |randoms| that contains 55 pseudo-random fractions.
Using the recurrence $x_n = (x_{n - 55} - x_{n - 31}) \bmod 2^{28}$, we generate
batches of 55 new $x_n$'s at a time by calling |new_randoms|. The global variable
|j_random| tells which element has most recently been consumed. The global
variable |random_seed| was introduced in version 0.9, for the sole reason of
stressing the fact that the initial value of the random seed is system-dependant.
The initialization code below will initialize this variable to |(internal
[mp_time] div unity) + internal [mp_day]|, but this is not good enough on modern
fast machines that are capable of running multiple \METAPOST\ processes within
the same second. @^system dependencies@>

@<Glob...@>=
mp_number randoms[55]; /* the last 55 random values generated */
int j_random;          /* the number of unused |randoms| */
int j_padding;         /* the number of unused |randoms| */

@ @<Option variables@>=
int random_seed; /* the default random seed */

@ @<Allocate or initialize ...@>=
mp->random_seed = opt->random_seed;
for (int i = 0; i < 55; i++) {
    new_fraction(mp->randoms[i]);
}

@ @<Dealloc...@>=
for (int i = 0; i < 55; i++) {
    free_number(mp->randoms[i]);
}

@ @<Internal library ...@>=
void mp_new_randoms (MP mp);

@ @c
void mp_new_randoms (MP mp)
{
    mp_number x; /* accumulator */
    new_number(x);
    for (int k = 0; k <= 23; k++) {
        set_number_from_subtraction(x, mp->randoms[k], mp->randoms[k + 31]);
        if (number_negative(x)) {
            number_add(x, fraction_one_t);
        }
        number_clone(mp->randoms[k], x);
    }
    for (int k = 24; k <= 54; k++) {
        set_number_from_subtraction(x, mp->randoms[k], mp->randoms[k - 24]);
        if (number_negative(x)) {
            number_add(x, fraction_one_t);
        }
        number_clone(mp->randoms[k], x);
    }
    free_number(x);
    mp->j_random = 54;
}

@ To consume a random fraction, the program below will say |next_random|. Now
each number system has its own implementation, true to the original as much as
possibile.

@ To produce a uniform random number in the range |0 <= u < x| or |0 >= u > x| or
|0 = u = x|, given a |scaled| value~|x|, we proceed as shown here.

Note that the call of |take_fraction| will produce the values 0 and~|x| with
about half the probability that it will produce any other particular values
between 0 and~|x|, because it rounds its answers. This is the original one, that
stays as reference: As said before, now each number system has its own
implementation.

@ Finally, a normal deviate with mean zero and unit standard deviation can
readily be obtained with the ratio method (Algorithm 3.4.1R in {\em The Art of
Computer Programming}). This is the original one, that stays as reference: Now
each number system has its own implementation, true to the original as much as
possibile.

@ The random related code is in the number system modules.

@* Packed data.

@d max_quarterword    0x3FFF /* largest allowable value in a |quarterword| */
@d max_halfword    0xFFFFFFF /* largest allowable value in a |halfword| */

@ The reader should study the following definitions closely: @^system
dependencies@>

@<Types...@>=
typedef struct mp_value_node_data *mp_value_node;
typedef struct mp_node_data       *mp_node;
typedef struct mp_symbol_entry    *mp_sym;

typedef unsigned short  quarterword;    /* 1/4 of a 64 bit word */
typedef int             halfword;       /* 1/2 of a 64 bit word */

typedef struct mp_independent_data {
    int scale;  /* only for |indep_scale|, used together with |serial| */
    int serial; /* only for |indep_value|, used together with |scale| */
} mp_independent_data;

typedef struct mp_value_data {
    mp_independent_data indep;
    mp_number           n;
    mp_string           str;
    mp_sym              sym;
    mp_node             node;
    mp_knot             p;
} mp_value_data;

typedef struct mp_value {
    mp_variable_type type;
    int              padding;
    mp_value_data    data;
} mp_value;

@ The global variable |math_mode| has four settings, representing the math value
type that will be used in this run.

The typedef for |mp_number| is here because it has to come very early.

@<Exported types@>=
typedef enum mp_math_mode {
    mp_math_scaled_mode,
    mp_math_double_mode,
    mp_math_binary_mode,
    mp_math_decimal_mode
} mp_math_mode;

@ @<Option variables@>=
int math_mode; /* math mode */

@ @<Allocate or initialize ...@>=
mp->math_mode = opt->math_mode;

@ Most important memory is kept in a chain so we don't need to allocate that
often. We could (at some point) decide to use mimalloc.

@<Declare helpers@>=
extern void *mp_memory_allocate       (size_t size);
extern void *mp_memory_clear_allocate (size_t size);
extern void *mp_memory_reallocate     (void *p, size_t size);
extern void  mp_memory_free           (void *p);

extern void *mp_allocate_node         (MP mp, size_t size);
extern void *mp_allocate_dash         (MP mp);

@ This is an attempt to spend less time in |malloc()|:

@d max_num_token_nodes    8000 /* maybe make this configureable */
@d max_num_pair_nodes     1000
@d max_num_knot_nodes     1000
@d max_num_value_nodes    1000
@d max_num_symbolic_nodes 1000

@<Global ...@>=
mp_node token_nodes;
mp_node pair_nodes;
int     num_token_nodes;
int     num_pair_nodes;
mp_knot knot_nodes;
mp_node value_nodes;
int     max_knot_nodes;
int     num_knot_nodes;
int     num_value_nodes;
mp_node symbolic_nodes;
int     num_symbolic_nodes;

@ @<Allocate or initialize ...@>=
mp->token_nodes        = NULL;
mp->num_token_nodes    = 0;
mp->pair_nodes         = NULL;
mp->num_pair_nodes     = 0;
mp->knot_nodes         = NULL;
mp->max_knot_nodes     = max_num_knot_nodes;
mp->num_knot_nodes     = 0;
mp->value_nodes        = NULL;
mp->num_value_nodes    = 0;
mp->symbolic_nodes     = NULL;
mp->num_symbolic_nodes = 0;

@ @<Dealloc ...@>=
while (mp->value_nodes) {
    mp_node p = mp->value_nodes;
    mp->value_nodes = p->link;
    mp_free_node(mp, p, sizeof(mp_value_node_data));
}
while (mp->symbolic_nodes) {
    mp_node p = mp->symbolic_nodes;
    mp->symbolic_nodes = p->link;
    mp_free_node(mp, p, sizeof(mp_node_data));
}
while (mp->pair_nodes) {
    mp_node p = mp->pair_nodes;
    mp->pair_nodes = p->link;
    mp_free_node(mp, p, sizeof(mp_pair_node_data));
}
while (mp->token_nodes) {
    mp_node p = mp->token_nodes;
    mp->token_nodes = p->link;
    mp_free_node(mp, p, sizeof(mp_node_data));
}
while (mp->knot_nodes) {
    mp_knot p = mp->knot_nodes;
    mp->knot_nodes = p->next;
    mp_free_knot(mp, p);
}

@ This is a nicer way of allocating nodes. Users who wish to study the memory
requirements of particular applications can can use the special features that
keep track of current and maximum memory usage. All kind of statistics are
available on request but we no longer display them in the library.

@ @<Glob...@>=
size_t var_used;     /* how much memory is in use */
size_t var_used_max; /* how much memory was in use max */

@ @c
void *mp_allocate_node (MP mp, size_t size)
{
    void *p = mp_memory_allocate(size);
    ((mp_node) p)->link = NULL;
    ((mp_node) p)->hasnumber = 0;
    mp->var_used += size;
    if (mp->var_used > mp->var_used_max) {
        mp->var_used_max = mp->var_used;
    }
    return p;
}

void *mp_allocate_dash (MP mp)
{
    void *p = mp_memory_allocate(sizeof(mp_dash_object));
    mp->var_used += sizeof(mp_dash_object);
    if (mp->var_used > mp->var_used_max) {
        mp->var_used_max = mp->var_used;
    }
    return p;
}

@ We want to be able to overload the allocator but then we also need to
pass to the avl handler and that one doesn't take the |mp| pointer so
we just do a hard exit.

@c
void *mp_memory_allocate (size_t size)
{
    void *w = lmt_memory_malloc(size);
    if (! w) {
        printf("mplib ran out of memory, case 1");
        exit(EXIT_FAILURE);
    }
    return w;
}

void *mp_memory_clear_allocate (size_t size)
{
    void *w = lmt_memory_calloc(1, size);
    if (! w) {
        printf("mplib ran out of memory, case 2");
        exit(EXIT_FAILURE);
    }
    return w;
}

void *mp_memory_reallocate (void *p, size_t size)
{
    void *w = lmt_memory_realloc(p, size);
    if (! w) {
        printf("mplib ran out of memory, case 3");
        exit(EXIT_FAILURE);
    }
    return w;
}

void mp_memory_free (void *p)
{
    lmt_memory_free(p);
}

@ @<Internal library declarations@>=
# define mp_snprintf snprintf

@* Dynamic memory allocation.

The \MP\ system does nearly all of its own memory allocation, so that it can
readily be transported into environments that do not have automatic facilities
for strings, garbage collection, etc., and so that it can be in control of what
error messages the user receives.

@d mp_link(A)      (A)->link      /* the |link| field of a node */
@d mp_type(A)      (A)->type      /* identifies what kind of value this is */
@d mp_name_type(A) (A)->name_type /* a clue to the name of this value */

@d mp_set_link(A,B) (A)->link = (mp_node) (B)

@ @<MPlib internal header stuff@>=
typedef struct mp_node_data {
    union {
        mp_command_code  command;
        mp_variable_type type;
    };
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_value_data        data;
} mp_node_data;

typedef struct mp_node_data *mp_symbolic_node;

@ These will become inline:

@c
# define mp_get_sym_info(A)   mp_get_indep_value(A)
# define mp_set_sym_info(A,B) mp_set_indep_value(A, (B))
# define mp_get_sym_sym(A)    (A)->data.sym
# define mp_set_sym_sym(A,B)  (A)->data.sym = (mp_sym)(B)

@ The function |get_symbolic_node| returns a pointer to a new symbolic node whose
|link| field is null. @^inner loop@>

@c
static mp_node mp_new_symbolic_node (MP mp)
{
    mp_symbolic_node p;
    if (mp->symbolic_nodes) {
        p = (mp_symbolic_node) mp->symbolic_nodes;
        mp->symbolic_nodes = p->link;
        mp->num_symbolic_nodes--;
        p->link = NULL;
    } else {
        p = mp_allocate_node(mp, sizeof(mp_node_data));
        new_number(p->data.n);
        p->hasnumber = 1;
    }
    p->type = mp_symbol_node_type;
    p->name_type = mp_normal_operation;
    return (mp_node) p;
}

@ Conversely, when some node |p| of size |s| is no longer needed, the operation
|free_node(p,s)| will make its words available, by inserting |p| as a new empty
node just before where |rover| now points.

A symbolic node is recycled by calling |free_symbolic_node|.

@c
static void mp_free_node (MP mp, mp_node p, size_t siz)
{
    /* node liberation */
    if (p) {
        mp->var_used -= siz;
        if (mp->math_mode > mp_math_double_mode) {
            if (p->hasnumber >= 1 && is_number(((mp_symbolic_node) p)->data.n)) {
                free_number(((mp_symbolic_node) p)->data.n);
            }
            if (p->hasnumber == 2 && is_number(((mp_value_node) p)->subscript)) {
                free_number(((mp_value_node) p)->subscript);
            }
            /*
                There was a quite large |switch| here first, but the |mp_dash_node|
                case was the only one that did anything ...
            */
            if (mp_type(p) == mp_dash_node_type) {
                free_number(((mp_dash_node) p)->start_x);
                free_number(((mp_dash_node) p)->stop_x);
                free_number(((mp_dash_node) p)->dash_y);
            }
        }
        mp_memory_free(p);
    }
}

static void mp_free_symbolic_node (MP mp, mp_node p)
{
    /* node liberation */
    if (p) {
        if (mp->num_symbolic_nodes < max_num_symbolic_nodes) {
            p->link = mp->symbolic_nodes;
            mp->symbolic_nodes = p;
            mp->num_symbolic_nodes++;
        } else {
            mp->var_used -= sizeof(mp_node_data);
            mp_memory_free(p);
        }
    }
}

static void mp_free_value_node (MP mp, mp_node p)
{
    /* node liberation */
    if (p) {
        if (mp->num_value_nodes < max_num_value_nodes) {
            p->link = mp->value_nodes;
            mp->value_nodes = p;
            mp->num_value_nodes++;
        } else {
            mp->var_used -= sizeof(mp_value_node_data);
            if (mp->math_mode > mp_math_double_mode) {
                free_number(((mp_value_node) p)->data.n);
                free_number(((mp_value_node) p)->subscript);
            }
            mp_memory_free(p);
        }
    }
}

@ @<declarations@>=
static void mp_free_node          (MP mp, mp_node p, size_t siz);
static void mp_free_symbolic_node (MP mp, mp_node p);
static void mp_free_value_node    (MP mp, mp_node p);

@* Memory layout.

Some nodes are created statically, since static allocation is more efficient than
dynamic allocation when we can get away with it.

@<Glob...@>=
mp_dash_node  null_dash;
mp_value_node dep_head;
mp_node       inf_val;
mp_node       zero_val;
mp_node       temp_val;
mp_node       end_attr;
mp_node       bad_vardef;
mp_node       temp_head;
mp_node       hold_head;
mp_node       spec_head;

@ The following code gets the memory off to a good start.

@<Initialize table entries@>=
mp->spec_head = mp_new_symbolic_node(mp);
mp->temp_head = mp_new_symbolic_node(mp);
mp->hold_head = mp_new_symbolic_node(mp);

@ @<Free table entries@>=
mp_free_symbolic_node(mp, mp->spec_head);
mp_free_symbolic_node(mp, mp->temp_head);
mp_free_symbolic_node(mp, mp->hold_head);

@ The procedure |flush_node_list(p)| frees an entire linked list of nodes that
starts at a given position, until coming to a |NULL| pointer. @^inner loop@>

@c
static void mp_flush_node_list (MP mp, mp_node p)
{
    while (p != NULL) {
        mp_node q = p;
        p = p->link;
        if (q->type != mp_symbol_node_type) {
            mp_free_token_node(mp, q);
        } else {
            mp_free_symbolic_node(mp, q);
        }
    }
}

@* The command codes.

Before we can go much further, we need to define symbolic names for the internal
code numbers that represent the various commands obeyed by \MP. These codes are
somewhat arbitrary, but not completely so. For example, some codes have been made
adjacent so that |case| statements in the program need not consider cases that
are widely spaced, or so that |case| statements can be replaced by |if|
statements. A command can begin an expression if and only if its code lies
between |min_primary_command| and |max_primary_command|, inclusive. The first
token of a statement that doesn't begin with an expression has a command code
between |min_command| and |max_statement_command|, inclusive. Anything less than
|min_command| is eliminated during macro expansions, and anything no more than
|max_pre_command| is eliminated when expanding \TEX\ material. Ranges such as
|min_secondary_command..max_secondary_command| are used when parsing expressions,
but the relative ordering within such a range is generally not critical.

The ordering of the highest-numbered commands (|comma<semicolon<end_group<stop|)
is crucial for the parsing and error-recovery methods of this program as is the
ordering |if_test<fi_or_else| for the smallest two commands. The ordering is also
important in the ranges |numeric_token..plus_or_minus| and
|left_brace..ampersand|.

At any rate, here is the list, for future reference.

@d mp_max_command_code       mp_stop
@d mp_max_pre_command        mp_etex_command
@d mp_min_command            (mp_defined_macro_command+1)
@d mp_max_statement_command  mp_type_name_command
@d mp_min_primary_command    mp_type_name_command
@d mp_min_suffix_token       mp_internal_command
@d mp_max_suffix_token       mp_numeric_command
@d mp_max_primary_command    mp_plus_or_minus_command /* should also be |numeric_token+1| */
@d mp_min_tertiary_command   mp_plus_or_minus_command
@d mp_max_tertiary_command   mp_tertiary_binary_command
@d mp_min_expression_command mp_left_brace_command
@d mp_max_expression_command mp_equals_command
@d mp_min_secondary_command  mp_and_command
@d mp_max_secondary_command  mp_secondary_binary_command
@d mp_end_of_statement       (cur_cmd>mp_comma_command)

@<Enumeration types@>=
typedef enum mp_command_code {
    mp_undefined_command,
    mp_btex_command,                /* begin \TeX\ material (|btex|, |verbatimtex|) */
    mp_etex_command,                /* end \TeX\ material (|etex|) */
    mp_if_test_command,             /* conditional text (|if|) */
    mp_fi_or_else_command,          /* delimiters for conditionals (|elseif|, |else|, |fi|) */
    mp_input_command,               /* input a source file (|input|, |endinput|) */
    mp_iteration_command,           /* iterate (|for|, |forsuffixes|, |forever|, |endfor|) */
    mp_repeat_loop_command,         /* special command substituted for |endfor| */
    mp_exit_test_command,           /* premature exit from a loop (|exitif|) */
    mp_relax_command,               /* do nothing (|\char`\\|) */
    mp_scan_tokens_command,         /* put a string into the input buffer */
    mp_runscript_command,           /* put a script result string into the input buffer */
    mp_maketext_command,            /* make a text (typesetting) */
    mp_expand_after_command,        /* look ahead one token */
    mp_defined_macro_command,       /* a macro defined by the user */
    mp_save_command,                /* save a list of tokens (|save|) */
    mp_interim_command,             /* save an internal quantity (|interim|) */
    mp_let_command,                 /* redefine a symbolic token (|let|) */
    mp_new_internal_command,        /* define a new internal quantity (|newinternal|) */
    mp_macro_def_command,           /* define a macro (|def|, |vardef|, etc.) */
    mp_ship_out_command,            /* output a character (|shipout|) */
    mp_add_to_command,              /* add to edges (|addto|) */
    mp_bounds_command,              /* add bounding path to edges (|setbounds|, |clip|) */
    mp_protection_command,          /* set protection flag (|outer|, |inner|) */
    mp_property_command,
    mp_show_command,                /* diagnostic output (|show|, |showvariable|, etc.) */
    mp_mode_command,                /* set interaction level (|batchmode|, etc.) */
    mp_only_set_command,            /* initialize random number generator (|randomseed|) */
    mp_message_command,             /* communicate to user (|message|, |errmessage|) */
    mp_every_job_command,           /* designate a starting token (|everyjob|) */
    mp_delimiters_command,          /* define a pair of delimiters (|delimiters|) */
    mp_write_command,               /* write text to a file (|write|) */
    mp_type_name_command,           /* declare a type (|numeric|, |pair|, etc.) */
    mp_left_delimiter_command,      /* the left delimiter of a matching pair */
    mp_begin_group_command,         /* beginning of a group (|begingroup|) */
    mp_nullary_command,             /* an operator without arguments (e.g., |normaldeviate|) */
    mp_unary_command,               /* an operator with one argument (e.g., |sqrt|) */
    mp_str_command,                 /* convert a suffix to a string (|str|) */
    mp_void_command,                /* convert a suffix to a boolean (|void|) */
    mp_cycle_command,               /* close a cyclic path (|cycle|) */
    mp_of_binary_command,           /* binary operation taking |of| (e.g., |point|) */
    mp_capsule_command,             /* a value that has been put into a token list */
    mp_string_command,              /* a string constant (e.g., |"hello"|) */
    mp_internal_command,   /* internal numeric parameter (e.g., |pausing|) */
    mp_tag_command,                 /* a symbolic token without a primitive meaning */
    mp_numeric_command,             /* a numeric constant (e.g., |3.14159|) */
    mp_plus_or_minus_command,       /* either |+| or |-| */
    mp_secondary_def_command,  /* a macro defined by |secondarydef| */
    mp_tertiary_binary_command,     /* an operator at the tertiary level (e.g., |++|) */
    mp_left_brace_command,          /* the operator `|\char||| */
    mp_path_join_command,           /* the operator |..| */
    mp_ampersand_command,           /* the operator `\.\&' */
    mp_tertiary_def_command, /* a macro defined by |tertiarydef| */
    mp_primary_binary_command,   /* an operator at the expression level (e.g., |<|) */
    mp_equals_command,              /* the operator |=| */
    mp_and_command,                 /* the operator |and| */
    mp_primary_def_command,   /* a macro defined by |primarydef| */
    mp_slash_command,               /* the operator |/| */
    mp_secondary_binary_command,    /* an operator at the binary level (e.g., |shifted|) */
    mp_parameter_commmand,          /* type of parameter (|primary|, |expr|, |suffix|, etc.) */
    mp_controls_command,            /* specify control points explicitly (|controls|) */
    mp_tension_command,             /* specify tension between knots (|tension|) */
    mp_at_least_command,            /* bounded tension value (|atleast|) */
    mp_curl_command,                /* specify curl at an end knot (|curl|) */
    mp_macro_special_command,       /* special macro operators (|quote|, |\#\AT!|, etc.) */
    mp_right_delimiter_command,     /* the right delimiter of a matching pair */
    mp_left_bracket_command,        /* the operator |[| */
    mp_right_bracket_command,       /* the operator |]| */
    mp_right_brace_command,         /* the operator `|\char|}| */
    mp_with_option_command,         /* option for filling (|withpen|, |withweight|, etc.) */
    mp_thing_to_add_command,        /* variant of |addto| (|contour|, |doublepath|, |also|) */
    mp_of_command,                  /* the operator |of| */
    mp_to_command,                  /* the operator |to| */
    mp_step_command,                /* the operator |step| */
    mp_until_command,               /* the operator |until| */
    mp_within_command,              /* the operator |within| */
    mp_assignment_command,          /* the operator |:=| */
    mp_colon_command,               /* the operator |:| */
    mp_comma_command,               /* the operator |,|, must be |colon+1| */
    mp_semicolon_command,           /* the operator |;|, must be |comma+1| */
    mp_end_group_command,           /* end a group (|endgroup|), must be |semicolon+1| */
    mp_stop_command,                /* end a job (|end|, |dump|), must be |end_group+1| */
 // mp_outer_tag_command,           /* protection code added to command code */
    mp_undefined_cs_command,        /* protection code added to command code */
} mp_command_code;

@ Variables and capsules in \MP\ have a variety of \quote {types,} distinguished by
the code numbers defined here. These numbers are also not completely arbitrary.
Things that get expanded must have types |> mp_independent|; a type remaining
after expansion is numeric if and only if its code number is at least
|numeric_type|; objects containing numeric parts must have types between
|transform_type| and |pair_type|; all other types must be smaller than
|transform_type|; and among the types that are not unknown or vacuous, the
smallest two must be |boolean_type| and |string_type| in that order.

@d unknown_tag 1 /* this constant is added to certain type codes below */

@<Enumeration types@>=
typedef enum mp_variable_type {
    mp_undefined_type,        /* no type has been declared */
    mp_vacuous_type,          /* no expression was present */
    mp_boolean_type,          /* |boolean| with a known value */
    mp_unknown_boolean_type,
    mp_string_type,           /* |string| with a known value */
    mp_unknown_string_type,
    mp_pen_type,              /* |pen| with a known value */
    mp_unknown_pen_type,
    mp_nep_type,              /* |pen| with a known value */
    mp_unknown_nep_type,
    mp_path_type,             /* |path| with a known value */
    mp_unknown_path_type,
    mp_picture_type,          /* |picture| with a known value */
    mp_unknown_picture_type,
    mp_transform_type,        /* |transform| variable or capsule */
    mp_color_type,            /* |color| variable or capsule */
    mp_cmykcolor_type,        /* |cmykcolor| variable or capsule */
    mp_pair_type,             /* |pair| variable or capsule */
    mp_numeric_type,          /* variable that has been declared |numeric| but not used */
    mp_known_type,            /* |numeric| with a known value */
    mp_dependent_type,        /* a linear combination with |fraction| coefficients */
    mp_proto_dependent_type,  /* a linear combination with |scaled| coefficients */
    mp_independent_type,      /* |numeric| with unknown value */
    mp_token_list_type,       /* variable name or suffix argument or text argument */
    mp_structured_type,       /* variable with subscripts and attributes */
    mp_unsuffixed_macro_type, /* variable defined with |vardef| but no |\AT!\#| */
    mp_suffixed_macro_type,   /* variable defined with |vardef| and |\AT!\#| */

    mp_symbol_node_type,
    mp_token_node_type,
    mp_value_node_type,
    mp_attribute_node_type,
    mp_subscript_node_type,
    mp_pair_node_type,
    mp_transform_node_type,
    mp_color_node_type,
    mp_cmykcolor_node_type,

    /*
        It is important that the next 7 items remain in this order, for export as
        well as switch/case offsets.
    */

    mp_fill_node_type,
    mp_stroked_node_type,
    mp_start_clip_node_type,
    mp_start_group_node_type,
    mp_start_bounds_node_type,

    mp_stop_clip_node_type,
    mp_stop_group_node_type,
    mp_stop_bounds_node_type,

    mp_dash_node_type,
    mp_dep_node_type,
    mp_if_node_type,
    mp_edge_header_node_type,
} mp_variable_type;

@ @<Declarations@>=
static void mp_print_type (MP mp, int t);

@ @c
static const char *mp_type_string(int t)
{
    const char *s = NULL;
    switch (t) {
        case mp_undefined_type:         s = "undefined";         break;
        case mp_vacuous_type:           s = "vacuous";           break;
        case mp_boolean_type:           s = "boolean";           break;
        case mp_unknown_boolean_type:   s = "unknown boolean";   break;
        case mp_string_type:            s = "string";            break;
        case mp_unknown_string_type:    s = "unknown string";    break;
        case mp_pen_type:               s = "pen";               break;
        case mp_unknown_pen_type:       s = "unknown pen";       break;
        case mp_nep_type:               s = "pen";               break;
        case mp_unknown_nep_type:       s = "unknown pen";       break;
        case mp_path_type:              s = "path";              break;
        case mp_unknown_path_type:      s = "unknown path";      break;
        case mp_picture_type:           s = "picture";           break;
        case mp_unknown_picture_type:   s = "unknown picture";   break;
        case mp_transform_type:         s = "transform";         break;
        case mp_color_type:             s = "color";             break;
        case mp_cmykcolor_type:         s = "cmykcolor";         break;
        case mp_pair_type:              s = "pair";              break;
        case mp_known_type:             s = "known numeric";     break;
        case mp_dependent_type:         s = "dependent";         break;
        case mp_proto_dependent_type:   s = "proto-dependent";   break;
        case mp_numeric_type:           s = "numeric";           break;
        case mp_independent_type:       s = "independent";       break;
        case mp_token_list_type:        s = "token list";        break;
        case mp_structured_type:        s = "mp_structured";     break;
        case mp_unsuffixed_macro_type:  s = "unsuffixed macro";  break;
        case mp_suffixed_macro_type:    s = "suffixed macro";    break;
        case mp_symbol_node_type:       s = "symbol node";       break;
        case mp_token_node_type:        s = "token node";        break;
        case mp_value_node_type:        s = "value node";        break;
        case mp_attribute_node_type:    s = "attribute node";    break;
        case mp_subscript_node_type:    s = "subscript node";    break;
        case mp_pair_node_type:         s = "pair node";         break;
        case mp_transform_node_type:    s = "transform node";    break;
        case mp_color_node_type:        s = "color node";        break;
        case mp_cmykcolor_node_type:    s = "cmykcolor node";    break;
        case mp_fill_node_type:         s = "fill node";         break;
        case mp_stroked_node_type:      s = "stroked node";      break;
        case mp_start_clip_node_type:   s = "start clip node";   break;
        case mp_start_group_node_type:  s = "start group node";  break;
        case mp_start_bounds_node_type: s = "start bounds node"; break;
        case mp_stop_clip_node_type:    s = "stop clip node";    break;
        case mp_stop_group_node_type:   s = "stop group node";   break;
        case mp_stop_bounds_node_type:  s = "stop bounds node";  break;
        case mp_dash_node_type:         s = "dash node";         break;
        case mp_dep_node_type:          s = "dependency node";   break;
        case mp_if_node_type:           s = "if node";           break;
        case mp_edge_header_node_type:  s = "edge header node";  break;
        default:
            {
                char ss[256];
                mp_snprintf(ss, 256, "<unknown type %d>", t);
                s = mp_strdup(ss);
            }
            break;
    }
    return s;
}

void mp_print_type (MP mp, int t)
{
    if (t >= 0 && t <= mp_edge_header_node_type) {
        mp_print_str(mp, mp_type_string(t));
    } else {
        mp_print_str(mp, "unknown");
    }
}

@ Values inside \MP\ are stored in non-symbolic nodes that have a |name_type| as
well as a |type|. The possibilities for |name_type| are defined here; they will
be explained in more detail later.

@<Enumeration types...@>=
typedef enum mp_name_type_type {
    mp_root_operation,            /* |name_type| at the top level of a variable */
    mp_saved_root_operation,      /* same, when the variable has been saved */
    mp_structured_root_operation, /* |name_type| where a |mp_structured| branch occurs */
    mp_subscript_operation,       /* |name_type| in a subscript node */
    mp_attribute_operation,       /* |name_type| in an attribute node */
    mp_x_part_operation,          /* |name_type| in the |xpart| of a node */
    mp_y_part_operation,          /* |name_type| in the |ypart| of a node */
    mp_xx_part_operation,         /* |name_type| in the |xxpart| of a node */
    mp_xy_part_operation,         /* |name_type| in the |xypart| of a node */
    mp_yx_part_operation,         /* |name_type| in the |yxpart| of a node */
    mp_yy_part_operation,         /* |name_type| in the |yypart| of a node */
    mp_red_part_operation,        /* |name_type| in the |redpart| of a node */
    mp_green_part_operation,      /* |name_type| in the |greenpart| of a node */
    mp_blue_part_operation,       /* |name_type| in the |bluepart| of a node */
    mp_cyan_part_operation,       /* |name_type| in the |redpart| of a node */
    mp_magenta_part_operation,    /* |name_type| in the |greenpart| of a node */
    mp_yellow_part_operation,     /* |name_type| in the |bluepart| of a node */
    mp_black_part_operation,      /* |name_type| in the |greenpart| of a node */
    mp_grey_part_operation,       /* |name_type| in the |greypart| of a node */
    mp_capsule_operation,         /* |name_type| in stashed-away subexpressions */
    mp_token_operation,           /* |name_type| in a numeric token or string token */

    mp_boolean_type_operation,    /* the order needs to match the types (as we use deltas) ! */
    mp_string_type_operation,
    mp_pen_type_operation,
    mp_nep_type_operation,
    mp_path_type_operation,
    mp_picture_type_operation,
    mp_transform_type_operation,
    mp_color_type_operation,
    mp_cmykcolor_type_operation,
    mp_pair_type_operation,
    mp_numeric_type_operation,

    /* Symbolic nodes also have |name_type|, which is a different enumeration */

    mp_normal_operation,
    mp_internal_operation,        /* for values of internals */
    mp_macro_operation,           /* for macro names */
    mp_expr_operation,            /* for macro parameters if type |expr| */
    mp_suffix_operation,          /* for macro parameters if type |suffix| */
    mp_text_operation,            /* for macro parameters if type |text| */
    @<Operation codes@>
} mp_name_type_type;

@ Primitive operations that produce values have a secondary identification code
in addition to their command code; it's something like genera and species. For
example, |*| has the command code |primary_binary|, and its secondary
identification is |times|. The secondary codes start such that they don't overlap
with the type codes; some type codes (e.g., |mp_string_type|) are used as
operators as well as type identifications. The relative values are not critical,
except for |true_code..false_code|, |or_op..and_op|, and |filled_op..bounded_op|.
The restrictions are that |and_op-false_code=or_op-true_code|, that the ordering
of |x_part...blue_part| must match that of |x_part_operation..mp_blue_part_operation|,
and the ordering of |filled_op..bounded_op| must match that of the code values
they test for.

Beware! The operation and type unumerations in some places run in parallel (with
an offset. That makes it possible the handle types with common code using a
delta. In some cases the delta is multiplied by 2 because we have knowns and
unknowns. A less sensitive to patches would be to just duplicate the code (or to
use a function call),

@d mp_min_of_operation mp_substring_operation

@<Operation codes@>=
mp_true_operation,             /* operation code for |true| */
mp_false_operation,            /* operation code for |false| */
mp_null_picture_operation,     /* operation code for |nullpicture| */
mp_null_pen_operation,         /* operation code for |nullpen| */
mp_read_string_operation,      /* operation code for |readstring| */
mp_pen_circle_operation,       /* operation code for |pencircle| */
mp_normal_deviate_operation,   /* operation code for |normaldeviate| */
mp_read_from_operation,        /* operation code for |readfrom| */
mp_close_from_operation,       /* operation code for |closefrom| */
mp_odd_operation,              /* operation code for |odd| */
mp_known_operation,            /* operation code for |known| */
mp_unknown_operation,          /* operation code for |unknown| */
mp_not_operation,              /* operation code for |not| */
mp_decimal_operation,          /* operation code for |decimal| */
mp_reverse_operation,          /* operation code for |reverse| */
mp_uncycle_operation,          /* operation code for |uncycle| */
mp_make_path_operation,        /* operation code for |makepath| */
mp_make_pen_operation,         /* operation code for |makepen| */
mp_make_nep_operation,         /* operation code for |makenep| */
mp_convexed_operation,         /* operation code for |convexed| */
mp_uncontrolled_operation,     /* operation code for |uncontrolled| */
mp_oct_operation,              /* operation code for |oct| */
mp_hex_operation,              /* operation code for |hex| */
mp_ASCII_operation,            /* operation code for |ASCII| */
mp_char_operation,             /* operation code for |char| */
mp_length_operation,           /* operation code for |length| */
mp_turning_operation,          /* operation code for |turningnumber| */
mp_color_model_operation,      /* operation code for |colormodel| */
mp_path_part_operation,        /* operation code for |pathpart| */
mp_pen_part_operation,         /* operation code for |penpart| */
mp_dash_part_operation,        /* operation code for |dashpart| */
mp_prescript_part_operation,   /* operation code for |prescriptpart| */
mp_postscript_part_operation,  /* operation code for |postscriptpart| */
mp_stacking_part_operation,    /* operation code for |stackingpart| */
mp_sqrt_operation,             /* operation code for |sqrt| */
mp_m_exp_operation,            /* operation code for |mexp| */
mp_m_log_operation,            /* operation code for |mlog| */
mp_sin_d_operation,            /* operation code for |sind| */
mp_cos_d_operation,            /* operation code for |cosd| */
mp_floor_operation,            /* operation code for |floor| */
mp_uniform_deviate_operation,  /* operation code for |uniformdeviate| */
mp_ll_corner_operation,        /* operation code for |llcorner| */
mp_lr_corner_operation,        /* operation code for |lrcorner| */
mp_ul_corner_operation,        /* operation code for |ulcorner| */
mp_ur_corner_operation,        /* operation code for |urcorner| */
mp_center_of_operation,        /* operation code for |centerof| */
mp_center_of_mass_operation,   /* operation code for |centerofmass| */
mp_corners_operation,          /* operation code for |corners| */
mp_x_range_operation,          /* operation code for |xrange| */
mp_y_range_operation,          /* operation code for |yrange| */
mp_delta_point_operation,      /* operation code for |deltapoint| */
mp_delta_precontrol_operation, /* operation code for |deltaprecontrol| */
mp_delta_postcontrol_operation,/* operation code for |deltapostcontrol| */
mp_delta_direction_operation,  /* operation code for |deltadirection| */
mp_arc_length_operation,       /* operation code for |arclength| */
mp_angle_operation,            /* operation code for |angle| */
mp_cycle_operation,            /* operation code for |cycle| */
mp_no_cycle_operation,         /* operation code for |nocycle| */
mp_filled_operation,           /* operation code for |filled| */
mp_stroked_operation,          /* operation code for |stroked| */
mp_clipped_operation,          /* operation code for |clipped| */
mp_grouped_operation,          /* operation code for |bounded| */
mp_bounded_operation,          /* operation code for |grouped| */
mp_plus_operation,             /* operation code for \.+ */
mp_minus_operation,            /* operation code for \.- */
mp_times_operation,            /* operation code for \.* */
mp_over_operation,             /* operation code for \./ */
mp_power_operation,            /* operation code for \.^ */
mp_pythag_add_operation,       /* operation code for |++| */
mp_pythag_sub_operation,       /* operation code for |+-+| */
mp_or_operation,               /* operation code for |or| */
mp_and_operation,              /* operation code for |and| */
mp_less_than_operation,        /* operation code for \.< */
mp_less_or_equal_operation,    /* operation code for |<=| */
mp_greater_than_operation,     /* operation code for \.> */
mp_greater_or_equal_operation, /* operation code for |>=| */
mp_equal_operation,            /* operation code for \.= */
mp_unequal_operation,          /* operation code for |<>| */
mp_concatenate_operation,      /* operation code for \.\& */
mp_just_append_operation,      /* operation code for \.\&\& */
mp_rotated_operation,          /* operation code for |rotated| */
mp_slanted_operation,          /* operation code for |slanted| */
mp_scaled_operation,           /* operation code for |scaled| */
mp_shifted_operation,          /* operation code for |shifted| */
mp_transformed_operation,      /* operation code for |transformed| */
mp_uncycled_operation,         /* operation code for |uncycled| */
mp_x_scaled_operation,         /* operation code for |xscaled| */
mp_y_scaled_operation,         /* operation code for |yscaled| */
mp_z_scaled_operation,         /* operation code for |zscaled| */
mp_intertimes_operation,       /* operation code for |intersectiontimes| */
mp_intertimes_list_operation,  /* operation code for |intersectiontimeslist| */
mp_double_dot_operation,       /* operation code for improper |..| */
mp_substring_operation,        /* operation code for |substring| */
mp_subpath_operation,          /* operation code for |subpath| */
mp_direction_time_operation,   /* operation code for |directiontime| */
mp_point_operation,            /* operation code for |point| */
mp_precontrol_operation,       /* operation code for |precontrol| */
mp_postcontrol_operation,      /* operation code for |postcontrol| */
mp_direction_operation,        /* operation code for |direction| */
mp_path_point_operation,       /* operation code for |pathpoint| */
mp_path_precontrol_operation,  /* operation code for |pathprecontrol| */
mp_path_postcontrol_operation, /* operation code for |pathpostcontrol| */
mp_path_direction_operation,   /* operation code for |pathdirection| */
mp_pen_offset_operation,       /* operation code for |penoffset| */
mp_arc_time_operation,         /* operation code for |arctime| */
mp_arc_point_operation,        /* operation code for |arcpoint| */
mp_arc_point_list_operation,   /* operation code for |arcpointlist| */
mp_subarc_length_operation,    /* operation code for |subarclength| */
mp_version_operation,          /* operation code for |mpversion| */
mp_envelope_operation,         /* operation code for |envelope| */
mp_boundingpath_operation,     /* operation code for |boundingpath| */

@ @c
static const char *mp_op_string (int c)
{
    if (c <= mp_numeric_type) {
        return mp_type_string(c);
    } else {
        switch (c) {
            case mp_true_operation             : return "true";
            case mp_false_operation            : return "false";
            case mp_null_picture_operation     : return "nullpicture";
            case mp_null_pen_operation         : return "nullpen";
            case mp_read_string_operation      : return "readstring";
            case mp_pen_circle_operation       : return "pencircle";
            case mp_normal_deviate_operation   : return "normaldeviate";
            case mp_read_from_operation        : return "readfrom";
            case mp_close_from_operation       : return "closefrom";
            case mp_odd_operation              : return "odd";
            case mp_known_operation            : return "known";
            case mp_unknown_operation          : return "unknown";
            case mp_not_operation              : return "not";
            case mp_decimal_operation          : return "decimal";
            case mp_reverse_operation          : return "reverse";
            case mp_uncycle_operation          : return "uncycle";
            case mp_make_path_operation        : return "makepath";
            case mp_make_pen_operation         : return "makepen";
            case mp_make_nep_operation         : return "makenep";
            case mp_convexed_operation         : return "convexed";
            case mp_uncontrolled_operation     : return "uncontrolled";
            case mp_oct_operation              : return "oct";
            case mp_hex_operation              : return "hex";
            case mp_ASCII_operation            : return "ASCII";
            case mp_char_operation             : return "char";
            case mp_length_operation           : return "length";
            case mp_turning_operation          : return "turningnumber";
            case mp_x_part_operation           : return "xpart";
            case mp_y_part_operation           : return "ypart";
            case mp_xx_part_operation          : return "xxpart";
            case mp_xy_part_operation          : return "xypart";
            case mp_yx_part_operation          : return "yxpart";
            case mp_yy_part_operation          : return "yypart";
            case mp_red_part_operation         : return "redpart";
            case mp_green_part_operation       : return "greenpart";
            case mp_blue_part_operation        : return "bluepart";
            case mp_cyan_part_operation        : return "cyanpart";
            case mp_magenta_part_operation     : return "magentapart";
            case mp_yellow_part_operation      : return "yellowpart";
            case mp_black_part_operation       : return "blackpart";
            case mp_grey_part_operation        : return "greypart";
            case mp_color_model_operation      : return "colormodel";
            case mp_prescript_part_operation   : return "prescriptpart";
            case mp_postscript_part_operation  : return "postscriptpart";
            case mp_stacking_part_operation    : return "stackingpart";
            case mp_path_part_operation        : return "pathpart";
            case mp_pen_part_operation         : return "penpart";
            case mp_dash_part_operation        : return "dashpart";
            case mp_sqrt_operation             : return "sqrt";
            case mp_m_exp_operation            : return "mexp";
            case mp_m_log_operation            : return "mlog";
            case mp_sin_d_operation            : return "sind";
            case mp_cos_d_operation            : return "cosd";
            case mp_floor_operation            : return "floor";
            case mp_uniform_deviate_operation  : return "uniformdeviate";
            case mp_ll_corner_operation        : return "llcorner";
            case mp_lr_corner_operation        : return "lrcorner";
            case mp_ul_corner_operation        : return "ulcorner";
            case mp_ur_corner_operation        : return "urcorner";
            case mp_center_of_operation        : return "centerof";
            case mp_center_of_mass_operation   : return "centerofmass";
            case mp_corners_operation          : return "corners";
            case mp_x_range_operation          : return "xrange";
            case mp_y_range_operation          : return "yrange";
            case mp_delta_point_operation      : return "deltapoint";
            case mp_delta_precontrol_operation : return "deltaprecontrol";
            case mp_delta_postcontrol_operation: return "deltapostcontrol";
            case mp_delta_direction_operation  : return "deltadirection";
            case mp_arc_length_operation       : return "arclength";
            case mp_angle_operation            : return "angle";
            case mp_cycle_operation            : return "cycle";
            case mp_no_cycle_operation         : return "nocycle";
            case mp_filled_operation           : return "filled";
            case mp_stroked_operation          : return "stroked";
            case mp_clipped_operation          : return "clipped";
            case mp_grouped_operation          : return "grouped";
            case mp_bounded_operation          : return "bounded";
            case mp_plus_operation             : return "+";
            case mp_minus_operation            : return "-";
            case mp_times_operation            : return "*";
            case mp_over_operation             : return "/";
            case mp_power_operation            : return "^";
            case mp_pythag_add_operation       : return "++";
            case mp_pythag_sub_operation       : return "+-+";
            case mp_or_operation               : return "or";
            case mp_and_operation              : return "and";
            case mp_less_than_operation        : return "<";
            case mp_less_or_equal_operation    : return "<=";
            case mp_greater_than_operation     : return ">";
            case mp_greater_or_equal_operation : return ">=";
            case mp_equal_operation            : return "=";
            case mp_unequal_operation          : return "<>";
            case mp_concatenate_operation      : return "&";
            case mp_just_append_operation      : return "&&";
            case mp_rotated_operation          : return "rotated";
            case mp_slanted_operation          : return "slanted";
            case mp_scaled_operation           : return "scaled";
            case mp_shifted_operation          : return "shifted";
            case mp_transformed_operation      : return "transformed";
            case mp_x_scaled_operation         : return "xscaled";
            case mp_y_scaled_operation         : return "yscaled";
            case mp_z_scaled_operation         : return "zscaled";
            case mp_intertimes_operation       : return "intersectiontimes";
            case mp_intertimes_list_operation  : return "intersectiontimeslist";
            case mp_substring_operation        : return "substring";
            case mp_subpath_operation          : return "subpath";
            case mp_direction_time_operation   : return "directiontime";
            case mp_point_operation            : return "point";
            case mp_precontrol_operation       : return "precontrol";
            case mp_postcontrol_operation      : return "postcontrol";
            case mp_direction_operation        : return "direction";
            case mp_path_point_operation       : return "pathpoint";
            case mp_path_precontrol_operation  : return "pathprecontrol";
            case mp_path_postcontrol_operation : return "pathpostcontrol";
            case mp_path_direction_operation   : return "pathdirection";
            case mp_pen_offset_operation       : return "penoffset";
            case mp_arc_time_operation         : return "arctime";
            case mp_arc_point_operation        : return "arcpoint";
            case mp_arc_point_list_operation   : return "arcpointlist";
            case mp_subarc_length_operation    : return "subarclength";
            case mp_version_operation          : return "mpversion";
            case mp_envelope_operation         : return "envelope";
            case mp_boundingpath_operation     : return "boundingpath";

            case mp_pen_type_operation         : return "pen";
            case mp_nep_type_operation         : return "nep";
            case mp_path_type_operation        : return "path";
            case mp_picture_type_operation     : return "picture";
            case mp_transform_type_operation   : return "transform";
            case mp_color_type_operation       : return "color";
            case mp_cmykcolor_type_operation   : return "cmykcolor";
            case mp_pair_type_operation        : return "pair";
            case mp_numeric_type_operation     : return "numeric";

            default                            : return "..";
        }
    }
}
static void mp_print_op (MP mp, int c)
{
    mp_print_str(mp, mp_op_string(c));
}

@ \MP\ also has a bunch of internal parameters that a user might want to fuss
with. Every such parameter has an identifying code number, defined here.

@<Types...@>=
typedef enum mp_given_internal {
    mp_number_system_internal = 1,   /* the number system as set up by |numbersystem| */
    mp_number_precision_internal,    /* the number system precision as set up by |numberprecision| */
    mp_job_name_internal,            /* the jobname as set up from the options stucture */
    mp_tracing_titles_internal,      /* show titles online when they appear */
    mp_tracing_equations_internal,   /* show each variable when it becomes known */
    mp_tracing_capsules_internal,    /* show capsules too */
    mp_tracing_choices_internal,     /* show the control points chosen for paths */
    mp_tracing_specs_internal,       /* show path subdivision prior to filling with polygonal a pen */
    mp_tracing_commands_internal,    /* show commands and operations before they are performed */
    mp_tracing_restores_internal,    /* show when a variable or internal is restored */
    mp_tracing_macros_internal,      /* show macros before they are expanded */
    mp_tracing_output_internal,      /* dummy */
    mp_tracing_stats_internal,       /* show memory usage at end of job */ /* now a dummy */
    mp_tracing_online_internal,      /* show long diagnostics on terminal and in the log file */
    mp_year_internal,                /* the current year (e.g., 1984) */
    mp_month_internal,               /* the current month (e.g., 3 $\equiv$ March) */
    mp_day_internal,                 /* the current day of the month */
    mp_time_internal,                /* the number of minutes past midnight when this job started */
    mp_hour_internal,                /* the number of hours past midnight when this job started */
    mp_minute_internal,              /* the number of minutes in that hour when this job started */
    mp_char_code_internal,           /* the number of the next character to be output */
    mp_char_wd_internal,             /* the width of the next character to be output */
    mp_char_ht_internal,             /* the height of the next character to be output */
    mp_char_dp_internal,             /* the depth of the next character to be output */
    mp_char_ic_internal,             /* the italic correction of the next character to be output */
    mp_pausing_internal,             /* dummy */
    mp_showstopping_internal,        /* positive to stop after each |show| command */
    mp_texscriptmode_internal,       /* controls spacing in texmode */
    mp_overloadmode_internal,
    mp_linejoin_internal,            /* as in \ps: 0 for mitered, 1 for round, 2 for beveled */
    mp_linecap_internal,             /* as in \ps: 0 for butt, 1 for round, 2 for square */
    mp_stacking_internal,
    mp_miterlimit_internal,          /* controls miter length as in \ps */
    mp_warning_check_internal,       /* controls error message when variable value is large */
    mp_true_corners_internal,        /* positive to make |llcorner| etc. ignore |setbounds| */
    mp_default_color_model_internal, /* the default color model for unspecified items */
    mp_restore_clip_color_internal,
} mp_given_internal;

typedef struct mp_internal {
    mp_value  v;
    char     *intname;
    int       run;
    int       padding;
} mp_internal;

@ @<MPlib internal header stuff@>=
typedef enum mp_linecap_codes {
    mp_butt_linecap_code,
    mp_rounded_linecap_code,
    mp_squared_linecap_code,
    /* see below */
    mp_weird_linecap_code,
} mp_linecap_codes;

typedef enum mp_linejoin_codes {
    mp_mitered_linejoin_code,
    mp_rounded_linejoin_code,
    mp_beveled_linejoin_code,
    /* we see this value being used */
    mp_weird_linejoin_code,
} mp_linejoin_codes;

@ @<MPlib internal header stuff@>=
# define internal_value(A)        mp->internal[(A)].v.data.n
# define internal_string(A)       mp->internal[A].v.data.str
# define set_internal_string(A,B) mp->internal[(A)].v.data.str=(B)
# define internal_name(A)         mp->internal[(A)].intname
# define set_internal_name(A,B)   mp->internal[(A)].intname=(B)
# define internal_type(A)         mp->internal[A].v.type
# define set_internal_type(A,B)   mp->internal[(A)].v.type=(B)
# define internal_run(A)          mp->internal[(A)].run
# define set_internal_run(A,B)    mp->internal[(A)].run=(B)

@ @d max_given_internal mp_restore_clip_color_internal

@<Glob...@>=
mp_internal *internal;     /* the values of internal quantities */
int          int_ptr;      /* the maximum internal quantity defined so far */
int          max_internal; /* current maximum number of internal quantities */

@ @<Allocate or initialize ...@>=
//mp->max_internal = 2 * max_given_internal;
mp->max_internal = 1000 + max_given_internal;
mp->internal     = mp_memory_allocate((size_t) (mp->max_internal + 1) * sizeof(mp_internal));

memset(mp->internal, 0, (size_t) (mp->max_internal + 1) * sizeof(mp_internal));
for (int i = 1; i <= mp->max_internal; i++) {
    new_number(mp->internal[i].v.data.n);
}
for (int i = 1; i <= max_given_internal; i++) {
    set_internal_type(i, mp_known_type);
}

set_internal_type(mp_number_system_internal, mp_string_type);
set_internal_type(mp_job_name_internal, mp_string_type);

@ @<Set initial ...@>=
mp->int_ptr = max_given_internal;

@ The symbolic names for internal quantities are put into \MP's hash table by
using a routine called |primitive|, which will be defined later. Let us enter
them now, so that we don't have to list all those names again anywhere else.

@<Put each of \MP's primitives into the hash table@>=
mp_primitive(mp, "tracingtitles", mp_internal_command, mp_tracing_titles_internal);
@:tracingtitles_}{|tracingtitles| primitive@>
mp_primitive(mp, "tracingequations", mp_internal_command, mp_tracing_equations_internal);
@:mp_tracing_equations_}{|tracingequations| primitive@>
mp_primitive(mp, "tracingcapsules", mp_internal_command, mp_tracing_capsules_internal);
@:mp_tracing_capsules_}{|tracingcapsules| primitive@>
mp_primitive(mp, "tracingchoices", mp_internal_command, mp_tracing_choices_internal);
@:mp_tracing_choices_}{|tracingchoices| primitive@>
mp_primitive(mp, "tracingspecs", mp_internal_command, mp_tracing_specs_internal);
@:mp_tracing_specs_}{|tracingspecs| primitive@>
mp_primitive(mp, "tracingcommands", mp_internal_command, mp_tracing_commands_internal);
@:mp_tracing_commands_}{|tracingcommands| primitive@>
mp_primitive(mp, "tracingrestores", mp_internal_command, mp_tracing_restores_internal);
@:mp_tracing_restores_}{|tracingrestores| primitive@>
mp_primitive(mp, "tracingmacros", mp_internal_command, mp_tracing_macros_internal);
@:mp_tracing_macros_}{|tracingmacros| primitive@>
mp_primitive(mp, "tracingoutput", mp_internal_command, mp_tracing_output_internal);
@:mp_tracing_output_}{|tracingoutput| primitive@>
mp_primitive(mp, "tracingstats", mp_internal_command, mp_tracing_stats_internal);
@:mp_tracing_stats_}{|tracingstats| primitive@>
mp_primitive(mp, "tracingonline", mp_internal_command, mp_tracing_online_internal);
@:mp_tracing_online_}{|tracingonline| primitive@>
mp_primitive(mp, "year", mp_internal_command, mp_year_internal);
@:mp_year_}{|year| primitive@>
mp_primitive(mp, "month", mp_internal_command, mp_month_internal);
@:mp_month_}{|month| primitive@>
mp_primitive(mp, "day", mp_internal_command, mp_day_internal);
@:mp_day_}{|day| primitive@>
mp_primitive(mp, "time", mp_internal_command, mp_time_internal);
@:time_}{|time| primitive@>
mp_primitive(mp, "hour", mp_internal_command, mp_hour_internal);
@:hour_}{|hour| primitive@>
mp_primitive(mp, "minute", mp_internal_command, mp_minute_internal);
@:minute_}{|minute| primitive@>
mp_primitive(mp, "charcode", mp_internal_command, mp_char_code_internal);
@:mp_char_code_}{|charcode| primitive@>
mp_primitive(mp, "charwd", mp_internal_command, mp_char_wd_internal);
@:mp_char_wd_}{|charwd| primitive@>
mp_primitive(mp, "charht", mp_internal_command, mp_char_ht_internal);
@:mp_char_ht_}{|charht| primitive@>
mp_primitive(mp, "chardp", mp_internal_command, mp_char_dp_internal);
@:mp_char_dp_}{|chardp| primitive@>
mp_primitive(mp, "charic", mp_internal_command, mp_char_ic_internal);
@:mp_char_ic_}{|charic| primitive@>
mp_primitive(mp, "pausing", mp_internal_command, mp_pausing_internal);
@:mp_pausing_}{|pausing| primitive@>
mp_primitive(mp, "showstopping", mp_internal_command, mp_showstopping_internal);
@:mp_showstopping_}{|showstopping| primitive@>
mp_primitive(mp, "texscriptmode", mp_internal_command, mp_texscriptmode_internal);
@:mp_texscriptmode_}{|texscriptmode| primitive@>
mp_primitive(mp, "overloadmode", mp_internal_command, mp_overloadmode_internal);
@:mp_overloadmode_}{|overloadmode| primitive@>
mp_primitive(mp, "linejoin", mp_internal_command, mp_linejoin_internal);
@:mp_linejoin_}{|linejoin| primitive@>
mp_primitive(mp, "linecap", mp_internal_command, mp_linecap_internal);
@:mp_linecap_}{|linecap| primitive@>
mp_primitive(mp, "stacking", mp_internal_command, mp_stacking_internal);
@:mp_stacking_}{|stacking| primitive@>
mp_primitive(mp, "miterlimit", mp_internal_command, mp_miterlimit_internal);
@:mp_miterlimit_}{|miterlimit| primitive@>
mp_primitive(mp, "warningcheck", mp_internal_command, mp_warning_check_internal);
@:mp_warning_check_}{|warningcheck| primitive@>
mp_primitive(mp, "truecorners", mp_internal_command, mp_true_corners_internal);
@:mp_true_corners_}{|truecorners| primitive@>
mp_primitive(mp, "defaultcolormodel", mp_internal_command, mp_default_color_model_internal);
@:mp_default_color_model_}{|defaultcolormodel| primitive@>
mp_primitive(mp, "restoreclipcolor", mp_internal_command, mp_restore_clip_color_internal);
@:mp_restore_clip_color_}{|restoreclipcolor| primitive@>
mp_primitive(mp, "numbersystem", mp_internal_command, mp_number_system_internal);
@:mp_number_system_}{|numbersystem| primitive@>
mp_primitive(mp, "numberprecision", mp_internal_command, mp_number_precision_internal);
@:mp_number_precision_}{|numberprecision| primitive@>
mp_primitive(mp, "jobname", mp_internal_command, mp_job_name_internal);
@:mp_job_name_}{|jobname| primitive@>

@ Colors can be specified in four color models. In the special case of
|no_model|, MetaPost does not output any color operator to the postscript output.

Note: these values are passed directly on to |with_option|. This only works
because the other possible values passed to |with_option| are 8 and 10
respectively (from |with_pen| and |with_picture|).

There is a first state, that is only used for |gs_colormodel|. It flags the fact
that there has not been any kind of color specification by the user so far in the
game.

@<MPlib header stuff@>=
typedef enum mp_color_model {
    mp_no_model,
    mp_grey_model,
    mp_rgb_model,
    mp_cmyk_model,
    mp_uninitialized_model,
} mp_color_model;

@ @<Initialize table entries@>=
number_clone(internal_value(mp_default_color_model_internal),unity_t);
number_multiply_int(internal_value(mp_default_color_model_internal), mp_rgb_model);
number_clone(internal_value(mp_restore_clip_color_internal), unity_t);
set_internal_string(mp_number_system_internal, mp_intern (mp, "scaled"));
number_clone(internal_value(mp_number_precision_internal), precision_default);
number_clone(internal_value(mp_texscriptmode_internal), unity_t);
number_clone(internal_value(mp_overloadmode_internal), zero_t);

@ Well, we do have to list the names one more time, for use in symbolic
printouts.

@<Initialize table...@>=
set_internal_name(mp_tracing_titles_internal,      mp_strdup("tracingtitles"));
set_internal_name(mp_tracing_equations_internal,   mp_strdup("tracingequations"));
set_internal_name(mp_tracing_capsules_internal,    mp_strdup("tracingcapsules"));
set_internal_name(mp_tracing_choices_internal,     mp_strdup("tracingchoices"));
set_internal_name(mp_tracing_specs_internal,       mp_strdup("tracingspecs"));
set_internal_name(mp_tracing_commands_internal,    mp_strdup("tracingcommands"));
set_internal_name(mp_tracing_restores_internal,    mp_strdup("tracingrestores"));
set_internal_name(mp_tracing_macros_internal,      mp_strdup("tracingmacros"));
set_internal_name(mp_tracing_output_internal,      mp_strdup("tracingoutput"));
set_internal_name(mp_tracing_stats_internal,       mp_strdup("tracingstats"));
set_internal_name(mp_tracing_online_internal,      mp_strdup("tracingonline"));
set_internal_name(mp_year_internal,                mp_strdup("year"));
set_internal_name(mp_month_internal,               mp_strdup("month"));
set_internal_name(mp_day_internal,                 mp_strdup("day"));
set_internal_name(mp_time_internal,                mp_strdup("time"));
set_internal_name(mp_hour_internal,                mp_strdup("hour"));
set_internal_name(mp_minute_internal,              mp_strdup("minute"));
set_internal_name(mp_char_code_internal,           mp_strdup("charcode"));
set_internal_name(mp_char_wd_internal,             mp_strdup("charwd"));
set_internal_name(mp_char_ht_internal,             mp_strdup("charht"));
set_internal_name(mp_char_dp_internal,             mp_strdup("chardp"));
set_internal_name(mp_char_ic_internal,             mp_strdup("charic"));
set_internal_name(mp_pausing_internal,             mp_strdup("pausing")); /* dummy */
set_internal_name(mp_showstopping_internal,        mp_strdup("showstopping"));
set_internal_name(mp_texscriptmode_internal,       mp_strdup("texscriptmode"));
set_internal_name(mp_overloadmode_internal,        mp_strdup("overloadmode"));
set_internal_name(mp_linejoin_internal,            mp_strdup("linejoin"));
set_internal_name(mp_linecap_internal,             mp_strdup("linecap"));
set_internal_name(mp_stacking_internal,            mp_strdup("stacking"));
set_internal_name(mp_miterlimit_internal,          mp_strdup("miterlimit"));
set_internal_name(mp_warning_check_internal,       mp_strdup("warningcheck"));
set_internal_name(mp_true_corners_internal,        mp_strdup("truecorners"));
set_internal_name(mp_default_color_model_internal, mp_strdup("defaultcolormodel"));
set_internal_name(mp_restore_clip_color_internal,  mp_strdup("restoreclipcolor"));
set_internal_name(mp_job_name_internal,            mp_strdup("jobname"));
set_internal_name(mp_number_system_internal,       mp_strdup("numbersystem"));
set_internal_name(mp_number_precision_internal,    mp_strdup("numberprecision"));

@ The following procedure, which is called just before \MP\ initializes its input
and output, establishes the initial values of the date and time. @^system
dependencies@>

Note that the values are |scaled| integers. Hence \MP\ can no longer be used
after the year 32767.

@c
static void mp_fix_date_and_time (MP mp)
{
    time_t aclock = time ((time_t *) 0);
    struct tm *tmptr = localtime (&aclock);
    number_clone(internal_value(mp_time_internal), unity_t);
    number_multiply_int(internal_value(mp_time_internal), (tmptr->tm_hour * 60 + tmptr->tm_min));
    number_clone(internal_value(mp_hour_internal), unity_t);
    number_multiply_int(internal_value(mp_hour_internal), (tmptr->tm_hour));
    number_clone(internal_value(mp_minute_internal), unity_t);
    number_multiply_int(internal_value(mp_minute_internal), (tmptr->tm_min));
    number_clone(internal_value(mp_day_internal), unity_t);
    number_multiply_int(internal_value(mp_day_internal), (tmptr->tm_mday));
    number_clone(internal_value(mp_month_internal), unity_t);
    number_multiply_int(internal_value(mp_month_internal), (tmptr->tm_mon + 1));
    number_clone(internal_value(mp_year_internal), unity_t);
    number_multiply_int(internal_value(mp_year_internal), (tmptr->tm_year + 1900));
}

@ @<Declarations@>=
static void mp_fix_date_and_time (MP mp);

@ \MP\ is occasionally supposed to print diagnostic information that goes only
into the transcript file, unless |mp_tracing_online| is positive. Now that we
have defined |mp_tracing_online| we can define two routines that adjust the
destination of print commands:

@<Declarations@>=
static void mp_begin_diagnostic (MP mp);
static void mp_end_diagnostic   (MP mp, int blank_line);
static void mp_print_diagnostic (MP mp, const char *s, const char *t, int nuline);

@ @c
static void mp_begin_diagnostic (MP mp)
{
    /* prepare to do some tracing */
    mp->old_selector = mp->selector;
    if (number_nonpositive(internal_value(mp_tracing_online_internal)) && (mp->selector == mp_term_and_log_selector)) {
        mp->selector = mp_log_only_selector;
        if (mp->history == mp_spotless) {
            mp->history = mp_warning_issued;
        }
    }
}

void mp_end_diagnostic (MP mp, int blank_line)
{
    /* restore proper conditions after tracing */
    mp_print_nl(mp, "");
    if (blank_line) {
        mp_print_ln(mp);
    }
    mp->selector = mp->old_selector;
}

@ @<Glob...@>=
unsigned int old_selector;

@ We will occasionally use |begin_diagnostic| in connection with line-number
printing, as follows. (The parameter |s| is typically |"Path"| or |"Cycle spec"|,
etc.)

@c
static void mp_print_diagnostic (MP mp, const char *s, const char *t, int nuline)
{
    mp_begin_diagnostic(mp);
    if (nuline) {
        mp_print_nl(mp, s);
    } else {
        mp_print_str(mp, s);
    }
    mp_print_str(mp, " at line ");
    mp_print_int(mp, mp_true_line(mp));
    mp_print_str(mp, t);
    mp_print_chr(mp, ':');
}

@ The 256 |unsigned char| characters are grouped into classes by means of the
|char_class| table. Individual class numbers have no semantic or syntactic
significance, except in a few instances defined here. There's also |max_class|,
which can be used as a basis for additional class numbers in nonstandard
extensions of \MP.

@<Enumeration types@>=
typedef enum mp_class_codes {
    mp_digit_class             =  0, /* the class number of |0123456789| */
    mp_period_class            =  1, /* the class number of |.| */
    mp_space_class             =  2, /* the class number of spaces and nonstandard characters */
    mp_percent_class           =  3, /* the class number of `\.\%' */
    mp_string_class            =  4, /* the class number of |"| */
    mp_comma_class             =  5, /* the , */
    mp_semicolon_class         =  6, /* the ; */
    mp_left_parenthesis_class  =  7, /* the class number of |(| */
    mp_right_parenthesis_class =  8, /* the class number of |)| */
    mp_letter_class            =  9, /* letters and the underline character */
    mp_suffix_class            = 15,
    mp_left_bracket_class      = 17, /* |[| */
    mp_right_bracket_class     = 18, /* |]| */
    mp_brace_class             = 19,
    mp_invalid_class           = 20, /* bad character in the input */
    mp_max_class               = 20, /* the largest class number */
} mp_class_codes;

@ The class numbers:

@<Glob...@>=
int char_class[256];

@ If changes are made to accommodate non-ASCII character sets, they should follow
the guidelines in Appendix~C of {\sl The {\logos METAFONT}book}.
@:METAFONTbook}{\sl The {\logos METAFONT}book@> @^system dependencies@>

@<Set initial ...@>=
for (int k = '0'; k <= '9'; k++) {
    mp->char_class[k] = mp_digit_class;
}
for (int k = 'A'; k <= 'Z'; k++) {
    mp->char_class[k] = mp_letter_class;
}
for (int k = 'a'; k <= 'z'; k++) {
    mp->char_class[k] = mp_letter_class;
}

mp->char_class['.']  = mp_period_class;
mp->char_class[' ']  = mp_space_class;
mp->char_class['%']  = mp_percent_class;
mp->char_class['"']  = mp_string_class;
mp->char_class[',']  = mp_comma_class;
mp->char_class[';']  = mp_semicolon_class;
mp->char_class['(']  = mp_left_parenthesis_class;
mp->char_class[')']  = mp_right_parenthesis_class;

mp->char_class['_']  = mp_letter_class;
mp->char_class['<']  = 10;
mp->char_class['=']  = 10;
mp->char_class['>']  = 10;
mp->char_class[':']  = 10;
mp->char_class['|']  = 10;
mp->char_class['`']  = 11;
mp->char_class['\''] = 11;
mp->char_class['+']  = 12;
mp->char_class['-']  = 12;
mp->char_class['/']  = 13;
mp->char_class['*']  = 13;
mp->char_class['\\'] = 13;
mp->char_class['^']  = 13;
mp->char_class['!']  = 14;
mp->char_class['?']  = 14;
mp->char_class['#']  = mp_suffix_class;
mp->char_class['&']  = mp_suffix_class;
mp->char_class['@@'] = mp_suffix_class; /* will become one after cwebbing */
mp->char_class['$']  = mp_suffix_class;
mp->char_class['^']  = 16;
mp->char_class['~']  = 16;
mp->char_class['[']  = mp_left_bracket_class;
mp->char_class[']']  = mp_right_bracket_class;
mp->char_class['{']  = mp_brace_class;
mp->char_class['}']  = mp_brace_class;

for (int k = 0; k < ' '; k++) {
    mp->char_class[k] = mp_invalid_class;
}

mp->char_class['\r'] = mp_space_class;
mp->char_class['\n'] = mp_space_class;
mp->char_class['\t'] = mp_space_class;
mp->char_class['\f'] = mp_space_class;

for (int k = 127; k <= 255; k++) {
    mp->char_class[k] = mp->utf8_mode ? mp_letter_class : mp_invalid_class;
}

if (mp->text_mode) {
    mp->char_class[2] = mp_string_class;    /* ascii 2 STX*/
 /* mp->char_class[3] = mp_string_class; */ /* ascii 3 ETX */
}

@* The hash table.

Symbolic tokens are stored in and retrieved from an AVL tree. This is not as fast
as an actual hash table, but it is easily extensible.

A symbolic token contains a pointer to the |mp_string| that contains the string
representation of the symbol, a |halfword| that holds the current command value
of the token, and an |mp_value| for the associated equivalent.

@d set_text(A) {
    (A)->text = (B) ;
}

@d set_eq_type(A,B) {
    (A)->type = (B) ;
}

@d set_eq_property(A,B) {
    (A)->property = (B) ;
}

@d set_equiv(A,B) {
    (A)->v.data.node = NULL ;
    (A)->v.data.indep.serial = (B);
}

@d set_equiv_node(A,B) {
    (A)->v.data.node = (B) ;
    (A)->v.data.indep.serial = 0;
}

@d set_equiv_sym(A,B) {
    (A)->v.data.node = (mp_node) (B);
    (A)->v.data.indep.serial = 0;
}

@ @c
# define text(A)        (A)->text
# define eq_type(A)     (A)->type
# define eq_property(A) (A)->property
# define equiv(A)       (A)->v.data.indep.serial
# define equiv_node(A)  (A)->v.data.node
# define equiv_sym(A)   (mp_sym)(A)->v.data.node

@ @<Types...@>=
typedef struct mp_symbol_entry {
    int        type;
    int        property; /* we had padding room anyway */
    mp_value   v;
    mp_string  text;
    void      *parent;
} mp_symbol_entry;

@ @<Glob...@>=
int          st_count;       /* total number of known identifiers */
avl_tree     symbols;        /* avl tree of symbolic tokens */
avl_tree     frozen_symbols; /* avl tree of frozen symbolic tokens */
avl_iterator symbol_iterator;

mp_sym frozen_bad_vardef;
mp_sym frozen_colon;
mp_sym frozen_end_def;
mp_sym frozen_end_for;
mp_sym frozen_end_group;
mp_sym frozen_etex;
mp_sym frozen_fi;
mp_sym frozen_inaccessible;
mp_sym frozen_left_bracket;
mp_sym frozen_repeat_loop;
mp_sym frozen_right_delimiter;
mp_sym frozen_semicolon;
mp_sym frozen_slash;
mp_sym frozen_undefined;
mp_sym frozen_dump;

@ Here are the functions needed for the avl construction.

@<Declarations@>=
static int   mp_compare_symbols_entry (void *p, const void *pa, const void *pb);
static void *mp_copy_symbols_entry    (const void *p);
static void *mp_delete_symbols_entry  (void *p);

@ The avl comparison function is a straightword version of |strcmp|,
except that checks for the string lengths first.

@c
static int mp_compare_symbols_entry (void *p, const void *pa, const void *pb)
{
    const mp_symbol_entry *a = (const mp_symbol_entry *) pa;
    const mp_symbol_entry *b = (const mp_symbol_entry *) pb;
    (void) p;
    if (a->text->len != b->text->len) {
        return (a->text->len > b->text->len ? 1 : -1);
    }
    return strncmp ((const char *) a->text->str, (const char *) b->text->str, a->text->len);
}

@ Copying a symbol happens when an item is inserted into an AVL tree. The |text|
and |mp_number| needs to be deep copied, every thing else can be reassigned.

@c
static void *mp_copy_symbols_entry (const void *p)
{
 // const mp_symbol_entry *fp = (const mp_symbol_entry *) p;
    mp_symbol_entry *fp = (mp_symbol_entry *) p;
    MP mp = (MP)fp->parent;
    mp_sym ff = mp_memory_allocate(sizeof(mp_symbol_entry));
    if (ff == NULL) {
        return NULL;
    }
    ff->text = mp_aux_copy_strings_entry(fp->text);
    if (ff->text == NULL) {
        return NULL;
    }
    ff->v = fp->v;
    ff->type = fp->type;
    ff->property = fp->property;
    ff->parent = mp;
    new_number_clone(ff->v.data.n, fp->v.data.n);
    return ff;
}

@ In the current implementation, symbols are not freed until the end of the run.

@c
static void *mp_delete_symbols_entry (void *p)
{
    mp_sym ff = (mp_sym) p;
    MP mp = (MP) ff->parent;
    free_number(ff->v.data.n);
    mp_memory_free(ff->text->str);
    mp_memory_free(ff->text);
    mp_memory_free(ff);
    return NULL;
}

@ @<Allocate or initialize ...@>=
mp->symbols = avl_create(mp_compare_symbols_entry, mp_copy_symbols_entry, mp_delete_symbols_entry, mp_memory_allocate, mp_memory_free, NULL);
mp->frozen_symbols = avl_create(mp_compare_symbols_entry, mp_copy_symbols_entry, mp_delete_symbols_entry, mp_memory_allocate, mp_memory_free, NULL);

@ @<Dealloc variables@>=
if (mp->symbols != NULL) {
    avl_destroy (mp->symbols);
}
if (mp->frozen_symbols != NULL) {
    avl_destroy (mp->frozen_symbols);
}

@ Actually creating symbols is done by |id_lookup|, but in order to do so it
needs a way to create a new, empty symbol structure.

@<Declarations@>=
static mp_sym new_symbols_entry (MP mp, unsigned char *nam, size_t len);

@ @c
static mp_sym new_symbols_entry (MP mp, unsigned char *nam, size_t len)
{
    mp_sym ff = mp_memory_clear_allocate(sizeof(mp_symbol_entry));
    ff->parent = mp;
    ff->text = mp_memory_allocate(sizeof(mp_lstring));
    ff->text->str = nam;
    ff->text->len = len;
    ff->type = mp_tag_command;
    ff->v.type = mp_known_type;
    new_number(ff->v.data.n);
    return ff;
}

@ There is one global variable so that |id_lookup| does not always have to create
a new entry just for testing. This is not freed because it creates a double-free
thanks to the |NULL| init.

@<Global ...@>=
mp_sym id_lookup_test;

@ @<Initialize table entries@>=
mp->id_lookup_test = new_symbols_entry(mp, NULL, 0);

@ Certain symbols are \quote {frozen} and not redefinable, since they are used in
error recovery.

@<Initialize table entries@>=
mp->st_count = 0;
mp->frozen_bad_vardef      = mp_frozen_primitive(mp, "a bad variable", mp_tag_command, 0);
mp->frozen_right_delimiter = mp_frozen_primitive(mp, ")",              mp_right_delimiter_command, 0);
mp->frozen_inaccessible    = mp_frozen_primitive(mp, " INACCESSIBLE",  mp_tag_command, 0);
mp->frozen_undefined       = mp_frozen_primitive(mp, " UNDEFINED",     mp_tag_command, 0);

@ Here is the subroutine that searches the avl tree for an identifier that
matches a given string of length~|l| appearing in |buffer[j.. (j+l-1)]|. If the
identifier is not found, it is inserted if |insert_new| is |true|, and the
corresponding symbol will be returned.

There are two variations on the lookup function: one for the normal symbol table,
and one for the table of error recovery symbols.

Note: simple symbols like |+|, |-|, |*| and |/| are also looked up. One can argue
that a user can redefine them but colons etc. are interpreted direct. Maybe
there's room for some optimization here. We could just put references (to
|mp_sym|) in the |mp| instance object for the handful. Okay, we also have |:=| so
maybe only for single character ones ... not worth the trouble.

@d mp_id_lookup(A,B,C,D) mp_do_id_lookup((A), mp->symbols, (B), (C), (D))

@c
static mp_sym mp_do_id_lookup (MP mp, avl_tree symbols, char *j, size_t l, int insert_new)
{
    mp_sym str;
    mp->id_lookup_test->text->str = (unsigned char *) j;
    mp->id_lookup_test->text->len = l;
    str = (mp_sym) avl_find(mp->id_lookup_test, symbols);
    if (str == NULL && insert_new) {
        unsigned char *nam = (unsigned char *) mp_strndup(j, l);
        mp_sym s = new_symbols_entry(mp, nam, l);
        mp->st_count++;
        avl_ins(s, symbols, avl_false);
        str = (mp_sym) avl_find(s, symbols);
        mp_delete_symbols_entry(s);
    }
    return str;
}

@ @<Exported function headers@>=
extern int   mp_initialize_symbol_traverse (MP mp);
extern void  mp_kill_symbol_traverse       (MP mp);
extern void *mp_fetch_symbol_traverse      (MP mp);
extern void *mp_fetch_symbol               (MP mp, char *s);

@ @c
int mp_initialize_symbol_traverse (MP mp)
{
    mp->symbol_iterator = avl_iterator_new(mp->symbols, AVL_ITERATOR_INI_PRE);
    return (mp->symbol_iterator != NULL);
}

void mp_kill_symbol_traverse (MP mp)
{
    avl_iterator_kill(mp->symbol_iterator);
}

void *mp_fetch_symbol_traverse (MP mp)
{
    return avl_iterator_next(mp->symbol_iterator);
}

void *mp_fetch_symbol (MP mp, char *s)
{
    return mp_id_lookup(mp, s, strlen(s), 0);
}

@ We need to put \MP's \quote {primitive} symbolic tokens into the hash table,
together with their command code (which will be the |eq_type|) and an operand
(which will be the |equiv|). The |primitive| procedure does this, in a way that
no \MP\ user can. The global value |cur_sym| contains the new |eqtb| pointer
after |primitive| has acted.

@c
static void mp_primitive (MP mp, const char *ss, int c, int o)
{
//  char *s = mp_strdup(ss);
//  set_cur_sym(mp_id_lookup(mp, s, strlen(s), 1));
//  mp_memory_free(s);
    set_cur_sym(mp_id_lookup(mp, (char *) ss, strlen(ss), 1));
    set_eq_type(cur_sym, c);
    set_eq_property(cur_sym, 0x1); /* todo: enumeration values */
    set_equiv(cur_sym, o);
}

@ Some other symbolic tokens only exist for error recovery.

@c
static mp_sym mp_frozen_primitive (MP mp, const char *ss, int c, int o)
{
//  char *s = mp_strdup(ss);
//  mp_sym str = mp_do_id_lookup(mp, mp->frozen_symbols, s, strlen(s), 1);
//  mp_memory_free(s);
    mp_sym str = mp_do_id_lookup(mp, mp->frozen_symbols, (char *) ss, strlen(ss), 1);
    str->type = c;
    str->property = 0x1; /* todo: enumeration values */
    str->v.data.indep.serial = o;
    return str;
}

@ This routine returns |true| if the argument is an un-redefinable symbol because
it is one of the error recovery tokens (as explained elsewhere,
|frozen_inaccessible| actuall is redefinable).

@c
static int mp_is_frozen (MP mp, mp_sym sym)
{
    mp_sym temp = mp_do_id_lookup(mp, mp->frozen_symbols, (char *) sym->text->str, sym->text->len, 0);
    if (temp == mp->frozen_inaccessible) {
        return 0;
    } else {
        return (temp == sym);
    }
}

@ Many of \MP's primitives need no |equiv|, since they are identifiable by their
|eq_type| alone. These primitives are loaded into the hash table as follows:

@<Put each of \MP's primitives into the hash table@>=
mp_primitive(mp, "..", mp_path_join_command, 0);
@:.._}{|..| primitive@>
mp_primitive(mp, "[", mp_left_bracket_command, 0);
mp->frozen_left_bracket = mp_frozen_primitive (mp, "[", mp_left_bracket_command, 0);
@:[ }{|[| primitive@>
mp_primitive(mp, "]", mp_right_bracket_command, 0);
@:] }{|]| primitive@>
mp_primitive(mp, "}", mp_right_brace_command, 0);
@:]]}{|\char`\|} primitive@>
mp_primitive(mp, "{", mp_left_brace_command, 0);
@:][}{|\char`\{| primitive@>
mp_primitive(mp, ":", mp_colon_command, 0);
mp->frozen_colon = mp_frozen_primitive (mp, ":", mp_colon_command, 0);
@:: }{|:| primitive@>
mp_primitive(mp, ":=", mp_assignment_command, 0);
@::=_}{|:=| primitive@>
mp_primitive(mp, ",", mp_comma_command, 0);
@:, }{\., primitive@>
mp_primitive(mp, ";", mp_semicolon_command, 0);
mp->frozen_semicolon = mp_frozen_primitive (mp, ";", mp_semicolon_command, 0);
@:; }{\.; primitive@>
mp_primitive(mp, "\\", mp_relax_command, 0);
@:]]\||\char`\\| primitive@>
mp_primitive(mp, "addto", mp_add_to_command, 0);
@:add_to_|{|addto| primitive@>
mp_primitive(mp, "atleast", mp_at_least_command, 0);
@:at_least_}{|atleast| primitive@>
mp_primitive(mp, "begingroup", mp_begin_group_command, 0);
mp->bg_loc = cur_sym;
@:begin_group_}{|begingroup| primitive@>
mp_primitive(mp, "controls", mp_controls_command, 0);
@:controls_}{|controls| primitive@>
mp_primitive(mp, "curl", mp_curl_command, 0);
@:curl_}{|curl| primitive@>
mp_primitive(mp, "delimiters", mp_delimiters_command, 0);
@:delimiters_}{|delimiters| primitive@>
mp_primitive(mp, "endgroup", mp_end_group_command, 0);

mp->eg_loc = cur_sym;
mp->frozen_end_group = mp_frozen_primitive (mp, "endgroup", mp_end_group_command, 0);

@:endgroup_}{|endgroup| primitive@>
mp_primitive(mp, "everyjob", mp_every_job_command, 0);
@:every_job_}{|everyjob| primitive@>
mp_primitive(mp, "exitif", mp_exit_test_command, 0);
@:exit_if_}{|exitif| primitive@>
mp_primitive(mp, "expandafter", mp_expand_after_command, 0);
@:expand_after_}{|expandafter| primitive@>
mp_primitive(mp, "interim", mp_interim_command, 0);
@:interim_}{|interim| primitive@>
mp_primitive(mp, "let", mp_let_command, 0);
@:let_}{|let| primitive@>
mp_primitive(mp, "newinternal", mp_new_internal_command, 0);
@:new_internal_}{|newinternal| primitive@>
mp_primitive(mp, "of", mp_of_command, 0);
@:of_}{|of| primitive@>
mp_primitive(mp, "randomseed", mp_only_set_command, mp_random_seed_code);
@:mp_random_seed_}{|randomseed| primitive@>
mp_primitive(mp, "maxknotpool", mp_only_set_command, mp_max_knot_pool_code);
@:mp_max_knot_pool_}{|maxknotpool| primitive@>
mp_primitive(mp, "save", mp_save_command, 0);
@:save_}{|save| primitive@>
mp_primitive(mp, "scantokens", mp_scan_tokens_command, 0);
@:scan_tokens_}{|scantokens| primitive@>
mp_primitive(mp, "runscript", mp_runscript_command, 0);
@:run_script_}{|runscript| primitive@>
mp_primitive(mp, "maketext", mp_maketext_command, 0);
@:make_text_}{|maketext| primitive@>
mp_primitive(mp, "shipout", mp_ship_out_command, 0);
@:ship_out_}{|shipout| primitive@>
mp_primitive(mp, "step", mp_step_command, 0);
@:step_}{|step| primitive@>
mp_primitive(mp, "str", mp_str_command, 0);
@:str_}{|str| primitive@>
mp_primitive(mp, "void", mp_void_command, 0);
@:void_}{|void| primitive@>
mp_primitive(mp, "tension", mp_tension_command, 0);
@:tension_}{|tension| primitive@>
mp_primitive(mp, "to", mp_to_command, 0);
@:to_}{|to| primitive@>
mp_primitive(mp, "until", mp_until_command, 0);
@:until_}{|until| primitive@>
mp_primitive(mp, "within", mp_within_command, 0);
@:within_}{|within| primitive@>
mp_primitive(mp, "write", mp_write_command, 0);
@:write_}{|write| primitive@>

@ Each primitive has a corresponding inverse, so that it is possible to display
the cryptic numeric contents of |eqtb| in symbolic form. Every call of
|primitive| in this program is therefore accompanied by some straightforward code
that forms part of the |print_cmd_mod| routine explained below.

@<Cases of |print_cmd_mod| for symbolic printing of primitives@>=
case mp_add_to_command:        return "addto";
case mp_assignment_command:    return ":=";
case mp_at_least_command:      return "atleast";
case mp_begin_group_command:   return "begingroup";
case mp_colon_command:         return ":";
case mp_comma_command:         return ",";
case mp_controls_command:      return "controls";
case mp_curl_command:          return "curl";
case mp_delimiters_command:    return "delimiters";
case mp_end_group_command:     return "endgroup";
case mp_every_job_command:     return "everyjob";
case mp_exit_test_command:     return "exitif";
case mp_expand_after_command:  return "expandafter";
case mp_interim_command:       return "interim";
case mp_left_brace_command:    return "{";
case mp_left_bracket_command:  return "[";
case mp_let_command:           return "let";
case mp_new_internal_command:  return "newinternal";
case mp_of_command:            return "of";
case mp_path_join_command:     return "..";
case mp_relax_command:         return "\\";
case mp_right_brace_command:   return "}";
case mp_right_bracket_command: return "]";
case mp_save_command:          return "save";
case mp_scan_tokens_command:   return "scantokens";
case mp_runscript_command:     return "runscript";
case mp_maketext_command:      return "maketext";
case mp_semicolon_command:     return ";";
case mp_ship_out_command:      return "shipout";
case mp_step_command:          return "step";
case mp_str_command:           return "str";
case mp_void_command:          return "void";
case mp_tension_command:       return "tension";
case mp_to_command:            return "to";
case mp_until_command:         return "until";
case mp_within_command:        return "within";
case mp_write_command:         return "write";

@ We will deal with the other primitives later, at some point in the program
where their |eq_type| and |equiv| values are more meaningful. For example, the
primitives for macro definitions will be loaded when we consider the routines
that define macros. It is easy to find where each particular primitive was
treated by looking in the index at the end; for example, the section where
|"def"| entered |eqtb| is listed under `|def| primitive'.

@* Token lists.

A \MP\ token is either symbolic or numeric or a string, or it denotes a macro
parameter or capsule or an internal; so there are six corresponding ways to
encode it internally: @^token@>

(1)~A symbolic token for symbol |p| is represented by the pointer |p|, in the
|sym_sym| field of a symbolic node in~|mem|. The |type| field is |symbol_node|;
and it has a |name_type| to differentiate various subtypes of symbolic tokens,
which is usually |normal_sym|, but |macro_sym| for macro names.

(2)~A numeric token whose |scaled| value is~|v| is represented in a non-symbolic
node of~|mem|; the |type| field is |known|, the |name_type| field is |token|, and
the |value| field holds~|v|.

(3)~A string token is also represented in a non-symbolic node; the |type| field
is |mp_string_type|, the |name_type| field is |token|, and the |value| field
holds the corresponding |mp_string|.

(4)~Capsules have |name_type=capsule|, and their |type| and |value| fields
represent arbitrary values, with |type| different from |symbol_node| (in ways to
be explained later).

(5)~Macro parameters appear in |sym_info| fields of symbolic nodes. The |type|
field is |symbol_node|; the $k$th parameter is represented by |k| in |sym_info|;
and |expr_sym| in |name_type|, if it is of type |expr|, or |suffix_sym| if it
is of type |suffix|, or by |text_sym| if it is of type |text|.

(6)~The $k$th internal is also represented by |k| in |sym_info|; the |type| field
is |symbol_node| as for the other symbolic tokens; and |internal_sym| is its
|name_type|;

Actual values of the parameters and internals are kept in a separate stack, as we
will see later.

Note that the |type| field of a node has nothing to do with \quote {type} in a
printer's sense. It's curious that the same word is used in such different ways.

@d mp_set_value_sym(A,B)    do_set_value_sym   (mp, (mp_token_node) (A), (B))
@d mp_set_value_number(A,B) do_set_value_number(mp, (mp_token_node) (A), &(B))
@d mp_set_value_node(A,B)   do_set_value_node  (mp, (mp_token_node) (A), (B))
@d mp_set_value_str(A,B)    do_set_value_str   (mp, (mp_token_node) (A), (B))
@d mp_set_value_knot(A,B)   do_set_value_knot  (mp, (mp_token_node) (A), (B))

@<MPlib internal header stuff@>=
typedef struct mp_node_data *mp_token_node;

@ @c
# define mp_get_value_sym(A)    ((mp_token_node) (A))->data.sym
# define mp_get_value_number(A) ((mp_token_node) (A))->data.n
# define mp_get_value_node(A)   ((mp_token_node) (A))->data.node
# define mp_get_value_str(A)    ((mp_token_node) (A))->data.str
# define mp_get_value_knot(A)   ((mp_token_node) (A))->data.p

inline static void do_set_value_sym (MP mp, mp_token_node A, mp_sym B)
{
    (void) mp;
    A->data.sym=(B);
}

inline static void do_set_value_number (MP mp, mp_token_node A, mp_number *B)
{
    (void) mp;
    A->data.p = NULL;
    A->data.str = NULL;
    A->data.node = NULL;
    number_clone(A->data.n, *B);
}

inline static void do_set_value_str (MP mp, mp_token_node A, mp_string B)
{
    (void) mp;
    A->data.p = NULL;
    A->data.str = (B);
    add_str_ref((B));
    A->data.node = NULL;
    number_clone(A->data.n, zero_t);
}

inline static void do_set_value_node (MP mp, mp_token_node A, mp_node B)
{
    (void) mp;
    /* store the value in a large token node */
    A->data.p = NULL;
    A->data.str = NULL;
    A->data.node = B;
    number_clone(A->data.n, zero_t);
}

inline static void do_set_value_knot (MP mp, mp_token_node A, mp_knot B)
{
    (void) mp;
    A->data.p = (B);
    A->data.str = NULL;
    A->data.node = NULL;
    number_clone(A->data.n, zero_t);
}

@ @<Declarations@>=
inline static void do_set_value_sym    (MP mp, mp_token_node A, mp_sym B);
inline static void do_set_value_number (MP mp, mp_token_node A, mp_number *B);
inline static void do_set_value_str    (MP mp, mp_token_node A, mp_string B);
inline static void do_set_value_node   (MP mp, mp_token_node A, mp_node B);
inline static void do_set_value_knot   (MP mp, mp_token_node A, mp_knot B);

@ @c
static mp_node mp_new_token_node (MP mp)
{
    mp_node p;
    if (mp->token_nodes) {
        p = mp->token_nodes;
        mp->token_nodes = p->link;
        mp->num_token_nodes--;
        p->link = NULL;
    } else {
        p = mp_allocate_node(mp, sizeof(mp_node_data));
        new_number(p->data.n);
        p->hasnumber = 1;
    }
    p->type = mp_token_node_type;
    return (mp_node) p;
}

@ @c
static void mp_free_token_node (MP mp, mp_node p)
{
    if (p) {
        if (mp->num_token_nodes < max_num_token_nodes) {
            p->link = mp->token_nodes;
            mp->token_nodes = p;
            mp->num_token_nodes++;
        } else {
            mp->var_used -= sizeof(mp_node_data);
            if (mp->math_mode > mp_math_double_mode) {
                free_number(((mp_value_node) p)->data.n);
            }
            mp_memory_free(p);
        }
    }
}

@ @<Declarations@>=
static void mp_free_token_node (MP mp, mp_node p);

@ A numeric token is created by the following trivial routine.

@c
static mp_node mp_new_num_tok (MP mp, mp_number *v)
{
    mp_node p = mp_new_token_node(mp);
    mp_set_value_number(p, *v);
    p->type = mp_known_type;
    p->name_type = mp_token_operation;
    return p;
}

@ @<Declarations@>=
static void mp_flush_token_list (MP mp, mp_node p);

@ A token list is a singly linked list of nodes in |mem|, where each node
contains a token and a link. Here's a subroutine that gets rid of a token list
when it is no longer needed.

@c
static void mp_flush_token_list (MP mp, mp_node p)
{
    while (p != NULL) {
        mp_node q = p; /* the node being recycled */
        p = mp_link(p);
        switch (mp_type(q)) {
            case mp_symbol_node_type:
                mp_free_symbolic_node(mp, q);
                continue;
            case mp_vacuous_type:
            case mp_boolean_type:
            case mp_known_type:
                break;
            case mp_string_type:
                delete_str_ref(mp_get_value_str(q));
                break;
            case mp_unknown_boolean_type:
            case mp_unknown_string_type:
            case mp_unknown_pen_type:
            case mp_unknown_nep_type:
            case mp_unknown_path_type:
            case mp_unknown_picture_type:
            case mp_pen_type:
            case mp_nep_type:
            case mp_path_type:
            case mp_picture_type:
            case mp_pair_type:
            case mp_color_type:
            case mp_cmykcolor_type:
            case mp_transform_type:
            case mp_dependent_type:
            case mp_proto_dependent_type:
            case mp_independent_type:
                mp_recycle_value(mp, q);
                break;
            default:
                mp_confusion(mp, "token");
                @:this can't happen token}{\quad token@>
        }
        mp_free_token_node(mp, q);
    }
}

@ The procedure |show_token_list|, which prints a symbolic form of the token list
that starts at a given node |p|, illustrates these conventions. The token list
being displayed should not begin with a reference count.

An additional parameter |q| is also given; this parameter is either NULL or it
points to a node in the token list where a certain magic computation takes place
that will be explained later. (Basically, |q| is non-NULL when we are printing
the two-line context information at the time of an error message; |q| marks the
place corresponding to where the second line should begin.)

@^recursion@>

Unusual entries are printed in the form of all-caps tokens preceded by a space,
e.g., |\char`\ BAD|.

@<Declarations@>=
static void mp_show_token_list       (MP mp, mp_node p, mp_node q);
static void mp_show_token_list_space (MP mp, mp_node p, mp_node q);

@ We go for a spacy layout because we have more screen estate today.
@c

void mp_show_token_list (MP mp, mp_node p, mp_node q)
{
    int cclass = mp_percent_class;
    (void) q;
    while (p != NULL) {
        int c = mp_letter_class;
        if (mp_type(p) != mp_symbol_node_type) {
            if (mp_name_type(p) == mp_token_operation) {
                if (mp_type(p) == mp_known_type) {
                    if (cclass == mp_digit_class) {
                        mp_print_chr(mp, ' ');
                    }
                    if (number_negative(mp_get_value_number(p))) {
                        if (cclass == mp_left_bracket_class) {
                            mp_print_chr(mp, ' ');
                        }
                        mp_print_chr(mp, '[');
                        print_number(mp_get_value_number(p));
                        mp_print_chr(mp, ']');
                        c = mp_right_bracket_class;
                    } else {
                        print_number(mp_get_value_number(p));
                        c = mp_digit_class;
                    }
                } else if (mp_type(p) == mp_string_type) {
                    mp_print_chr(mp, '"');
                    mp_print_mp_str(mp, mp_get_value_str(p));
                    mp_print_chr(mp, '"');
                    c = mp_string_class;
                } else {
                    mp_print_str(mp, " BAD");
                }
            } else if ((mp_name_type(p) != mp_capsule_operation) || (mp_type(p) < mp_vacuous_type) || (mp_type(p) > mp_independent_type)) {
                mp_print_str(mp, " BAD");
            } else {
                mp_print_capsule(mp, p);
                c = mp_right_parenthesis_class;
            }
        } else if (mp_name_type(p) == mp_expr_operation || mp_name_type(p) == mp_suffix_operation || mp_name_type(p) == mp_text_operation) {
            int r = mp_get_sym_info(p);
            if (mp_name_type(p) == mp_expr_operation) {
                mp_print_str(mp, "(EXPR");
            } else if (mp_name_type(p) == mp_suffix_operation) {
                mp_print_str(mp, "(SUFFIX");
            } else {
                mp_print_str(mp, "(TEXT");
            }
            mp_print_int(mp, r);
            mp_print_chr(mp, ')');
            c = mp_right_parenthesis_class;
        } else {
            mp_sym sr = mp_get_sym_sym(p);
            if (sr == mp_collective_subscript) {
                if (cclass == mp_left_bracket_class) {
                    mp_print_chr(mp, ' ');
                }
                mp_print_str(mp, "[]");
                c = mp_right_bracket_class;
            } else {
                mp_string rr = text(sr);
                if (rr == NULL || rr->str == NULL) {
                    mp_print_str(mp, " NONEXISTENT");
                } else {
                    c = mp->char_class[(rr->str[0])];
                    if (c == cclass) {
                        switch (c) {
                            case mp_letter_class:
                                mp_print_chr(mp, '.');
                                break;
                            case mp_comma_class:
                            case mp_semicolon_class:
                            case mp_left_parenthesis_class:
                            case mp_right_parenthesis_class:
                                break;
                            default:
                                mp_print_chr(mp, ' ');
                                break;
                            }
                    }
                    mp_print_mp_str(mp, rr);
                }
            }
        }
        cclass = c;
        p = mp_link(p);
    }
    return;
}

void mp_show_token_list_space (MP mp, mp_node p, mp_node q)
{
    (void) q;
    while (p != NULL) {
        if (mp_type(p) != mp_symbol_node_type) {
            if (mp_name_type(p) == mp_token_operation) {
                if (mp_type(p) == mp_known_type) {
                    if (number_negative(mp_get_value_number(p))) {
                        mp_print_str(mp, "[ ");
                        print_number(mp_get_value_number(p));
                        mp_print_str(mp, " ]");
                    } else {
                        print_number(mp_get_value_number(p));
                    }
                } else if (mp_type(p) == mp_string_type) {
                    mp_print_chr(mp, '"');
                    mp_print_mp_str(mp, mp_get_value_str(p));
                    mp_print_chr(mp, '"');
                } else {
                    mp_print_str(mp, "BAD");
                }
            } else if ((mp_name_type(p) != mp_capsule_operation) || (mp_type(p) < mp_vacuous_type) || (mp_type(p) > mp_independent_type)) {
                mp_print_str(mp, "BAD");
            } else {
                mp_print_capsule(mp, p);
            }
        } else if (mp_name_type(p) == mp_expr_operation || mp_name_type(p) == mp_suffix_operation || mp_name_type(p) == mp_text_operation) {
            int r = mp_get_sym_info(p);
            if (mp_name_type(p) == mp_expr_operation) {
                mp_print_str(mp, "(EXPR ");
            } else if (mp_name_type(p) == mp_suffix_operation) {
                mp_print_str(mp, "(SUFFIX ");
            } else {
                mp_print_str(mp, "(TEXT ");
            }
            mp_print_int(mp, r);
            mp_print_chr(mp, ')');
        } else {
            mp_sym sr = mp_get_sym_sym(p);
            if (sr == mp_collective_subscript) {
                mp_print_str(mp, "[]");
            } else {
                mp_string rr = text(sr);
                if (rr == NULL || rr->str == NULL) {
                    mp_print_str(mp, "NONEXISTENT");
                } else {
                    mp_print_mp_str(mp, rr);
                }
            }
        }
        p = mp_link(p);
        if (p) {
            mp_print_chr(mp, ' ');
        }
    }
    return;
}

@ @<Declarations@>=
static void mp_print_capsule (MP mp, mp_node p);

@ @<Declare miscellaneous procedures that were declared |forward|@>=
void mp_print_capsule (MP mp, mp_node p)
{
    mp_print_chr(mp, '(');
    mp_print_exp(mp, p, 0);
    mp_print_chr(mp, ')');
}

@ Macro definitions are kept in \MP's memory in the form of token lists that have
a few extra symbolic nodes at the beginning.

The first node contains a reference count that is used to tell when the list is
no longer needed. To emphasize the fact that a reference count is present, we
shall refer to the |sym_info| field of this special node as the |ref_count|
field. @^reference counts@>

The next node or nodes after the reference count serve to describe the formal
parameters. They consist of zero or more parameter tokens followed by a code for
the type of macro.

/* reference count preceding a macro definition or picture header */

@d mp_get_ref_count(A)   mp_get_indep_value(A)
@d mp_set_ref_count(A,B) mp_set_indep_value(A,B)
@d mp_add_mac_ref(A)     mp_set_ref_count((A), mp_get_ref_count((A))+1) /* make a new reference to a macro list */
@d mp_decr_mac_ref(A)    mp_set_ref_count((A), mp_get_ref_count((A))-1) /* remove a reference to a macro list */

@<Types...@>=
typedef enum mp_macro_info {
    mp_general_macro,    /* preface to a macro defined with a parameter list */
    mp_primary_macro,    /* preface to a macro with a |primary| parameter */
    mp_secondary_macro,  /* preface to a macro with a |secondary| parameter */
    mp_tertiary_macro,   /* preface to a macro with a |tertiary| parameter */
    mp_expr_macro,       /* preface to a macro with an undelimited |expr| parameter */
    mp_of_macro,         /* preface to a macro with undelimited `|expr| |x| |of|~|y|' parameters */
    mp_suffix_macro,     /* preface to a macro with an undelimited |suffix| parameter */
    mp_text_macro,       /* preface to a macro with an undelimited |text| parameter */
    mp_expr_parameter,   /* used by |expr| primitive */
    mp_suffix_parameter, /* used by |suffix| primitive */
    mp_text_parameter    /* used by |text| primitive */
} mp_macro_info;

@ @c
static void mp_delete_mac_ref (MP mp, mp_node p)
{
    /* |p| points to the reference count of a macro list that is losing one reference */
    if (mp_get_ref_count(p) == 0) {
        mp_flush_token_list(mp, p);
    } else {
        mp_decr_mac_ref(p);
    }
}

@ The following subroutine displays a macro, given a pointer to its reference
count.

@c
static void mp_show_macro (MP mp, mp_node p, mp_node q)
{
    p = mp_link(p); /* bypass the reference count */
    while (mp_name_type(p) != mp_macro_operation) {
        mp_node r = mp_link(p);
        mp_link(p) = NULL;
        mp_show_token_list(mp, p, NULL);
        mp_link(p) = r;
        p = r;
    }
    switch (mp_get_sym_info(p)) {
        case mp_general_macro:
            mp_print_str(mp, "-> ");
            break;
            @.->@>
        case mp_primary_macro:
        case mp_secondary_macro:
        case mp_tertiary_macro:
            mp_print_str(mp, "<");
            mp_print_cmd_mod(mp, mp_parameter_commmand, mp_get_sym_info(p));
            mp_print_str(mp, "> -> ");
            break;
        case mp_expr_macro:
            mp_print_str(mp, "<expr> -> ");
            break;
        case mp_of_macro:
            mp_print_str(mp, "<expr> of <primary> -> ");
            break;
        case mp_suffix_macro:
            mp_print_str(mp, "<suffix> -> ");
            break;
        case mp_text_macro:
            mp_print_str(mp, "<text> -> ");
            break;
    }
    mp_show_token_list(mp, mp_link(p), q);
}

@* Data structures for variables.

The variables of \MP\ programs can be simple, like |x|, or they can combine the
structural property of arrays and records, like |x20a.b|. A \MP\ user assigns a
type to a variable like |x20a.b| by saying, for example, `|boolean| |x[]a.b|'.
It's time for us to study how such things are represented inside of the computer.

Each variable value occupies two consecutive words, either in a non-symbolic node
called a value node, or as a non-symbolic subfield of a larger node. One of those
two words is called the |value| field; it is an integer, containing either a
|scaled| numeric value or the representation of some other type of quantity. (It
might also be subdivided into halfwords, in which case it is referred to by other
names instead of |value|.) The other word is broken into subfields called |type|,
|name_type|, and |link|. The |type| field is a quarterword that specifies the
variable's type, and |name_type| is a quarterword from which \MP\ can reconstruct
the variable's name (sometimes by using the |link| field as well). Thus, only
1.25 words are actually devoted to the value itself; the other three-quarters of
a word are overhead, but they aren't wasted because they allow \MP\ to deal with
sparse arrays and to provide meaningful diagnostics.

In this section we shall be concerned only with the structural aspects of
variables, not their values. Later parts of the program will change the |type|
and |value| fields, but we shall treat those fields as black boxes whose contents
should not be touched.

However, if the |type| field is |mp_structured|, there is no |value| field, and
the second word is broken into two pointer fields called |attr_head| and
|subscr_head|. Those fields point to additional nodes that contain structural
information, as we shall see.

TH Note: DEK and JDH had a nice theoretical split between |value|, |attr| and
|subscr| nodes, as documented above and further below. However, all three types
had a bad habit of transmuting into each other in practice while pointers to them
still lived on elsewhere, so using three different C structures is simply not
workable. All three are now represented as a single C structure called
|mp_value_node|.

There is a potential union in this structure in the interest of space saving:
|subscript| and |hashloc| are mutually exclusive.

Actually, so are |attr_head| + |subscr_head| on one side and and |value_| on the
other, but because of all the access macros that are used in the code base to get
at values, those cannot be folded into a union (yet); this would have required
creating a similar union in |mp_token_node| where it would only serve to confuse
things.

Finally, |parent| only applies in |attr| nodes (the ones that have |hashloc|),
but creating an extra substructure inside the union just for that does not save
space and the extra complication in the structure is not worth the minimal extra
code clarification.

@d mp_get_attribute_head(A)     mp_do_get_attribute_head(mp, (mp_value_node) (A))
@d mp_set_attribute_head(A,B)   mp_do_set_attribute_head(mp, (mp_value_node) (A),(mp_node) (B))

@d mp_get_subscr_head(A)   mp_do_get_subscr_head(mp,(mp_value_node) (A))
@d mp_set_subscr_head(A,B) mp_do_set_subscr_head(mp,(mp_value_node) (A),(mp_node) (B))

@<MPlib internal header stuff@>=
typedef struct mp_value_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_value_data        data;
    mp_number            subscript;
    mp_sym               hashloc_;
    mp_node              parent;
    mp_node              attr_head;
    mp_node              subscr_head;
} mp_value_node_data;

@ @c
static mp_node mp_do_get_attribute_head (MP mp, mp_value_node A)
{
    (void) mp;
    return A->attr_head;
}

static mp_node mp_do_get_subscr_head (MP mp, mp_value_node A)
{
    return A->subscr_head;
    (void) mp;
}

static void mp_do_set_attribute_head (MP mp, mp_value_node A, mp_node d)
{
    (void) mp;
    A->attr_head = d;
}

static void mp_do_set_subscr_head (MP mp, mp_value_node A, mp_node d)
{
    (void) mp;
    A->subscr_head = d;
}

@ @<Declarations@>=
static mp_node mp_do_get_subscr_head (MP mp, mp_value_node A);
static mp_node mp_do_get_attribute_head   (MP mp, mp_value_node A);
static void    mp_do_set_attribute_head   (MP mp, mp_value_node A, mp_node d);
static void    mp_do_set_subscr_head (MP mp, mp_value_node A, mp_node d);

@ It would have been nicer to make |mp_new_value_node| return |mp_value_node|
variables, but with |eqtb| as it stands that became messy: lots of typecasts. So,
it returns a simple |mp_node| for now.

@c
static mp_node mp_new_value_node (MP mp)
{
    mp_value_node p;
    if (mp->value_nodes) {
        p = (mp_value_node) mp->value_nodes;
        mp->value_nodes = p->link;
        mp->num_value_nodes--;
        p->link = NULL;
    } else {
        p = mp_allocate_node(mp, sizeof(mp_value_node_data));
        new_number(p->data.n);
        new_number(p->subscript);
        p->hasnumber = 2;
    }
    mp_type(p) = mp_value_node_type;
    return (mp_node) p;
}

@ @<Declarations@>=
static mp_node mp_new_value_node (MP mp);

@ An attribute node is three words long. Two of these words contain |type| and
|value| fields as described above, and the third word contains additional
information: There is an |hashloc| field, which contains the hash address of the
token that names this attribute; and there's also a |parent| field, which points
to the value node of |mp_structured| type at the next higher level (i.e., at the
level to which this attribute is subsidiary). The |name_type| in an attribute
node is |attr|. The |link| field points to the next attribute with the same
parent; these are arranged in increasing order, so that |mp_get_hashloc
(mp_link(p)) > mp_get_hashloc (p)|. The final attribute node links to the
constant |end_attr|, whose |hashloc| field is greater than any legal hash
address. The |attr_head| in the parent points to a node whose |name_type| is
|mp_structured_root_operation|; this node represents the NULL attribute, i.e.,
the variable that is relevant when no attributes are attached to the parent. The
|attr_head| node has the fields of either a value node, a subscript node, or an
attribute node, depending on what the parent would be if it were not structured;
but the subscript and attribute fields are ignored, so it effectively contains
only the data of a value node. The |link| field in this special node points to an
attribute node whose |hashloc| field is zero; the latter node represents a
collective subscript |[]| attached to the parent, and its |link| field points to
the first non-special attribute node (or to |end_attr| if there are none).

A subscript node likewise occupies three words, with |type| and |value| fields
plus extra information; its |name_type| is |subscr|. In this case the third word
is called the |subscript| field, which is a |scaled| integer. The |link| field
points to the subscript node with the next larger subscript, if any; otherwise
the |link| points to the attribute node for collective subscripts at this level.
We have seen that the latter node contains an upward pointer, so that the parent
can be deduced.

The |name_type| in a parent-less value node is |root|, and the |link| is the hash
address of the token that names this value.

In other words, variables have a hierarchical structure that includes enough
threads running around so that the program is able to move easily between
siblings, parents, and children. An example should be helpful: (The reader is
advised to draw a picture while reading the following description, since that
will help to firm up the ideas.) Suppose that |x| and |x.a| and |x[]b| and |x5|
and |x20b| have been mentioned in a user's program, where |x[]b| has been
declared to be of |boolean| type. Let |h(x)|, |h(a)|, and |h(b)| be the hash
addresses of \.x, \.a, and~\.b. Then |eq_type(h(x)) = name| and |equiv(h(x)) =
p|, where |p|~is a non-symbolic value node with |mp_name_type(p) = root| and
|mp_link(p)=h(x)|. We have |type(p) = mp_structured|, |mp_get_attribute_head(p) =
q|, and |mp_get_subscr_head(p) = r|, where |q| points to a value node and |r| to
a subscript node. (Are you still following this? Use a pencil to draw a diagram.)
The lone variable |x| is represented by |type(q)| and |value(q)|; furthermore
|mp_name_type(q) = mp_structured_root_operation| and |mp_link(q) = q1|, where
|q1| points to an attribute node representing |x[]|. Thus |mp_name_type(q1) =
attr|, |mp_get_hashloc(q1) = mp_collective_subscript = 0|, |mp_get_parent(q1) =
p|, |type(q1) = mp_structured|, |mp_get_attribute_head(q1) = qq|, and
|mp_get_subscr_head(q1) = qq1|; |qq| is a three-word \quote {attribute-as-value}
node with |type(qq) = numeric_type| (assuming that |x5| is numeric, because |qq|
represents |x[]| with no further attributes), |mp_name_type(qq) =
structured_root|, |mp_get_hashloc(qq)=0|, |mp_get_parent(qq) = p|, and
|mp_link(qq) = qq1|. (Now pay attention to the next part.) Node |qq1| is an
attribute node representing |x[][]|, which has never yet occurred; its |type|
field is |undefined|, and its |value| field is undefined. We have
|mp_name_type(qq1) = attr|, |mp_get_hashloc(qq1)=mp_collective_subscript|,
|mp_get_parent(qq1) = q1|, and |mp_link(qq1) = qq2|. Since |qq2| represents
|x[]b|, |type(qq2) = mp_unknown_boolean|; also |mp_get_hashloc(qq2) = h(b)|,
|mp_get_parent(qq2) = q1|, |mp_name_type(qq2) = attr|, |mp_link(qq2) = end_attr|.
(Maybe colored lines will help untangle your picture.) Node |r| is a subscript
node with |type| and |value| representing |x5|; |mp_name_type(r) = subscr|,
|subscript(r) = 5.0|, and |mp_link(r) = r1| is another subscript node. To
complete the picture, see if you can guess what |mp_link(r1)| is; give up?
It's~|q1|. Furthermore |subscript(r1) = 20.0|, |mp_name_type(r1) = subscr|,
|type(r1)=mp_structured|, |mp_get_attribute_head(r1) = qqq|,
|mp_get_subscr_head(r1) = qqq1|, and we finish things off with three more nodes
|qqq|, |qqq1|, and |qqq2| hung onto~|r1|. (Perhaps you should start again with a
larger sheet of paper.) The value of variable |x20b| appears in node~|qqq2|, as
you can well imagine.

If the example in the previous paragraph doesn't make things crystal clear, a
glance at some of the simpler subroutines below will reveal how things work out
in practice.

The only really unusual thing about these conventions is the use of collective
subscript attributes. The idea is to avoid repeating a lot of type information
when many elements of an array are identical macros (for which distinct values
need not be stored) or when they don't have all of the possible attributes.
Branches of the structure below collective subscript attributes do not carry
actual values except for macro identifiers; branches of the structure below
subscript nodes do not carry significant information in their collective
subscript attributes.

@c
# define mp_get_hashloc(A)   ((mp_value_node)(A))->hashloc_
# define mp_set_hashloc(A,B) ((mp_value_node)(A))->hashloc_ = B
# define mp_get_parent(A)    ((mp_value_node)(A))->parent
# define mp_set_parent(A,B)  ((mp_value_node)(A))->parent = B

@ @c
static mp_value_node mp_get_attribute_node (MP mp)
{
    mp_value_node p = (mp_value_node) mp_new_value_node(mp);
    mp_type(p) = mp_attribute_node_type;
    return p;
}

@ Setting the |hashloc| field of |end_attr| to a value greater than any legal
hash address is done by assigning $-1$ typecasted to |mp_sym|, hopefully
resulting in all bits being set. On systems that support negative pointer values
or where typecasting $-1$ does not result in all bits in a pointer being set,
something else needs to be done. @^system dependencies@>

@<Initialize table...@>=
mp->end_attr = (mp_node) mp_get_attribute_node(mp);
mp_set_hashloc(mp->end_attr, (mp_sym)-1);
mp_set_parent((mp_value_node) mp->end_attr, NULL);

@ @<Free table...@>=
mp_free_value_node(mp, mp->end_attr);

@d mp_collective_subscript (void *)0 /* code for the attribute |[]| */
@d mp_subscript(A)         ((mp_value_node)(A))->subscript

@ @c
static mp_value_node mp_get_subscr_node (MP mp)
{
    mp_value_node p = (mp_value_node) mp_new_value_node(mp);
    mp_type(p) = mp_subscript_node_type;
    return p;
}

@ Variables of type |pair| will have values that point to four-word nodes
containing two numeric values. The first of these values has |name_type =
mp_x_part_operation| and the second has |name_type = mp_y_part_operation|; the
|link| in the first points back to the node whose |value| points to this
four-word node.

@d mp_x_part(A) ((mp_pair_node) (A))->x_part /* where the |xpart| is found in a pair node */
@d mp_y_part(A) ((mp_pair_node) (A))->y_part /* where the |ypart| is found in a pair node */

@<MPlib internal header stuff@>=
typedef struct mp_pair_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_node              x_part;
    mp_node              y_part;
} mp_pair_node_data;

typedef struct mp_pair_node_data *mp_pair_node;

@ @c
static mp_node mp_get_pair_node (MP mp)
{
    mp_node p;
    if (mp->pair_nodes) {
        p = mp->pair_nodes;
        mp->pair_nodes = p->link;
        mp->num_pair_nodes--;
        p->link = NULL;
    } else {
        p = mp_allocate_node(mp, sizeof(mp_pair_node_data));
    }
    mp_type(p) = mp_pair_node_type;
    return (mp_node) p;
}

@ @c
static void mp_free_pair_node (MP mp, mp_node p)
{
    if (p) {
        if (mp->num_pair_nodes < max_num_pair_nodes) {
            p->link = mp->pair_nodes;
            mp->pair_nodes = p;
            mp->num_pair_nodes++;
        } else {
            mp->var_used -= sizeof(mp_pair_node_data);
            mp_memory_free(p);
        }
    }
}

@ If |type(p) = mp_pair_type| or if |value(p) = NULL|, the procedure call
|init_pair_node(p)| will allocate a pair node for~|p|. The individual parts of
such nodes are initially of type |mp_independent|.

@c
static void mp_init_pair_node (MP mp, mp_node p)
{
    mp_node q; /* the new node */
    mp_type(p) = mp_pair_type;
    q = mp_get_pair_node(mp);
    mp_y_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_y_part(q)); /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_y_part(q)) = mp_y_part_operation;
    mp_link(mp_y_part(q)) = p;
    mp_x_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_x_part(q)); /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_x_part(q)) = mp_x_part_operation;
    mp_link(mp_x_part(q)) = p;
    mp_set_value_node(p, q);
}

@ Variables of type |transform| are similar, but in this case their |value|
points to a 12-word node containing six values, identified by |x_part_operation|,
|y_part_operation|, |mp_xx_part_operation|, |mp_xy_part_operation|,
|mp_yx_part_operation|, and |mp_yy_part_operation|.

@d mp_tx_part(A) ((mp_transform_node) (A))->tx_part /* where the |xpart| is found in a transform node */
@d mp_ty_part(A) ((mp_transform_node) (A))->ty_part /* where the |ypart| is found in a transform node */
@d mp_xx_part(A) ((mp_transform_node) (A))->xx_part /* where the |xxpart| is found in a transform node */
@d mp_xy_part(A) ((mp_transform_node) (A))->xy_part /* where the |xypart| is found in a transform node */
@d mp_yx_part(A) ((mp_transform_node) (A))->yx_part /* where the |yxpart| is found in a transform node */
@d mp_yy_part(A) ((mp_transform_node) (A))->yy_part /* where the |yypart| is found in a transform node */

@<MPlib internal header stuff@>=
typedef struct mp_transform_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_node              tx_part;
    mp_node              ty_part;
    mp_node              xx_part;
    mp_node              yx_part;
    mp_node              xy_part;
    mp_node              yy_part;
} mp_transform_node_data;

typedef struct mp_transform_node_data *mp_transform_node;

@ @c
static mp_node mp_get_transform_node (MP mp)
{
    mp_transform_node p = (mp_transform_node) mp_allocate_node(mp, sizeof(mp_transform_node_data));
    mp_type(p) = mp_transform_node_type;
    return (mp_node) p;
}

@ @c
static void mp_init_transform_node (MP mp, mp_node p)
{
    mp_node q;    /* the new node */
    mp_type(p) = mp_transform_type;
    q = mp_get_transform_node(mp);       /* big node */
    mp_yy_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_yy_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_yy_part(q)) = mp_yy_part_operation;
    mp_link(mp_yy_part(q)) = p;
    mp_yx_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_yx_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_yx_part(q)) = mp_yx_part_operation;
    mp_link(mp_yx_part(q)) = p;
    mp_xy_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_xy_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_xy_part(q)) = mp_xy_part_operation;
    mp_link(mp_xy_part(q)) = p;
    mp_xx_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_xx_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_xx_part(q)) = mp_xx_part_operation;
    mp_link(mp_xx_part(q)) = p;
    mp_ty_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_ty_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_ty_part(q)) = mp_y_part_operation;
    mp_link(mp_ty_part(q)) = p;
    mp_tx_part(q) = mp_new_value_node(mp);
    mp_new_indep(mp, mp_tx_part(q));  /* sets |type(q)| and |value(q)| */
    mp_name_type(mp_tx_part(q)) = mp_x_part_operation;
    mp_link(mp_tx_part(q)) = p;
    mp_set_value_node(p, q);
}

@ Variables of type |color| have 3~values in 6~words identified by
|mp_red_part_operation|, |mp_green_part_operation|, and |mp_blue_part_operation|.

@d mp_red_part(A)     ((mp_color_node) (A))->red_part     /* where the |redpart| is found in a color node */
@d mp_green_part(A)   ((mp_color_node) (A))->green_part   /* where the |greenpart| is found in a color node */
@d mp_blue_part(A)    ((mp_color_node) (A))->blue_part    /* where the |bluepart| is found in a color node */
@d mp_grey_part(A)    ((mp_color_node) (A))->grey_part    /* where the |greypart| is found in a color node */
@d mp_cyan_part(A)    ((mp_color_node) (A))->cyan_part    /* where the |cyanpart| is found in a color node */
@d mp_magenta_part(A) ((mp_color_node) (A))->magenta_part /* where the |magentapart| is found in a color node */
@d mp_yellow_part(A)  ((mp_color_node) (A))->yellow_part  /* where the |yellowpart| is found in a color node */
@d mp_black_part(A)   ((mp_color_node) (A))->black_part   /* where the |blackpart| is found in a color node */

@<MPlib internal header stuff@>=
typedef struct mp_color_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    union {
        mp_node red_part;
        mp_node cyan_part;
    };
    union {
        mp_node green_part;
        mp_node magenta_part;
    };
    union {
        mp_node blue_part;
        mp_node yellow_part;
    };
    union {
        mp_node grey_part;
        mp_node black_part;
    };
} mp_color_node_data;

typedef struct mp_color_node_data *mp_color_node;

@ @c
static void mp_init_color_node (MP mp, mp_node p, int type)
{
    mp_node q = (mp_node) mp_allocate_node(mp, sizeof(mp_color_node_data));
    q->link = NULL;
    mp_type(p) = type;
    switch (type) {
        case mp_color_type:
            mp_type(q) = mp_color_node_type;
            /* */
            mp_red_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_red_part(q));
            mp_name_type(mp_red_part(q)) = mp_red_part_operation;
            mp_link(mp_red_part(q)) = p;
            /* */
            mp_green_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_green_part(q));
            mp_name_type(mp_green_part(q)) = mp_green_part_operation;
            mp_link(mp_green_part(q)) = p;
            /* */
            mp_blue_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_blue_part(q));
            mp_name_type(mp_blue_part(q)) = mp_blue_part_operation;
            mp_link(mp_blue_part(q)) = p;
            break;
        case mp_cmykcolor_type:
            mp_type(q) = mp_cmykcolor_node_type;
            /* */
            mp_cyan_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_cyan_part(q));
            mp_name_type(mp_cyan_part(q)) = mp_cyan_part_operation;
            mp_link(mp_cyan_part(q)) = p;
            /* */
            mp_magenta_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_magenta_part(q));
            mp_name_type(mp_magenta_part(q)) = mp_magenta_part_operation;
            mp_link(mp_magenta_part(q)) = p;
            /* */
            mp_yellow_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_yellow_part(q));
            mp_name_type(mp_yellow_part(q)) = mp_yellow_part_operation;
            mp_link(mp_yellow_part(q)) = p;
            /* */
            mp_black_part(q) = mp_new_value_node(mp);
            mp_new_indep(mp, mp_black_part(q));
            mp_name_type(mp_black_part(q)) = mp_black_part_operation;
            mp_link(mp_black_part(q)) = p;
            break;
    }
    mp_set_value_node(p, q);
}

@ When an entire structured variable is saved, the |root| indication is
temporarily replaced by |saved_root|. Some variables have no name; they just are
used for temporary storage while expressions are being evaluated. We call them
{\sl capsules}.

@ The |id_transform| function creates a capsule for the identity transformation.

@c
static mp_node mp_id_transform (MP mp)
{
    mp_node q;
    mp_node p = mp_new_value_node(mp);
    mp_name_type(p) = mp_capsule_operation;
    mp_set_value_number(p, zero_t); /* todo: this was |null| */
    mp_init_transform_node(mp, p);
    q = mp_get_value_node(p);
    mp_type(mp_tx_part(q)) = mp_known_type;
    mp_set_value_number(mp_tx_part(q), zero_t);
    mp_type(mp_ty_part(q)) = mp_known_type;
    mp_set_value_number(mp_ty_part(q), zero_t);
    mp_type(mp_xy_part(q)) = mp_known_type;
    mp_set_value_number(mp_xy_part(q), zero_t);
    mp_type(mp_yx_part(q)) = mp_known_type;
    mp_set_value_number(mp_yx_part(q), zero_t);
    mp_type(mp_xx_part(q)) = mp_known_type;
    mp_set_value_number(mp_xx_part(q), unity_t);
    mp_type(mp_yy_part(q)) = mp_known_type;
    mp_set_value_number(mp_yy_part(q), unity_t);
    return p;
}

@ Tokens are of type |tag_token| when they first appear, but they point to |NULL|
until they are first used as the root of a variable. The following subroutine
establishes the root node on such grand occasions.

@c
static void mp_new_root (MP mp, mp_sym x)
{
    mp_node p = mp_new_value_node(mp);
    mp_type(p) = mp_undefined_type;
    mp_name_type(p) = mp_root_operation;
    mp_set_value_sym(p, x);
    set_equiv_node(x, p);
}

@ These conventions for variable representation are illustrated by the
|print_variable_name| routine, which displays the full name of a variable given
only a pointer to its value.

@<Declarations@>=
static void mp_print_variable_name (MP mp, mp_node p);

@ @c
void mp_print_variable_name (MP mp, mp_node p)
{
    mp_node q = NULL; /* a token list that will name the variable's suffix */
    mp_node r = NULL; /* temporary for token list creation */
    while (mp_name_type(p) >= mp_x_part_operation) {
        switch (mp_name_type(p)) {
            case mp_x_part_operation      : mp_print_str(mp, "xpart ");         break;
            case mp_y_part_operation      : mp_print_str(mp, "ypart ");         break;
            case mp_xx_part_operation     : mp_print_str(mp, "xxpart ");        break;
            case mp_xy_part_operation     : mp_print_str(mp, "xypart ");        break;
            case mp_yx_part_operation     : mp_print_str(mp, "yxpart ");        break;
            case mp_yy_part_operation     : mp_print_str(mp, "yypart ");        break;
            case mp_red_part_operation    : mp_print_str(mp, "redpart ");       break;
            case mp_green_part_operation  : mp_print_str(mp, "greenpart ");     break;
            case mp_blue_part_operation   : mp_print_str(mp, "bluepart ");      break;
            case mp_cyan_part_operation   : mp_print_str(mp, "cyanpart ");      break;
            case mp_magenta_part_operation: mp_print_str(mp, "magentapart ");   break;
            case mp_yellow_part_operation : mp_print_str(mp, "yellowpart ");    break;
            case mp_black_part_operation  : mp_print_str(mp, "blackpart ");     break;
            case mp_grey_part_operation   : mp_print_str(mp, "greypart ");      break;
            case mp_capsule_operation     : mp_print_fmt(mp, "%%CAPSULE%p", p); return;
            default                       :                                     break;
        }
        p = mp_link(p);
    }
    while (mp_name_type(p) > mp_saved_root_operation) {
        /*
            Ascend one level, pushing a token onto list |q| and replacing |p| by
            its parent
        */
        if (mp_name_type(p) == mp_subscript_operation) {
            r = mp_new_num_tok(mp, &(mp_subscript(p)));
            do {
                p = mp_link(p);
            } while (mp_name_type(p) != mp_attribute_operation);
        } else if (mp_name_type(p) == mp_structured_root_operation) {
            p = mp_link(p);
            goto FOUND;
        } else if (mp_name_type(p) != mp_attribute_operation) {
            mp_confusion(mp, "variable");
        } else {
            r = mp_new_symbolic_node(mp);
            /* the hash address */
            mp_set_sym_sym(r, mp_get_hashloc(p));
        }
        mp_set_link(r, q);
        q = r;
    FOUND:
        p = mp_get_parent((mp_value_node) p);

    }
    /*
        now |link(p)| is the hash address of |p|, and |name_type(p)| is either
        |root| or |saved_root|. Have to prepend a token to |q| for
        |show_token_list|.
    */
    r = mp_new_symbolic_node(mp);
    mp_set_sym_sym(r, mp_get_value_sym(p));
    mp_link(r) = q;
    if (mp_name_type(p) == mp_saved_root_operation) {
        mp_print_str(mp, "(SAVED)");
    }
    mp_show_token_list(mp, r, NULL);
    mp_flush_token_list(mp, r);
}

@ The |interesting| function returns |true| if a given variable is not in a
capsule, or if the user wants to trace capsules.

@c
static int mp_interesting (MP mp, mp_node p)
{
    if (number_positive(internal_value(mp_tracing_capsules_internal))) {
        return 1;
    } else {
        mp_name_type_type t = mp_name_type(p);
        if (t >= mp_x_part_operation && t != mp_capsule_operation) {
            mp_node tt = mp_get_value_node(mp_link(p));
            switch (t) {
                case mp_x_part_operation:       t = mp_name_type(mp_x_part      (tt)); break;
                case mp_y_part_operation:       t = mp_name_type(mp_y_part      (tt)); break;
                case mp_xx_part_operation:      t = mp_name_type(mp_xx_part     (tt)); break;
                case mp_xy_part_operation:      t = mp_name_type(mp_xy_part     (tt)); break;
                case mp_yx_part_operation:      t = mp_name_type(mp_yx_part     (tt)); break;
                case mp_yy_part_operation:      t = mp_name_type(mp_yy_part     (tt)); break;
                case mp_red_part_operation:     t = mp_name_type(mp_red_part    (tt)); break;
                case mp_green_part_operation:   t = mp_name_type(mp_green_part  (tt)); break;
                case mp_blue_part_operation:    t = mp_name_type(mp_blue_part   (tt)); break;
                case mp_cyan_part_operation:    t = mp_name_type(mp_cyan_part   (tt)); break;
                case mp_magenta_part_operation: t = mp_name_type(mp_magenta_part(tt)); break;
                case mp_yellow_part_operation:  t = mp_name_type(mp_yellow_part (tt)); break;
                case mp_black_part_operation:   t = mp_name_type(mp_black_part  (tt)); break;
                case mp_grey_part_operation:    t = mp_name_type(mp_grey_part   (tt)); break;
                default:                                                               break;
            }
        }
        return (t != mp_capsule_operation);
    }
}

@ Now here is a subroutine that converts an unstructured type into an equivalent
structured type, by inserting a |mp_structured| node that is capable of growing.
This operation is done only when |mp_name_type(p)=root|, |subscr|, or |attr|.

The procedure returns a pointer to the new node that has taken node~|p|'s place
in the structure. Node~|p| itself does not move, nor are its |value| or |type|
fields changed in any way.

@c
static mp_node mp_new_structure (MP mp, mp_node p)
{
    mp_node r = NULL;
    switch (mp_name_type(p)) {
        case mp_root_operation:
            {
                mp_sym q = mp_get_value_sym(p);
                r = mp_new_value_node(mp);
                set_equiv_node(q, r);
            }
            break;
        case mp_subscript_operation:
            /* Link a new subscript node |r| in place of node |p| */
            {
                mp_node q_new;
                mp_node q = p;
                do {
                    q = mp_link(q);
                } while (mp_name_type(q) != mp_attribute_operation);
                q = mp_get_parent((mp_value_node) q);
                r = mp->temp_head;
                mp_set_link(r, mp_get_subscr_head(q));
                do {
                    q_new = r;
                    r = mp_link(r);
                } while (r != p);
                r = (mp_node) mp_get_subscr_node(mp);
                if (q_new == mp->temp_head) {
                    mp_set_subscr_head(q, r);
                } else {
                    mp_set_link(q_new, r);
                }
                number_clone(mp_subscript(r), mp_subscript(p));
            }
            break;
        case mp_attribute_operation:
            /*
                Link a new attribute node |r| in place of node |p| If the
                attribute is |collective_subscript|, there are two pointers to
                node~|p|, so we must change both of them.
            */
            {
                mp_value_node rr;
                mp_node q = mp_get_parent((mp_value_node) p);
                r = mp_get_attribute_head(q);
                do {
                    q = r;
                    r = mp_link(r);
                } while (r != p);
                rr = mp_get_attribute_node(mp);
                r = (mp_node) rr;
                mp_set_link(q, rr);
                mp_set_hashloc(rr, mp_get_hashloc(p));
                mp_set_parent(rr, mp_get_parent((mp_value_node) p));
                if (mp_get_hashloc(p) == mp_collective_subscript) {
                    q = mp->temp_head;
                    mp_set_link(q, mp_get_subscr_head(mp_get_parent((mp_value_node) p)));
                    while (mp_link(q) != p) {
                        q = mp_link(q);
                    }
                    if (q == mp->temp_head) {
                        mp_set_subscr_head(mp_get_parent((mp_value_node) p), (mp_node) rr);
                    } else {
                        mp_set_link(q, rr);
                    }
                }
            }
            break;
        default:
            mp_confusion(mp, "structure");
            break;
    }
    if (r) {
        mp_value_node q;
        mp_set_link(r, mp_link(p));
        mp_set_value_sym(r, mp_get_value_sym(p));
        mp_type(r) = mp_structured_type;
        mp_name_type(r) = mp_name_type(p);
        mp_set_attribute_head(r, p);
        mp_name_type(p) = mp_structured_root_operation;
        q = mp_get_attribute_node(mp);
        mp_set_link(p, q);
        mp_set_subscr_head(r, (mp_node) q);
        mp_set_parent(q, r);
        mp_type(q) = mp_undefined_type;
        mp_name_type(q) = mp_attribute_operation;
        mp_set_link(q, mp->end_attr);
        mp_set_hashloc(q, mp_collective_subscript);
    }
    return r;
}

@ The |find_variable| routine is given a pointer~|t| to a nonempty token list of
suffixes; it returns a pointer to the corresponding non-symbolic value. For
example, if |t| points to token |x| followed by a numeric token containing the
value~7, |find_variable| finds where the value of |x7| is stored in memory. This
may seem a simple task, and it usually is, except when |x7| has never been
referenced before. Indeed, |x| may never have even been subscripted before;
complexities arise with respect to updating the collective subscript information.

If a macro type is detected anywhere along path~|t|, or if the first item on |t|
isn't a |tag_token|, the value |NULL| is returned. Otherwise |p| will be a
non-NULL pointer to a node such that |undefined < type(p) < mp_structured|.

@c
static mp_node mp_find_variable (MP mp, mp_node t)
{
    mp_sym p_sym = mp_get_sym_sym(t);
    @^inner loop@>
 // if ((eq_type(p_sym) % mp_outer_tag_command) != mp_tag_command) {
    if (eq_type(p_sym) != mp_tag_command) {
        return NULL;
    } else {
        mp_node p, q, r, s;     /* nodes in the \quote {value} line */
        mp_node pp, qq, rr, ss; /* nodes in the \quote {collective} line */
        t = mp_link(t);
        if (equiv_node(p_sym) == NULL) {
            mp_new_root (mp, p_sym);
        }
        p = equiv_node(p_sym);
        pp = p;
        while (t != NULL) {
            /*
                Make sure that both nodes |p| and |pp| are of |mp_structured| type
                Although |pp| and |p| begin together, they diverge when a subscript
                occurs; |pp|~stays in the collective line while |p|~goes through
                actual subscript values.
            */
            if (mp_type(pp) != mp_structured_type) {
                if (mp_type(pp) > mp_structured_type) {
                    return NULL;
                } else {
                    ss = mp_new_structure(mp, pp);
                    if (p == pp) {
                        p = ss;
                    }
                    pp = ss;
                }
            }
            /* now |type(pp)=mp_structured| */
            if (mp_type(p) != mp_structured_type) {
                /* it cannot be |>mp_structured| */
                p = mp_new_structure(mp, p);
                /* now |type(p)=mp_structured| */
            }
            if (mp_type(t) != mp_symbol_node_type) {
                /*
                    Descend one level for the subscript |value (t)| We want this part
                    of the program to be reasonably fast, in case there are lots of
                    subscripts at the same level of the data structure. Therefore we
                    store an \quote {infinite} value in the word that appears at the end
                    of the subscript list, even though that word isn't part of a
                    subscript node.
                */
                mp_number nn, save_subscript; /* temporary storage */
                new_number_clone(nn, mp_get_value_number(t));
                pp = mp_link(mp_get_attribute_head(pp));
                /* now |mp_get_hashloc(pp)=mp_collective_subscript| */
                q = mp_link(mp_get_attribute_head(p));
                new_number_clone(save_subscript, mp_subscript(q));
                set_number_to_inf(mp_subscript(q));
                s = mp->temp_head;
                mp_set_link(s, mp_get_subscr_head(p));
                do {
                    r = s;
                    s = mp_link(s);
                } while (number_greater(nn, mp_subscript(s)));
                if (number_equal(nn, mp_subscript(s))) {
                    p = s;
                } else {
                    mp_value_node p1 = mp_get_subscr_node(mp);
                    if (r == mp->temp_head) {
                        mp_set_subscr_head(p, (mp_node) p1);
                    } else {
                        mp_set_link(r, p1);
                    }
                    mp_set_link(p1, s);
                    number_clone(mp_subscript(p1), nn);
                    mp_name_type(p1) = mp_subscript_operation;
                    mp_type(p1) = mp_undefined_type;
                    p = (mp_node) p1;
                }
                number_clone(mp_subscript(q), save_subscript);
                free_number(save_subscript);
                free_number(nn);
            } else {
                /* Descend one level for the attribute |mp_get_sym_info(t)| */
                mp_sym nn1 = mp_get_sym_sym(t);
                ss = mp_get_attribute_head(pp);
                do {
                    rr = ss;
                    ss = mp_link(ss);
                } while (nn1 > mp_get_hashloc(ss));
                if (nn1 < mp_get_hashloc(ss)) {
                    qq = (mp_node) mp_get_attribute_node(mp);
                    mp_set_link(rr, qq);
                    mp_set_link(qq, ss);
                    mp_set_hashloc(qq, nn1);
                    mp_name_type(qq) = mp_attribute_operation;
                    mp_type(qq) = mp_undefined_type;
                    mp_set_parent((mp_value_node) qq, pp);
                    ss = qq;
                }
                if (p == pp) {
                    p = ss;
                    pp = ss;
                } else {
                    pp = ss;
                    s = mp_get_attribute_head(p);
                    do {
                        r = s;
                        s = mp_link(s);
                    } while (nn1 > mp_get_hashloc(s));
                    if (nn1 == mp_get_hashloc(s)) {
                        p = s;
                    } else {
                        q = (mp_node) mp_get_attribute_node(mp);
                        mp_set_link(r, q);
                        mp_set_link(q, s);
                        mp_set_hashloc(q, nn1);
                        mp_name_type(q) = mp_attribute_operation;
                        mp_type(q) = mp_undefined_type;
                        mp_set_parent((mp_value_node) q, p);
                        p = q;
                    }
                }
            }
            t = mp_link(t);
        }
        if (mp_type(pp) >= mp_structured_type) {
            if (mp_type(pp) == mp_structured_type) {
                pp = mp_get_attribute_head(pp);
            } else {
                return NULL;
            }
        }
        if (mp_type(p) == mp_structured_type) {
            p = mp_get_attribute_head(p);
        }
        if (mp_type(p) == mp_undefined_type) {
            if (mp_type(pp) == mp_undefined_type) {
                mp_type(pp) = mp_numeric_type;
                mp_set_value_number(pp, zero_t);
            }
            mp_type(p) = mp_type(pp);
            mp_set_value_number(p, zero_t);
        }
        return p;
    }
}

@ Variables lose their former values when they appear in a type declaration, or
when they are defined to be macros or |let| equal to something else. A
subroutine will be defined later that recycles the storage associated with any
particular |type| or |value|; our goal now is to study a higher level process
called |flush_variable|, which selectively frees parts of a variable structure.

This routine has some complexity because of examples such as |numeric x[]a[]b|
which recycles all variables of the form |x[i]a[j]b| (and no others), while
|vardef x[]a[] = ...| discards all variables of the form |x[i]a[j]| followed by
an arbitrary suffix, except for the collective node |x[]a[]| itself. The obvious
way to handle such examples is to use recursion; so that's what we~do.
@^recursion@>

Parameter |p| points to the root information of the variable; parameter |t|
points to a list of symbolic nodes that represent suffixes, with |info =
mp_collective_subscript| for subscripts.

@<Declarations@>=
static void mp_flush_cur_exp (MP mp, mp_value v);

@ @c
static void mp_flush_variable (MP mp, mp_node p, mp_node t, int discard_suffixes)
{
    while (t != NULL) {
        if (mp_type(p) != mp_structured_type) {
            return;
        } else {
            /* attribute to match */
            mp_sym n = mp_get_sym_sym(t);
            t = mp_link(t);
            if (n == mp_collective_subscript) {
                mp_node q = mp_get_subscr_head(p);
                mp_node r = NULL;
                while (mp_name_type(q) == mp_subscript_operation) {
                    mp_flush_variable(mp, q, t, discard_suffixes);
                    if (t != NULL) {
                        r = q;
                    } else if (mp_type(q) == mp_structured_type) {
                        r = q;
                    } else {
                        if (r == NULL) {
                            mp_set_subscr_head(p, mp_link(q));
                        } else {
                            mp_set_link(r, mp_link(q));
                        }
                        mp_free_value_node(mp, q);
                    }
                    q = r == NULL ? mp_get_subscr_head(p) : mp_link(r);
                }
            }
            p = mp_get_attribute_head(p);
            do {
                p = mp_link(p);
            } while (mp_get_hashloc(p) < n);
            if (mp_get_hashloc(p) != n) {
                return;
            }
        }
    }
    if (discard_suffixes) {
        mp_flush_below_variable(mp, p);
    } else {
        if (mp_type(p) == mp_structured_type) {
            p = mp_get_attribute_head(p);
        }
        mp_recycle_value(mp, p);
    }
}

@ The next procedure is simpler; it wipes out everything but |p| itself, which
becomes undefined.

@<Declarations@>=
static void mp_flush_below_variable (MP mp, mp_node p);

@ @c
void mp_flush_below_variable (MP mp, mp_node p)
{
    if (mp_type(p) != mp_structured_type) {
        mp_recycle_value(mp, p); /* this sets |type(p)=undefined| */
    } else {
        mp_node r;
        mp_node q = mp_get_subscr_head(p);
        while (mp_name_type(q) == mp_subscript_operation) {
            mp_flush_below_variable(mp, q);
            r = q;
            q = mp_link(q);
            mp_free_value_node(mp, r);
        }
        r = mp_get_attribute_head(p);
        q = mp_link(r);
        mp_recycle_value(mp, r);
        mp_free_value_node(mp, r);
        do {
            mp_flush_below_variable(mp, q);
            r = q;
            q = mp_link(q);
            mp_free_value_node(mp, r);
        } while (q != mp->end_attr);
        mp_type(p) = mp_undefined_type;
    }
}

@ Just before assigning a new value to a variable, we will recycle the old value
and make the old value undefined. The |und_type| routine determines what type of
undefined value should be given, based on the current type before recycling.

@c
static int mp_und_type (MP mp, mp_node p)
{
    (void) mp;
    switch (mp_type(p)) {
        case mp_vacuous_type:
            return mp_undefined_type;
        case mp_boolean_type:
        case mp_unknown_boolean_type:
            return mp_unknown_boolean_type;
        case mp_string_type:
        case mp_unknown_string_type:
            return mp_unknown_string_type;
        case mp_pen_type:
        case mp_unknown_pen_type:
            return mp_unknown_pen_type;
        case mp_nep_type:
        case mp_unknown_nep_type:
            return mp_unknown_nep_type;
        case mp_path_type:
        case mp_unknown_path_type:
            return mp_unknown_path_type;
        case mp_picture_type:
        case mp_unknown_picture_type:
            return mp_unknown_picture_type;
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
        case mp_numeric_type:
            return mp_type(p);
        case mp_known_type:
        case mp_dependent_type:
        case mp_proto_dependent_type:
        case mp_independent_type:
            return mp_numeric_type;
        default:
            return 0;
    }
}

@ The |clear_symbol| routine is used when we want to redefine the equivalent of a
symbolic token. It must remove any variable structure or macro definition that is
currently attached to that symbol. If the |saving| parameter is true, a
subsidiary structure is saved instead of destroyed.

@c
static void mp_clear_symbol (MP mp, mp_sym p, int saving)
{
    mp_node q = equiv_node(p);
    if (eq_property(p) > 0) {
        mp_check_overload(mp, p);
    }
 // switch (eq_type(p) % mp_outer_tag_command) {
    switch (eq_type(p)) {
        case mp_defined_macro_command:
        case mp_primary_def_command:
        case mp_secondary_def_command:
        case mp_tertiary_def_command:
            if (!saving) {
                mp_delete_mac_ref(mp, q);
            }
            break;
        case mp_tag_command:
            if (q != NULL) {
                if (saving) {
                    mp_name_type(q) = mp_saved_root_operation;
                } else {
                    mp_flush_below_variable(mp, q);
                    mp_free_value_node(mp, q);
                }
            }
            break;
        default:
            break;
    }
    set_equiv(p, mp->frozen_undefined->v.data.indep.serial);
    set_eq_type(p, mp->frozen_undefined->type);
}

@* Saving and restoring equivalents.

The nested structure given by |begingroup| and |endgroup| allows |eqtb| entries
to be saved and restored, so that temporary changes can be made without
difficulty. When the user requests a current value to be saved, \MP\ puts that
value into its \quote {save stack.} An appearance of |endgroup| ultimately causes
the old values to be removed from the save stack and put back in their former
places.

The save stack is a linked list containing three kinds of entries, distinguished
by their |type| fields. If |p| points to a saved item, then

\smallskip \hang |p->type = 0| stands for a group boundary; each |begingroup|
contributes such an item to the save stack and each |endgroup| cuts back the
stack until the most recent such entry has been removed.

\smallskip \hang |p->type = mp_normal_operation| means that |p->value| holds the
former contents of |eqtb[q]| (saved in the |knot| field of the value, which is
otherwise unused for variables). Such save stack entries are generated by |save|
commands.

\smallskip \hang |p->type = mp_internal_operation| means that |p->value| is a
|mp_internal| to be restored to internal parameter number~|q| (saved in the
|serial| field of the value, which is otherwise unused for internals). Such
entries are generated by |interim| commands.

\smallskip \noindent The global variable |save_ptr| points to the top item on the
save stack.

@<Types...@>=
typedef struct mp_save_data {
    int                  type;
    int                  padding;
    mp_internal          value;
    struct mp_save_data *link;
} mp_save_data;

@ @<Glob...@>=
mp_save_data *save_ptr; /* the most recently saved item */

@ @<Set init...@>=
mp->save_ptr = NULL;

@ Saving a boundary item
@c
static void mp_save_boundary (MP mp)
{
    mp_save_data *p = mp_memory_allocate(sizeof(mp_save_data));
    p->type = 0;
    p->link = mp->save_ptr;
    mp->save_ptr = p;
}

@ The |save_variable| routine is given a hash address |q|; it salts this address
in the save stack, together with its current equivalent, then makes token~|q|
behave as though it were brand new.

Nothing is stacked when |save_ptr = NULL|, however; there's no way to remove
things from the stack when the program is not inside a group, so there's no point
in wasting the space.

@c
static void mp_save_variable (MP mp, mp_sym q)
{
    if (mp->save_ptr != NULL) {
        mp_save_data *p = mp_memory_allocate(sizeof(mp_save_data));
        p->type = mp_normal_operation;
        p->link = mp->save_ptr;
        p->value.v.data.indep.scale = eq_type(q);
        p->value.v.data.indep.serial = equiv(q);
        p->value.v.data.node = equiv_node(q);
        p->value.v.data.p = (mp_knot)q;
        mp->save_ptr = p;
    }
    mp_clear_symbol(mp, q, (mp->save_ptr != NULL));
}

static void mp_unsave_variable (MP mp)
{
    mp_sym q = (mp_sym)mp->save_ptr->value.v.data.p;
    if (number_positive(internal_value(mp_tracing_restores_internal))) {
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "{restoring ");
        mp_print_mp_str(mp,text(q));
        mp_print_chr(mp, '}');
        mp_end_diagnostic(mp, 0);
    }
    mp_clear_symbol(mp, q, 0);
    set_eq_type(q, mp->save_ptr->value.v.data.indep.scale);
    set_equiv(q,mp->save_ptr->value.v.data.indep.serial);
    q->v.data.node = mp->save_ptr->value.v.data.node;
 // if (eq_type(q) % mp_outer_tag_command == mp_tag_command) {
    if (eq_type(q) == mp_tag_command) {
        mp_node pp = q->v.data.node;
        if (pp != NULL) {
            mp_name_type(pp) = mp_root_operation;
        }
    }
}

@ Similarly, |save_internal| is given the location |q| of an internal quantity
like |mp_tracing_pens|. It creates a save stack entry of the third kind.

Todo: check what happens with strings! We need to mess with the ref counter and
there is no need to copy a number when we have a string.

@c
static void mp_save_internal (MP mp, int q)
{
    if (mp->save_ptr != NULL) {
        mp_save_data *p = mp_memory_allocate(sizeof(mp_save_data));
        p->type = mp_internal_operation;
        p->link = mp->save_ptr;
        p->value = mp->internal[q];
        p->value.v.data.indep.serial = q;
        if (internal_run(q) == 1) {
            mp->run_internal(mp, 1, q, internal_type(q), internal_name(q));
        }
        new_number_clone(p->value.v.data.n, mp->internal[q].v.data.n);
        mp->save_ptr = p;
    }
}

static void mp_unsave_internal (MP mp)
{
    int q = mp->save_ptr->value.v.data.indep.serial;
    mp_internal saved = mp->save_ptr->value;
    if (number_positive(internal_value(mp_tracing_restores_internal))) {
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "{restoring ");
        mp_print_str(mp, internal_name(q));
        mp_print_chr(mp, '=');
        switch (internal_type(q)) {
            case mp_known_type:
            case mp_numeric_type:
                print_number(saved.v.data.n);
                break;
            case mp_boolean_type:
                mp_print_str(mp, number_to_boolean(saved.v.data.n) == mp_true_operation ? "true" : "false");
                break;
            case mp_string_type:
                {
                    char *s = mp_str(mp, saved.v.data.str);
                    mp_print_str(mp, s);
                    break;
                }
            default:
                mp_confusion(mp, "internal restore");
                break;
        }
        mp_print_chr(mp, '}');
        mp_end_diagnostic(mp, 0);
    }
    free_number(mp->internal[q].v.data.n);
    if (internal_run(q) == 1) {
        mp->run_internal(mp, 2, q, internal_type(q), internal_name(q));
    }
    mp->internal[q] = saved;
}

@ At the end of a group, the |unsave| routine restores all of the saved
equivalents in reverse order. This routine will be called only when there is at
least one boundary item on the save stack.

@c
static void mp_unsave (MP mp)
{
    mp_save_data *p; /* saved item */
    while (mp->save_ptr->type != 0) {
        if (mp->save_ptr->type == mp_internal_operation) {
            mp_unsave_internal(mp);
        } else {
            mp_unsave_variable(mp);
        }
        p = mp->save_ptr->link;
        mp_memory_free(mp->save_ptr);
        mp->save_ptr = p;
    }
    p = mp->save_ptr->link;
    mp_memory_free(mp->save_ptr);
    mp->save_ptr = p;
}

@* Data structures for paths.

When a \MP\ user specifies a path, \MP\ will create a list of knots and control
points for the associated cubic spline curves. If the knots are $z_0$, $z_1$,
\dots, $z_n$, there are control points $z_k^+$ and $z_{k+1}^-$ such that the
cubic splines between knots $z_k$ and $z_{k+1}$ are defined by B\'ezier's formula
@:Bezier}{B\'ezier, Pierre Etienne@>

$$\eqalign{z(t)&=B(z_k,z_k^+,z_{k+1}^-,z_{k+1};t)\cr
&=(1-t)^3z_k+3(1-t)^2tz_k^++3(1-t)t^2z_{k+1}^-+t^3z_{k+1}\cr}$$

for |0<=t<=1|.

There is a 8-word node for each knot $z_k$, containing one word of control
information and six words for the |x| and |y| coordinates of $z_k^-$ and $z_k$
and~$z_k^+$. The control information appears in the |mp_left_type| and
|mp_right_type| fields, which each occupy a quarter of the first word in the
node; they specify properties of the curve as it enters and leaves the knot.
There's also a halfword |link| field, which points to the following knot, and a
final supplementary word (of which only a quarter is used).

If the path is a closed contour, knots 0 and |n| are identical; i.e., the |link|
in knot |n-1| points to knot~0. But if the path is not closed, the |mp_left_type|
of knot~0 and the |mp_right_type| of knot~|n| are equal to |endpoint|. In the
latter case the |link| in knot~|n| points to knot~0, and the control points
$z_0^-$ and $z_n^+$ are not used.

@d mp_next_knot(A)  (A)->next       /* the next knot in this list */
@d mp_left_type(A)  (A)->left_type  /* characterizes the path entering this knot */
@d mp_right_type(A) (A)->right_type /* characterizes the path leaving this knot */
@d mp_prev_knot(A)  (A)->prev       /* the previous knot in this list (only for pens) */
@d mp_knot_info(A)  (A)->info       /* temporary info, used during splitting */

@<Exported types...@>=
typedef struct mp_knot_data *mp_knot;

typedef struct mp_knot_data {
    mp_number     x_coord;       /* the |x| coordinate of this knot */
    mp_number     y_coord;       /* the |y| coordinate of this knot */
    union {
        mp_number left_x;        /* the |x| coordinate of previous control point */
        mp_number left_curl;     /* curl information when entering this knot */
        mp_number left_given;    /* given direction when entering this knot */
    };
    union {
        mp_number left_y;        /* the |y| coordinate of previous control point */
        mp_number left_tension;  /* tension information when entering this knot */
    };
    union {
        mp_number right_x;       /* the |x| coordinate of next control point */
        mp_number right_curl;    /* curl information when leaving this knot */
        mp_number right_given;   /* given direction when leaving this knot */
    };
    union {
        mp_number right_y;       /* the |y| coordinate of next control point */
        mp_number right_tension; /* tension information when leaving this knot */
    };
    mp_knot       next;
    mp_knot       prev;
    unsigned char left_type;
    unsigned char right_type;
    unsigned char originator;
    unsigned char state;
    signed   int  info;
    /* we now have some 3 bytes slack that we can use */
} mp_knot_data;

@ @<Exported types...@>=
typedef struct mp_gr_knot_data *mp_gr_knot;

typedef struct mp_gr_knot_data {
    double        x_coord;
    double        y_coord;
    double        left_x;
    double        left_y;
    double        right_x;
    double        right_y;
    mp_gr_knot    next;
    mp_gr_knot    prev;
    unsigned char left_type;
    unsigned char right_type;
    unsigned char originator;
    unsigned char state;
    signed int    info;
} mp_gr_knot_data;

@ @<MPlib header stuff@>=
typedef enum mp_knot_type {
    mp_endpoint_knot,  /* |mp_left_type| at path beginning and |mp_right_type| at path end */
    mp_explicit_knot,  /* |mp_left_type| or |mp_right_type| when control points are known */
    mp_given_knot,     /* |mp_left_type| or |mp_right_type| when a direction is given */
    mp_curl_knot,      /* |mp_left_type| or |mp_right_type| when a curl is desired */
    mp_open_knot,      /* |mp_left_type| or |mp_right_type| when \MP\ should choose the direction */
    mp_end_cycle_knot
} mp_knot_type;

@ Before the B\'ezier control points have been calculated, the memory space they
will ultimately occupy is taken up by information that can be used to compute
them. There are four cases:

\yskip \textindent{$\bullet$} If |mp_right_type=mp_open|, the curve should leave
the knot in the same direction it entered; \MP\ will figure out a suitable
direction.

\yskip \textindent{$\bullet$} If |mp_right_type=mp_curl|, the curve should leave
the knot in a direction depending on the angle at which it enters the next knot
and on the curl parameter stored in |right_curl|.

\yskip \textindent{$\bullet$} If |mp_right_type=mp_given|, the curve should leave
the knot in a nonzero direction stored as an |angle| in |right_given|.

\yskip \textindent{$\bullet$} If |mp_right_type=mp_explicit|, the B\'ezier
control point for leaving this knot has already been computed; it is in the
|mp_right_x| and |mp_right_y| fields.

\yskip\noindent The rules for |mp_left_type| are similar, but they refer to the
curve entering the knot, and to |left| fields instead of |right| fields.

Non-|explicit| control points will be chosen based on \quote {tension} parameters
in the |left_tension| and |right_tension| fields. The |atleast| option is
represented by negative tension values. @:at_least_}{|atleast| primitive@>

For example, the \MP\ path specification

$$|z0..z1..tension atleast 1..\{curl 2\|z2..z3\{-1,-2\}..tension 3 and 4..p},$$

where \.p is the path |z4..controls z45 and z54..z5|, will be represented by
the six knots \def\lodash{\hbox to 1.1em{\thinspace\hrulefill\thinspace}}

$$\vbox{\halign{#\hfil&&\qquad#\hfil\cr |mp_left_type|&|left|
info&|x_coord,y_coord|&|mp_right_type|&|right| info\cr \noalign{\yskip}
|endpoint|&\lodash$,\,$\lodash&$x_0,y_0$&|curl|&$1.0,1.0$\cr
|open|&\lodash$,1.0$&$x_1,y_1$&|open|&\lodash$,-1.0$\cr
|curl|&$2.0,-1.0$&$x_2,y_2$&|curl|&$2.0,1.0$\cr
|given|&$d,1.0$&$x_3,y_3$&|given|&$d,3.0$\cr
|open|&\lodash$,4.0$&$x_4,y_4$&|explicit|&$x_{45},y_{45}$\cr
|explicit|&$x_{54},y_{54}$&$x_5,y_5$&|endpoint|&\lodash$,\,$\lodash\cr}}$$

Here |d| is the |angle| obtained by calling |n_arg(-unity,-two)|. Of course, this
example is more complicated than anything a normal user would ever write.

These types must satisfy certain restrictions because of the form of \MP's path
syntax: (i)~|open| type never appears in the same node together with |endpoint|,
|given|, or |curl|. (ii)~The |mp_right_type| of a node is |explicit| if and only
if the |mp_left_type| of the following node is |explicit|. (iii)~|endpoint| types
occur only at the ends, as mentioned above.

@ Knots can be user-supplied, or they can be created by program code, like the
|split_cubic| function, or |copy_path|. The distinction is needed for the cleanup
routine that runs after |split_cubic|, because it should only delete knots it has
previously inserted, and never anything that was user-supplied. In order to be
able to differentiate one knot from another, we will set |originator(p) :=
mp_metapost_user| when it appeared in the actual metapost program, and
|originator(p) := mp_program_code| in all other cases.

@d mp_originator(A) (A)->originator /* the creator of this knot */
@d mp_knotstate(A)  (A)->state

@<Exported types@>=
enum mp_knot_originator {
    mp_program_code,  /* not created by a user */
    mp_metapost_user  /* created by a user */
};
enum mp_knot_states {
    mp_regular_knot,
    mp_begin_knot,
    mp_end_knot,
    mp_single_knot,
};

@ Here is a routine that prints a given knot list in symbolic form. It
illustrates the conventions discussed above, and checks for anomalies that might
arise while \MP\ is being debugged.

@<Declarations@>=
static void mp_pr_path (MP mp, mp_knot h);

@ @c
void mp_pr_path (MP mp, mp_knot h)
{
    mp_knot p = h;
    do {
        mp_knot q = mp_next_knot(p);
        if ((p == NULL) || (q == NULL)) {
            mp_print_nl(mp, "???");
            return; /* this won't happen */
            @.???@>
        } else {
            @<Print information for adjacent knots |p| and |q|@>
          DONE1:
            p = q;
            if (p && ((p != h) || (mp_left_type(h) != mp_endpoint_knot))) {
                @<Print two dots, followed by |given| or |curl| if present@>
            }
        }
    } while (p != h);
    if (mp_left_type(h) != mp_endpoint_knot) {
        mp_print_str(mp, " cycle");
    }
}

@ @<Print information for adjacent knots...@>=
mp_print_two(mp, &(p->x_coord), &(p->y_coord));
switch (mp_knotstate(p)) {
    case mp_begin_knot:
        mp_print_str(mp, " {begin}");
        break;
    case mp_end_knot:
        mp_print_str(mp, " {end}");
        break;
}
switch (mp_right_type(p)) {
    case mp_endpoint_knot:
        {
            if (mp_left_type(p) == mp_open_knot) {
                mp_print_str(mp, " {open?}"); /* can't happen */
                @.open?@>
            }
            if ((mp_left_type(q) != mp_endpoint_knot) || (q != h)) {
                q = NULL; /* force an error */
            }
            goto DONE1;
        }
        break;
    case mp_explicit_knot:
        {
            @<Print control points between |p| and |q|, then |goto done1|@>
        }
        break;
    case mp_open_knot:
        {
            @<Print information for a curve that begins |open|@>
        }
        break;
    case mp_curl_knot:
    case mp_given_knot:
        {
            @<Print information for a curve that begins |curl| or |given|@>
        }
        break;
    default:
        {
            mp_print_str(mp, "???"); /* can't happen */
            @.???@>
        }
        break;
}
if (mp_left_type(q) <= mp_explicit_knot) {
    mp_print_str(mp, " .. control ?"); /* can't happen */
    @.control?@>
} else if ((! number_equal(p->right_tension, unity_t)) || (! number_equal(q->left_tension, unity_t))) {
    @<Print tension between |p| and |q|@>
}

@ Since |n_sin_cos| produces |fraction| results, which we will print as if they
were |scaled|, the magnitude of a |given| direction vector will be~4096.

@<Print two dots...@>=
mp_number n_sin, n_cos;
new_fraction(n_sin);
new_fraction(n_cos);
mp_print_nl(mp, " .. ");
if (mp_left_type(p) == mp_given_knot) {
    n_sin_cos(p->left_given, n_cos, n_sin);
    mp_print_str(mp, "{");
    print_number(n_cos);
    mp_print_chr(mp, ',');
    print_number(n_sin);
    mp_print_chr(mp, '}');
} else if (mp_left_type(p) == mp_curl_knot) {
    mp_print_str(mp, "{curl ");
    print_number(p->left_curl);
    mp_print_chr(mp, '}');
}
free_number(n_sin);
free_number(n_cos);

@ @<Print tension between |p| and |q|@>=
mp_number v1;
mp_print_str(mp, " .. tension");
if (number_negative(p->right_tension)) {
    mp_print_str(mp, " atleast");
}
new_number_abs(v1, p->right_tension);
print_number(v1);
if (! number_equal(p->right_tension, q->left_tension)) {
    mp_print_str(mp, " and");
    if (number_negative(q->left_tension)) {
        mp_print_str(mp, " atleast");
    }
    number_abs_clone(v1, p->left_tension);
    print_number(v1);
}
free_number(v1);

@ @<Print control points between |p| and |q|, then |goto done1|@>=
mp_print_str(mp, " .. controls ");
mp_print_two(mp, &(p->right_x), &(p->right_y));
mp_print_str(mp, " and ");
if (mp_left_type(q) != mp_explicit_knot) {
    mp_print_str(mp, "??"); /* can't happen */
    @.??@>
} else {
    mp_print_two(mp, &(q->left_x), &(q->left_y));
}
goto DONE1;

@ @<Print information for a curve that begins |open|@>=
if ((mp_left_type(p) != mp_explicit_knot) && (mp_left_type(p) != mp_open_knot)) {
    mp_print_str(mp, " {open?}"); /* can't happen */
    @.open?@>
}

@ A curl of 1 is shown explicitly, so that the user sees clearly that \MP's
default curl is present.

@<Print information for a curve that begins |curl|...@>=
if (mp_left_type(p) == mp_open_knot) {
    mp_print_str(mp, " ??"); /* can't happen */
    @.??@>
}
if (mp_right_type(p) == mp_curl_knot) {
    mp_print_str(mp, " {curl");
    print_number(p->right_curl);
} else {
    mp_number n_sin, n_cos;
    new_fraction(n_sin);
    new_fraction(n_cos);
    n_sin_cos(p->right_given, n_cos, n_sin);
    mp_print_str(mp, " {");
    print_number(n_cos);
    mp_print_chr(mp, ',');
    print_number(n_sin);
    free_number(n_sin);
    free_number(n_cos);
}
mp_print_str(mp, "} ");

@ It is convenient to have another version of |pr_path| that prints the path as a
diagnostic message.

@<Declarations@>=
static void mp_print_path (MP mp, mp_knot h, const char *s, int nuline);

@ @c
void mp_print_path (MP mp, mp_knot h, const char *s, int nuline)
{
    mp_print_diagnostic(mp, "Path", s, nuline);
    mp_print_ln(mp);
    @.Path at line...@>
    mp_pr_path(mp, h);
    mp_end_diagnostic(mp, 1);
}

@ @<Declarations@>=
static mp_knot mp_new_knot (MP mp);

@ @c
static mp_knot mp_new_knot (MP mp)
{
    mp_knot q;
    if (mp->knot_nodes) {
        q = mp->knot_nodes;
        mp->knot_nodes = q->next;
        mp->num_knot_nodes--;
    } else {
        q = mp_memory_clear_allocate(sizeof(struct mp_knot_data));
    }
    new_number(q->x_coord);
    new_number(q->y_coord);
    new_number(q->left_x);
    new_number(q->left_y);
    new_number(q->right_x);
    new_number(q->right_y);
    return q;
}

@ @<Declarations@>=
static mp_gr_knot mp_gr_new_knot (MP mp);

@ @c
static mp_gr_knot mp_gr_new_knot (MP mp)
{
    mp_gr_knot q = mp_memory_allocate(sizeof(struct mp_gr_knot_data));
    (void) mp;
    return q;
}

@ If we want to duplicate a knot node, we can say |copy_knot|:

@c
static mp_knot mp_copy_knot (MP mp, mp_knot p)
{
    mp_knot q;
    if (mp->knot_nodes) {
        q = mp->knot_nodes;
        mp->knot_nodes = q->next;
        mp->num_knot_nodes--;
    } else {
        q = mp_memory_allocate(sizeof(struct mp_knot_data));
    }
    memcpy(q, p, sizeof(struct mp_knot_data));
    if (mp->math_mode > mp_math_double_mode) {
        new_number_clone(q->x_coord, p->x_coord);
        new_number_clone(q->y_coord, p->y_coord);
        new_number_clone(q->left_x, p->left_x);
        new_number_clone(q->left_y, p->left_y);
        new_number_clone(q->right_x, p->right_x);
        new_number_clone(q->right_y, p->right_y);
    }
    mp_prev_knot(q) = NULL;
    mp_next_knot(q) = NULL;
    return q;
}

@ If we want to export a knot node, we can say |export_knot|:

@c
static mp_gr_knot mp_export_knot (MP mp, mp_knot p)
{
    mp_gr_knot q = mp_gr_new_knot(mp);
    q->x_coord    = number_to_double(p->x_coord);
    q->y_coord    = number_to_double(p->y_coord);
    q->left_x     = number_to_double(p->left_x);
    q->left_y     = number_to_double(p->left_y);
    q->right_x    = number_to_double(p->right_x);
    q->right_y    = number_to_double(p->right_y);
    q->left_type  = p->left_type;
    q->right_type = p->right_type;
    q->info       = p->info;
    q->originator = p->originator;
    q->state      = p->state;
    q->prev       = NULL;
    q->next       = NULL;
    return q;
}

@ The |copy_path| routine makes a clone of a given path.

@c
static mp_knot mp_copy_path (MP mp, mp_knot p)
{
    if (p == NULL) {
        return NULL;
    } else {
        mp_knot q = mp_copy_knot(mp, p);
        mp_knot qq = q;
        mp_knot pp = mp_next_knot(p);
        while (pp != p) {
            mp_knot k = mp_copy_knot(mp, pp);
            mp_next_knot(qq) = k;
            mp_prev_knot(k) = qq;
            qq = mp_next_knot(qq);
            pp = mp_next_knot(pp);
        }
        mp_next_knot(qq) = q;
        mp_prev_knot(q) = qq;
        return q;
    }
}

@ The |export_path| routine makes a clone of a given path
and converts the |value|s therein to |double|s.

@c
static mp_gr_knot mp_export_path (MP mp, mp_knot p)
{
    if (p == NULL) {
        return NULL;
    } else {
        mp_gr_knot q = mp_export_knot(mp, p);
        mp_gr_knot qq = q;
        mp_knot pp = mp_next_knot(p);
        while (pp != p) {
            mp_gr_knot k = mp_export_knot(mp, pp);
            mp_prev_knot(k) = qq;
            mp_next_knot(qq) = k;
            qq = k;
            pp = mp_next_knot(pp);
        }
        mp_prev_knot(q) = qq;
        mp_next_knot(qq) = q;
        return q;
    }
}

@ Just before |ship_out|, knot lists are exported for printing.

@ The |export_knot_list| routine therefore also makes a clone of a given path.

@c
static mp_gr_knot mp_export_knot_list (MP mp, mp_knot p)
{
    if (p == NULL) {
        return NULL;
    } else {
        mp_gr_knot q = mp_export_path(mp, p);
        return q;
    }
}

@ Similarly, there's a way to copy the {\em reverse} of a path. This procedure
returns a pointer to the first node of the copy, if the path is a cycle, but to
the final node of a non-cyclic copy. The global variable |path_tail| will point
to the final node of the original path; this trick makes it easier to implement
|doublepath|.

All node types are assumed to be |endpoint| or |explicit| only.

@c
static mp_knot mp_htap_ypoc (MP mp, mp_knot p)
{
    mp_knot q = mp_new_knot(mp);  /* this will correspond to |p| */
    mp_knot qq = q;
    mp_knot pp = p;
    while (1) {
        mp_right_type(qq) = mp_left_type(pp);
        mp_left_type(qq) = mp_right_type(pp);
        number_clone(qq->x_coord, pp->x_coord);
        number_clone(qq->y_coord, pp->y_coord);
        number_clone(qq->right_x, pp->left_x);
        number_clone(qq->right_y, pp->left_y);
        number_clone(qq->left_x, pp->right_x);
        number_clone(qq->left_y, pp->right_y);
        mp_originator(qq) = mp_originator(pp);
        mp_knotstate(qq) = mp_knotstate(pp);
        if (mp_next_knot(pp) == p) {
            mp_prev_knot(qq) = q;
            mp_next_knot(q) = qq;
            mp->path_tail = pp;
            return q;
        } else {
            mp_knot rr = mp_new_knot(mp);
            mp_prev_knot(qq) = rr;
            mp_next_knot(rr) = qq;
            qq = rr;
            pp = mp_next_knot(pp);
        }
    }
}

@ @<Glob...@>=
mp_knot path_tail; /* the node that links to the beginning of a path */

@ When a cyclic list of knot nodes is no longer needed, it can be recycled by
calling the following subroutine.

@<Declarations@>=
static void mp_toss_knot_list (MP mp, mp_knot p);
static void mp_toss_knot      (MP mp, mp_knot p);
static void mp_free_knot      (MP mp, mp_knot p);

@ Numbers are unions of a scaled (integer), double or pointer. The pointer is
used for e.g.\ decimal numbers. These are structs with a size that is set at
compile time. A decimal number struct is allocated in the new_number function and
all the \METAPOST\ data structures that have number handle clean up and renewal.
Keeping the numbers in the free know list entries is just not worth the effort so
in decimal mode quite a bit of (de/re)allocation goes on.

@c
static void mp_free_knot (MP mp, mp_knot q)
{
    if (mp->math_mode > mp_math_double_mode) {
        free_number(q->x_coord);
        free_number(q->y_coord);
        free_number(q->left_x);
        free_number(q->left_y);
        free_number(q->right_x);
        free_number(q->right_y);
    }
    mp_memory_free(q);
}

static void mp_toss_knot (MP mp, mp_knot q)
{
    if (mp->num_knot_nodes < mp->max_knot_nodes) {
        mp_next_knot(q) = mp->knot_nodes;
        mp->knot_nodes = q;
        mp->num_knot_nodes++;
        if (mp->math_mode > mp_math_double_mode) {
            free_number(q->x_coord);
            free_number(q->y_coord);
            free_number(q->left_x);
            free_number(q->left_y);
            free_number(q->right_x);
            free_number(q->right_y);
        }
    } else {
        mp_free_knot(mp, q);
    }
}

static void mp_toss_knot_list (MP mp, mp_knot p)
{
    if (p == NULL) {
        return;
    } else {
        mp_knot q = p;
        do {
            mp_knot r = mp_next_knot(q);
            mp_toss_knot(mp, q);
            q = r;
        } while (q != p);
    }
}

@* Choosing control points.

Now we must actually delve into one of \MP's more difficult routines, the
|make_choices| procedure that chooses angles and control points for the splines
of a curve when the user has not specified them explicitly. The parameter to
|make_choices| points to a list of knots and path information, as described
above.

A path decomposes into independent segments at \quote {breakpoint} knots, which are
knots whose left and right angles are both prespecified in some way (i.e., their
|mp_left_type| and |mp_right_type| aren't both open).

@c
void mp_make_choices  (MP mp, mp_knot knots)
{
    mp_knot h;    /* the first breakpoint */
    mp_knot p, q; /* consecutive breakpoints being processed */
    @<Other local variables for |make_choices|@>
    /* make sure that |arith_error=false| */
    check_arith();
    if (number_positive(internal_value(mp_tracing_choices_internal))) {
        mp_print_path(mp, knots, ", before choices", 1);
    }
    @<If consecutive knots are equal, join them explicitly@>
    @<Find the first breakpoint, |h|, on the path; insert an artificial breakpoint if the path is an unbroken cycle@>
    p = h;
    do {
        @<Fill in the control points between |p| and the next breakpoint, thenadvance |p| to that breakpoint@>
    } while (p != h);
    if (number_positive(internal_value(mp_tracing_choices_internal))) {
        mp_print_path(mp, knots, ", after choices", 1);
    }
    if (mp->arith_error) {
        @<Report an unexpected problem during the choice-making@>
    }
}

@ @<Internal ...@>=
void mp_make_choices (MP mp, mp_knot knots);

@ @<Report an unexpected problem during the choice...@>=
mp_back_error(
    mp,
    "Some number got too big",
    "The path that I just computed is out of range. So it will probably look funny.\n"
    "Proceed, for a laugh."
);
@.Some number got too big@>
mp_get_x_next(mp);
mp->arith_error = 0;

@ Two knots in a row with the same coordinates will always be joined by an
explicit \quote {curve} whose control points are identical with the knots.

@<If consecutive knots are equal, join them explicitly@>=
p = knots;
do {
    q = mp_next_knot(p);
    if (number_equal(p->x_coord, q->x_coord) && number_equal(p->y_coord, q->y_coord) && mp_right_type(p) > mp_explicit_knot) {
        mp_right_type(p) = mp_explicit_knot;
        if (mp_left_type(p) == mp_open_knot) {
            mp_left_type(p) = mp_curl_knot;
            set_number_to_unity(p->left_curl);
        }
        mp_left_type(q) = mp_explicit_knot;
        if (mp_right_type(q) == mp_open_knot) {
            mp_right_type(q) = mp_curl_knot;
            set_number_to_unity(q->right_curl);
        }
        number_clone(p->right_x, p->x_coord);
        number_clone(q->left_x, p->x_coord);
        number_clone(p->right_y, p->y_coord);
        number_clone(q->left_y, p->y_coord);
    }
    p = q;
} while (p != knots);

@ If there are no breakpoints, it is necessary to compute the direction angles
around an entire cycle. In this case the |mp_left_type| of the first node is
temporarily changed to |end_cycle|.

@<Find the first breakpoint, |h|, on the path...@>=
h = knots;
while (1) {
    if (mp_left_type(h) != mp_open_knot) {
        break;
    } else if (mp_right_type(h) != mp_open_knot) {
        break;
    } else {
        h = mp_next_knot(h);
        if (h == knots) {
            mp_left_type(h) = mp_end_cycle_knot;
            break;
        }
    }
}

@ If |mp_right_type(p) < given| and |q = mp_link(p)|, we must have
|mp_right_type(p) = mp_left_type(q) = mp_explicit| or |endpoint|.

@<Fill in the control points between |p| and the next breakpoint...@>=
q = mp_next_knot(p);
if (mp_right_type(p) >= mp_given_knot) {
    while ((mp_left_type(q) == mp_open_knot) && (mp_right_type(q) == mp_open_knot)) {
        q = mp_next_knot(q);
    }
    @<Fill in the control information between consecutive breakpoints |p| and |q|@>
} else if (mp_right_type(p) == mp_endpoint_knot) {
    @<Give reasonable values for the unused control points between |p| and~|q|@>
}
p = q;

@ This step makes it possible to transform an explicitly computed path without
checking the |mp_left_type| and |mp_right_type| fields.

@<Give reasonable values for the unused control points between |p| and~|q|@>=
number_clone(p->right_x, p->x_coord);
number_clone(p->right_y, p->y_coord);
number_clone(q->left_x, q->x_coord);
number_clone(q->left_y, q->y_coord);

@ Before we can go further into the way choices are made, we need to consider the
underlying theory. The basic ideas implemented in |make_choices| are due to John
Hobby, who introduced the notion of \quote {mock curvature} @^Hobby, John
Douglas@> at a knot. Angles are chosen so that they preserve mock curvature when
a knot is passed, and this has been found to produce excellent results.

It is convenient to introduce some notations that simplify the necessary
formulas. Let $d_{k,k+1}=\vert z\k-z_k\vert$ be the (nonzero) distance between
knots |k| and |k+1|; and let

$${z\k-z_k\over z_k-z_{k-1}}={d_{k,k+1}\over d_{k-1,k}}e^{i\psi_k}$$

so that a polygonal line from $z_{k-1}$ to $z_k$ to $z\k$ turns left through an
angle of~$\psi_k$. We assume that $\vert\psi_k\vert\L180^\circ$. The control
points for the spline from $z_k$ to $z\k$ will be denoted by

$$\eqalign{z_k^+&=z_k+ \textstyle{1\over3}\rho_k e^{i\theta_k}(z\k-z_k),\cr
z\k^-&=z\k- \textstyle{1\over3}\sigma\k e^{-i\phi\k}(z\k-z_k),\cr}$$

where $\rho_k$ and $\sigma\k$ are nonnegative \quote {velocity ratios} at the
beginning and end of the curve, while $\theta_k$ and $\phi\k$ are the
corresponding \quote {offset angles.} These angles satisfy the condition

$$\theta_k+\phi_k+\psi_k=0,\eqno(*)$$

whenever the curve leaves an intermediate knot~|k| in the direction that it
enters.

@ Let $\alpha_k$ and $\beta\k$ be the reciprocals of the \quote {tension} of the curve
at its beginning and ending points. This means that $\rho_k=\alpha_k
f(\theta_k,\phi\k)$ and $\sigma\k=\beta\k f(\phi\k,\theta_k)$, where
$f(\theta,\phi)$ is \MP's standard velocity function defined in the |velocity|
subroutine. The cubic spline $B(z_k^{\phantom+},z_k^+, z\k^-,z\k^{\phantom+};t)$
has curvature @^curvature@>

$${2\sigma\k\sin(\theta_k+\phi\k)-6\sin\theta_k\over\rho_k^2d_{k,k+1}} \qquad{\rm
and}\qquad {2\rho_k\sin(\theta_k+\phi\k)-6\sin\phi\k\over\sigma\k^2d_{k,k+1}}$$

at |t=0| and |t=1|, respectively. The mock curvature is the linear @^mock
curvature@> approximation to this true curvature that arises in the limit for
small $\theta_k$ and~$\phi\k$, if second-order terms are discarded. The standard
velocity function satisfies $$f(\theta,\phi)=1+O(\theta^2+\theta\phi+\phi^2);$$
hence the mock curvatures are respectively

$${2\beta\k(\theta_k+\phi\k)-6\theta_k\over\alpha_k^2d_{k,k+1}} \qquad{\rm
and}\qquad
{2\alpha_k(\theta_k+\phi\k)-6\phi\k\over\beta\k^2d_{k,k+1}}.\eqno(**)$$

@ The turning angles $\psi_k$ are given, and equation $(*)$ above determines
$\phi_k$ when $\theta_k$ is known, so the task of angle selection is essentially
to choose appropriate values for each $\theta_k$. When equation~$(*)$ is used to
eliminate $\phi$~variables from $(**)$, we obtain a system of linear equations of
the form

$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k,$$

where

$$A_k={\alpha_{k-1}\over\beta_k^2d_{k-1,k}}, \qquad
B_k={3-\alpha_{k-1}\over\beta_k^2d_{k-1,k}}, \qquad
C_k={3-\beta\k\over\alpha_k^2d_{k,k+1}}, \qquad
D_k={\beta\k\over\alpha_k^2d_{k,k+1}}.$$

The tensions are always $3\over4$ or more, hence each $\alpha$ and~$\beta$ will
be at most $4\over3$. It follows that $B_k|5\over4|A_k$ and
$C_k|5\over4|D_k$; hence the equations are diagonally dominant; hence they have
a unique solution. Moreover, in most cases the tensions are equal to~1, so that
$B_k=2A_k$ and $C_k=2D_k$. This makes the solution numerically stable, and there
is an exponential damping effect: The data at knot $k\pm j$ affects the angle at
knot~$k$ by a factor of~$O(2^{-j})$.

@ However, we still must consider the angles at the starting and ending knots of
a non-cyclic path. These angles might be given explicitly, or they might be
specified implicitly in terms of an amount of \quote {curl.}

Let's assume that angles need to be determined for a non-cyclic path starting at
$z_0$ and ending at~$z_n$. Then equations of the form

$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta_{k+1}=R_k$$

have been given for
$0<k<n$, and it will be convenient to introduce equations of the same form for
$k=0$ and $k=n$, where

$$A_0=B_0=C_n=D_n=0.$$

If $\theta_0$ is supposed to have a given value $E_0$, we simply define $C_0=1$,
$D_0=0$, and $R_0=E_0$. Otherwise a curl parameter, $\gamma_0$, has been
specified at~$z_0$; this means that the mock curvature at $z_0$ should be
$\gamma_0$ times the mock curvature at $z_1$; i.e.,

$${2\beta_1(\theta_0+\phi_1)-6\theta_0\over\alpha_0^2d_{01}}
=\gamma_0{2\alpha_0(\theta_0+\phi_1)-6\phi_1\over\beta_1^2d_{01}}.$$

This equation simplifies to

$$(\alpha_0\chi_0+3-\beta_1)\theta_0+
\bigl((3-\alpha_0)\chi_0+\beta_1\bigr)\theta_1=
-\bigl((3-\alpha_0)\chi_0+\beta_1\bigr)\psi_1,$$

where $\chi_0=\alpha_0^2\gamma_0/\beta_1^2$; so we can set $C_0=
\chi_0\alpha_0+3-\beta_1$, $D_0=(3-\alpha_0)\chi_0+\beta_1$, $R_0=-D_0\psi_1$. It
can be shown that $C_0>0$ and $C_0B_1-A_1D_0>0$ when $\gamma_0\G0$, hence the
linear equations remain nonsingular.

Similar considerations apply at the right end, when the final angle $\phi_n$ may
or may not need to be determined. It is convenient to let $\psi_n=0$, hence
$\theta_n=-\phi_n$. We either have an explicit equation $\theta_n=E_n$, or we
have

$$\bigl((3-\beta_n)\chi_n+\alpha_{n-1}\bigr)\theta_{n-1}+
(\beta_n\chi_n+3-\alpha_{n-1})\theta_n=0,\qquad
\chi_n={\beta_n^2\gamma_n\over\alpha_{n-1}^2}.$$

When |make_choices| chooses angles, it must compute the coefficients of these
linear equations, then solve the equations. To compute the coefficients, it is
necessary to compute arctangents of the given turning angles~$\psi_k$. When the
equations are solved, the chosen directions $\theta_k$ are put back into the form
of control points by essentially computing sines and cosines.

@ OK, we are ready to make the hard choices of |make_choices|. Most of the work
is relegated to an auxiliary procedure called |solve_choices|, which has been
introduced to keep |make_choices| from being extremely long.

@<Fill in the control information between...@>=
@<FillInAllocate@>
@<Calculate the turning angles $\psi_k$ and the distances $d_{k,k+1}$; set $n$ to the length of the path@>
@<Remove |open| types at the breakpoints@>
@<FillInDeallocate@>
mp_solve_choices(mp, p, q, n);

@ It's convenient to precompute quantities that will be needed several times
later. The values of |delta_x[k]| and |delta_y[k]| will be the coordinates of
$z\k-z_k$, and the magnitude of this vector will be |delta[k]=@t$d_{k,k+1}$@>|.
The path angle $\psi_k$ between $z_k-z_{k-1}$ and $z\k-z_k$ will be stored in
|psi[k]|.

@<Glob...@>=
int path_size;      /* maximum number of knots between breakpoints of a path */
int path_padding;   /* be nice */

mp_number *delta_x;
mp_number *delta_y;
mp_number *delta;   /* knot differences */
mp_number *psi;     /* turning angles */

@ @<Dealloc variables@>=
for (int k = 0; k<mp->path_size; k++) {
    free_number(mp->delta_x[k]);
    free_number(mp->delta_y[k]);
    free_number(mp->delta[k]);
    free_number(mp->psi[k]);
}
mp_memory_free(mp->delta_x);
mp_memory_free(mp->delta_y);
mp_memory_free(mp->delta);
mp_memory_free(mp->psi);

@ @<Other local variables for |make_choices|@>=
int k, n;     /* current and final knot numbers */
mp_knot s, t; /* registers for list traversal */

@ @<FillInAllocate@>=
mp_number sine, cosine; /* trig functions of various angles */
mp_number arg1, arg2, r1, r2;
mp_number delx, dely; /* directions where |open| meets |explicit| */
new_fraction(sine);
new_fraction(cosine);
new_number(arg1);
new_number(arg2);
new_fraction(r1);
new_fraction(r2);
new_number(delx);
new_number(dely);

@ @<FillInDeallocate@>=
free_number(sine);
free_number(cosine);
free_number(arg1);
free_number(arg2);
free_number(r1);
free_number(r2);
free_number(delx);
free_number(dely);

@ @<Calculate the turning angles...@>=
{
  RESTART:
    k = 0;
    s = p;
    n = mp->path_size;
    do {
        t = mp_next_knot(s);
        set_number_from_subtraction(mp->delta_x[k], t->x_coord, s->x_coord);
        set_number_from_subtraction(mp->delta_y[k], t->y_coord, s->y_coord);
        pyth_add(mp->delta[k], mp->delta_x[k], mp->delta_y[k]);
        if (k > 0) {
            make_fraction(r1, mp->delta_y[k - 1], mp->delta[k - 1]);
            number_clone(sine, r1);
            make_fraction(r2, mp->delta_x[k - 1], mp->delta[k - 1]);
            number_clone(cosine, r2);
            take_fraction(r1, mp->delta_x[k], cosine);
            take_fraction(r2, mp->delta_y[k], sine);
            set_number_from_addition(arg1, r1, r2);
            take_fraction(r1, mp->delta_y[k], cosine);
            take_fraction(r2, mp->delta_x[k], sine);
            set_number_from_subtraction(arg2, r1, r2);
            n_arg(mp->psi[k], arg1, arg2 );
        }
        ++k;
        s = t;
        if (k == mp->path_size) {
            mp_reallocate_paths(mp, mp->path_size + (mp->path_size / 4));
            goto RESTART; /* retry, loop size has changed */
        } else if (s == q) {
            n = k;
        }
    } while (! ((k >= n) && (mp_left_type(s) != mp_end_cycle_knot)));
    if (k == n) {
        set_number_to_zero(mp->psi[k]);
    } else {
        number_clone(mp->psi[k], mp->psi[1]);
    }
}

@ When we get to this point of the code, |mp_right_type(p)| is either |given| or
|curl| or |open|. If it is |open|, we must have |mp_left_type(p)=mp_end_cycle| or
|mp_left_type(p)=mp_explicit|. In the latter case, the |open| type is converted
to |given|; however, if the velocity coming into this knot is zero, the |open|
type is converted to a |curl|, since we don't know the incoming direction.

Similarly, |mp_left_type(q)| is either |given| or |curl| or |open| or
|mp_end_cycle|. The |open| possibility is reduced either to |given| or to |curl|.

@<Remove |open| types at the breakpoints@>=
{
    if (mp_left_type(q) == mp_open_knot) {
        set_number_from_subtraction(delx, q->right_x, q->x_coord);
        set_number_from_subtraction(dely, q->right_y, q->y_coord);
        if (number_zero(delx) && number_zero(dely)) {
            mp_left_type(q) = mp_curl_knot;
            set_number_to_unity(q->left_curl);
        } else {
            mp_left_type(q) = mp_given_knot;
            n_arg(q->left_given, delx, dely);
        }
    }
    if ((mp_right_type(p) == mp_open_knot) && (mp_left_type(p) == mp_explicit_knot)) {
        set_number_from_subtraction(delx, p->x_coord, p->left_x);
        set_number_from_subtraction(dely, p->y_coord, p->left_y);
        if (number_zero(delx) && number_zero(dely)) {
            mp_right_type(p) = mp_curl_knot;
            set_number_to_unity(p->right_curl);
        } else {
            mp_right_type(p) = mp_given_knot;
            n_arg(p->right_given, delx, dely);
        }
    }
}

@ Linear equations need to be solved whenever |n>1|; and also when |n=1| and
exactly one of the breakpoints involves a curl. The simplest case occurs when
|n=1| and there is a curl at both breakpoints; then we simply draw a straight
line.

But before coding up the simple cases, we might as well face the general case,
since we must deal with it sooner or later, and since the general case is likely
to give some insight into the way simple cases can be handled best.

When there is no cycle, the linear equations to be solved form a tridiagonal
system, and we can apply the standard technique of Gaussian elimination to
convert that system to a sequence of equations of the form

$$\theta_0+u_0\theta_1=v_0,\quad \theta_1+u_1\theta_2=v_1,\quad\ldots,\quad
\theta_{n-1}+u_{n-1}\theta_n=v_{n-1},\quad \theta_n=v_n.$$

It is possible to do this diagonalization while generating the equations. Once
$\theta_n$ is known, it is easy to determine $\theta_{n-1}$, \dots, $\theta_1$,
$\theta_0$; thus, the equations will be solved.

The procedure is slightly more complex when there is a cycle, but the basic idea
will be nearly the same. In the cyclic case the right-hand sides will be
$v_k+w_k\theta_0$ instead of simply $v_k$, and we will start the process off with
$u_0=v_0=0$, $w_0=1$. The final equation will be not $\theta_n=v_n$ but
$\theta_n+u_n\theta_1=v_n+w_n\theta_0$; an appropriate ending routine will take
account of the fact that $\theta_n=\theta_0$ and eliminate the $w$'s from the
system, after which the solution can be obtained as before.

When $u_k$, $v_k$, and $w_k$ are being computed, the three pointer variables |r|,
|s|,~|t| will point respectively to knots |k-1|, |k|, and~|k+1|. The $u$'s and
$w$'s are scaled by $2^{28}$, i.e., they are of type |fraction|; the $\theta$'s
and $v$'s are of type |angle|.

@<Glob...@>=
mp_number *theta; /* values of $\theta_k$ */
mp_number *uu;    /* values of $u_k$ */
mp_number *vv;    /* values of $v_k$ */
mp_number *ww;    /* values of $w_k$ */

@ @<Dealloc variables@>=
for (int k = 0; k < mp->path_size; k++) {
    free_number(mp->theta[k]);
    free_number(mp->uu[k]);
    free_number(mp->vv[k]);
    free_number(mp->ww[k]);
}
mp_memory_free(mp->theta);
mp_memory_free(mp->uu);
mp_memory_free(mp->vv);
mp_memory_free(mp->ww);

@ @<Declarations@>=
static void mp_reallocate_paths (MP mp, int l);

@ @c
void mp_reallocate_paths (MP mp, int l)
{
    mp->delta_x = mp_memory_reallocate(mp->delta_x, (size_t) (l + 1) * sizeof(mp_number));
    mp->delta_y = mp_memory_reallocate(mp->delta_y, (size_t) (l + 1) * sizeof(mp_number));
    mp->delta = mp_memory_reallocate(mp->delta, (size_t) (l + 1) * sizeof(mp_number));
    mp->psi = mp_memory_reallocate(mp->psi, (size_t) (l + 1) * sizeof(mp_number));
    mp->theta = mp_memory_reallocate(mp->theta, (size_t) (l + 1) * sizeof(mp_number));
    mp->uu = mp_memory_reallocate(mp->uu, (size_t) (l + 1) * sizeof(mp_number));
    mp->vv = mp_memory_reallocate(mp->vv, (size_t) (l + 1) * sizeof(mp_number));
    mp->ww = mp_memory_reallocate(mp->ww, (size_t) (l + 1) * sizeof(mp_number));
    for (int k = mp->path_size; k<l; k++) {
        new_number(mp->delta_x[k]);
        new_number(mp->delta_y[k]);
        new_number(mp->delta[k]);
        new_angle(mp->psi[k]);
        new_angle(mp->theta[k]);
        new_fraction(mp->uu[k]);
        new_angle(mp->vv[k]);
        new_fraction(mp->ww[k]);
    }
    mp->path_size = l;
}

@ Our immediate problem is to get the ball rolling by setting up the first
equation or by realizing that no equations are needed, and to fit this
initialization into a framework suitable for the overall computation.

@<Declarations@>=
static void mp_solve_choices (MP mp, mp_knot p, mp_knot q, int n);

@ @c
void mp_solve_choices (MP mp, mp_knot p, mp_knot q, int n)
{
    int k = 0;     /* current knot number */
    mp_knot r = 0;
    mp_knot s = p;
    mp_number ff;
    new_fraction(ff);
    while (1) {
        mp_knot t = mp_next_knot(s);
        if (k == 0) {
            @<Get the linear equations started; or |return| with the control points in place, if linear equations needn't be solved@>
        } else {
            switch (mp_left_type(s)) {
                case mp_end_cycle_knot:
                case mp_open_knot:
                    @<Set up the equation to match mock curvatures at $z_k$; then |goto found| with $\theta_n$ adjusted to equal $\theta_0$, if a cycle has ended@>
                    break;
                case mp_curl_knot:
                    @<Set up the equation for a curl at $\theta_n$ and |goto found|@>
                    break;
                case mp_given_knot:
                    @<Calculate the given value of $\theta_n$ and |goto found|@>
                    break;
            }
        }
        r = s;
        s = t;
        ++k;
    }
FOUND:
    @<Finish choosing angles and assigning control points@>
    free_number(ff);
}

@ On the first time through the loop, we have |k=0| and |r| is not yet defined.
The first linear equation, if any, will have $A_0=B_0=0$.

@<Get the linear equations started...@>=
switch (mp_right_type(s)) {
    case mp_given_knot:
        if (mp_left_type(t) == mp_given_knot) {
            @<Reduce to simple case of two givens  and |return|@>
        } else {
            @<Set up the equation for a given value of $\theta_0$@>
        }
        break;
    case mp_curl_knot:
        if (mp_left_type(t) == mp_curl_knot) {
            @<Reduce to simple case of straight line and |return|@>
        } else {
            @<Set up the equation for a curl at $\theta_0$@>
        }
        break;
    case mp_open_knot:
        set_number_to_zero(mp->uu[0]);
        set_number_to_zero(mp->vv[0]);
        number_clone(mp->ww[0], fraction_one_t);
        /* this begins a cycle */
        break;
}

@ The general equation that specifies equality of mock curvature at $z_k$ is

$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k,$$

as derived above. We want to combine this with the already-derived equation
$\theta_{k-1}+u_{k-1}\theta_k=v_{k-1}+w_{k-1}\theta_0$ in order to obtain a new
equation $\theta_k+u_k\theta\k=v_k+w_k\theta_0$. This can be done by dividing the
equation

$$(B_k-u_{k-1}A_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k-A_kv_{k-1}
-A_kw_{k-1}\theta_0$$

by $B_k-u_{k-1}A_k+C_k$. The trick is to do this carefully with fixed-point
arithmetic, avoiding the chance of overflow while retaining suitable precision.

The calculations will be performed in several registers that provide temporary
storage for intermediate quantities.

@ @<Set up the equation to match mock curvatures...@>=
{
    mp_number aa, bb, cc, acc; /* temporary registers */
    mp_number dd, ee;          /* likewise, but |scaled| */
    new_fraction(aa);
    new_fraction(bb);
    new_fraction(cc);
    new_fraction(acc);
    new_number(dd);
    new_number(ee);
    @<Calculate the values $|aa|=A_k/B_k$, $|bb|=D_k/C_k$, $|dd|=(3-\alpha_{k-1})d_{k,k+1}$, $|ee|=(3-\beta\k)d_{k-1,k}$,  and $|cc|=(B_k-u_{k-1}A_k)/B_k$@>
    @<Calculate the ratio $|ff|=C_k/(C_k+B_k-u_{k-1}A_k)$@>
    take_fraction(mp->uu[k], ff, bb);
    @<Calculate the values of $v_k$ and $w_k$@>
    if (mp_left_type(s) == mp_end_cycle_knot) {
        @<Adjust $\theta_n$ to equal $\theta_0$ and |goto found|@>
    }
    free_number(aa);
    free_number(bb);
    free_number(cc);
    free_number(acc);
    free_number(dd);
    free_number(ee);
}

@ Since tension values are never less than 3/4, the values |aa| and |bb| computed
here are never more than 4/5.

@<Calculate the values $|aa|=...@>=
{
    mp_number absval;
    new_number_abs(absval, r->right_tension);
    if (number_equal(absval, unity_t)) {
        number_clone(aa, fraction_half_t);
        number_clone(dd, mp->delta[k]);
        number_double(dd);
    } else {
        mp_number arg1, arg2, ret;
        new_number(arg1);
        new_number_abs(arg2, r->right_tension);
        number_multiply_int(arg2, 3);
        number_subtract(arg2, unity_t);
        make_fraction(aa, unity_t, arg2);
        number_abs_clone(arg2, r->right_tension);
        new_fraction(ret);
        make_fraction(ret, unity_t, arg2);
        set_number_from_subtraction(arg1, fraction_three_t, ret);
        take_fraction(arg2, mp->delta[k], arg1);
        number_clone(dd, arg2);
        free_number(ret);
        free_number(arg1);
        free_number(arg2);
    }
    number_abs_clone(absval, t->left_tension);
    if (number_equal(absval, unity_t)) {
        number_clone(bb, fraction_half_t);
        number_clone(ee, mp->delta[k - 1]);
        number_double(ee);
    } else {
        mp_number arg1, arg2, ret;
        new_number(arg1);
        new_number_abs(arg2, t->left_tension);
        number_multiply_int(arg2, 3);
        number_subtract(arg2, unity_t);
        make_fraction(bb, unity_t, arg2);
        number_abs_clone(arg2, t->left_tension);
        new_fraction(ret);
        make_fraction(ret, unity_t, arg2);
        set_number_from_subtraction(arg1, fraction_three_t, ret);
        take_fraction(ee, mp->delta[k - 1], arg1);
        free_number(ret);
        free_number(arg1);
        free_number(arg2);
    }
    free_number(absval);
}
{
    mp_number r1;
    new_number(r1);
    take_fraction(r1, mp->uu[k - 1], aa);
    set_number_from_subtraction(cc, fraction_one_t, r1);
    free_number(r1);
}

@ The ratio to be calculated in this step can be written in the form

$$\beta_k^2\cdot|ee|\over\beta_k^2\cdot|ee|+\alpha_k^2\cdot
|cc|\cdot|dd|,$$

because of the quantities just calculated. The values of |dd| and |ee| will not
be needed after this step has been performed.

@<Calculate the ratio $|ff|=C_k/(C_k+B_k-u_{k-1}A_k)$@>=
{
    mp_number rt, lt;
    mp_number arg2;
    new_number_clone(arg2, dd);
    take_fraction(dd, arg2, cc);
    new_number_abs(lt, s->left_tension);
    new_number_abs(rt, s->right_tension);
    if (! number_equal(lt, rt)) {
        /* $\beta_k^{-1}\ne\alpha_k^{-1}$ */
        mp_number r1;
        new_number(r1);
        if (number_less(lt, rt)) {
            /* $\alpha_k^2/\beta_k^2$ */
            make_fraction(r1, lt, rt);
            take_fraction(ff, r1, r1);
            number_clone(r1, dd);
            take_fraction(dd, r1, ff);
        } else {
            /* $\beta_k^2/\alpha_k^2$ */
            make_fraction(r1, rt, lt);
            take_fraction(ff, r1, r1);
            number_clone(r1, ee);
            take_fraction(ee, r1, ff);
        }
        free_number(r1);
    }
    free_number(rt);
    free_number(lt);
    set_number_from_addition(arg2, dd, ee);
    make_fraction(ff, ee, arg2);
    free_number(arg2);
}

@ The value of $u_{k-1}$ will be |<=1| except when $k=1$ and the previous
equation was specified by a curl. In that case we must use a special method of
computation to prevent overflow.

Fortunately, the calculations turn out to be even simpler in this \quote {hard} case.
The curl equation makes $w_0=0$ and $v_0=-u_0\psi_1$, hence
$-B_1\psi_1-A_1v_0=-(B_1-u_0A_1)\psi_1=-|cc|\cdot B_1\psi_1$.

@<Calculate the values of $v_k$ and $w_k$@>=
take_fraction(acc, mp->psi[k + 1], mp->uu[k]);
number_negate(acc);
if (mp_right_type(r) == mp_curl_knot) {
    mp_number r1, arg2;
    new_fraction(r1);
    new_number(arg2);
    set_number_from_subtraction(arg2, fraction_one_t, ff);
    take_fraction(r1, mp->psi[1], arg2);
    set_number_to_zero(mp->ww[k]);
    set_number_from_subtraction(mp->vv[k], acc, r1);
    free_number(r1);
    free_number(arg2);
} else {
    mp_number arg1, r1;
    new_fraction(r1);
    new_number(arg1);
    set_number_from_subtraction(arg1, fraction_one_t, ff);
    /* this is $B_k/(C_k+B_k-u_{k-1}A_k)<5$ */
    make_fraction(ff, arg1, cc);
    free_number(arg1);
    take_fraction(r1, mp->psi[k], ff);
    number_subtract(acc, r1);
    number_clone(r1, ff);
    /* this is $A_k/(C_k+B_k-u_{k-1}A_k)$ */
    take_fraction(ff, r1, aa);
    take_fraction(r1, mp->vv[k - 1], ff);
    set_number_from_subtraction(mp->vv[k], acc, r1 );
    if (number_zero(mp->ww[k - 1])) {
        set_number_to_zero(mp->ww[k]);
    } else {
        take_fraction(mp->ww[k], mp->ww[k - 1], ff);
        number_negate(mp->ww[k]);
    }
    free_number(r1);
}

@ When a complete cycle has been traversed, we have $\theta_k+u_k\theta\k=
v_k+w_k\theta_0$, for |1<=k<=n|. We would like to determine the value of
$\theta_n$ and reduce the system to the form $\theta_k+u_k\theta\k=v_k$ for
|0<=k<n|, so that the cyclic case can be finished up just as if there were no
cycle.

The idea in the following code is to observe that

$$\eqalign{\theta_n&=v_n+w_n\theta_0-u_n\theta_1=\cdots\cr
&=v_n+w_n\theta_0-u_n\bigl(v_1+w_1\theta_0-u_1(v_2+\cdots
-u_{n-2}(v_{n-1}+w_{n-1}\theta_0-u_{n-1}\theta_0))\bigr),\cr}$$

so we can solve for $\theta_n=\theta_0$.

@<Adjust $\theta_n$ to equal $\theta_0$ and |goto found|@>=
mp_number arg2, r1;
new_number(arg2);
new_number(r1);
set_number_to_zero(aa);
number_clone(bb, fraction_one_t); /* we have |k=n| */
do {
    --k;
    if (k == 0) {
        k = n;
    }
    take_fraction(r1, aa, mp->uu[k]);
    set_number_from_subtraction(aa, mp->vv[k], r1);
    take_fraction(r1, bb, mp->uu[k]);
    set_number_from_subtraction(bb, mp->ww[k], r1);
} while (k != n);
/* now $\theta_n=|aa|+|bb|\cdot\theta_n$ */
set_number_from_subtraction(arg2, fraction_one_t, bb);
make_fraction(r1, aa, arg2);
number_clone(aa, r1);
number_clone(mp->theta[n], aa);
number_clone(mp->vv[0], aa);
for (k = 1; k < n; k++) {
    take_fraction(r1, aa, mp->ww[k]);
    number_add(mp->vv[k], r1);
}
free_number(arg2);
free_number(r1);
free_number(aa);
free_number(bb);
free_number(cc);
free_number(acc);
free_number(dd);
free_number(ee);
goto FOUND;

@ @c
static void mp_reduce_angle (MP mp, mp_number *a)
{
    mp_number abs_a;
    new_number_abs(abs_a, *a);
    if (number_greater(abs_a, one_eighty_deg_t)) {
        if (number_positive(*a)) {
            number_subtract(*a, three_sixty_deg_t);
        } else {
            number_add(*a, three_sixty_deg_t);
        }
    }
    free_number(abs_a);
}

@ @<Declarations@>=
static void mp_reduce_angle (MP mp, mp_number *a);

@ @<Calculate the given value of $\theta_n$...@>=
{
    mp_number narg;
    new_angle(narg);
    n_arg(narg, mp->delta_x[n - 1], mp->delta_y[n - 1]);
    set_number_from_subtraction(mp->theta[n], s->left_given, narg);
    free_number(narg);
    mp_reduce_angle(mp, &mp->theta[n]);
    goto FOUND;
}

@ @<Set up the equation for a given value of $\theta_0$@>=
{
    mp_number narg;
    new_angle(narg);
    n_arg(narg, mp->delta_x[0], mp->delta_y[0]);
    set_number_from_subtraction(mp->vv[0], s->right_given, narg);
    free_number(narg);
    mp_reduce_angle(mp, &mp->vv[0]);
    set_number_to_zero(mp->uu[0]);
    set_number_to_zero(mp->ww[0]);
}

@ @<Set up the equation for a curl at $\theta_0$@>=
{
    mp_number lt, rt, cc; /* tension values */
    new_number_clone(cc, s->right_curl);
    new_number_abs(lt, t->left_tension);
    new_number_abs(rt, s->right_tension);
    if (number_unity(rt) && number_unity(lt)) {
        mp_number arg1, arg2;
        new_number_clone(arg1, cc);
        new_number_clone(arg2, cc);
        number_double(arg1);
        number_add(arg1, unity_t);
        number_add(arg2, two_t);
        make_fraction(mp->uu[0], arg1, arg2);
        free_number(arg1);
        free_number(arg2);
    } else {
        mp_curl_ratio(mp, &mp->uu[0], &cc, &rt, &lt);
    }
    take_fraction(mp->vv[0], mp->psi[1], mp->uu[0]);
    number_negate(mp->vv[0]);
    set_number_to_zero(mp->ww[0]);
    free_number(rt);
    free_number(lt);
    free_number(cc);
}

@ @<Set up the equation for a curl at $\theta_n$...@>=
{
    mp_number lt, rt, cc; /* tension values */
    new_number_clone(cc, s->left_curl);
    new_number_abs(lt, s->left_tension);
    new_number_abs(rt, r->right_tension);
    if (number_unity(rt) && number_unity(lt)) {
        mp_number arg1, arg2;
        new_number_clone(arg1, cc);
        new_number_clone(arg2, cc);
        number_double(arg1);
        number_add(arg1, unity_t);
        number_add(arg2, two_t);
        make_fraction(ff, arg1, arg2);
        free_number(arg1);
        free_number(arg2);
    } else {
        mp_curl_ratio(mp, &ff, &cc, &lt, &rt);
    }
    {
        mp_number arg1, arg2, r1;
        new_fraction(r1);
        new_fraction(arg1);
        new_number(arg2);
        take_fraction(arg1, mp->vv[n - 1], ff);
        take_fraction(r1, ff, mp->uu[n - 1]);
        set_number_from_subtraction(arg2, fraction_one_t, r1);
        make_fraction(mp->theta[n], arg1, arg2);
        number_negate(mp->theta[n]);
        free_number(r1);
        free_number(arg1);
        free_number(arg2);
    }
    free_number(rt);
    free_number(lt);
    free_number(cc);
    goto FOUND;
}

@ The |curl_ratio| subroutine has three arguments, which our previous notation
encourages us to call $\gamma$, $\alpha^{-1}$, and $\beta^{-1}$. It is a somewhat
tedious program to calculate

$${(3-\alpha)\alpha^2\gamma+\beta^3\over \alpha^3\gamma+(3-\beta)\beta^2},$$

with the result reduced to 4 if it exceeds 4. (This reduction of curl is
necessary only if the curl and tension are both large.) The values of $\alpha$
and $\beta$ will be at most~4/3.

@<Declarations@>=
static void mp_curl_ratio (MP mp, mp_number *ret, mp_number *gamma, mp_number *a_tension, mp_number *b_tension);

@ @c
void mp_curl_ratio (MP mp, mp_number *ret, mp_number *gamma_orig, mp_number *a_tension, mp_number *b_tension)
{
    mp_number alpha, beta, gamma, num, denom, ff; /* registers */
    mp_number arg1;
    new_number(arg1);
    new_fraction(alpha);
    new_fraction(beta);
    new_fraction(gamma);
    new_fraction(ff);
    new_fraction(denom);
    new_fraction(num);
    make_fraction(alpha, unity_t, *a_tension);
    make_fraction(beta, unity_t, *b_tension);
    number_clone(gamma, *gamma_orig);
    if (number_lessequal(alpha, beta)) {
        make_fraction(ff, alpha, beta);
        number_clone(arg1, ff);
        take_fraction(ff, arg1, arg1);
        number_clone(arg1, gamma);
        take_fraction(gamma, arg1, ff);
        convert_fraction_to_scaled(beta);
        take_fraction(denom, gamma, alpha);
        number_add(denom, three_t);
    } else {
        make_fraction(ff, beta, alpha);
        number_clone(arg1, ff);
        take_fraction(ff, arg1, arg1);
        take_fraction(arg1, beta, ff);
        convert_fraction_to_scaled(arg1);
        number_clone(beta, arg1);
        take_fraction(denom, gamma, alpha);
        set_number_from_div(arg1, ff, twelvebits_3);
        number_add(denom, arg1);
    }
    number_subtract(denom, beta);
    set_number_from_subtraction(arg1, fraction_three_t, alpha);
    take_fraction(num, gamma, arg1);
    number_add(num, beta);
    number_clone(arg1, denom);
    number_double(arg1);
    number_double(arg1); /* arg1 = 4*denom */
    if (number_greaterequal(num, arg1)) {
        number_clone(*ret, fraction_four_t);
    } else {
        make_fraction(*ret, num, denom);
    }
    free_number(alpha);
    free_number(beta);
    free_number(gamma);
    free_number(num);
    free_number(denom);
    free_number(ff);
    free_number(arg1);
}

@ We're in the home stretch now.

@<Finish choosing angles and assigning control points@>=
{
    mp_number r1;
    new_number(r1);
    for (k = n - 1; k >= 0; k--) {
        take_fraction(r1, mp->theta[k + 1], mp->uu[k]);
        set_number_from_subtraction(mp->theta[k], mp->vv[k], r1);
    }
    free_number(r1);
}
s = p;
k = 0;
{
    mp_number arg;
    new_number(arg);
    do {
        mp_knot t = mp_next_knot(s);
        n_sin_cos(mp->theta[k], mp->ct, mp->st);
        number_negated_clone(arg, mp->psi[k + 1]);
        number_subtract(arg, mp->theta[k + 1]);
        n_sin_cos(arg, mp->cf, mp->sf);
        mp_set_controls (mp, s, t, k);
        ++k;
        s = t;
    } while (k != n);
    free_number(arg);
}

@ The |set_controls| routine actually puts the control points into a pair of
consecutive nodes |p| and~|q|. Global variables are used to record the values of
$\sin\theta$, $\cos\theta$, $\sin\phi$, and $\cos\phi$ needed in this
calculation.

@<Glob...@>=
mp_number st;
mp_number ct;
mp_number sf;
mp_number cf; /* sines and cosines */

@ @<Initialize table...@>=
new_fraction(mp->st);
new_fraction(mp->ct);
new_fraction(mp->sf);
new_fraction(mp->cf);

@ @<Dealloc ...@>=
free_number(mp->st);
free_number(mp->ct);
free_number(mp->sf);
free_number(mp->cf);

@ @<Declarations@>=
static void mp_set_controls (MP mp, mp_knot p, mp_knot q, int k);

@ @c
void mp_set_controls (MP mp, mp_knot p, mp_knot q, int k)
{
    mp_number rr, ss; /* velocities, divided by thrice the tension */
    mp_number lt, rt; /* tensions */
    mp_number sine;   /* $\sin(\theta+\phi)$ */
    mp_number tmp;
    mp_number r1, r2;
    new_number(tmp);
    new_number(r1);
    new_number(r2);
    new_number_abs(lt, q->left_tension);
    new_number_abs(rt, p->right_tension);
    new_fraction(sine);
    new_fraction(rr);
    new_fraction(ss);
    velocity(rr, mp->st, mp->ct, mp->sf, mp->cf, rt);
    velocity(ss, mp->sf, mp->cf, mp->st, mp->ct, lt);
    if (number_negative(p->right_tension) || number_negative(q->left_tension)) {
        @<Decrease the velocities, if necessary, to stay inside the bounding triangle@>
    }
    take_fraction(r1, mp->delta_x [k], mp->ct);
    take_fraction(r2, mp->delta_y [k], mp->st);
    number_subtract(r1, r2);
    take_fraction(tmp, r1, rr);
    set_number_from_addition(p->right_x, p->x_coord, tmp);
    take_fraction(r1, mp->delta_y[k], mp->ct);
    take_fraction(r2, mp->delta_x[k], mp->st);
    number_add(r1, r2);
    take_fraction(tmp, r1, rr);
    set_number_from_addition(p->right_y, p->y_coord, tmp);
    take_fraction(r1, mp->delta_x[k], mp->cf);
    take_fraction(r2, mp->delta_y[k], mp->sf);
    number_add(r1, r2);
    take_fraction(tmp, r1, ss);
    set_number_from_subtraction(q->left_x, q->x_coord, tmp);
    take_fraction(r1, mp->delta_y[k], mp->cf);
    take_fraction(r2, mp->delta_x[k], mp->sf);
    number_subtract(r1, r2);
    take_fraction(tmp, r1, ss);
    set_number_from_subtraction(q->left_y, q->y_coord, tmp);
    mp_right_type(p) = mp_explicit_knot;
    mp_left_type(q) = mp_explicit_knot;
    free_number(tmp);
    free_number(r1);
    free_number(r2);
    free_number(lt);
    free_number(rt);
    free_number(rr);
    free_number(ss);
    free_number(sine);
}

@ The boundedness conditions $|rr|\L\sin\phi\,/\sin(\theta+\phi)$ and
$|ss|\L\sin\theta\,/\sin(\theta+\phi)$ are to be enforced if $\sin\theta$,
$\sin\phi$, and $\sin(\theta+\phi)$ all have the same sign. Otherwise there is no
\quote {bounding triangle.}

@<Decrease the velocities, if necessary...@>=
if ((number_nonnegative(mp->st) && number_nonnegative(mp->sf)) || (number_nonpositive(mp->st) && number_nonpositive(mp->sf))) {
    mp_number r1, r2, arg1;
    new_fraction(r1);
    new_fraction(r2);
    new_number_abs(arg1, mp->st);
    take_fraction(r1, arg1, mp->cf);
    number_abs_clone(arg1, mp->sf);
    take_fraction(r2, arg1, mp->ct);
    set_number_from_addition(sine, r1, r2);
    if (number_positive(sine)) {
        set_number_from_addition(arg1, fraction_one_t, unity_t);  /* safety factor */
        number_clone(r1, sine);
        take_fraction(sine, r1, arg1);
        if (number_negative(p->right_tension)) {
            number_abs_clone(arg1, mp->sf);
            if (ab_vs_cd(arg1, fraction_one_t, rr, sine) < 0) {
                number_abs_clone(arg1, mp->sf);
                make_fraction(rr, arg1, sine);
            }
        }
        if (number_negative(q->left_tension)) {
            number_abs_clone(arg1, mp->st);
            if (ab_vs_cd(arg1, fraction_one_t, ss, sine) < 0) {
                number_abs_clone(arg1, mp->st);
                make_fraction(ss, arg1, sine);
            }
        }
    }
    free_number(arg1);
    free_number(r1);
    free_number(r2);
}

@ Only the simple cases remain to be handled.

@<Reduce to simple case of two givens and |return|@>=
{
    mp_number arg1;
    mp_number narg;
    new_angle(narg);
    n_arg(narg, mp->delta_x[0], mp->delta_y[0]);
    new_number(arg1);
    set_number_from_subtraction(arg1, p->right_given, narg);
    n_sin_cos(arg1, mp->ct, mp->st);
    set_number_from_subtraction(arg1, q->left_given, narg);
    n_sin_cos(arg1, mp->cf, mp->sf);
    number_negate(mp->sf);
    mp_set_controls (mp, p, q, 0);
    free_number(narg);
    free_number(arg1);
    free_number(ff);
    return;
}

@ @<Reduce to simple case of straight line and |return|@>=
{
    mp_number lt, rt; /* tension values */
    mp_right_type(p) = mp_explicit_knot;
    mp_left_type(q) = mp_explicit_knot;
    new_number_abs(lt, q->left_tension);
    new_number_abs(rt, p->right_tension);
    if (number_unity(rt)) {
        mp_number arg2;
        new_number(arg2);
        if (number_nonnegative(mp->delta_x[0])) {
            set_number_from_addition(arg2, mp->delta_x[0], epsilon_t);
        } else {
            set_number_from_subtraction(arg2, mp->delta_x[0], epsilon_t);
        }
        number_int_div(arg2, 3);
        set_number_from_addition(p->right_x, p->x_coord, arg2);
        if (number_nonnegative(mp->delta_y[0])) {
            set_number_from_addition(arg2, mp->delta_y[0], epsilon_t);
        } else {
            set_number_from_subtraction(arg2, mp->delta_y[0], epsilon_t);
        }
        number_int_div(arg2, 3);
        set_number_from_addition(p->right_y, p->y_coord, arg2);
        free_number(arg2);
    } else {
        mp_number arg2, r1;
        new_fraction(r1);
        new_number_clone(arg2, rt);
        number_multiply_int(arg2, 3);
        make_fraction(ff, unity_t, arg2);    /* $\alpha/3$ */
        free_number(arg2);
        take_fraction(r1, mp->delta_x[0], ff);
        set_number_from_addition(p->right_x, p->x_coord, r1);
        take_fraction(r1, mp->delta_y[0], ff);
        set_number_from_addition(p->right_y, p->y_coord, r1);
    }
    if (number_unity(lt)) {
        mp_number arg2;
        new_number(arg2);
        if (number_nonnegative(mp->delta_x[0])) {
            set_number_from_addition(arg2, mp->delta_x[0], epsilon_t);
        } else {
            set_number_from_subtraction(arg2, mp->delta_x[0], epsilon_t);
        }
        number_int_div(arg2, 3);
        set_number_from_subtraction(q->left_x, q->x_coord, arg2);
        if (number_nonnegative(mp->delta_y[0])) {
            set_number_from_addition(arg2, mp->delta_y[0], epsilon_t);
        } else {
            set_number_from_subtraction(arg2, mp->delta_y[0], epsilon_t);
        }
        number_int_div(arg2, 3);
        set_number_from_subtraction(q->left_y, q->y_coord, arg2);
        free_number(arg2);
    } else {
        mp_number arg2, r1;
        new_fraction(r1);
        new_number_clone(arg2, lt);
        number_multiply_int(arg2, 3);
        make_fraction(ff, unity_t, arg2); /* $\beta/3$ */
        free_number(arg2);
        take_fraction(r1, mp->delta_x[0], ff);
        set_number_from_subtraction(q->left_x, q->x_coord, r1);
        take_fraction(r1, mp->delta_y[0], ff);
        set_number_from_subtraction(q->left_y, q->y_coord, r1);
        free_number(r1);
    }
    free_number(ff);
    free_number(lt);
    free_number(rt);
    return;
}

@ Various subroutines that are useful for the new (1.770) exported api for
solving path choices

@c
# define TOO_LARGE(a) (fabs((a))>4096.0)
# define PI           3.1415926535897932384626433832795028841971

static int out_of_range (MP mp, double a)
{
    (void) mp;
    mp_number t;
    new_number_from_double(mp, t, fabs(a));
    if (number_greaterequal(t, inf_t)) {
        free_number(t);
        return 1;
    } else {
        free_number(t);
        return 0;
    }
}

static int mp_link_knotpair (MP mp, mp_knot p, mp_knot q)
{
    (void) mp;
    if (p == NULL || q == NULL) {
        return 0;
    } else {
        mp_prev_knot(q) = p;
        mp_next_knot(p) = q;
        set_number_from_double(p->right_tension, 1.0);
        if (mp_right_type(p) == mp_endpoint_knot) {
            mp_right_type(p) = mp_open_knot;
        }
        set_number_from_double(q->left_tension, 1.0);
        if (mp_left_type(q) == mp_endpoint_knot) {
            mp_left_type(q) = mp_open_knot;
        }
        return 1;
    }
}

static int mp_link_knotpair_xy (MP mp, mp_knot p, mp_knot q)
{
    (void) mp;
    if (p == NULL || q == NULL) {
        return 0;
    } else {
        mp_prev_knot(q) = p;
        mp_next_knot(p) = q;
        return 1;
    }
}

int mp_close_path_cycle (MP mp, mp_knot p, mp_knot q)
{
    return mp_link_knotpair(mp, p, q);
}

int mp_close_path (MP mp, mp_knot q, mp_knot first)
{
    if (q == NULL || first == NULL) {
        return 0;
    } else {
        mp_prev_knot(first) = q;
        mp_next_knot(q) = first;
        mp_right_type(q) = mp_endpoint_knot;
        set_number_from_double(q->right_tension, 1.0);
        mp_left_type(first) = mp_endpoint_knot;
        set_number_from_double(first->left_tension, 1.0);
        return 1;
    }
}

mp_knot mp_create_knot (MP mp)
{
    mp_knot q = mp_new_knot(mp);
    mp_left_type(q) = mp_endpoint_knot;
    mp_right_type(q) = mp_endpoint_knot;
    return q;
}

int mp_set_knot (MP mp, mp_knot p, double x, double y)
{
    if (p == NULL) {
        return 0;
    } else if (out_of_range(mp, x)) {
        return 0;
    } else if (out_of_range(mp, y)) {
        return 0;
    } else {
        set_number_from_double(p->x_coord, x);
        set_number_from_double(p->y_coord, y);
        return 1;
    }
}

mp_knot mp_append_knot (MP mp, mp_knot p, double x, double y)
{
    mp_knot q = mp_create_knot(mp);
    if (q == NULL) {
        return NULL;
    } else if (! mp_set_knot(mp, q, x, y)) {
        mp_memory_free(q);
        return NULL;
    } else if (p == NULL) {
        return q;
    } else if (mp_link_knotpair(mp, p, q)) {
        return q;
    } else {
        mp_memory_free(q);
        return NULL;
    }
}

mp_knot mp_append_knot_xy (MP mp, mp_knot p, double x, double y)
{
    mp_knot q = mp_create_knot(mp);
    if (q == NULL) {
        return NULL;
    } else if (! mp_set_knot(mp, q, x, y)) {
        mp_memory_free(q);
        return NULL;
    } else if (p == NULL) {
        return q;
    } else if (mp_link_knotpair_xy(mp, p, q)) {
        mp_right_type(p) = mp_explicit_knot;
        mp_left_type(p) = mp_explicit_knot;
        return q;
    } else {
        mp_memory_free(q);
        return NULL;
    }
}

int mp_set_knot_curl (MP mp, mp_knot q, double value) /* same as mp_set_knot_right_curl */
{
    if (q == NULL) {
        return 0;
    } else if (TOO_LARGE(value)) {
        return 0;
    } else {
        mp_right_type(q) = mp_curl_knot;
        set_number_from_double(q->right_curl, value);
        if (mp_left_type(q) == mp_open_knot) {
            mp_left_type(q) = mp_curl_knot;
            set_number_from_double(q->left_curl, value);
        }
        return 1;
    }
}

int mp_set_knot_left_curl (MP mp, mp_knot q, double value)
{
    if (q == NULL) {
        return 0;
    } else if (TOO_LARGE(value)) {
        return 0;
    } else {
        mp_left_type(q) = mp_curl_knot;
        set_number_from_double(q->left_curl, value);
        if (mp_right_type(q) == mp_open_knot) {
            mp_right_type(q) = mp_curl_knot;
            set_number_from_double(q->right_curl, value);
        }
        return 1;
    }
}

int mp_set_knot_right_curl (MP mp, mp_knot q, double value)
{
    if (q == NULL) {
        return 0;
    } else if (TOO_LARGE(value)) {
        return 0;
    } else {
        mp_right_type(q) = mp_curl_knot;
        set_number_from_double(q->right_curl, value);
        if (mp_left_type(q) == mp_open_knot) {
            mp_left_type(q) = mp_curl_knot;
            set_number_from_double(q->left_curl, value);
        }
        return 1;
    }
}

int mp_set_knot_simple_curl (MP mp, mp_knot q)
{
    if (q == NULL) {
        return 0;
    } else {
        /* no need for double */
        mp_right_type(q) = mp_curl_knot;
        set_number_from_double(q->right_curl, 1.0);
        mp_left_type(q) = mp_curl_knot;
        set_number_from_double(q->left_curl, 1.0);
        return 1;
    }
}

int mp_set_knotpair_curls (MP mp, mp_knot p, mp_knot q, double t1, double t2)
{
    if (p == NULL || q == NULL) {
        return 0;
    } else if (mp_set_knot_curl(mp, p, t1)) {
        return mp_set_knot_curl(mp, q, t2);
    } else {
        return 0;
    }
}

int mp_set_knotpair_tensions (MP mp, mp_knot p, mp_knot q, double t1, double t2)
{
    if (p == NULL || q == NULL) {
        return 0;
    } else if (TOO_LARGE(t1)) {
        return 0;
    } else if (TOO_LARGE(t2)) {
        return 0;
    } else if ((fabs(t1) < 0.75)) {
        return 0;
    } else if ((fabs(t2) < 0.75)) {
        return 0;
    } else {
        set_number_from_double(p->right_tension, t1);
        set_number_from_double(q->left_tension, t2);
        return 1;
    }
}

int mp_set_knot_left_tension (MP mp, mp_knot p, double t1)
{
    if (p == NULL) {
        return 0;
    } else if (TOO_LARGE(t1)) {
        return 0;
    } else if ((fabs(t1) < 0.75)) {
        return 0;
    } else  {
        set_number_from_double(p->left_tension, t1);
        return 1;
    }
}

int mp_set_knot_right_tension (MP mp, mp_knot p, double t1)
{
    if (p == NULL) {
        return 0;
    } else if (TOO_LARGE(t1)) {
        return 0;
    } else if ((fabs(t1) < 0.75)) {
        return 0;
    } else {
        set_number_from_double(p->right_tension, t1);
        return 1;
    }
}

int mp_set_knotpair_controls (MP mp, mp_knot p, mp_knot q, double x1, double y1, double x2, double y2)
{
    if (p == NULL || q == NULL) {
        return 0;
    } else if (out_of_range(mp, x1)) {
        return 0;
    } else if (out_of_range(mp, y1)) {
        return 0;
    } else if (out_of_range(mp, x2)) {
        return 0;
    } else if (out_of_range(mp, y2)) {
        return 0;
    } else {
        mp_right_type(p) = mp_explicit_knot;
        set_number_from_double(p->right_x, x1);
        set_number_from_double(p->right_y, y1);
        mp_left_type(q) = mp_explicit_knot;
        set_number_from_double(q->left_x, x2);
        set_number_from_double(q->left_y, y2);
        return 1;
    }
}

int mp_set_knot_left_control (MP mp, mp_knot p, double x1, double y1)
{
    if (p == NULL) {
        return 0;
    } else if (out_of_range(mp, x1)) {
        return 0;
    } else if (out_of_range(mp, y1)) {
        return 0;
    } else {
        mp_left_type(p) = mp_explicit_knot;
        set_number_from_double(p->left_x, x1);
        set_number_from_double(p->left_y, y1);
        return 1;
    }
}

int mp_set_knot_right_control (MP mp, mp_knot p, double x1, double y1)
{
    if (p == NULL) {
        return 0;
    } else if (out_of_range(mp, x1)) {
        return 0;
    } else if (out_of_range(mp, y1)) {
        return 0;
    } else {
        mp_right_type(p) = mp_explicit_knot;
        set_number_from_double(p->right_x, x1);
        set_number_from_double(p->right_y, y1);
        return 1;
    }
}

int mp_set_knot_direction (MP mp, mp_knot q, double x, double y)
{
    if (q == NULL) {
        return 0;
    } else if (TOO_LARGE(x)) {
        return 0;
    } else if (TOO_LARGE(y)) {
        return 0;
    } else {
        double value = 0;
        if (!(x == 0 && y == 0)) {
            value = atan2(y, x) * (180.0 / PI)  * 16.0;
        }
        mp_right_type(q) = mp_given_knot;
        set_number_from_double(q->right_curl, value);
        if (mp_left_type(q) == mp_open_knot) {
            mp_left_type(q) = mp_given_knot;
            set_number_from_double(q->left_curl, value);
        }
        return 1;
    }
}

int mp_set_knotpair_directions (MP mp, mp_knot p, mp_knot q, double x1, double y1, double x2, double y2)
{
    if (p == NULL || q == NULL) {
        return 0;
    } else if (mp_set_knot_direction(mp,p, x1, y1)) {
        return mp_set_knot_direction(mp,q, x2, y2);
    } else {
        return 0;
    }
}

@ @c
static int path_needs_fixing(mp_knot source)
{
    mp_knot sourcehead = source;
    do {
        source = source->next;
    } while (source && source != sourcehead);
    if (! source) {
        return 1;
    } else {
        return 0;
    }
}

int mp_solve_path (MP mp, mp_knot first)
{
    if (first == NULL) {
        return 0;
    } else if (path_needs_fixing(first)) {
        return 0;
    } else {
        int saved_arith_error = mp->arith_error;
        int retval = 1;
        jmp_buf *saved_jump_buf = mp->jump_buf;
        mp->jump_buf = mp_memory_allocate(sizeof(jmp_buf));
        if (mp->jump_buf == NULL || setjmp(*(mp->jump_buf)) != 0) {
            return 0;
        } else {
            mp->arith_error = 0;
            mp_make_choices(mp, first);
            if (mp->arith_error) {
                retval = 0;
            }
            mp->arith_error = saved_arith_error;
            mp_memory_free(mp->jump_buf);
            mp->jump_buf = saved_jump_buf;
            return retval;
        }
    }
}

void mp_free_path (MP mp, mp_knot p)
{
    mp_toss_knot_list(mp, p);
}

@ @<Exported function headers@>=
int     mp_close_path_cycle        (MP mp, mp_knot p, mp_knot q);
int     mp_close_path              (MP mp, mp_knot q, mp_knot first);
mp_knot mp_create_knot             (MP mp);
int     mp_set_knot                (MP mp, mp_knot p, double x, double y);
mp_knot mp_append_knot             (MP mp, mp_knot p, double x, double y);
mp_knot mp_append_knot_xy          (MP mp, mp_knot p, double x, double y);
int     mp_set_knot_curl           (MP mp, mp_knot q, double value);
int     mp_set_knot_left_curl      (MP mp, mp_knot q, double value);
int     mp_set_knot_right_curl     (MP mp, mp_knot q, double value);
int     mp_set_knot_simple_curl    (MP mp, mp_knot q);
int     mp_set_knotpair_curls      (MP mp, mp_knot p, mp_knot q, double t1, double t2) ;
int     mp_set_knotpair_tensions   (MP mp, mp_knot p, mp_knot q, double t1, double t2) ;
int     mp_set_knot_left_tension   (MP mp, mp_knot p, double t1);
int     mp_set_knot_right_tension  (MP mp, mp_knot p, double t1);
int     mp_set_knot_left_control   (MP mp, mp_knot p, double t1, double t2);
int     mp_set_knot_right_control  (MP mp, mp_knot p, double t1, double t2);
int     mp_set_knotpair_controls   (MP mp, mp_knot p, mp_knot q, double x1, double y1, double x2, double y2) ;
int     mp_set_knot_direction      (MP mp, mp_knot q, double x, double y) ;
int     mp_set_knotpair_directions (MP mp, mp_knot p, mp_knot q, double x1, double y1, double x2, double y2) ;
int     mp_solve_path              (MP mp, mp_knot first);
void    mp_free_path               (MP mp, mp_knot p);

@ Simple accessors for |mp_knot|.

@c
double mp_number_as_double (MP mp, mp_number n) {
    (void) mp;
    return number_to_double(n);
}

@ @<Exported function headers@>=
double mp_number_as_double (MP mp, mp_number n);

@* Measuring paths.

\MP's |llcorner|, |lrcorner|, |ulcorner|, and |urcorner| operators allow
the user to measure the bounding box of anything that can go into a picture. It's
easy to get rough bounds on the $x$ and $y$ extent of a path by just finding the
bounding box of the knots and the control points. We need a more accurate version
of the bounding box, but we can still use the easy estimate to save time by
focusing on the interesting parts of the path.

@ Computing an accurate bounding box involves a theme that will come up again and
again. Given a Bernshte{\u\i}n polynomial @^Bernshte{\u\i}n, Serge{\u\i}
Natanovich@>

$$B(z_0,z_1,\ldots,z_n;t)=\sum_k{n\choose k}t^k(1-t)^{n-k}z_k,$$

we can conveniently bisect its range as follows:

\smallskip \textindent{1)} Let $z_k^{(0)}=z_k$, for |0<=k<=n|.

\smallskip \textindent{2)} Let $z_k^{(j+1)}={1\over2}(z_k^{(j)}+z\k^{(j)})$, for
|0<=k<n-j|, for |0<=j<n|.

\smallskip\noindent Then

$$B(z_0,z_1,\ldots,z_n;t)=B(z_0^{(0)},z_0^{(1)},\ldots,z_0^{(n)};2t)
=B(z_0^{(n)},z_1^{(n-1)},\ldots,z_n^{(0)};2t-1).$$

This formula gives us the coefficients of polynomials to use over the ranges $0\L
t|1\over2|$ and ${1\over2}\L t\L1$.

@ Here is a routine that computes the $x$ or $y$ coordinate of the point on a
cubic corresponding to the |fraction| value~|t|.

@c
static void mp_eval_cubic (MP mp, mp_number *r, mp_knot p, mp_knot q, int c, mp_number *t)
{
    mp_number x1, x2, x3; /* intermediate values */
    new_number(x1);
    new_number(x2);
    new_number(x3);
    if (c == mp_x_code) {
        set_number_from_of_the_way(x1, *t, p->x_coord, p->right_x);
        set_number_from_of_the_way(x2, *t, p->right_x, q->left_x);
        set_number_from_of_the_way(x3, *t, q->left_x, q->x_coord);
    } else {
        set_number_from_of_the_way(x1, *t, p->y_coord, p->right_y);
        set_number_from_of_the_way(x2, *t, p->right_y, q->left_y);
        set_number_from_of_the_way(x3, *t, q->left_y, q->y_coord);
    }
    set_number_from_of_the_way(x1, *t, x1, x2);
    set_number_from_of_the_way(x2, *t, x2, x3);
    set_number_from_of_the_way(*r, *t, x1, x2);
    free_number(x1);
    free_number(x2);
    free_number(x3);
}

@ The actual bounding box information is stored in global variables. Since it is
convenient to address the $x$ and $y$ information separately, we define arrays
indexed by |x_code..y_code| and use macros to give them more convenient names.

@<Types...@>=
enum mp_bb_code {
    mp_x_code, /* index for |minx| and |maxx| */
    mp_y_code  /* index for |miny| and |maxy| */
};

@
@d mp_minx mp->bbmin[mp_x_code]
@d mp_maxx mp->bbmax[mp_x_code]
@d mp_miny mp->bbmin[mp_y_code]
@d mp_maxy mp->bbmax[mp_y_code]

@<Glob...@>=
/* the result of procedures that compute bounding box information */
mp_number bbmin[mp_y_code + 1];
mp_number bbmax[mp_y_code + 1];

@ @<Initialize table ...@>=
for (int i = 0; i <= mp_y_code; i++) {
    new_number(mp->bbmin[i]);
    new_number(mp->bbmax[i]);
}

@ @<Dealloc...@>=
for (int i = 0; i <= mp_y_code; i++) {
    free_number(mp->bbmin[i]);
    free_number(mp->bbmax[i]);
}

@ Now we're ready for the key part of the bounding box computation. The
|bound_cubic| procedure updates |bbmin[c]| and |bbmax[c]| based on

$$B(\hbox{|knot_coord(p)|}, \hbox{|right_coord(p)|}, \hbox{|left_coord(q)|},
\hbox{|knot_coord(q)|};t) $$

for $0<t\le1$. In other words, the procedure adjusts the bounds to accommodate
|knot_coord(q)| and any extremes over the range $0<t<1$. The |c| parameter is
|x_code| or |y_code|.

@c
static void mp_bound_cubic (MP mp, mp_knot p, mp_knot q, int c)
{
    int wavy;                              /* whether we need to look for extremes */
    mp_number del1, del2, del3, del, dmax; /* proportional to the control points of a quadratic derived from a cubic */
    mp_number t, tt;                       /* where a quadratic crosses zero */
    mp_number x;                           /* a value that |bbmin[c]| and |bbmax[c]| must accommodate */
    new_fraction(t);
    new_fraction(tt);
    if (c == mp_x_code) {
        new_number_clone(x, q->x_coord);
    } else {
        new_number_clone(x, q->y_coord);
    }
    new_number(del1);
    new_number(del2);
    new_number(del3);
    new_number(del);
    new_number(dmax);
    @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>
    @<Check the control points against the bounding box and set |wavy:=1| if any of them lie outside@>
    if (wavy) {
        if (c == mp_x_code) {
            set_number_from_subtraction(del1, p->right_x, p->x_coord);
            set_number_from_subtraction(del2, q->left_x, p->right_x);
            set_number_from_subtraction(del3, q->x_coord, q->left_x);
        } else {
            set_number_from_subtraction(del1, p->right_y, p->y_coord);
            set_number_from_subtraction(del2, q->left_y, p->right_y);
            set_number_from_subtraction(del3, q->y_coord, q->left_y);
        }
        @<Scale up |del1|, |del2|, and |del3| for greater accuracy; also set |del| to the first nonzero element of |(del1,del2,del3)|@>
        if (number_negative(del)) {
            number_negate(del1);
            number_negate(del2);
            number_negate(del3);
        }
        crossing_point(t, del1, del2, del3);
        if (number_less(t, fraction_one_t)) {
            @<Test the extremes of the cubic against the bounding box@>
        }
    }
    free_number(del3);
    free_number(del2);
    free_number(del1);
    free_number(del);
    free_number(dmax);
    free_number(x);
    free_number(t);
    free_number(tt);
}

@ @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>=
if (number_less(x, mp->bbmin[c])) {
    number_clone(mp->bbmin[c], x);
}
if (number_greater(x, mp->bbmax[c])) {
    number_clone(mp->bbmax[c], x);
}

@ @<Check the control points against the bounding box and set...@>=
wavy = 1;
if (c == mp_x_code) {
    if (number_lessequal(mp->bbmin[c], p->right_x) && number_lessequal(p->right_x, mp->bbmax[c])) {
        if (number_lessequal(mp->bbmin[c], q->left_x) && number_lessequal(q->left_x, mp->bbmax[c])) {
            wavy = 0;
        }
    }
} else {
    if (number_lessequal(mp->bbmin[c], p->right_y) && number_lessequal(p->right_y, mp->bbmax[c])) {
        if (number_lessequal(mp->bbmin[c], q->left_y) && number_lessequal(q->left_y, mp->bbmax[c])) {
            wavy = 0;
        }
    }
}

@ If |del1=del2=del3=0|, it's impossible to obey the title of this section. We
just set |del=0| in that case.

@<Scale up |del1|, |del2|, and |del3| for greater accuracy...@>=
if (number_nonzero(del1)) {
    number_clone(del, del1);
} else if (number_nonzero(del2)) {
    number_clone(del, del2);
} else {
    number_clone(del, del3);
}
if (number_nonzero(del)) {
    mp_number absval1;
    new_number(absval1);
    number_abs_clone(dmax, del1);
    number_abs_clone(absval1, del2);
    if (number_greater(absval1, dmax)) {
        number_clone(dmax, absval1);
    }
    number_abs_clone(absval1, del3);
    if (number_greater(absval1, dmax)) {
        number_clone(dmax, absval1);
    }
    while (number_less(dmax, fraction_half_t)) {
        number_double(dmax);
        number_double(del1);
        number_double(del2);
        number_double(del3);
    }
    free_number(absval1);
}

@ Since |crossing_point| has tried to choose |t| so that $B(|del1|, |del2|,
|del3|; \tau)$ crosses zero at $\tau = |t|$ with negative slope, the value of
|del2| computed below should not be positive. But rounding error could make it
slightly positive in which case we must cut it to zero to avoid confusion.

@<Test the extremes of the cubic against the bounding box@>=
{
    mp_eval_cubic(mp, &x, p, q, c, &t);
    @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>
    set_number_from_of_the_way(del2, t, del2, del3);
    /* now |0,del2,del3| represent the derivative on the remaining interval */
    if (number_positive(del2)) {
        set_number_to_zero(del2);
    }
    {
        mp_number arg2, arg3;
        new_number(arg2);
        new_number(arg3);
        number_negated_clone(arg2, del2);
        number_negated_clone(arg3, del3);
        crossing_point(tt, zero_t, arg2, arg3);
        free_number(arg2);
        free_number(arg3);
    }
    if (number_less(tt, fraction_one_t)) {
        /* Test the second extreme against the bounding box. */
        mp_number arg;
        new_number(arg);
        set_number_from_of_the_way(arg, t, tt, fraction_one_t);
        mp_eval_cubic(mp, &x, p, q, c, &arg);
        free_number(arg);
        @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>
    }
}

@ Finding the bounding box of a path is basically a matter of applying
|bound_cubic| twice for each pair of adjacent knots.

@c
static void mp_path_bbox (MP mp, mp_knot h)
{
    mp_knot p = h;
    number_clone(mp_minx, h->x_coord);
    number_clone(mp_miny, h->y_coord);
    number_clone(mp_maxx, mp_minx);
    number_clone(mp_maxy, mp_miny);
    do {
        if (mp_right_type(p) == mp_endpoint_knot) {
            return;
        } else {
            mp_knot q = mp_next_knot(p);
            mp_bound_cubic(mp, p, q, mp_x_code);
            mp_bound_cubic(mp, p, q, mp_y_code);
            p = q;
        }
    } while (p != h);
}

static void mp_path_xbox (MP mp, mp_knot h)
{
    mp_knot p = h;
    number_clone(mp_minx, h->x_coord);
    number_clone(mp_maxx, mp_minx);
    set_number_to_zero(mp_miny);
    set_number_to_zero(mp_maxy);
    do {
        if (mp_right_type(p) == mp_endpoint_knot) {
            return;
        } else {
            mp_knot q = mp_next_knot(p);
            mp_bound_cubic(mp, p, q, mp_x_code);
            p = q;
        }
    } while (p != h);
}

static void mp_path_ybox (MP mp, mp_knot h)
{
    mp_knot p = h;
    set_number_to_zero(mp_minx);
    set_number_to_zero(mp_maxx);
    number_clone(mp_miny, h->y_coord);
    number_clone(mp_maxy, mp_miny);
    do {
        if (mp_right_type(p) == mp_endpoint_knot) {
            return;
        } else {
            mp_knot q = mp_next_knot(p);
            mp_bound_cubic(mp, p, q, mp_y_code);
            p = q;
        }
    } while (p != h);
}

@ Another important way to measure a path is to find its arc length. This is best
done by using the general bisection algorithm to subdivide the path until
obtaining \quote {well behaved} subpaths whose arc lengths can be approximated by
simple means.

Since the arc length is the integral with respect to time of the magnitude of the
velocity, it is natural to use Simpson's rule for the approximation. @^Simpson's
rule@> If $\dot B(t)$ is the spline velocity, Simpson's rule gives

$$ \vb\dot B(0)\vb + 4\vb\dot B({1\over2})\vb + \vb\dot B(1)\vb \over 6 $$

for the arc length of a path of length~1. For a cubic spline
$B(z_0,z_1,z_2,z_3;t)$, the time derivative $\dot B(t)$ is
$3B(dz_0,dz_1,dz_2;t)$, where $dz_i=z_{i+1}-z_i$. Hence the arc length
approximation is

$$ {\vb dz_0\vb \over 2} + 2\vb dz_{02}\vb + {\vb dz_2\vb \over 2}, $$

where

$$ dz_{02}={1\over2}\left({dz_0+dz_1\over 2}+{dz_1+dz_2\over 2}\right)$$

is the result of the bisection algorithm.

@ The remaining problem is how to decide when a subpath is \quote {well behaved.} This
could be done via the theoretical error bound for Simpson's rule, @^Simpson's
rule@> but this is impractical because it requires an estimate of the fourth
derivative of the quantity being integrated. It is much easier to just perform a
bisection step and see how much the arc length estimate changes. Since the error
for Simpson's rule is proportional to the fourth power of the sample spacing, the
remaining error is typically about $1\over16$ of the amount of the change. We say
\quote {typically} because the error has a pseudo-random behavior that could cause the
two estimates to agree when each contain large errors.

To protect against disasters such as undetected cusps, the bisection process
should always continue until all the $dz_i$ vectors belong to a single $90^\circ$
sector. This ensures that no point on the spline can have velocity less than 70\%
of the minimum of $\vb dz_0\vb$, $\vb dz_1\vb$ and $\vb dz_2\vb$. If such a
spline happens to produce an erroneous arc length estimate that is little changed
by bisection, the amount of the error is likely to be fairly small. We will try
to arrange things so that freak accidents of this type do not destroy the inverse
relationship between the |arclength| and |arctime| operations.
@:arclength_}{|arclength| primitive@> @:arctime_}{|arctime| primitive@>

@ The |arclength| and |arctime| operations are both based on a recursive
@^recursion@> function that finds the arc length of a cubic spline given $dz_0$,
$dz_1$, $dz_2$. This |arc_test| routine also takes an arc length goal |a_goal|
and returns the time when the arc length reaches |a_goal| if there is such a
time. Thus the return value is either an arc length less than |a_goal| or, if the
arc length would be at least |a_goal|, it returns a time value decreased by
|two|. This allows the caller to use the sign of the result to distinguish
between arc lengths and time values. On certain types of overflow, it is possible
for |a_goal| and the result of |arc_test| both to be |EL_GORDO|. Otherwise, the
result is always less than |a_goal|.

Rather than halving the control point coordinates on each recursive call to
|arc_test|, it is better to keep them proportional to velocity on the original
curve and halve the results instead. This means that recursive calls can
potentially use larger error tolerances in their arc length estimates. How much
larger depends on to what extent the errors behave as though they are independent
of each other. To save computing time, we use optimistic assumptions and increase
the tolerance by a factor of about $\sqrt2$ for each recursive call.

In addition to the tolerance parameter, |arc_test| should also have parameters
for ${1\over3}\vb\dot B(0)\vb$, ${2\over3}\vb\dot B({1\over2})\vb$, and
${1\over3}\vb\dot B(1)\vb$. These quantities are relatively expensive to compute
and they are needed in different instances of |arc_test|.

@c
static void mp_arc_test (MP mp,
    mp_number *ret, mp_number *dx0, mp_number *dy0, mp_number *dx1,
    mp_number *dy1, mp_number *dx2, mp_number *dy2, mp_number *v0,
    mp_number *v02, mp_number *v2, mp_number *a_goal, mp_number *tol_orig
)
{
    int simple;           /* are the control points confined to a $90^\circ$ sector? */
    mp_number dx01, dy01, dx12, dy12, dx02, dy02; /* bisection results */
    mp_number v002, v022; /* twice the velocity magnitudes at $t={1\over4}$ and $t={3\over4}$ */
    mp_number arc;        /* best arc length estimate before recursion */
    mp_number arc1;       /* arc length estimate for the first half */
    mp_number simply;
    mp_number tol;
    new_number(arc );
    new_number(arc1);
    new_number(dx01);
    new_number(dy01);
    new_number(dx12);
    new_number(dy12);
    new_number(dx02);
    new_number(dy02);
    new_number(v002);
    new_number(v022);
    new_number(simply);
    new_number_clone(tol, *tol_orig);
    @<Bisect the B\'ezier quadratic given by |dx0|, |dy0|, |dx1|, |dy1|, |dx2|, |dy2|@>
    @<Initialize |v002|, |v022|, and the arc length estimate |arc|; if it overflows set |arc_test| and |return|@>
    @<Test if the control points are confined to one quadrant or rotating them $45^\circ$ would put them in one quadrant. Then set |simple| appropriately@>
    set_number_half_from_addition(simply, *v0, *v2);
    number_negate(simply);
    number_add(simply, arc);
    number_subtract(simply, *v02);
    number_abs(simply);
    if (simple && number_lessequal(simply, tol)) {
        if (number_less(arc, *a_goal)){
            number_clone(*ret, arc);
        } else {
            @<Estimate when the arc length reaches |a_goal| and set |arc_test| to that time minus |two|@>
        }
    } else {
        @<Use one or two recursive calls to compute the |arc_test| function@>
    }
  DONE:
    free_number(arc);
    free_number(arc1);
    free_number(dx01);
    free_number(dy01);
    free_number(dx12);
    free_number(dy12);
    free_number(dx02);
    free_number(dy02);
    free_number(v002);
    free_number(v022);
    free_number(simply);
    free_number(tol);
}

@ The |tol| value should by multiplied by $\sqrt 2$ before making recursive
calls, but $1.5$ is an adequate approximation. It is best to avoid using
|make_fraction| in this inner loop. @^inner loop@>

@<Use one or two recursive calls to compute the |arc_test| function@>=
mp_number a_new, a_aux; /* the sum of these gives the |a_goal| */
mp_number a, b;         /* results of recursive calls */
mp_number half_v02;     /* |half(v02)|, a recursion argument */
new_number(a_new);
new_number(a_aux);
new_number(half_v02);
@<Set |a_new| and |a_aux| so their sum is |2*a_goal| and |a_new| is as large as possible@>
{
    mp_number half_tol;
    new_number_clone(half_tol, tol);
    number_half(half_tol);
    number_add(tol, half_tol);
    free_number(half_tol);
}
number_clone(half_v02, *v02);
number_half(half_v02);
new_number(a);
mp_arc_test(mp, &a, dx0, dy0, &dx01, &dy01, &dx02, &dy02, v0, &v002, &half_v02, &a_new, &tol);
if (number_negative(a)) {
    set_number_to_unity(*ret);
    number_double(*ret); /* two */
    number_subtract(*ret, a); /* two - a */
    number_half(*ret);
    number_negate(*ret); /* -half(two - a) */
} else {
    @<Update |a_new| to reduce |a_new+a_aux| by |a|@>
    new_number(b);
    mp_arc_test(mp, &b, &dx02, &dy02, &dx12, &dy12, dx2, dy2, &half_v02, &v022, v2, &a_new, &tol);
    if (number_negative(b)) {
        mp_number tmp ;
        new_number(tmp);
        number_negated_clone(tmp, b);
        number_half(tmp);
        number_negate(tmp);
        number_clone(*ret, tmp);
        set_number_to_unity(tmp);
        number_half(tmp);
        number_subtract(*ret, tmp); /* (-(half(-b)) - 1/2) */
        free_number(tmp);
    } else {
        set_number_from_subtraction(*ret, b, a);
        number_half(*ret);
        set_number_from_addition(*ret, a, *ret); /* (a + half(b - a)) */
    }
    free_number(b);
}
free_number(half_v02);
free_number(a_aux);
free_number(a_new);
free_number(a);

@ @<Set |a_new| and |a_aux| so their sum is |2*a_goal| and |a_new| is...@>=
set_number_to_inf(a_aux);
number_subtract(a_aux, *a_goal);
if (number_greater(*a_goal, a_aux)) {
    set_number_from_subtraction(a_aux, *a_goal, a_aux);
    set_number_to_inf(a_new);
} else {
    set_number_from_addition(a_new, *a_goal, *a_goal);
    set_number_to_zero(a_aux);
}

@ There is no need to maintain |a_aux| at this point so we use it as a temporary
to force the additions and subtractions to be done in an order that avoids
overflow.

@<Update |a_new| to reduce |a_new+a_aux| by |a|@>=
if (number_greater(a, a_aux)) {
    number_subtract(a_aux, a);
    number_add(a_new, a_aux);
}

@ This code assumes all {\it dx} and {\it dy} variables have magnitude less than
|fraction_four|. To simplify the rest of the |arc_test| routine, we strengthen
this assumption by requiring the norm of each $({\it dx},{\it dy})$ pair to obey
this bound. Note that recursive calls will maintain this invariant.

@<Bisect the B\'ezier quadratic given by |dx0|, |dy0|, |dx1|, |dy1|,...@>=
set_number_half_from_addition(dx01, *dx0, *dx1);
set_number_half_from_addition(dx12, *dx1, *dx2);
set_number_half_from_addition(dx02, dx01, dx12);
set_number_half_from_addition(dy01, *dy0, *dy1);
set_number_half_from_addition(dy12, *dy1, *dy2);
set_number_half_from_addition(dy02, dy01, dy12);

@ We should be careful to keep |arc<EL_GORDO| so that calling |arc_test| with
|a_goal=EL_GORDO| is guaranteed to yield the arc length.

@<Initialize |v002|, |v022|, and the arc length estimate |arc|;...@>=
{
    mp_number tmp, arg1, arg2 ;
    new_number(tmp);
    new_number(arg1);
    new_number(arg2);
    set_number_half_from_addition(arg1, *dx0, dx02);
    number_add(arg1, dx01);
    set_number_half_from_addition(arg2, *dy0, dy02);
    number_add(arg2, dy01);
    pyth_add(v002, arg1, arg2);

    set_number_half_from_addition(arg1, dx02, *dx2);
    number_add(arg1, dx12);
    set_number_half_from_addition(arg2, dy02, *dy2);
    number_add(arg2, dy12);
    pyth_add(v022, arg1, arg2);
    free_number(arg1);
    free_number(arg2);

    number_clone(tmp, *v02);
    number_add_scaled(tmp, 2);
    number_half(tmp);

    set_number_half_from_addition(arc1, *v0, tmp);
    number_subtract(arc1, v002);
    number_half(arc1);
    set_number_from_addition(arc1, v002, arc1);

    set_number_half_from_addition(arc, *v2, tmp);
    number_subtract(arc, v022);
    number_half(arc);
    set_number_from_addition(arc, v022, arc);

    /* reuse |tmp| for the next |if| test: */
    set_number_to_inf(tmp);
    number_subtract(tmp,arc1);
    if (number_less(arc, tmp)) {
        free_number(tmp);
        number_add(arc, arc1);
    } else {
        free_number(tmp);
        mp->arith_error = 1;
        if (number_infinite(*a_goal)) {
            set_number_to_inf(*ret);
        } else {
            set_number_to_unity(*ret);
            number_double(*ret);
            number_negate(*ret); /* -two */
        }
        goto DONE;
    }
}

@ @<Test if the control points are confined to one quadrant or rotating...@>=
simple = (number_nonnegative(*dx0) && number_nonnegative(*dx1) && number_nonnegative(*dx2))
      || (number_nonpositive(*dx0) && number_nonpositive(*dx1) && number_nonpositive(*dx2));
if (simple) {
    simple = (number_nonnegative(*dy0) && number_nonnegative(*dy1) && number_nonnegative(*dy2))
          || (number_nonpositive(*dy0) && number_nonpositive(*dy1) && number_nonpositive(*dy2));
}
if (!simple) {
    simple = (number_greaterequal(*dx0, *dy0) && number_greaterequal(*dx1, *dy1) && number_greaterequal(*dx2, *dy2))
          || (number_lessequal   (*dx0, *dy0) && number_lessequal   (*dx1, *dy1) && number_lessequal   (*dx2, *dy2));
    if (simple) {
        mp_number neg_dx0, neg_dx1, neg_dx2;
        new_number(neg_dx0);
        new_number(neg_dx1);
        new_number(neg_dx2);
        number_negated_clone(neg_dx0, *dx0);
        number_negated_clone(neg_dx1, *dx1);
        number_negated_clone(neg_dx2, *dx2);
        simple = (number_greaterequal(neg_dx0, *dy0) && number_greaterequal(neg_dx1, *dy1) && number_greaterequal(neg_dx2, *dy2))
              || (number_lessequal   (neg_dx0, *dy0) && number_lessequal   (neg_dx1, *dy1) && number_lessequal   (neg_dx2, *dy2));
        free_number(neg_dx0);
        free_number(neg_dx1);
        free_number(neg_dx2);
    }
}

@ Since Simpson's rule is based on approximating the integrand by a parabola,
@^Simpson's rule@> it is appropriate to use the same approximation to decide when
the integral reaches the intermediate value |a_goal|. At this point

$$\eqalign{
    {\vb\dot B(0)\vb\over 3} &= \hbox{|v0|}, \qquad
    {\vb\dot B({1\over4})\vb\over 3} = {\hbox{|v002|}\over 2}, \qquad
    {\vb\dot B({1\over2})\vb\over 3} = {\hbox{|v02|}\over 2}, \cr
    {\vb\dot B({3\over4})\vb\over 3} &= {\hbox{|v022|}\over 2}, \qquad
    {\vb\dot B(1)\vb\over 3} = \hbox{|v2|} \cr
}
$$

and

$$ {\vb\dot B(t)\vb\over 3} \approx
  \cases{B\left(\hbox{|v0|},
      \hbox{|v002|}-{1\over 2}\hbox{|v0|}-{1\over 4}\hbox{|v02|},
      {1\over 2}\hbox{|v02|}; 2t \right)&
    if $t\le{1\over 2}$\cr
  B\left({1\over 2}\hbox{|v02|},
      \hbox{|v022|}-{1\over 4}\hbox{|v02|}-{1\over 2}\hbox{|v2|},
      \hbox{|v2|}; 2t-1 \right)&
    if $t\ge{1\over 2}$.\cr}
 \eqno (*)
$$

We can integrate $\vb\dot B(t)\vb$ by using

$$\int 3B(a,b,c;\tau)\,dt =
  {B(0,a,a+b,a+b+c;\tau) + {\rm constant} \over {d\tau\over dt}}.
$$

This construction allows us to find the time when the arc length reaches |a_goal|
by solving a cubic equation of the form $$ B(0,a,a+b,a+b+c;\tau) = x, $$ where
$\tau$ is $2t$ or $2t+1$, $x$ is |a_goal| or |a_goal-arc1|, and $a$, $b$, and $c$
are the Bernshte{\u\i}n coefficients from $(*)$ divided by @^Bernshte{\u\i}n,
Serge{\u\i} Natanovich@> $d\tau\over dt$. We shall define a function
|solve_rising_cubic| that finds $\tau$ given $a$, $b$, $c$, and $x$.

@<Estimate when the arc length reaches |a_goal| and set |arc_test| to...@>=
mp_number tmp;
mp_number tmp2;
mp_number tmp3;
mp_number tmp4;
mp_number tmp5;
new_number_clone(tmp, *v02);
new_number(tmp2);
new_number(tmp3);
new_number(tmp4);
new_number(tmp5);
number_add_scaled(tmp, 2);
number_half(tmp);
number_half(tmp); /* (v02+2) / 4 */
if (number_lessequal(*a_goal, arc1)) {
    number_clone(tmp2, *v0);
    number_half(tmp2);
    set_number_from_subtraction(tmp3, arc1, tmp2);
    number_subtract(tmp3, tmp);
    mp_solve_rising_cubic(mp, &tmp5, &tmp2, &tmp3, &tmp, a_goal);
    number_half(tmp5);
    set_number_to_unity(tmp3);
    number_subtract(tmp5, tmp3);
    number_subtract(tmp5, tmp3);
    number_clone(*ret, tmp5);
} else {
    number_clone(tmp2, *v2);
    number_half(tmp2);
    set_number_from_subtraction(tmp3, arc, arc1);
    number_subtract(tmp3, tmp);
    number_subtract(tmp3, tmp2);
    set_number_from_subtraction(tmp4, *a_goal, arc1);
    mp_solve_rising_cubic(mp, &tmp5, &tmp, &tmp3, &tmp2, &tmp4);
    number_half(tmp5);
    set_number_to_unity(tmp2);
    set_number_to_unity(tmp3);
    number_half(tmp2);
    number_subtract(tmp2, tmp3);
    number_subtract(tmp2, tmp3);
    set_number_from_addition(*ret, tmp2, tmp5);
}
free_number(tmp);
free_number(tmp2);
free_number(tmp3);
free_number(tmp4);
free_number(tmp5);

@ Here is the |solve_rising_cubic| routine that finds the time~$t$ when $$ B(0,
a, a+b, a+b+c; t) = x. $$ This routine is based on |crossing_point| but is
simplified by the assumptions that $B(a,b,c;t)\ge0$ for $0\le t\le1$ and that
|0<=x<=a+b+c|. If rounding error causes this condition to be violated slightly,
we just ignore it and proceed with binary search. This finds a time when the
function value reaches |x| and the slope is positive.

@<Declarations@>=
static void mp_solve_rising_cubic (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig, mp_number *c_orig, mp_number *x_orig);

@ @c
void mp_solve_rising_cubic (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig, mp_number *c_orig, mp_number *x_orig)
{
    mp_number abc;
    mp_number a, b, c, x; /* local versions of arguments */
    mp_number ab, bc, ac; /* bisection results */
    mp_number t;          /* $2^k+q$ where unscaled answer is in $[q2^{-k},(q+1)2^{-k})$ */
    mp_number xx;         /* temporary for updating |x| */
    mp_number neg_x;      /* temporary for an |if| */
    if (number_negative(*a_orig) || number_negative(*c_orig)) {
        mp_confusion(mp, "rising cubic");
        @:this can't happen rising?}{\quad rising?@>
    }
    new_number(t);
    new_number(abc);
    new_number_clone(a, *a_orig);
    new_number_clone(b, *b_orig);
    new_number_clone(c, *c_orig);
    new_number_clone(x, *x_orig);
    new_number(ab);
    new_number(bc);
    new_number(ac);
    new_number(xx);
    new_number(neg_x);
    set_number_from_addition(abc, a, b);
    number_add(abc, c);
    if (number_nonpositive(x)) {
        set_number_to_zero(*ret);
    } else if (number_greaterequal(x, abc)) {
        set_number_to_unity(*ret);
    } else {
        number_clone(t, epsilon_t);
        @<Rescale if necessary to make sure |a|, |b|, and |c| are all less than |EL_GORDO div 3|@>
        do {
            number_add(t, t);
            @<Subdivide the B\'ezier quadratic defined by |a|, |b|, |c|@>
            number_clone(xx,x);
            number_subtract(xx, a);
            number_subtract(xx, ab);
            number_subtract(xx, ac);
            number_negated_clone(neg_x, x);
            if (number_less(xx, neg_x)) {
                number_double(x);
                number_clone(b, ab);
                number_clone(c, ac);
            } else {
                number_add(x, xx);
                number_clone(a, ac);
                number_clone(b, bc);
                number_add(t, epsilon_t);
            }
        } while (number_less(t, unity_t));
        set_number_from_subtraction(*ret, t, unity_t);
    }
    free_number(abc);
    free_number(t);
    free_number(a);
    free_number(b);
    free_number(c);
    free_number(ab);
    free_number(bc);
    free_number(ac);
    free_number(xx);
    free_number(x);
    free_number(neg_x);
}

@ @<Subdivide the B\'ezier quadratic defined by |a|, |b|, |c|@>=
set_number_half_from_addition(ab, a, b);
set_number_half_from_addition(bc, b, c);
set_number_half_from_addition(ac, ab, bc);

@ The upper bound on |a|, |b|, and |c|:

@d one_third_inf_t mp->math->md_one_third_inf_t

@<Rescale if necessary to make sure |a|, |b|, and |c| are all less than...@>=
while (number_greater(a, one_third_inf_t) || number_greater(b, one_third_inf_t) || number_greater(c, one_third_inf_t)) {
    number_half(a);
    number_half(b);
    number_half(c);
    number_half(x);
}

@ It is convenient to have a simpler interface to |arc_test| that requires no
unnecessary arguments and ensures that each $({\it dx},{\it dy})$ pair has
length less than |fraction_four|.

@c
static void mp_do_arc_test (MP mp,
    mp_number *ret, mp_number *dx0, mp_number *dy0, mp_number *dx1,
    mp_number *dy1, mp_number *dx2, mp_number *dy2, mp_number *a_goal
)
{
    mp_number v0, v1, v2; /* length of each $({\it dx},{\it dy})$ pair */
    mp_number v02;        /* twice the norm of the quadratic at $t={1\over2}$ */
    new_number(v0);
    new_number(v1);
    new_number(v2);
    pyth_add(v0, *dx0, *dy0);
    pyth_add(v1, *dx1, *dy1);
    pyth_add(v2, *dx2, *dy2);
    if ((number_greaterequal(v0, fraction_four_t)) || (number_greaterequal(v1, fraction_four_t)) || (number_greaterequal(v2, fraction_four_t))) {
        mp->arith_error = 1;
        if (number_infinite(*a_goal)) {
            set_number_to_inf(*ret);
        } else {
            set_number_to_unity(*ret);
            number_double(*ret);
            number_negate(*ret);
        }
    } else {
        mp_number arg1, arg2;
        new_number(v02);
        new_number(arg1);
        new_number(arg2);
        set_number_half_from_addition(arg1, *dx0, *dx2);
        number_add(arg1, *dx1);
        set_number_half_from_addition(arg2, *dy0, *dy2);
        number_add(arg2, *dy1);
        pyth_add(v02, arg1, arg2);
        free_number(arg1);
        free_number(arg2);
        mp_arc_test(mp, ret, dx0, dy0, dx1, dy1, dx2, dy2, &v0, &v02, &v2, a_goal, &arc_tol_k);
        free_number(v02);
    }
    free_number(v0);
    free_number(v1);
    free_number(v2);
}

@ Now it is easy to find the arc length of an entire path.

@c
static void mp_get_arc_length (MP mp, mp_number *ret, mp_knot h)
{
    mp_number a;     /* current arc length */
    mp_number a_tot; /* total arc length */
    mp_number arg1, arg2, arg3, arg4, arg5, arg6;
    mp_number arcgoal;
    mp_knot p = h;   /* for traversing the path */
    new_number(a_tot);
    new_number(arg1);
    new_number(arg2);
    new_number(arg3);
    new_number(arg4);
    new_number(arg5);
    new_number(arg6);
    new_number(a);
    new_number(arcgoal);
    set_number_to_inf(arcgoal);
    while (mp_right_type(p) != mp_endpoint_knot) {
        mp_knot q = mp_next_knot(p);
        @<Add arclength of path segment@>
        if (q == h) {
            break;
        } else {
            p = q;
        }
    }
    free_number(arcgoal);
    free_number(a);
    free_number(arg1);
    free_number(arg2);
    free_number(arg3);
    free_number(arg4);
    free_number(arg5);
    free_number(arg6);
    check_arith();
    number_clone(*ret, a_tot);
    free_number(a_tot);
}

static void mp_get_subarc_length (MP mp, mp_number *ret, mp_knot h, mp_number *first, mp_number *last)
{
    mp_number a;
    mp_number a_tot, a_cnt;
    mp_number arg1, arg2, arg3, arg4, arg5, arg6;
    mp_number arcgoal;
    mp_knot p = h;
    new_number(a_tot);
    new_number(a_cnt);
    new_number(arg1);
    new_number(arg2);
    new_number(arg3);
    new_number(arg4);
    new_number(arg5);
    new_number(arg6);
    new_number(a);
    new_number(arcgoal);
    set_number_to_inf(arcgoal);
    while (mp_right_type(p) != mp_endpoint_knot) {
        mp_knot q = mp_next_knot(p);
        if (number_greaterequal(a_cnt, *last)) {
            break;
        } else if (number_greaterequal(a_cnt, *first)) {
            @<Add arclength of path segment@>
        }
        if (q == h) {
            break;
        } else {
            p = q;
            number_add(a_cnt, unity_t);
        }
    }
    free_number(arcgoal);
    free_number(a);
    free_number(arg1);
    free_number(arg2);
    free_number(arg3);
    free_number(arg4);
    free_number(arg5);
    free_number(arg6);
    check_arith();
    number_clone(*ret, a_tot);
    free_number(a_cnt);
    free_number(a_tot);
}

@<Add arclength of path segment@>=
set_number_from_subtraction(arg1, p->right_x, p->x_coord);
set_number_from_subtraction(arg2, p->right_y, p->y_coord);
set_number_from_subtraction(arg3, q->left_x,  p->right_x);
set_number_from_subtraction(arg4, q->left_y,  p->right_y);
set_number_from_subtraction(arg5, q->x_coord, q->left_x);
set_number_from_subtraction(arg6, q->y_coord, q->left_y);
mp_do_arc_test(mp, &a, &arg1, &arg2, &arg3, &arg4, &arg5, &arg6, &arcgoal);
slow_add(a_tot, a, a_tot);

@ The inverse operation of finding the time on a path~|h| when the arc length
reaches some value |arc0| can also be accomplished via |do_arc_test|. Some care
is required to handle very large times or negative times on cyclic paths. For
non-cyclic paths, |arc0| values that are negative or too large cause
|get_arc_time| to return 0 or the length of path~|h|.

If |arc0| is greater than the arc length of a cyclic path~|h|, the result is a
time value greater than the length of the path. Since it could be much greater,
we must be prepared to compute the arc length of path~|h| and divide this into
|arc0| to find how many multiples of the length of path~|h| to add.

@c
static mp_knot mp_get_arc_time(MP mp, mp_number *ret, mp_knot h, mp_number *arc0_orig, int local)
{
    if (number_negative(*arc0_orig)) {
        @<Deal with a negative |arc0_orig| value and |return|@>
    } else {
        mp_knot p, q, k;                              /* for traversing the path */
        mp_number t_tot;                              /* accumulator for the result */
        mp_number t;                                  /* the result of |do_arc_test| */
        mp_number arc, arc0;                          /* portion of |arc0| not used up so far */
        mp_number arg1, arg2, arg3, arg4, arg5, arg6; /* |do_arc_test| arguments */
        new_number(t_tot);
        new_number_clone(arc0, *arc0_orig);
        if (number_infinite(arc0)) {
            number_add_scaled(arc0, -1);
        }
        new_number_clone(arc, arc0);
        p = h;
        k = h;
        new_number(arg1);
        new_number(arg2);
        new_number(arg3);
        new_number(arg4);
        new_number(arg5);
        new_number(arg6);
        new_number(t);
        while ((mp_right_type(p) != mp_endpoint_knot) && number_positive(arc)) {
            k = p;
            q = mp_next_knot(p);
            set_number_from_subtraction(arg1, p->right_x, p->x_coord);
            set_number_from_subtraction(arg2, p->right_y, p->y_coord);
            set_number_from_subtraction(arg3, q->left_x,  p->right_x);
            set_number_from_subtraction(arg4, q->left_y,  p->right_y);
            set_number_from_subtraction(arg5, q->x_coord, q->left_x);
            set_number_from_subtraction(arg6, q->y_coord, q->left_y);
            mp_do_arc_test(mp, &t, &arg1, &arg2, &arg3, &arg4, &arg5, &arg6, &arc);
            @<Update |arc| and |t_tot| after |do_arc_test| has just returned |t|@>
            if (q == h) {
                @<Update |t_tot| and |arc| to avoid going around the cyclic path too many times but set |arith_error:=1| and |goto done| on overflow@>
            }
            p = q;
        }
        check_arith();
        if (local) {
            number_add(t, two_t);
            number_clone(*ret, t);
        } else {
            number_clone(*ret, t_tot);
        }
        h = k;
      RETURN:
        free_number(t_tot);
        free_number(t);
        free_number(arc);
        free_number(arc0);
        free_number(arg1);
        free_number(arg2);
        free_number(arg3);
        free_number(arg4);
        free_number(arg5);
        free_number(arg6);
    }
    return h;
}

@ @<Update |arc| and |t_tot| after |do_arc_test| has just returned |t|@>=
if (number_negative(t)) {
    number_add(t_tot, t);
    number_add(t_tot, two_t);
    set_number_to_zero(arc);
} else {
    number_add(t_tot, unity_t);
    number_subtract(arc, t);
}

@ @<Deal with a negative |arc0_orig| value and |return|@>=
if (mp_left_type(h) == mp_endpoint_knot) {
    set_number_to_zero(*ret);
} else {
    mp_number neg_arc0;
    mp_knot p = mp_htap_ypoc(mp, h);
    new_number(neg_arc0);
    number_negated_clone(neg_arc0, *arc0_orig);
    mp_get_arc_time(mp, ret, p, &neg_arc0, 0);
    number_negate(*ret);
    mp_toss_knot_list(mp, p);
    free_number(neg_arc0);
}
check_arith();

@ @<Update |t_tot| and |arc| to avoid going around the cyclic...@>=
if (number_positive(arc)) {
    mp_number n, n1, d1, v1;
    new_number(n);
    new_number(n1);
    new_number(d1);
    new_number(v1);

    set_number_from_subtraction(d1, arc0, arc); /* d1 = arc0 - arc */
    set_number_from_div(n1, arc, d1);           /* n1 = (arc / d1) */
    number_clone(n, n1);
    set_number_from_mul(n1, n1, d1);            /* n1 = (n1 * d1) */
    number_subtract(arc, n1);                   /* arc = arc - n1 */

    number_clone(d1, inf_t);                    /* reuse d1 */
    number_clone(v1, n);                        /* v1 = n */
    number_add(v1, epsilon_t);                  /* v1 = n1+1 */
    set_number_from_div(d1, d1, v1);            /* |d1 = EL_GORDO / v1| */
    if (number_greater(t_tot, d1)) {
        mp->arith_error = 1;
        check_arith();
        set_number_to_inf(*ret);
        free_number(n);
        free_number(n1);
        free_number(d1);
        free_number(v1);
        goto RETURN;
    }
    set_number_from_mul(t_tot, t_tot, v1);
    free_number(n);
    free_number(n1);
    free_number(d1);
    free_number(v1);
}

@* Data structures for pens.

A Pen in \MP\ can be either elliptical or polygonal. Elliptical pens result in
\ps\ |stroke| commands, while anything drawn with a polygonal pen is
@:stroke}{|stroke| command@> converted into an area fill as described in the
next part of this program. The mathematics behind this process is based on simple
aspects of the theory of tracings developed by Leo Guibas, Lyle Ramshaw, and
Jorge Stolfi [\quote {A kinematic framework for computational geometry,} Proc.\ IEEE
Symp.\ Foundations of Computer Science {\bf 24} (1983), 100--111].

Polygonal pens are created from paths via \MP's |makepen| primitive.
@:makepen_}{|makepen| primitive@> This path representation is almost sufficient
for our purposes except that a pen path should always be a convex polygon with
the vertices in counter-clockwise order. Since we will need to scan pen polygons
both forward and backward, a pen should be represented as a doubly linked ring of
knot nodes. There is room for the extra back pointer because we do not need the
|mp_left_type| or |mp_right_type| fields. In fact, we don't need the |left_x|,
|left_y|, |right_x|, or |right_y| fields either but we leave these alone so that
certain procedures can operate on both pens and paths. In particular, pens can be
copied using |copy_path| and recycled using |toss_knot_list|.

@ The |make_pen| procedure turns a path into a pen by initializing the
|prev_knot| pointers and making sure the knots form a convex polygon. Thus each
cubic in the given path becomes a straight line and the control points are
ignored. If the path is not cyclic, the ends are connected by a straight line.

@d mp_copy_pen(mp,A) mp_make_pen(mp, mp_copy_path(mp, (A)),0)

@c
static mp_knot mp_make_pen (MP mp, mp_knot h, int need_hull)
{
    mp_knot q = h;
    /* this can go ... we are already double linked */
    do {
        mp_knot p = q;
        q = mp_next_knot(q);
        mp_prev_knot(q) = p;
    } while (q != h);
    if (need_hull) {
        h = mp_convex_hull(mp, h);
        @<Make sure |h| isn't confused with an elliptical pen@>
    }
    return h;
}

@ The only information required about an elliptical pen is the overall
transformation that has been applied to the original |pencircle|.
@:pencircle_}{|pencircle| primitive@> Since it suffices to keep track of how
the three points $(0,0)$, $(1,0)$, and $(0,1)$ are transformed, an elliptical pen
can be stored in a single knot node and transformed as if it were a path.

@d mp_pen_is_elliptical(A) ((A)==mp_next_knot((A)))

@ @c
static mp_knot mp_get_pen_circle (MP mp, mp_number *diam)
{
    mp_knot h = mp_new_knot(mp); /* the knot node to return */
    mp_next_knot(h) = h;
    mp_prev_knot(h) = h;
    mp_originator(h) = mp_program_code;
    mp_knotstate(h) = mp_regular_knot;
    set_number_to_zero(h->x_coord);
    set_number_to_zero(h->y_coord);
    number_clone(h->left_x, *diam);
    set_number_to_zero(h->left_y);
    set_number_to_zero(h->right_x);
    number_clone(h->right_y, *diam);
    return h;
}

@ If the polygon being returned by |make_pen| has only one vertex, it will be
interpreted as an elliptical pen. This is no problem since a degenerate polygon
can equally well be thought of as a degenerate ellipse. We need only initialize
the |left_x|, |left_y|, |right_x|, and |right_y| fields.


@<Make sure |h| isn't confused with an elliptical pen@>=
if (mp_pen_is_elliptical(h)) {
    number_clone(h->left_x, h->x_coord);
    number_clone(h->left_y, h->y_coord);
    number_clone(h->right_x, h->x_coord);
    number_clone(h->right_y, h->y_coord);
}

@ Printing a polygonal pen is very much like printing a path

@<Declarations@>=
static void mp_pr_pen (MP mp, mp_knot h);

@ @c
void mp_pr_pen (MP mp, mp_knot h)
{
    if (mp_pen_is_elliptical(h)) {
        @<Print the elliptical pen |h|@>
    } else {
        mp_knot p = h;
        do {
            /* Advance |p| making sure the links are OK and |return| if there is a problem. */
            mp_knot q = mp_next_knot(p);
            mp_print_two(mp, &(p->x_coord), &(p->y_coord));
            mp_print_nl(mp, " .. ");
            if ((q == NULL) || (mp_prev_knot(q) != p)) {
                mp_print_nl(mp, "???");
                return; /* this won't happen */
                @.???@>
            }
            p = q;
        } while (p != h);
        mp_print_str(mp, "cycle");
    }
}

@ @<Print the elliptical pen |h|@>=
{
    mp_number v1;
    new_number(v1);
    mp_print_str(mp, "pencircle transformed (");
    print_number(h->x_coord);
    mp_print_chr(mp, ',');
    print_number(h->y_coord);
    mp_print_chr(mp, ',');
    set_number_from_subtraction(v1, h->left_x, h->x_coord);
    print_number(v1);
    mp_print_chr(mp, ',');
    set_number_from_subtraction(v1, h->right_x, h->x_coord);
    print_number(v1);
    mp_print_chr(mp, ',');
    set_number_from_subtraction(v1, h->left_y, h->y_coord);
    print_number(v1);
    mp_print_chr(mp, ',');
    set_number_from_subtraction(v1, h->right_y, h->y_coord);
    print_number(v1);
    mp_print_chr(mp, ')');
    free_number(v1);
}

@ Here us another version of |pr_pen| that prints the pen as a diagnostic
message.

@<Declarations@>=
static void mp_print_pen (MP mp, mp_knot h, const char *s, int nuline);

@ @c
void mp_print_pen (MP mp, mp_knot h, const char *s, int nuline) {
    mp_print_diagnostic(mp, "Pen", s, nuline);
    mp_print_ln(mp);
    @.Pen at line...@>
    mp_pr_pen(mp, h);
    mp_end_diagnostic(mp, 1);
}

@ Making a polygonal pen into a path involves restoring the |mp_left_type| and
|mp_right_type| fields and setting the control points so as to make a polygonal
path.

@c
static void mp_make_path (MP mp, mp_knot h)
{
    if (mp_pen_is_elliptical(h)) {
        @<Make the elliptical pen |h| into a path@>
    } else {
        mp_knot p = h;
        do {
            mp_left_type(p) = mp_explicit_knot;
            mp_right_type(p) = mp_explicit_knot;
            number_clone(p->left_x, p->x_coord);
            number_clone(p->left_y, p->y_coord);
            number_clone(p->right_x, p->x_coord);
            number_clone(p->right_y, p->y_coord);
            p = mp_next_knot(p);
        } while (p != h);
    }
}

@ We need an eight knot path to get a good approximation to an ellipse.

@<Make the elliptical pen |h| into a path@>=
mp_knot p;                    /* for traversing the knot list */
mp_number center_x, center_y; /* translation parameters for an elliptical pen */
mp_number width_x, width_y;   /* the effect of a unit change in $x$ */
mp_number height_x, height_y; /* the effect of a unit change in $y$ */
mp_number dx, dy;             /* the vector from knot |p| to its right control point */
new_number(width_x);
new_number(width_y);
new_number(height_x);
new_number(height_y);
new_number(dx);
new_number(dy);
new_number_clone(center_x, h->x_coord);
new_number_clone(center_y, h->y_coord);
set_number_from_subtraction(width_x, h->left_x, center_x);
set_number_from_subtraction(width_y, h->left_y, center_y);
set_number_from_subtraction(height_x, h->right_x, center_x);
set_number_from_subtraction(height_y, h->right_y, center_y);
p = h;
for (int k = 0; k <= 7; k++) {
    @<Initialize |p| as the |k|th knot of a circle of unit diameter, transforming it appropriately@>
    if (k == 7) {
        mp_prev_knot(h) = p;
        mp_next_knot(p) = h;
    } else {
        mp_knot k = mp_new_knot(mp);
        mp_prev_knot(k) = p;
        mp_next_knot(p) = k;
    }
    p = mp_next_knot(p);
}
free_number(dx);
free_number(dy);
free_number(center_x);
free_number(center_y);
free_number(width_x);
free_number(width_y);
free_number(height_x);
free_number(height_y);

@ The only tricky thing here are the tables |half_cos| and |d_cos| used to find
the point $k/8$ of the way around the circle and the direction vector to use
there. With |kk| we track |k| advancing $270^\circ$ around the ring (cf. $\sin
\theta = \cos (\theta+270)$).

@<Initialize |p| as the |k|th knot of a circle of unit diameter,...@>=
/* This is the body of a loop with variable k: */
int kk = (k + 6) % 8;
mp_number r1, r2;
new_fraction(r1);
new_fraction(r2);
take_fraction(r1, mp->half_cos[k], width_x);
take_fraction(r2, mp->half_cos[kk], height_x);
number_add(r1, r2);
set_number_from_addition(p->x_coord, center_x, r1);
take_fraction(r1, mp->half_cos[k],  width_y);
take_fraction(r2, mp->half_cos[kk], height_y);
number_add(r1, r2);
set_number_from_addition(p->y_coord, center_y, r1);
take_fraction(r1, mp->d_cos[kk], width_x);
take_fraction(r2, mp->d_cos[k], height_x);
number_negated_clone(dx, r1);
number_add(dx, r2);
take_fraction(r1, mp->d_cos[kk], width_y);
take_fraction(r2, mp->d_cos[k], height_y);
number_negated_clone(dy, r1);
number_add(dy, r2);
set_number_from_addition(p->right_x, p->x_coord, dx);
set_number_from_addition(p->right_y, p->y_coord, dy);
set_number_from_subtraction(p->left_x, p->x_coord, dx);
set_number_from_subtraction(p->left_y, p->y_coord, dy);
free_number(r1);
free_number(r2);
mp_left_type(p) = mp_explicit_knot;
mp_right_type(p) = mp_explicit_knot;
mp_originator(p) = mp_program_code;
mp_knotstate(p) = mp_regular_knot;

@ @<Glob...@>=
mp_number half_cos[8]; /* ${1\over2}\cos(45k)$ */
mp_number d_cos[8];    /* a magic constant times $\cos(45k)$ */

@ The magic constant for |d_cos| is the distance between $({1\over2},0)$ and
$({1\over4}\sqrt2,{1\over4}\sqrt2)$ times the result of the |velocity| function
for $\theta=\phi=22.5^\circ$. This comes out to be

$$ d = {\sqrt{2-\sqrt2}\over 3+3\cos22.5^\circ} \approx 0.132608244919772. $$

@<Set init...@>=
for (int k = 0; k <= 7; k++) {
    new_fraction(mp->half_cos[k]);
    new_fraction(mp->d_cos[k]);
}

number_clone(mp->half_cos[0], fraction_half_t);
number_clone(mp->half_cos[1], twentysixbits_sqrt2_t);
number_clone(mp->half_cos[2], zero_t);
number_clone(mp->d_cos[0],    twentyeightbits_d_t);
number_clone(mp->d_cos[1],    twentysevenbits_sqrt2_d_t);
number_clone(mp->d_cos[2],    zero_t);

for (int k = 3; k <= 4; k++) {
    number_negated_clone(mp->half_cos[k], mp->half_cos[4 - k]);
    number_negated_clone(mp->d_cos[k], mp->d_cos[4 - k]);
}

for (int k = 5; k <= 7; k++) {
    number_clone(mp->half_cos[k], mp->half_cos[8 - k]);
    number_clone(mp->d_cos[k], mp->d_cos[8 - k]);
}

@ @<Dealloc...@>=
for (int k = 0; k <= 7; k++) {
    free_number(mp->half_cos[k]);
    free_number(mp->d_cos[k]);
}

@ The |convex_hull| function forces a pen polygon to be convex when it is
returned by |make_pen| and after any subsequent transformation where rounding
error might allow the convexity to be lost. The convex hull algorithm used here
is described by F.~P. Preparata and M.~I. Shamos [{\sl Computational Geometry},
Springer-Verlag, 1985].

@<Declarations@>=
static mp_knot mp_convex_hull (MP mp, mp_knot h);

@ @c
mp_knot mp_convex_hull (MP mp, mp_knot h)
{
    if (mp_pen_is_elliptical(h)) {
        return h;
    } else {
        /* Make a polygonal pen convex */
        mp_knot l, r;     /* the leftmost and rightmost knots */
        mp_knot p, q;     /* knots being scanned */
        mp_knot s;        /* the starting point for an upcoming scan */
        mp_number dx, dy; /* a temporary pointer */
        new_number(dx);
        new_number(dy);
        @<Set |l| to the leftmost knot in polygon~|h|@>
        @<Set |r| to the rightmost knot in polygon~|h|@>
        if (l != r) {
            mp_knot s = mp_next_knot(r);
            @<Find any knots on the path from |l| to |r| above the |l|-|r| line and move them past~|r|@>
            @<Find any knots on the path from |s| to |l| below the |l|-|r| line and move them past~|l|@>
            @<Sort the path from |l| to |r| by increasing $x$@>
            @<Sort the path from |r| to |l| by decreasing $x$@>
        }
        if (l != mp_next_knot(l)) {
            @<Do a Gramm scan and remove vertices where there is no left turn@>
        }
        free_number(dx);
        free_number(dy);
        return l;
    }
}

@<Declarations@>=
void mp_simplify_path (MP mp, mp_knot h);

@ @c
void mp_simplify_path (MP mp, mp_knot h)
{
    mp_knot p = h;
    (void) mp;
    do {
        p->left_x = p->x_coord;
        p->left_y = p->y_coord;
        p->right_x = p->x_coord;
        p->right_y = p->y_coord;
        p = mp_next_knot(p);
    } while (p != h);
}

@ All comparisons are done primarily on $x$ and secondarily on $y$.

@<Set |l| to the leftmost knot in polygon~|h|@>=
l = h;
p = mp_next_knot(h);
while (p != h) {
    if (number_lessequal(p->x_coord, l->x_coord) && (number_less(p->x_coord, l->x_coord) || number_less(p->y_coord, l->y_coord))) {
        l = p;
    }
    p = mp_next_knot(p);
}

@ @<Set |r| to the rightmost knot in polygon~|h|@>=
r = h;
p = mp_next_knot(h);
while (p != h) {
    if (number_greaterequal(p->x_coord, r->x_coord) && (number_greater(p->x_coord, r->x_coord) || number_greater(p->y_coord, r->y_coord))) {
        r = p;
    }
    p = mp_next_knot(p);
}

@ @<Find any knots on the path from |l| to |r| above the |l|-|r| line...@>=
{
    mp_number arg1, arg2;
    new_number(arg1);
    new_number(arg2);
    set_number_from_subtraction(dx, r->x_coord, l->x_coord);
    set_number_from_subtraction(dy, r->y_coord, l->y_coord);
    p = mp_next_knot(l);
    while (p != r) {
        q = mp_next_knot(p);
        set_number_from_subtraction(arg1, p->y_coord, l->y_coord);
        set_number_from_subtraction(arg2, p->x_coord, l->x_coord);
        if (ab_vs_cd(dx, arg1, dy, arg2) > 0) {
            mp_move_knot(mp, p, r);
        }
        p = q;
    }
    free_number(arg1);
    free_number(arg2);
}

@ The |move_knot| procedure removes |p| from a doubly linked list and inserts
it after |q|.

@ @<Declarations@>=
static void mp_move_knot (MP mp, mp_knot p, mp_knot q);

@ @c
void mp_move_knot (MP mp, mp_knot p, mp_knot q)
{
    (void) mp;
    mp_next_knot(mp_prev_knot(p)) = mp_next_knot(p);
    mp_prev_knot(mp_next_knot(p)) = mp_prev_knot(p);
    mp_prev_knot(p) = q;
    mp_next_knot(p) = mp_next_knot(q);
    mp_next_knot(q) = p;
    mp_prev_knot(mp_next_knot(p)) = p;
}

@ @<Find any knots on the path from |s| to |l| below the |l|-|r| line...@>=
{
    mp_number arg1, arg2;
    new_number(arg1);
    new_number(arg2);
    p = s;
    while (p != l) {
        q = mp_next_knot(p);
        set_number_from_subtraction(arg1, p->y_coord, l->y_coord);
        set_number_from_subtraction(arg2, p->x_coord, l->x_coord);
        if (ab_vs_cd(dx, arg1, dy, arg2) < 0) {
            mp_move_knot(mp, p, l);
        }
        p = q;
    }
    free_number(arg1);
    free_number(arg2);
}

@ The list is likely to be in order already so we just do linear insertions.
Secondary comparisons on $y$ ensure that the sort is consistent with the choice
of |l| and |r|.

@<Sort the path from |l| to |r| by increasing $x$@>=
p = mp_next_knot(l);
while (p != r) {
    q = mp_prev_knot(p);
    while (number_greater(q->x_coord, p->x_coord)) {
        q = mp_prev_knot(q);
    }
    while (number_equal(q->x_coord, p->x_coord)) {
        if (number_greater(q->y_coord, p->y_coord)) {
            q = mp_prev_knot(q);
        } else {
            break;
        }
    }
    if (q == mp_prev_knot(p)) {
        p = mp_next_knot(p);
    } else {
        p = mp_next_knot(p);
        mp_move_knot(mp, mp_prev_knot(p), q);
    }
}

@ @<Sort the path from |r| to |l| by decreasing $x$@>=
p = mp_next_knot(r);
while (p != l) {
    q = mp_prev_knot(p);
    while (number_less(q->x_coord, p->x_coord)) {
        q = mp_prev_knot(q);
    }
    while (number_equal(q->x_coord, p->x_coord)) {
        if (number_less(q->y_coord, p->y_coord)) {
            q = mp_prev_knot(q);
        } else {
            break;
        }
    }
    if (q == mp_prev_knot(p)) {
        p = mp_next_knot(p);
    } else {
        p = mp_next_knot(p);
        mp_move_knot(mp, mp_prev_knot(p), q);
    }
}

@ The condition involving |ab_vs_cd| tests if there is not a left turn at knot
|q|. There usually will be a left turn so we streamline the case where the |then|
clause is not executed.

@<Do a Gramm scan and remove vertices where there...@>=
mp_number arg1, arg2;
new_number(arg1);
new_number(arg2);
p = l;
q = mp_next_knot(l);
while (1) {
    set_number_from_subtraction(dx, q->x_coord, p->x_coord);
    set_number_from_subtraction(dy, q->y_coord, p->y_coord);
    p = q;
    q = mp_next_knot(q);
    if (p == l) {
        break;
    } else if (p != r) {
        set_number_from_subtraction(arg1, q->y_coord, p->y_coord);
        set_number_from_subtraction(arg2, q->x_coord, p->x_coord);
        if (ab_vs_cd(dx, arg1, dy, arg2) <= 0) {
            /* Remove knot |p| and back up |p| and |q| but don't go past |l|. */
            s = mp_prev_knot(p);
            mp_memory_free(p);
            mp_next_knot(s) = q;
            mp_prev_knot(q) = s;
            if (s == l) {
                p = s;
            } else {
                p = mp_prev_knot(s);
                q = s;
            }
        }
    }
}
free_number(arg1);
free_number(arg2);

@ The |find_offset| procedure sets global variables |(cur_x,cur_y)| to the offset
associated with the given direction |(x,y)|. If two different offsets apply, it
chooses one of them.

@c
static void mp_find_offset (MP mp, mp_number *x_orig, mp_number *y_orig, mp_knot h)
{
    if (mp_pen_is_elliptical(h)) {
        mp_fraction xx, yy;       /* untransformed offset for an elliptical pen */
        mp_number wx, wy, hx, hy; /* the transformation matrix for an elliptical pen */
        mp_fraction d;            /* a temporary register */
        new_fraction(xx);
        new_fraction(yy);
        new_number(wx);
        new_number(wy);
        new_number(hx);
        new_number(hy);
        new_fraction(d);
        @<Find the offset for |(x,y)| on the elliptical pen~|h|@>
        free_number(xx);
        free_number(yy);
        free_number(wx);
        free_number(wy);
        free_number(hx);
        free_number(hy);
        free_number(d);
    } else {
        mp_knot p, q; /* consecutive knots */
        mp_number arg1, arg2;
        new_number(arg1);
        new_number(arg2);
        q = h;
        do {
            p = q;
            q = mp_next_knot(q);
            set_number_from_subtraction(arg1, q->x_coord, p->x_coord);
            set_number_from_subtraction(arg2, q->y_coord, p->y_coord);
        } while (ab_vs_cd(arg1, *y_orig, arg2, *x_orig) < 0);
        do {
            p = q;
            q = mp_next_knot(q);
            set_number_from_subtraction(arg1, q->x_coord, p->x_coord);
            set_number_from_subtraction(arg2, q->y_coord, p->y_coord);
        } while (ab_vs_cd(arg1, *y_orig, arg2, *x_orig) > 0);
        number_clone(mp->cur_x, p->x_coord);
        number_clone(mp->cur_y, p->y_coord);
        free_number(arg1);
        free_number(arg2);
    }
}

@ @<Glob...@>=
mp_number cur_x;
mp_number cur_y; /* all-purpose return value registers */

@ @<Initialize table entries@>=
new_number(mp->cur_x);
new_number(mp->cur_y);

@ @<Dealloc...@>=
free_number(mp->cur_x);
free_number(mp->cur_y);

@ @<Find the offset for |(x,y)| on the elliptical pen~|h|@>=
if (number_zero(*x_orig) && number_zero(*y_orig)) {
    number_clone(mp->cur_x, h->x_coord);
    number_clone(mp->cur_y, h->y_coord);
} else {
    mp_number x, y, abs_x, abs_y;
    new_number_clone(x, *x_orig);
    new_number_clone(y, *y_orig);
    @<Find the non-constant part of the transformation for |h|@>
    new_number_abs(abs_x, x);
    new_number_abs(abs_y, y);
    while (number_less(abs_x, fraction_half_t) && number_less(abs_y, fraction_half_t)) {
        number_double(x);
        number_double(y);
        number_abs_clone(abs_x, x);
        number_abs_clone(abs_y, y);
    }
    @<Make |(xx,yy)| the offset on the untransformed |pencircle| for the untransformed version of |(x,y)|@>
    {
        mp_number r1, r2;
        new_fraction(r1);
        new_fraction(r2);
        take_fraction(r1, xx, wx);
        take_fraction(r2, yy, hx);
        number_add(r1, r2);
        set_number_from_addition(mp->cur_x, h->x_coord, r1);
        take_fraction(r1, xx, wy);
        take_fraction(r2, yy, hy);
        number_add(r1, r2);
        set_number_from_addition(mp->cur_y, h->y_coord, r1);
        free_number(r1);
        free_number(r2);
    }
    free_number(abs_x);
    free_number(abs_y);
    free_number(x);
    free_number(y);
}

@ @<Find the non-constant part of the transformation for |h|@>=
set_number_from_subtraction(wx, h->left_x,  h->x_coord);
set_number_from_subtraction(wy, h->left_y,  h->y_coord);
set_number_from_subtraction(hx, h->right_x, h->x_coord);
set_number_from_subtraction(hy, h->right_y, h->y_coord);

@ @<Make |(xx,yy)| the offset on the untransformed |pencircle| for the...@>=
{
    mp_number r1, r2, arg1;
    new_number(arg1);
    new_fraction(r1);
    new_fraction(r2);
    take_fraction(r1, x, hy);
    number_negated_clone(arg1, hx);
    take_fraction(r2, y, arg1);
    number_add(r1, r2);
    number_negate(r1);
    number_clone(yy, r1);
    number_negated_clone(arg1, wy);
    take_fraction(r1, x, arg1);
    take_fraction(r2, y, wx);
    number_add(r1, r2);
    number_clone(xx, r1);
    free_number(arg1);
    free_number(r1);
    free_number(r2);
}
pyth_add(d, xx, yy);
if (number_positive(d)) {
    mp_number ret;
    new_fraction(ret);
    make_fraction(ret, xx, d);
    number_half(ret);
    number_clone(xx, ret);
    make_fraction(ret, yy, d);
    number_half(ret);
    number_clone(yy, ret);
    free_number(ret);
}

@ Finding the bounding box of a pen is easy except if the pen is elliptical. But
we can handle that case by just calling |find_offset| twice. The answer is stored
in the global variables |minx|, |maxx|, |miny|, and |maxy|.

@c
static void mp_pen_bbox (MP mp, mp_knot h)
{
    if (mp_pen_is_elliptical(h)) {
        mp_number arg1, arg2;
        new_number(arg1);
        new_fraction(arg2);
        number_clone(arg2, fraction_one_t);
        mp_find_offset(mp, &arg1, &arg2, h);
        number_clone(mp_maxx, mp->cur_x);
        number_clone(mp_minx, h->x_coord);
        number_double(mp_minx);
        number_subtract(mp_minx, mp->cur_x);
        number_negate(arg2);
        mp_find_offset(mp, &arg2, &arg1, h);
        number_clone(mp_maxy, mp->cur_y);
        number_clone(mp_miny, h->y_coord);
        number_double(mp_miny);
        number_subtract(mp_miny, mp->cur_y);
        free_number(arg1);
        free_number(arg2);
    } else {
        mp_knot p = mp_next_knot(h); /* for scanning the knot list */
        number_clone(mp_minx, h->x_coord);
        number_clone(mp_maxx, mp_minx);
        number_clone(mp_miny, h->y_coord);
        number_clone(mp_maxy, mp_miny);
        while (p != h) {
            if (number_less(p->x_coord, mp_minx)) {
                number_clone(mp_minx, p->x_coord);
            }
            if (number_less(p->y_coord, mp_miny)) {
                number_clone(mp_miny, p->y_coord);
            }
            if (number_greater(p->x_coord, mp_maxx)) {
                number_clone(mp_maxx, p->x_coord);
            }
            if (number_greater(p->y_coord, mp_maxy)) {
                number_clone(mp_maxy, p->y_coord);
            }
            p = mp_next_knot(p);
        }
    }
}

@* Numerical values.

This first set goes into the header

@<MPlib internal header stuff@>=
@d mp_fraction mp_number
@d mp_angle    mp_number

@d new_number(A)                           mp->math->md_allocate(mp, &(A), mp_scaled_type)
@d new_fraction(A)                         mp->math->md_allocate(mp, &(A), mp_fraction_type)
@d new_angle(A)                            mp->math->md_allocate(mp, &(A), mp_angle_type)

@d new_number_clone(A,B)                   mp->math->md_allocate_clone(mp, &(A), mp_scaled_type, &(B))
@d new_fraction_clone(A,B)                 mp->math->md_allocate_clone(mp, &(A), mp_fraction_type, &(B))
@d new_angle_clone(A,B)                    mp->math->md_allocate_clone(mp, &(A), mp_angle_type, &(B))

@d new_number_from_double(mp,A,B)          mp->math->md_allocate_double(mp, &(A), B)
@d new_number_abs(A,B)                     mp->math->md_allocate_abs(mp, &(A), mp_scaled_type, &(B))

@d free_number(A)                          mp->math->md_free(mp, &(A))

@d set_precision()                         mp->math->md_set_precision(mp)
@d free_math()                             mp->math->md_free_math(mp)
@d scan_numeric_token(A)                   mp->math->md_scan_numeric(mp,A)
@d scan_fractional_token(A)                mp->math->md_scan_fractional(mp,A)
@d set_number_from_of_the_way(A,t,B,C)     mp->math->md_from_oftheway(mp,&(A),&(t),&(B),&(C))
@d set_number_from_int(A,B)                mp->math->md_from_int(&(A),B)
@d set_number_from_scaled(A,B)             mp->math->md_from_scaled(&(A),B)
@d set_number_from_boolean(A,B)            mp->math->md_from_boolean(&(A),B)
@d set_number_from_double(A,B)             mp->math->md_from_double(&(A),B)
@d set_number_from_addition(A,B,C)         mp->math->md_from_addition(&(A),&(B),&(C))
@d set_number_half_from_addition(A,B,C)    mp->math->md_half_from_addition(&(A),&(B),&(C))
@d set_number_from_subtraction(A,B,C)      mp->math->md_from_subtraction(&(A),&(B),&(C))
@d set_number_half_from_subtraction(A,B,C) mp->math->md_half_from_subtraction(&(A),&(B),&(C))
@d set_number_from_div(A,B,C)              mp->math->md_from_div(&(A),&(B),&(C))
@d set_number_from_mul(A,B,C)              mp->math->md_from_mul(&(A),&(B),&(C))
@d number_int_div(A,C)                     mp->math->md_from_int_div(&(A),&(A),C)
@d set_number_from_int_mul(A,B,C)          mp->math->md_from_int_mul(&(A),&(B),C)

@d set_number_to_unity(A)                  mp->math->md_clone(&(A), &unity_t)
@d set_number_to_zero(A)                   mp->math->md_clone(&(A), &zero_t)
@d set_number_to_inf(A)                    mp->math->md_clone(&(A), &inf_t)
@d set_number_to_negative_inf(A)           mp->math->md_clone(&(A), &negative_inf_t)
@d old_set_number_to_neg_inf(A)	           do { set_number_to_inf(A); number_negate(A); } while (0)

@d init_randoms(A)                         mp->math->md_init_randoms(mp,A)
@d print_number(A)                         mp->math->md_print(mp,&(A))
@d number_tostring(A)                      mp->math->md_tostring(mp,&(A))
@d make_scaled(R,A,B)                      mp->math->md_make_scaled(mp,&(R),&(A),&(B))
@d take_scaled(R,A,B)                      mp->math->md_take_scaled(mp,&(R),&(A),&(B))
@d make_fraction(R,A,B)                    mp->math->md_make_fraction(mp,&(R),&(A),&(B))
@d take_fraction(R,A,B)                    mp->math->md_take_fraction(mp,&(R),&(A),&(B))
@d pyth_add(R,A,B)                         mp->math->md_pyth_add(mp,&(R),&(A),&(B))
@d pyth_sub(R,A,B)                         mp->math->md_pyth_sub(mp,&(R),&(A),&(B))
@d power_of(R,A,B)                         mp->math->md_power_of(mp,&(R),&(A),&(B))
@d n_arg(R,A,B)                            mp->math->md_n_arg(mp,&(R),&(A),&(B))
@d m_log(R,A)                              mp->math->md_m_log(mp,&(R),&(A))
@d m_exp(R,A)                              mp->math->md_m_exp(mp,&(R),&(A))
@d m_unif_rand(R,A)                        mp->math->md_m_unif_rand(mp,&(R),&(A))
@d m_norm_rand(R)                          mp->math->md_m_norm_rand(mp,&(R))
@d velocity(R,A,B,C,D,E)                   mp->math->md_velocity(mp,&(R),&(A),&(B),&(C),&(D),&(E))
@d ab_vs_cd(A,B,C,D)                       mp->math->md_ab_vs_cd(&(A),&(B),&(C),&(D))
@d crossing_point(R,A,B,C)                 mp->math->md_crossing_point(mp,&(R),&(A),&(B),&(C))
@d n_sin_cos(A,S,C)                        mp->math->md_sin_cos(mp,&(A),&(S),&(C))
@d square_rt(A,S)                          mp->math->md_sqrt(mp,&(A),&(S))
@d slow_add(R,A,B)                         mp->math->md_slow_add(mp,&(R),&(A),&(B))
@d round_unscaled(A)                       mp->math->md_round_unscaled(&(A))
@d floor_scaled(A)                         mp->math->md_floor_scaled(&(A))
@d fraction_to_round_scaled(A)             mp->math->md_fraction_to_round_scaled(&(A))
@d number_to_int(A)                        mp->math->md_to_int(&(A))
@d number_to_boolean(A)                    mp->math->md_to_boolean(&(A))
@d number_to_scaled(A)                     mp->math->md_to_scaled(&(A))
@d number_to_double(A)                     mp->math->md_to_double(&(A))
@d number_negate(A)                        mp->math->md_negate(&(A))
@d number_add(A,B)                         mp->math->md_add(&(A),&(B))
@d number_subtract(A,B)                    mp->math->md_subtract(&(A),&(B))
@d number_half(A)                          mp->math->md_half(&(A))
@d number_double(A)                        mp->math->md_do_double(&(A))
@d number_add_scaled(A,B)                  mp->math->md_add_scaled(&(A),B)
@d number_multiply_int(A,B)                mp->math->md_multiply_int(&(A),B)
@d number_divide_int(A,B)                  mp->math->md_divide_int(&(A),B)
@d number_abs(A)                           mp->math->md_abs(&(A))
@d number_modulo(A,B)                      mp->math->md_modulo(&(A),&(B))
@d number_nonequalabs(A,B)                 mp->math->md_nonequalabs(&(A),&(B))
@d number_odd(A)                           mp->math->md_odd(&(A))
@d number_equal(A,B)                       mp->math->md_equal(&(A),&(B))
@d number_greater(A,B)                     mp->math->md_greater(&(A),&(B))
@d number_less(A,B)                        mp->math->md_less(&(A),&(B))
@d number_clone(A,B)                       mp->math->md_clone(&(A),&(B))
@d number_negated_clone(A,B)               mp->math->md_negated_clone(&(A),&(B))
@d number_abs_clone(A,B)                   mp->math->md_abs_clone(&(A),&(B))
@d number_swap(A,B)                        mp->math->md_swap(&(A),&(B));
@d convert_scaled_to_angle(A)              mp->math->md_scaled_to_angle(&(A));
@d convert_angle_to_scaled(A)              mp->math->md_angle_to_scaled(&(A));
@d convert_fraction_to_scaled(A)           mp->math->md_fraction_to_scaled(&(A));
@d convert_scaled_to_fraction(A)           mp->math->md_scaled_to_fraction(&(A));

@d number_zero(A)           number_equal(A, zero_t)
@d number_infinite(A)       number_equal(A, inf_t)
@d number_unity(A)          number_equal(A, unity_t)
@d number_negative(A)       number_less(A, zero_t)
@d number_nonnegative(A)    (! number_negative(A))
@d number_positive(A)       number_greater(A, zero_t)
@d number_nonpositive(A)    (! number_positive(A))
@d number_nonzero(A)        (! number_zero(A))
@d number_greaterequal(A,B) (! number_less(A,B))
@d number_lessequal(A,B)    (! number_greater(A,B))

@* Edge structures.

Now we come to \MP's internal scheme for representing pictures. The
representation is very different from \MF's edge structures because \MP\ pictures
contain \ps\ graphics objects instead of pixel images. However, the basic idea is
somewhat similar in that shapes are represented via their boundaries.

The main purpose of edge structures is to keep track of graphical objects until
it is time to translate them into \ps. Since \MP\ does not need to know anything
about an edge structure other than how to translate it into \ps\ and how to find
its bounding box, edge structures can be just linked lists of graphical objects.
\MP\ has no easy way to determine whether two such objects overlap, but it
suffices to draw the first one first and let the second one overwrite it if
necessary.

@<MPlib header stuff@>=
enum mp_graphical_object_code {
    mp_unset_code,
    mp_fill_code,
    mp_stroked_code,
    mp_start_clip_code,   /* |type| of a node that starts clipping */
    mp_start_group_code,  /* |type| of a node that gives a |setgroup| path */
    mp_start_bounds_code, /* |type| of a node that gives a |setbounds| path */
    mp_stop_clip_code,    /* |type| of a node that stops clipping */
    mp_stop_group_code,   /* |type| of a node that stops grouping */
    mp_stop_bounds_code,  /* |type| of a node that stops |setbounds| */
    mp_final_graphic
};

@ Let's consider the types of graphical objects one at a time. First of all, a
filled contour is represented by a eight-word node. The first word contains
|type| and |link| fields, and the next six words contain a pointer to a cyclic
path and the value to use for \ps' |currentrgbcolor| parameter. If a pen is
used for filling |pen_p|, |linejoin| and |miterlimit| give the relevant information.

We can actually be more sparse: |color_model|, |line_join| and |pen_type| can be
chars: a todo.

We don't save that much by distinguishing between a stroke and a fill object and
we can save some code when we make then the same. Todo: use char for some.

@<MPlib internal header stuff@>=
typedef struct mp_shape_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  stacking;
    struct mp_node_data *link;
    /*common */
    mp_string            pre_script;
    mp_string            post_script;
    union {
        mp_number        red;
        mp_number        cyan;
    };
    union {
        mp_number        green;
        mp_number        magenta;
    };
    union {
        mp_number        blue;
        mp_number        yellow;
    };
    union {
        mp_number        black;
        mp_number        grey;
    };
    /*specific to paths */
    mp_knot              path;
    mp_knot              pen;
    mp_node              dash;
    mp_number            dashscale;
    mp_number            miterlimit;
    unsigned char        color_model;
    unsigned char        linejoin;
    unsigned char        linecap;
    unsigned char        pen_type;
} mp_shape_node_data;

typedef struct mp_shape_node_data *mp_shape_node;

@d mp_path_ptr(A)       (A)->path
@d mp_pen_ptr(A)        (A)->pen
@d mp_dash_ptr(A)       ((mp_shape_node) (A))->dash
@d mp_line_cap(A)       ((mp_shape_node) (A))->linecap
@d mp_line_join(A)      ((mp_shape_node) (A))->linejoin
@d mp_miterlimit(A)     ((mp_shape_node) (A))->miterlimit

@d mp_set_linecap(A,B)  ((mp_shape_node) (A))->linecap = (short) (B)
@d mp_set_linejoin(A,B) ((mp_shape_node) (A))->linejoin = (short) (B)

@d mp_pre_script(A)     ((mp_shape_node) (A))->pre_script
@d mp_post_script(A)    ((mp_shape_node) (A))->post_script
@d mp_color_model(A)    ((mp_shape_node) (A))->color_model
@d mp_stacking(A)       ((mp_shape_node) (A))->stacking
@d mp_pen_type(A)       ((mp_shape_node) (A))->pen_type

@d mp_cyan_color(A)     ((mp_shape_node) (A))->cyan
@d mp_magenta_color(A)  ((mp_shape_node) (A))->magenta
@d mp_yellow_color(A)   ((mp_shape_node) (A))->yellow
@d mp_black_color(A)    ((mp_shape_node) (A))->black
@d mp_red_color(A)      ((mp_shape_node) (A))->red
@d mp_green_color(A)    ((mp_shape_node) (A))->green
@d mp_blue_color(A)     ((mp_shape_node) (A))->blue
@d mp_gray_color(A)     ((mp_shape_node) (A))->grey
@d mp_grey_color(A)     ((mp_shape_node) (A))->grey

@ Make a shape node. A fill node is a cyclic path |p|. A stroked path is a node
that is like a filled contour node except that it contains the current |linecap|
value, a scale factor for the dash pattern, and a pointer that is non-NULL if the
stroke is to be dashed. The purpose of the scale factor is to allow a picture to
be transformed without touching the picture that |dash_p| points to.

@c
static mp_node mp_new_shape_node (MP mp, mp_knot p, int type)
{
    mp_shape_node t = mp_allocate_node(mp, sizeof(mp_shape_node_data));
    mp_type(t) = type;
    mp_path_ptr(t) = p;
    mp_pen_ptr(t) = NULL; /* |NULL| means don't use a pen */
    mp_dash_ptr(t) = NULL;
    new_number(t->red);
    new_number(t->green);
    new_number(t->blue);
    new_number(t->black);
    new_number(t->miterlimit);
    new_number(t->dashscale);
    set_number_to_unity(t->dashscale);
    mp_color_model(t) = mp_uninitialized_model;
    mp_pen_type(t) = 0;
    mp_pre_script(t) = NULL;
    mp_post_script(t) = NULL;
    /* Set the |linejoin| and |miterlimit| fields in object |t| */
    if (number_greater(internal_value(mp_linejoin_internal), unity_t)) {
        t->linejoin = mp_beveled_linejoin_code;
    } else if (number_positive(internal_value(mp_linejoin_internal))) {
        t->linejoin = mp_rounded_linejoin_code;
    } else {
        t->linejoin = mp_mitered_linejoin_code;
    }
    t->stacking = round_unscaled(internal_value(mp_stacking_internal));
    if (number_less(internal_value(mp_miterlimit_internal), unity_t)) {
        set_number_to_unity(t->miterlimit);
    } else {
        number_clone(t->miterlimit, internal_value(mp_miterlimit_internal));
    }
    if (number_greater(internal_value(mp_linecap_internal), unity_t)) {
        t->linecap = mp_squared_linecap_code;
    } else if (number_positive(internal_value(mp_linecap_internal))) {
        t->linecap = mp_rounded_linecap_code;
    } else {
        t->linecap = mp_butt_linecap_code;
    }
    return (mp_node) t;
}

@ @c
static mp_edge_header_node mp_free_shape_node (MP mp, mp_shape_node p)
{
    mp_edge_header_node e = NULL;
    mp_toss_knot_list(mp, mp_path_ptr(p));
    if (mp_pen_ptr(p) != NULL) {
        mp_toss_knot_list(mp, mp_pen_ptr(p));
    }
    if (mp_pre_script(p) != NULL) {
        delete_str_ref(mp_pre_script(p));
    }
    if (mp_post_script(p) != NULL) {
        delete_str_ref(mp_post_script(p));
    }
    e = (mp_edge_header_node) mp_dash_ptr(p);
    free_number(p->red);
    free_number(p->green);
    free_number(p->blue);
    free_number(p->black);
    free_number(p->miterlimit);
    free_number(p->dashscale);
    mp_free_node(mp, (mp_node) p, sizeof(mp_shape_node_data));
    return e ;
}

@ When a dashed line is computed in a transformed coordinate system, the dash
lengths get scaled like the pen shape and we need to compensate for this. Since
there is no unique scale factor for an arbitrary transformation, we use the the
square root of the determinant. The properties of the determinant make it easier
to maintain the |dashscale|. The computation is fairly straight-forward except
for the initialization of the scale factor |s|. The factor of 64 is needed
because |square_rt| scales its result by $2^8$ while we need $2^{14}$ to
counteract the effect of |take_fraction|.

@c
void mp_sqrt_det (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig, mp_number *c_orig, mp_number *d_orig)
{
    mp_number a, b, c, d;
    mp_number maxabs; /* $max(|a|,|b|,|c|,|d|)$ */
    unsigned s = 64;  /* amount by which the result of |square_rt| needs to be scaled */
    mp_number tmp;
    new_number_clone(a, *a_orig);
    new_number_clone(b, *b_orig);
    new_number_clone(c, *c_orig);
    new_number_clone(d, *d_orig);
    /* Initialize |maxabs| */
    new_number_abs(maxabs, a);
    new_number_abs(tmp, b);
    if (number_greater(tmp, maxabs)) {
        number_clone(maxabs, tmp);
    }
    number_abs_clone(tmp, c);
    if (number_greater(tmp, maxabs)) {
        number_clone(maxabs, tmp);
    }
    number_abs_clone(tmp, d);
    if (number_greater(tmp, maxabs)) {
        number_clone(maxabs, tmp);
    }
    free_number(tmp);
    while ((number_less(maxabs, fraction_one_t)) && (s > 1)) {
        number_double(a);
        number_double(b);
        number_double(c);
        number_double(d);
        number_double(maxabs);
        s = s/2;
    }
    {
        mp_number r1, r2;
        new_fraction(r1);
        new_fraction(r2);
        take_fraction(r1, a, d);
        take_fraction(r2, b, c);
        number_subtract(r1, r2);
        number_abs(r1);
        square_rt(*ret, r1);
        number_multiply_int(*ret, s);
        free_number(r1);
        free_number(r2);
    }
    free_number(a);
    free_number(b);
    free_number(c);
    free_number(d);
    free_number(maxabs);
}

static void mp_get_pen_scale (MP mp, mp_number *ret, mp_knot p)
{
    if (p == NULL) {
        set_number_to_zero(*ret);
    } else {
        mp_number a, b, c, d;
        new_number(a);
        new_number(b);
        new_number(c);
        new_number(d);
        set_number_from_subtraction(a, p->left_x, p->x_coord);
        set_number_from_subtraction(b, p->right_x, p->x_coord);
        set_number_from_subtraction(c, p->left_y,    p->y_coord);
        set_number_from_subtraction(d, p->right_y, p->y_coord);
        mp_sqrt_det(mp, ret, &a, &b, &c, &d);
        free_number(a);
        free_number(b);
        free_number(c);
        free_number(d);
    }
}

@ @<Declarations@>=
static void mp_sqrt_det (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig, mp_number *c_orig, mp_number *d_orig);

@ The last two types of graphical objects that can occur in an edge structure are
clipping paths and |setbounds| paths. These are slightly more difficult
@:set_bounds_}{|setbounds| primitive@> to implement because we must keep track
of exactly what is being clipped or bounded when pictures get merged together.
For this reason, each clipping or |setbounds| operation is represented by a
pair of nodes: first comes a node whose |path_ptr| gives the relevant path, then
there is the list of objects to clip or bound followed by a closing node.

@d mp_has_color(A)  (mp_type((A))<mp_start_clip_node_type)    /* does a graphical object have color fields? */
@d mp_has_script(A) (mp_type((A))<=mp_start_bounds_node_type) /* does a graphical object have color fields? */
@d mp_has_pen(A)    (mp_type((A))<=mp_stroked_node_type)      /* does a graphical object have a |mp_pen_ptr| field? */

@d mp_is_start_or_stop(A) (mp_type((A))>=mp_start_clip_node_type)
@d mp_is_stop(A)          (mp_type((A))>=mp_stop_clip_node_type)

@<MPlib internal header stuff@>=
typedef struct mp_start_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  stacking;
    struct mp_node_data *link;
    /*specific */
    mp_string            pre_script;
    mp_string            post_script;
    mp_knot              path;
} mp_start_node_data;

typedef struct mp_start_node_data *mp_start_node;

typedef struct mp_stop_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  stacking;
    struct mp_node_data *link;
    /*specific */
} mp_stop_node_data;

typedef struct mp_stop_node_data *mp_stop_node;

@ Make a node of type |c| where |p| is the clipping or |setbounds| path.

@c
static mp_node mp_new_bounds_node (MP mp, mp_knot p, int c)
{
    switch (c) {
        case mp_start_clip_node_type:
        case mp_start_group_node_type:
        case mp_start_bounds_node_type:
            {
                mp_start_node t = (mp_start_node) mp_allocate_node(mp, sizeof(mp_start_node_data));
                mp_type(t) = c;
                t->path = p;
                t->link = NULL;
                t->stacking = round_unscaled(internal_value(mp_stacking_internal));
                mp_pre_script(t) = NULL;
                mp_post_script(t) = NULL;
                return (mp_node) t;
            }
            break;
        case mp_stop_clip_node_type:
        case mp_stop_group_node_type:
        case mp_stop_bounds_node_type:
            {
                mp_stop_node t = (mp_stop_node) mp_allocate_node(mp, sizeof(mp_stop_node_data));
                mp_type(t) = c;
                t->link = NULL;
                t->stacking = round_unscaled(internal_value(mp_stacking_internal));
                return (mp_node) t;
            }
            break;
        default:
            /* maybe some message */
            break;
    }
    return NULL;
}

@ @c
static void mp_free_start_node (MP mp, mp_start_node p)
{
    mp_toss_knot_list(mp, mp_path_ptr(p));
    if (mp_pre_script(p) != NULL) {
        delete_str_ref(mp_pre_script(p));
    }
    if (mp_post_script(p) != NULL) {
        delete_str_ref(mp_post_script(p));
    }
    mp_free_node(mp, (mp_node) p, sizeof(mp_start_node_data));
}

static void mp_free_stop_node (MP mp, mp_stop_node p)
{
    mp_free_node(mp, (mp_node) p, sizeof(mp_stop_node_data));
}

@ All the essential information in an edge structure is encoded as a linked list
of graphical objects as we have just seen, but it is helpful to add some
redundant information. A single edge structure might be used as a dash pattern
many times, and it would be nice to avoid scanning the same structure repeatedly.
Thus, an edge structure known to be a suitable dash pattern has a header that
gives a list of dashes in a sorted order designed for rapid translation into \ps.

Each dash is represented by a three-word node containing the initial and final
$x$~coordinates as well as the usual |link| field. The |link| fields points to
the dash node with the next higher $x$-coordinates and the final link points to a
special location called |null_dash|. (There should be no overlap between dashes).
Since the $y$~coordinate of the dash pattern is needed to determine the period of
repetition, this needs to be stored in the edge header along with a pointer to
the list of dash nodes.

The |dash_info| is explained below.

@d mp_get_dash_list(A)   (mp_dash_node) (((mp_dash_node) (A))->link) /* in an edge header this points to the first dash node */
@d mp_set_dash_list(A,B) ((mp_dash_node) (A))->link = (mp_node) ((B))  /* in an edge header this points to the first dash node */

@<MPlib internal header stuff@>=
typedef struct mp_dash_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_number            start_x; /* the starting $x$~coordinate in a dash node */
    mp_number            stop_x;  /* the ending $x$~coordinate in a dash node */
    mp_number            dash_y;  /* $y$ value for the dash list in an edge header */
    mp_node              dash_info;
} mp_dash_node_data;

@ @<Types...@>=
typedef struct mp_dash_node_data *mp_dash_node;

@ @<Initialize table entries@>=
mp->null_dash = mp_get_dash_node(mp);

@ @<Free table entries@>=
mp_free_node(mp, (mp_node) mp->null_dash, sizeof(mp_dash_node_data));

@c
static mp_dash_node mp_get_dash_node (MP mp)
{
    mp_dash_node p = (mp_dash_node) mp_allocate_node(mp, sizeof(mp_dash_node_data));
    p->hasnumber = 0;
    new_number(p->start_x);
    new_number(p->stop_x);
    new_number(p->dash_y);
    mp_type(p) = mp_dash_node_type;
    return p;
}

@ It is also convenient for an edge header to contain the bounding box
information needed by the |llcorner| and |urcorner| operators so that this
does not have to be recomputed unnecessarily. This is done by adding fields for
the $x$~and $y$ extremes as well as a pointer that indicates how far the bounding
box computation has gotten. Thus if the user asks for the bounding box and then
adds some more text to the picture before asking for more bounding box
information, the second computation need only look at the additional text.

When the bounding box has not been computed, the |bblast| pointer points to a
dummy link at the head of the graphical object list while the |minx_val| and
|miny_val| fields contain |EL_GORDO| and the |maxx_val| and |maxy_val| fields
contain |-EL_GORDO|.

Since the bounding box of pictures containing objects of type
|mp_start_bounds_node| depends on the value of |truecorners|, the bounding box
@:mp_true_corners_}{|truecorners| primitive@> data might not be valid for all
values of this parameter. Hence, the |bbtype| field is needed to keep track of
this.

@d mp_bblast(A)    ((mp_edge_header_node) (A))->bblast /* last item considered in bounding box computation */
@d mp_edge_list(A) ((mp_edge_header_node) (A))->list   /* where the object list begins in an edge header */

@<MPlib internal header stuff@>=
typedef struct mp_edge_header_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  padding;
    struct mp_node_data *link;
    /*specific */
    mp_number            start_x;
    mp_number            stop_x;
    mp_number            dash_y;
    mp_node              dash_info;
    mp_number            minx;
    mp_number            miny;
    mp_number            maxx;
    mp_number            maxy;
    mp_node              bblast;
    int                  bbtype;     /* tells how bounding box data depends on |truecorners| */
    int                  ref_count;  /* explained below */
    mp_node              list;
    mp_node              obj_tail;   /* explained below */
} mp_edge_header_node_data;

typedef struct mp_edge_header_node_data *mp_edge_header_node;

typedef enum mp_bound_codes {
    mp_no_bounds_code,    /* |bbtype| value when bounding box data is valid for all |truecorners| values */
    mp_bounds_set_code,   /* |bbtype| value when bounding box data is for |truecorners|${}\le 0$ */
    mp_bounds_unset_code, /* |bbtype| value when bounding box data is for |truecorners|${}>0$ */
} mp_bound_codes;

@ @c
static void mp_init_bbox (MP mp, mp_edge_header_node h)
{
    /* Initialize the bounding box information in edge structure |h| */
    (void) mp;
    mp_bblast(h) = mp_edge_list(h);
    h->bbtype = mp_no_bounds_code;
    set_number_to_inf(h->minx);
    set_number_to_inf(h->miny);
    set_number_to_negative_inf(h->maxx);
    set_number_to_negative_inf(h->maxy);
}

@ The only other entries in an edge header are a reference count in the first
word and a pointer to the tail of the object list in the last word.

@d mp_obj_tail(A)       ((mp_edge_header_node) (A))->obj_tail  /* points to the last entry in the object list */
@d mp_edge_ref_count(A) ((mp_edge_header_node) (A))->ref_count

@ @c
static mp_edge_header_node mp_get_edge_header_node (MP mp)
{
    mp_edge_header_node p = (mp_edge_header_node) mp_allocate_node(mp, sizeof(mp_edge_header_node_data));
    mp_type(p) = mp_edge_header_node_type;
    new_number(p->start_x);
    new_number(p->stop_x);
    new_number(p->dash_y);
    new_number(p->minx);
    new_number(p->miny);
    new_number(p->maxx);
    new_number(p->maxy);
    p->list = mp_new_token_node(mp); /* or whatever, just a need a link handle */
    return p;
}

static void mp_init_edges (MP mp, mp_edge_header_node h)
{
  /* initialize an edge header to NULL values */
  mp_set_dash_list(h, mp->null_dash);
  mp_obj_tail(h) = mp_edge_list(h);
  mp_link(mp_edge_list(h)) = NULL;
  mp_edge_ref_count(h) = 0;
  mp_init_bbox(mp, h);
}

@ Here is how edge structures are deleted. The process can be recursive because
of the need to dereference edge structures that are used as dash patterns.
@^recursion@>

@d mp_add_edge_ref(mp,A) mp_edge_ref_count((A)) += 1

@d mp_delete_edge_ref(mp,A) {
    if (mp_edge_ref_count((A)) == 0) {
        mp_toss_edges(mp, (mp_edge_header_node) (A));
    } else {
        mp_edge_ref_count((A)) -= 1;
    }
}

@<Declarations@>=
static void                mp_flush_dash_list (MP mp, mp_edge_header_node h);
static mp_edge_header_node mp_toss_gr_object  (MP mp, mp_node p);
static void                mp_toss_edges      (MP mp, mp_edge_header_node h);

@ @c
void mp_toss_edges (MP mp, mp_edge_header_node h)
{
    mp_node q;             /* pointers that scan the list being recycled */
    mp_edge_header_node r; /* an edge structure that object |p| refers to */
    mp_flush_dash_list(mp, h);
    q = mp_link(mp_edge_list(h));
    while (q != NULL) {
        mp_node p = q;
        q = mp_link(q);
        r = mp_toss_gr_object(mp, p);
        if (r != NULL) {
            mp_delete_edge_ref(mp, r);
        }
    }
    free_number(h->start_x);
    free_number(h->stop_x);
    free_number(h->dash_y);
    free_number(h->minx);
    free_number(h->miny);
    free_number(h->maxx);
    free_number(h->maxy);
    mp_free_token_node(mp, h->list);
    mp_free_node(mp, (mp_node) h, sizeof(mp_edge_header_node_data));
}

void mp_flush_dash_list (MP mp, mp_edge_header_node h)
{
    mp_dash_node q = mp_get_dash_list(h);
    while (q != mp->null_dash) {
        mp_dash_node p = q;
        q = (mp_dash_node) mp_link(q);
        mp_free_node(mp, (mp_node) p, sizeof(mp_dash_node_data));
    }
    mp_set_dash_list(h, mp->null_dash);
}

mp_edge_header_node mp_toss_gr_object (MP mp, mp_node p)
{
    /* returns an edge structure that needs to be dereferenced */
    switch (mp_type(p)) {
        case mp_fill_node_type:
        case mp_stroked_node_type:
            return mp_free_shape_node(mp, (mp_shape_node) p);
        case mp_start_clip_node_type:
        case mp_start_group_node_type:
        case mp_start_bounds_node_type:
            mp_free_start_node(mp, (mp_start_node) p);
            return NULL;
        case mp_stop_clip_node_type:
        case mp_stop_group_node_type:
        case mp_stop_bounds_node_type:
            mp_free_stop_node(mp, (mp_stop_node) p);
            return NULL;
        default:
            return NULL;
    }
}

@ If we use |add_edge_ref| to \quote {copy} edge structures, the real copying needs to
be done before making a significant change to an edge structure. Much of the work
is done in a separate routine |copy_objects| that copies a list of graphical
objects into a new edge header.

@c
static mp_edge_header_node mp_private_edges (MP mp, mp_edge_header_node h)
{
    /* make a private copy of the edge structure headed by |h| */
    if (mp_edge_ref_count(h) == 0) {
        return h;
    } else {
        mp_edge_header_node hh; /* the edge header for the new copy */
        mp_dash_node p, pp;     /* pointers for copying the dash list */
        mp_edge_ref_count(h) -= 1;
        hh = (mp_edge_header_node) mp_copy_objects (mp, mp_link(mp_edge_list(h)), NULL);
        @<Copy the dash list from |h| to |hh|@>
        @<Copy the bounding box information from |h| to |hh| and make |mp_bblast(hh)| point into the new object list@>
        return hh;
    }
}

@ Here we use the fact that |mp_get_dash_list(hh)=mp_link(hh)|. @^data structure
assumptions@>

@<Copy the dash list from |h| to |hh|@>=
pp = (mp_dash_node) hh;
p = mp_get_dash_list(h);
while ((p != mp->null_dash)) {
    mp_link(pp) = (mp_node) mp_get_dash_node(mp);
    pp = (mp_dash_node) mp_link(pp);
    number_clone(pp->start_x, p->start_x);
    number_clone(pp->stop_x, p->stop_x);
    p = (mp_dash_node) mp_link(p);
}
mp_link(pp) = (mp_node) mp->null_dash;
number_clone(hh->dash_y, h->dash_y);

@ |h| is an edge structure

@c
static mp_dash_object *mp_export_dashes (MP mp, mp_shape_node q, mp_number *w)
{
    mp_dash_node h = (mp_dash_node) mp_dash_ptr(q);
    if (h == NULL || mp_get_dash_list(h) == mp->null_dash) {
        return NULL;
    } else {
        mp_dash_object *d;
        mp_dash_node p;
        mp_number scf; /* scale factor */
        mp_number dashoff;
        double *dashes = NULL;
        int num_dashes = 1;
        new_number(scf);
        p = mp_get_dash_list(h);
        mp_get_pen_scale(mp, &scf, mp_pen_ptr(q));
        if (number_zero(scf)) {
            if (number_zero(*w)) {
                number_clone(scf, q->dashscale);
            } else {
                free_number(scf);
                return NULL;
            }
        } else {
            mp_number ret;
            new_number(ret);
            make_scaled(ret, *w, scf);
            take_scaled(scf, ret, q->dashscale);
            free_number(ret);
        }
        number_clone(*w, scf);
        d = mp_allocate_dash(mp);
        set_number_from_addition(mp->null_dash->start_x, p->start_x, h->dash_y);
        {
            mp_number ret, arg1;
            new_number(ret);
            new_number(arg1);
            new_number(dashoff);
            while (p != mp->null_dash) {
                dashes = mp_memory_reallocate(dashes, (size_t) (num_dashes + 2) * sizeof(double));
                set_number_from_subtraction(arg1, p->stop_x, p->start_x);
                take_scaled(ret, arg1, scf);
                dashes[(num_dashes - 1)] = number_to_double(ret);
                set_number_from_subtraction(arg1, ((mp_dash_node) mp_link(p))->start_x, p->stop_x);
                take_scaled(ret, arg1, scf);
                dashes[(num_dashes)] = number_to_double(ret);
                dashes[(num_dashes + 1)] = -1.0; /* terminus */
                num_dashes += 2;
                p = (mp_dash_node) mp_link(p);
            }
            d->array = dashes;
            mp_dash_offset(mp, &dashoff, h);
            take_scaled(ret, dashoff, scf);
            d->offset = number_to_double(ret);
            free_number(ret);
            free_number(arg1);
        }
        free_number(dashoff);
        free_number(scf);
        return d;
    }
}

@ @<Copy the bounding box information from |h| to |hh|...@>=
number_clone(hh->minx, h->minx);
number_clone(hh->miny, h->miny);
number_clone(hh->maxx, h->maxx);
number_clone(hh->maxy, h->maxy);
hh->bbtype = h->bbtype;
p = (mp_dash_node) mp_edge_list(h);
pp = (mp_dash_node) mp_edge_list(hh);
while ((p != (mp_dash_node) mp_bblast(h))) {
    if (p == NULL) {
        mp_confusion(mp, "boundingbox last");
        @:this can't happen bblast}{\quad bblast@>
    } else {
        p = (mp_dash_node) mp_link(p);
        pp = (mp_dash_node) mp_link(pp);
    }
}
mp_bblast(hh) = (mp_node) pp;

@ Here is the promised routine for copying graphical objects into a new edge
structure. It starts copying at object~|p| and stops just before object~|q|. If
|q| is NULL, it copies the entire sublist headed at |p|. The resulting edge
structure requires further initialization by |init_bbox|.

@<Declarations@>=
static mp_edge_header_node mp_copy_objects (MP mp, mp_node p, mp_node q);

@ @c
mp_edge_header_node mp_copy_objects (MP mp, mp_node p, mp_node q) {
    mp_node pp;             /* the last newly copied object */
    int k = 0;              /* temporary register */
    mp_edge_header_node hh = mp_get_edge_header_node(mp); /* the new edge header */
    mp_set_dash_list(hh, mp->null_dash);
    mp_edge_ref_count(hh) = 0;
    pp = mp_edge_list(hh);
    while (p != q) {
        @<Make |mp_link(pp)| point to a copy of object |p|, and update |p| and |pp|@>
    }
    mp_obj_tail(hh) = pp;
    mp_link(pp) = NULL;
    return hh;
}

@ @<Make |mp_link(pp)| point to a copy of object |p|, and update |p| and |pp|@>=
{
    switch (mp_type(p)) {
        case mp_fill_node_type:
        case mp_stroked_node_type:
            k = sizeof(mp_shape_node_data);
            break;
        case mp_start_clip_node_type:
        case mp_start_group_node_type:
        case mp_start_bounds_node_type:
            k = sizeof(mp_start_node_data);
            break;
        case mp_stop_clip_node_type:
        case mp_stop_group_node_type:
        case mp_stop_bounds_node_type:
            k = sizeof(mp_stop_node_data);
            break;
        default:
            break;
    }
    mp_link(pp) = mp_allocate_node(mp, (size_t) k); /* |gr_object| */
    pp = mp_link(pp);
    memcpy(pp, p, (size_t) k);
    pp->link = NULL;
    @<Fix anything in graphical object |pp| that should differ from the corresponding field in |p|@>
    p = mp_link(p);
}

@ @<Fix anything in graphical object |pp| that should differ from the...@>=
switch (mp_type(p)) {
    case mp_fill_node_type:
    case mp_stroked_node_type:
        {
            mp_shape_node tt = (mp_shape_node) pp;
            mp_shape_node t = (mp_shape_node) p;
            new_number_clone(tt->red, t->red);
            new_number_clone(tt->green, t->green);
            new_number_clone(tt->blue, t->blue);
            new_number_clone(tt->black, t->black);
            new_number_clone(tt->miterlimit, t->miterlimit);
            new_number_clone(tt->dashscale, t->dashscale);
            mp_path_ptr(tt) = mp_copy_path(mp, mp_path_ptr(t));
            if (mp_pre_script(p) != NULL) {
                add_str_ref(mp_pre_script(p));
            }
            if (mp_post_script(p) != NULL) {
                add_str_ref(mp_post_script(p));
            }
            if (mp_pen_ptr(t) != NULL) {
                mp_pen_ptr(tt) = mp_copy_pen(mp, mp_pen_ptr(t));
            }
            if (mp_dash_ptr(p) != NULL) {
                mp_add_edge_ref(mp, mp_dash_ptr(pp));
            }
        }
        break;
    case mp_start_clip_node_type:
    case mp_start_group_node_type:
    case mp_start_bounds_node_type:
        {
            mp_start_node tt = (mp_start_node) pp;
            mp_start_node t = (mp_start_node) p;
            mp_path_ptr(tt) = mp_copy_path(mp, mp_path_ptr(t));
            if (mp_pre_script(p) != NULL) {
                add_str_ref(mp_pre_script(p));
            }
            if (mp_post_script(p) != NULL) {
                add_str_ref(mp_post_script(p));
            }
        }
        break;
    case mp_stop_clip_node_type:
    case mp_stop_group_node_type:
    case mp_stop_bounds_node_type:
        break;
    default:
        break;
}

@ Here is one way to find an acceptable value for the second argument to
|copy_objects|. Given a non-NULL graphical object list, |skip_1component| skips
past one picture component, where a \quote {picture component} is a single graphical
object, or a start bounds or start clip object and everything up through the
matching stop bounds or stop clip object.

@c
static mp_node mp_skip_1component (MP mp, mp_node p)
{
    int lev = 0; /* current nesting level */
    (void) mp;
    do {
        if (mp_is_start_or_stop (p)) {
            if (mp_is_stop(p)) {
                --lev;
            } else {
                ++lev;
            }
        }
        p = mp_link(p);
    } while (lev != 0);
    return p;
}

@ Here is a diagnostic routine for printing an edge structure in symbolic form.

@<Declarations@>=
static void mp_print_edges (MP mp, mp_node h, const char *s, int nuline);

@ @c
void mp_print_edges (MP mp, mp_node h, const char *s, int nuline)
{
    mp_node p = mp_edge_list(h); /* a graphical object to be printed */
    mp_number scf;               /* a scale factor for the dash pattern */
    new_number(scf);
    mp_print_diagnostic(mp, "Edge structure", s, nuline);
    while (mp_link(p) != NULL) {
        p = mp_link(p);
        mp_print_ln(mp);
        switch (mp_type(p)) {
            @<Cases for printing graphical object node |p|@>
            default:
                mp_print_str(mp, "[unknown object type!]");
                break;
        }
    }
    mp_print_nl(mp, "End edges");
    if (p != mp_obj_tail(h)) {
        mp_print_str(mp, "?");
        @.End edges?@>
    }
    mp_end_diagnostic(mp, 1);
    free_number(scf);
}

@ @<Cases for printing graphical object node |p|@>=
case mp_fill_node_type:
    mp_print_str(mp, "Filled contour ");
    mp_print_obj_color (mp, p);
    mp_print_chr(mp, ':');
    mp_print_ln(mp);
    mp_pr_path(mp, mp_path_ptr((mp_shape_node) p));
    mp_print_ln(mp);
    if ((mp_pen_ptr((mp_shape_node) p) != NULL)) {
        @<Print join type for graphical object |p|@>
        mp_print_str(mp, " with pen");
        mp_print_ln(mp);
        mp_pr_pen(mp, mp_pen_ptr((mp_shape_node) p));
    }
    break;

@ @<Print join type for graphical object |p|@>=
switch (((mp_shape_node) p)->linejoin) {
    case mp_mitered_linejoin_code:
        mp_print_str(mp, "mitered joins limited ");
        print_number(((mp_shape_node) p)->miterlimit);
        break;
    case mp_rounded_linejoin_code:
        mp_print_str(mp, "round joins");
        break;
    case mp_beveled_linejoin_code:
        mp_print_str(mp, "beveled joins");
        break;
    default:
        mp_print_str(mp, "?? joins");
        break;
        @.??@>
}

@ For stroked nodes, we need to print |linecap_val(p)| as well.

@<Print join and cap types for stroked node |p|@>=
switch (((mp_shape_node) p)->linecap) {
    case mp_butt_linecap_code:
        mp_print_str(mp, "butt");
        break;
    case mp_rounded_linecap_code:
        mp_print_str(mp, "round");
        break;
    case mp_squared_linecap_code:
        mp_print_str(mp, "square");
        break;
    default:
        mp_print_str(mp, "??");
        break;
        @.??@>
}
mp_print_str(mp, " ends, ");
@<Print join type for graphical object |p|@>

@ Here is a routine that prints the color of a graphical object if it isn't black
(the default color).

@<Declarations@>=
static void mp_print_obj_color (MP mp, mp_node p);

@ @c
void mp_print_obj_color (MP mp, mp_node p)
{
    mp_shape_node p0 = (mp_shape_node) p;
    switch (mp_color_model(p)) {
        case mp_grey_model:
            if (number_positive(p0->grey)) {
                mp_print_str(mp, "greyed ");
                mp_print_chr(mp, '(');
                print_number(p0->grey);
                mp_print_chr(mp, ')');
            };
            break;
        case mp_cmyk_model:
            if (number_positive(p0->cyan)   || number_positive(p0->magenta)
             || number_positive(p0->yellow) || number_positive(p0->black)) {
                mp_print_str(mp, "processcolored ");
                mp_print_chr(mp, '(');
                print_number(p0->cyan);
                mp_print_chr(mp, ',');
                print_number(p0->magenta);
                mp_print_chr(mp, ',');
                print_number(p0->yellow);
                mp_print_chr(mp, ',');
                print_number(p0->black);
                mp_print_chr(mp, ')');
            };
            break;
        case mp_rgb_model:
            if (number_positive(p0->red) || number_positive(p0->green) || number_positive(p0->blue)) {
                mp_print_str(mp, "colored ");
                mp_print_chr(mp, '(');
                print_number(p0->red);
                mp_print_chr(mp, ',');
                print_number(p0->green);
                mp_print_chr(mp, ',');
                print_number(p0->blue);
                mp_print_chr(mp, ')');
            }
            break;
        default:
            break;
    }
}

@ @<Cases for printing graphical object node |p|@>=
case mp_stroked_node_type:
    mp_print_str(mp, "Filled pen stroke ");
    mp_print_obj_color (mp, p);
    mp_print_chr(mp, ':');
    mp_print_ln(mp);
    mp_pr_path(mp, mp_path_ptr((mp_shape_node) p));
    if (mp_dash_ptr(p) != NULL) {
        @<Finish printing the dash pattern that |p| refers to@>
    }
    mp_print_ln(mp);
    @<Print join and cap types for stroked node |p|@>
    mp_print_str(mp, " with pen");
    mp_print_ln(mp);
    if (mp_pen_ptr((mp_shape_node) p) == NULL) {
        mp_print_str(mp, "???"); /* shouldn't happen */
        @.???@>
    } else {
        mp_pr_pen(mp, mp_pen_ptr((mp_shape_node) p));
    }
    break;

@ Normally, the |dash_list| field in an edge header is set to |null_dash| when it
is not known to define a suitable dash pattern. This is disallowed here because
the |mp_dash_ptr| field should never point to such an edge header. Note that memory
is allocated for |start_x(null_dash)| and we are free to give it any convenient
value.

@<Finish printing the dash pattern that |p| refers to@>=
mp_dash_node ppd, hhd;
int ok_to_dash = mp_pen_is_elliptical(mp_pen_ptr((mp_shape_node) p));
mp_print_nl(mp, "dashed (");
if (! ok_to_dash) {
    set_number_to_unity(scf);
} else {
    number_clone(scf, ((mp_shape_node) p)->dashscale);
}
hhd = (mp_dash_node) mp_dash_ptr(p);
ppd = mp_get_dash_list(hhd);
if ((ppd == mp->null_dash) || number_negative(hhd->dash_y)) {
    mp_print_str(mp, " ??");
} else {
    mp_number dashoff;
    mp_number ret, arg1;
    new_number(ret);
    new_number(arg1);
    new_number(dashoff);
    set_number_from_addition(mp->null_dash->start_x, ppd->start_x, hhd->dash_y );
    while (ppd != mp->null_dash) {
        mp_print_str(mp, "on ");
        set_number_from_subtraction(arg1, ppd->stop_x, ppd->start_x);
        take_scaled(ret, arg1, scf);
        print_number( ret);
        mp_print_str(mp, " off ");
        set_number_from_subtraction(arg1, ((mp_dash_node) mp_link(ppd))->start_x, ppd->stop_x);
        take_scaled(ret, arg1, scf);
        print_number(ret);
        ppd = (mp_dash_node) mp_link(ppd);
        if (ppd != mp->null_dash) {
            mp_print_chr(mp, ' ');
        }
    }
    mp_print_str(mp, ") shifted ");
    mp_dash_offset(mp, &dashoff, hhd);
    take_scaled(ret, dashoff, scf);
    number_negate(ret);
    print_number(ret);
    free_number(dashoff);
    free_number(ret);
    free_number(arg1);
    if (!ok_to_dash || number_zero(hhd->dash_y)) {
        mp_print_str(mp, " (this will be ignored)");
    }
}

@ @<Declarations@>=
static void mp_dash_offset (MP mp, mp_number *x, mp_dash_node h);

@ @c
void mp_dash_offset (MP mp, mp_number *x, mp_dash_node h)
{
    if (mp_get_dash_list(h) == mp->null_dash || number_negative(h->dash_y)) {
        mp_confusion(mp, "dash offset");
        @:this can't happen dash0}{\quad dash0@>
    } else if (number_zero(h->dash_y)) {
        set_number_to_zero(*x);
    } else {
        number_clone(*x, (mp_get_dash_list(h))->start_x);
        number_modulo(*x, h->dash_y);
        number_negate(*x);
        if (number_negative(*x)) {
            number_add(*x, h->dash_y);
        }
    }
}

@ @<Cases for printing graphical object node |p|@>=
case mp_start_clip_node_type:
    mp_print_str(mp, "clipping path:");
    goto COMMONSTART;
case mp_start_group_node_type:
    mp_print_str(mp, "setgroup path:");
    goto COMMONSTART;
case mp_start_bounds_node_type:
    mp_print_str(mp, "setbounds path:");
  COMMONSTART:
    mp_print_ln(mp);
    mp_pr_path(mp, mp_path_ptr((mp_start_node) p));
    break;
case mp_stop_clip_node_type:
    mp_print_str(mp, "stop clipping");
    break;
case mp_stop_group_node_type:
    mp_print_str(mp, "stop group");
    break;
case mp_stop_bounds_node_type:
    mp_print_str(mp, "end of setbounds");
    break;

@ To initialize the |dash_list| field in an edge header~|h|, we need a subroutine
that scans an edge structure and tries to interpret it as a dash pattern. This
can only be done when there are no filled regions or clipping paths and all the
pen strokes have the same color. The first step is to let $y_0$ be the initial
$y$~coordinate of the first pen stroke. Then we implicitly project all the pen
stroke paths onto the line $y=y_0$ and require that there be no retracing. If the
resulting paths cover a range of $x$~coordinates of length $\Delta x$, we set
|dash_y(h)| to the length of the dash pattern by finding the maximum of $\Delta
x$ and the absolute value of~$y_0$.

@c
static mp_edge_header_node mp_make_dashes (MP mp, mp_edge_header_node h)
{
    if (mp_get_dash_list(h) != mp->null_dash) {
        return h;
    } else {
        /* returns |h| or |NULL| */
        mp_node p;          /* this scans the stroked nodes in the object list */
        mp_node p0;         /* if not |NULL| this points to the first stroked node */
        mp_knot pp, qq, rr; /* pointers into |mp_path_ptr(p)| */
        mp_dash_node d, dd; /* pointers used to create the dash list */
        mp_number y0;
        @<Other local variables in |make_dashes|@>
        new_number(y0); /* the initial $y$ coordinate */
        p0 = NULL;
        p = mp_link(mp_edge_list(h));
        while (p != NULL) {
            if (mp_type(p) != mp_stroked_node_type) {
                @<Complain that the edge structure contains a node of the wrong type and |goto not_found|@>
            }
            pp = mp_path_ptr((mp_shape_node) p);
            if (p0 == NULL) {
                p0 = p;
                number_clone(y0, pp->y_coord);
            }
            @<Make |d| point to a new dash node created from stroke |p| and path |pp| or |goto not_found| if there is an error@>
            @<Insert |d| into the dash list and |goto not_found| if there is an error@>
            p = mp_link(p);
        }
        if (mp_get_dash_list(h) == mp->null_dash) {
            goto NOT_FOUND; /* No error message */
        } else {
            @<Scan |mp_get_dash_list(h)| and deal with any dashes that are themselves dashed@>
            @<Set |dash_y(h)| and merge the first and last dashes if necessary@>
            free_number(y0);
            return h;
        }
      NOT_FOUND:
        free_number(y0);
        @<Flush the dash list, recycle |h| and return |NULL|@>
    }
}

@ @<Complain that the edge structure contains a node of the wrong type...@>=
mp_back_error(
    mp,
    "Picture is too complicated to use as a dash pattern",
    "When you say 'dashed p', picture p should not contain any text, filled regions,\n"
    "or clipping paths. This time it did so I'll just make it a solid line instead."
);
mp_get_x_next(mp);
goto NOT_FOUND;

@ A similar error occurs when monotonicity fails.

@<Declarations@>=
static void mp_x_retrace_error (MP mp);

@ @c
void mp_x_retrace_error (MP mp)
{
    mp_back_error(
        mp,
        "Picture is too complicated to use as a dash pattern",
        "When you say 'dashed p', every path in p should be monotone in x and there must\n"
        "be no overlapping. This failed so I'll just make it a solid line instead."
    );
    mp_get_x_next(mp);
}

@ We stash |p| in |dash_info(d)| if |mp_dash_ptr(p)<>0| so that subsequent
processing can handle the case where the pen stroke |p| is itself dashed.

@d mp_dash_info(A) ((mp_dash_node) (A))->dash_info  /* in an edge header this points to the first dash node */

@<Make |d| point to a new dash node created from stroke |p| and path...@>=
@<Make sure |p| and |p0| are the same color and |goto not_found| if there is an error@>
rr = pp;
if (mp_next_knot(pp) != pp) {
    do {
        qq = rr;
        rr = mp_next_knot(rr);
        @<Check for retracing between knots |qq| and |rr| and |goto not_found| if there is a problem@>
    } while (mp_right_type(rr) != mp_endpoint_knot);
}
d = (mp_dash_node) mp_get_dash_node(mp);
if (mp_dash_ptr(p) == NULL) {
    mp_dash_info(d) = NULL;
} else {
    mp_dash_info(d) = p;
}
if (number_less(pp->x_coord, rr->x_coord)) {
    number_clone(d->start_x, pp->x_coord);
    number_clone(d->stop_x, rr->x_coord);
} else {
    number_clone(d->start_x, rr->x_coord);
    number_clone(d->stop_x, pp->x_coord);
}

@ We also need to check for the case where the segment from |qq| to |rr| is
monotone in $x$ but is reversed relative to the path from |pp| to |qq|.

@<Check for retracing between knots |qq| and |rr| and |goto not_found|...@>=
{
    mp_number x0, x1, x2, x3; /* $x$ coordinates of the segment from |qq| to |rr| */
    new_number_clone(x0, qq->x_coord);
    new_number_clone(x1, qq->right_x);
    new_number_clone(x2, rr->left_x);
    new_number_clone(x3, rr->x_coord);
    if (number_greater(x0, x1) || number_greater(x1, x2) || number_greater(x2, x3)) {
        if (number_less(x0, x1) || number_less(x1, x2) || number_less(x2, x3)) {
            mp_number a1, a2, a3, a4;
            int test;
            new_number(a1);
            new_number(a2);
            new_number(a3);
            new_number(a4);
            set_number_from_subtraction(a1, x2, x1);
            set_number_from_subtraction(a2, x2, x1);
            set_number_from_subtraction(a3, x1, x0);
            set_number_from_subtraction(a4, x3, x2);
            test = ab_vs_cd(a1, a2, a3, a4);
            free_number(a1);
            free_number(a2);
            free_number(a3);
            free_number(a4);
            if (test > 0) {
                mp_x_retrace_error(mp);
                free_number(x0);
                free_number(x1);
                free_number(x2);
                free_number(x3);
                goto NOT_FOUND;
            }
        }
    }
    if (number_greater(pp->x_coord, x0) || number_greater(x0, x3)) {
        if (number_less(pp->x_coord, x0) || number_less(x0, x3)) {
            mp_x_retrace_error(mp);
            free_number(x0);
            free_number(x1);
            free_number(x2);
            free_number(x3);
            goto NOT_FOUND;
        }
    }
    free_number(x0);
    free_number(x1);
    free_number(x2);
    free_number(x3);
}

@ @<Make sure |p| and |p0| are the same color and |goto not_found|...@>=
if (! number_equal(((mp_shape_node) p)->red,   ((mp_shape_node) p0)->red)
 || ! number_equal(((mp_shape_node) p)->black, ((mp_shape_node) p0)->black)
 || ! number_equal(((mp_shape_node) p)->green, ((mp_shape_node) p0)->green)
 || ! number_equal(((mp_shape_node) p)->blue,  ((mp_shape_node) p0)->blue)
    ) {
    mp_back_error(
        mp,
        "Picture is too complicated to use as a dash pattern",
        "When you say 'dashed p', everything in picture p should be the same color. I\n"
        "can't handle your color changes so I'll just make it a solid line instead."
    );
    mp_get_x_next(mp);
    goto NOT_FOUND;
}

@ @<Insert |d| into the dash list and |goto not_found| if there is an error@>=
number_clone(mp->null_dash->start_x, d->stop_x);
dd = (mp_dash_node) h; /* this makes |mp_link(dd)=mp_get_dash_list(h)| */
while (number_less(((mp_dash_node) mp_link(dd))->start_x, d->stop_x)) {
    dd = (mp_dash_node) mp_link(dd);
}
if ((dd != (mp_dash_node) h) && number_greater(dd->stop_x, d->start_x)) {
    mp_x_retrace_error(mp);
    goto NOT_FOUND;
}
mp_link(d) = mp_link(dd);
mp_link(dd) = (mp_node) d;

@ @<Set |dash_y(h)| and merge the first and last dashes if necessary@>=
d = mp_get_dash_list(h);
while (mp_link(d) != (mp_node) mp->null_dash) {
    d = (mp_dash_node) mp_link(d);
}
dd = mp_get_dash_list(h);
set_number_from_subtraction(h->dash_y, d->stop_x, dd->start_x);
{
    mp_number absval;
    new_number(absval);
    number_abs_clone(absval, y0);
    if (number_greater(absval, h->dash_y) ) {
        number_clone(h->dash_y, absval);
    } else if (d != dd) {
        mp_set_dash_list(h, mp_link(dd));
        set_number_from_addition(d->stop_x, dd->stop_x, h->dash_y);
        mp_free_node(mp, (mp_node) dd, sizeof(mp_dash_node_data));
    }
    free_number(absval);
}

@ We get here when the argument is a NULL picture or when there is an error.
Recovering from an error involves making |mp_get_dash_list(h)| empty to indicate that
|h| is not known to be a valid dash pattern. We also dereference |h| since it is
not being used for the return value.

@<Flush the dash list, recycle |h| and return |NULL|@>=
mp_flush_dash_list(mp, h);
mp_delete_edge_ref(mp, h);
return NULL;

@ Having carefully saved the dashed stroked nodes in the corresponding dash
nodes, we must be prepared to break up these dashes into smaller dashes.

@<Scan |mp_get_dash_list(h)| and deal with any dashes that are themselves dashed@>=
{
mp_number hsf; /* the dash pattern from |hh| gets scaled by this */
new_number(hsf);
d = (mp_dash_node) h; /* now |mp_link(d)=mp_get_dash_list(h)| */
while (mp_link(d) != (mp_node) mp->null_dash) {
    ds = mp_dash_info(mp_link(d));
    if (ds == NULL) {
        d = (mp_dash_node) mp_link(d);
    } else {
        hh = (mp_edge_header_node) mp_dash_ptr(ds);
        number_clone(hsf, ((mp_shape_node) ds)->dashscale);
        if (hh == NULL) {
            mp_confusion(mp, "dash pattern");
            @:this can't happen dash0}{\quad dash1@>
            return NULL;
        } else if (number_zero(((mp_dash_node) hh)->dash_y )) {
            d = (mp_dash_node) mp_link(d);
        } else if (mp_get_dash_list (hh) == NULL) {
            mp_confusion(mp, "dash list");
            @:this can't happen dash1}{\quad dash1@>
            return NULL;
        } else {
            @<Replace |mp_link(d)| by a dashed version as determined by edge header |hh| and scale factor |ds|@>
        }
    }
}
free_number(hsf);
}

@ @<Other local variables in |make_dashes|@>=
mp_dash_node dln;       /* |mp_link(d)| */
mp_edge_header_node hh; /* an edge header that tells how to break up |dln| */
mp_node ds;             /* the stroked node from which |hh| and |hsf| are derived */

@ @<Replace |mp_link(d)| by a dashed version as determined by edge header...@>=
mp_number xoff; /* added to $x$ values in |mp_get_dash_list(hh)| to match |dln| */
mp_number dashoff;
mp_number r1, r2;
new_number(r1);
new_number(r2);
dln = (mp_dash_node) mp_link(d);
dd = mp_get_dash_list(hh);
new_number(xoff);
new_number(dashoff);
mp_dash_offset(mp, &dashoff, (mp_dash_node) hh);
take_scaled(r1, hsf, dd->start_x);
take_scaled(r2, hsf, dashoff);
number_add(r1, r2);
set_number_from_subtraction(xoff, dln->start_x, r1);
free_number(dashoff);
take_scaled(r1, hsf, dd->start_x);
take_scaled(r2, hsf, hh->dash_y);
set_number_from_addition(mp->null_dash->start_x, r1, r2);
number_clone(mp->null_dash->stop_x, mp->null_dash->start_x);
@<Advance |dd| until finding the first dash that overlaps |dln| when offset by |xoff|@>
while (number_lessequal(dln->start_x, dln->stop_x)) {
    @<If |dd| has `fallen off the end', back up to the beginning and fix |xoff|@>
    @<Insert a dash between |d| and |dln| for the overlap with the offset version of |dd|@>
    dd = (mp_dash_node) mp_link(dd);
    take_scaled(r1, hsf, dd->start_x);
    set_number_from_addition(dln->start_x , xoff, r1);
}
free_number(xoff);
free_number(r1);
free_number(r2);
mp_link(d) = mp_link(dln);
mp_free_node(mp, (mp_node) dln, sizeof(mp_dash_node_data));

@ The name of this module is a bit of a lie because we just find the first |dd|
where |take_scaled(hsf, stop_x(dd))| is large enough to make an overlap
possible. It could be that the unoffset version of dash |dln| falls in the gap
between |dd| and its predecessor.

@<Advance |dd| until finding the first dash that overlaps |dln| when...@>=
{
    mp_number r1;
    new_number(r1);
    take_scaled(r1, hsf, dd->stop_x);
    number_add(r1, xoff);
    while (number_less(r1, dln->start_x)) {
        dd = (mp_dash_node) mp_link(dd);
        take_scaled(r1, hsf, dd->stop_x);
        number_add(r1, xoff);
    }
    free_number(r1);
}

@ @<If |dd| has `fallen off the end', back up to the beginning and fix...@>=
if (dd == mp->null_dash) {
    mp_number ret;
    new_number(ret);
    dd = mp_get_dash_list(hh);
    take_scaled(ret, hsf, hh->dash_y);
    number_add(xoff, ret);
    free_number(ret);
}

@ At this point we already know that |start_x(dln)<=xoff+take_scaled(hsf,stop_x(dd))|.

@<Insert a dash between |d| and |dln| for the overlap with the offset...@>=
{
    mp_number r1;
    new_number(r1);
    take_scaled(r1, hsf, dd->start_x);
    number_add(r1, xoff);
    if (number_lessequal(r1, dln->stop_x)) {
        mp_link(d) = (mp_node) mp_get_dash_node(mp);
        d = (mp_dash_node) mp_link(d);
        mp_link(d) = (mp_node) dln;
        take_scaled(r1, hsf, dd->start_x );
        number_add(r1, xoff);
        if (number_greater(dln->start_x, r1)) {
            number_clone(d->start_x, dln->start_x);
        } else {
            number_clone(d->start_x, r1);
        }
        take_scaled(r1, hsf, dd->stop_x);
        number_add(r1, xoff);
        if (number_less(dln->stop_x, r1)) {
            number_clone(d->stop_x, dln->stop_x );
        } else {
            number_clone(d->stop_x, r1);
        }
    }
    free_number(r1);
}

@ The next major task is to update the bounding box information in an edge
header~|h|. This is done via a procedure |adjust_bbox| that enlarges an edge
header's bounding box to accommodate the box computed by |path_bbox| or
|pen_bbox|. (This is stored in global variables |minx|, |miny|, |maxx|, and
|maxy|.)

@c
static void mp_adjust_bbox (MP mp, mp_edge_header_node h)
{
    if (number_less(mp_minx, h->minx)) {
        number_clone(h->minx, mp_minx);
    }
    if (number_less(mp_miny, h->miny)) {
        number_clone(h->miny, mp_miny);
    }
    if (number_greater(mp_maxx, h->maxx)) {
        number_clone(h->maxx, mp_maxx);
    }
    if (number_greater(mp_maxy, h->maxy)) {
        number_clone(h->maxy, mp_maxy);
    }
}

@ Here is a special routine for updating the bounding box information in edge
header~|h| to account for the squared-off ends of a non-cyclic path~|p| that is
to be stroked with the pen~|pp|.

@c
static void mp_box_ends (MP mp, mp_knot p, mp_knot pp, mp_edge_header_node h)
{
    if (mp_right_type(p) != mp_endpoint_knot) {
        mp_fraction dx, dy; /* a unit vector in the direction out of the path at~|p| */
        mp_number d;        /* a factor for adjusting the length of |(dx,dy)| */
        mp_number z;        /* a coordinate being tested against the bounding box */
        mp_number xx, yy;   /* the extreme pen vertex in the |(dx,dy)| direction */
        new_fraction(dx);
        new_fraction(dy);
        new_number(xx);
        new_number(yy);
        new_number(z);
        new_number(d);
        mp_knot q = mp_next_knot(p); /* a knot node adjacent to knot |p| */
        while (1) {
            @<Make |(dx,dy)| the final direction for the path segment from |q| to~|p|; set~|d|@>
            pyth_add(d, dx, dy);
            if (number_positive(d)) {
                @<Normalize the direction |(dx,dy)| and find the pen offset |(xx,yy)|@>
                for (int i = 1; i <= 2; i++) {
                    @<Use |(dx,dy)| to generate a vertex of the square end cap and update the bounding box to accommodate it@>
                    number_negate(dx);
                    number_negate(dy);
                }
            }
            if (mp_right_type(p) == mp_endpoint_knot) {
                goto DONE;
            } else {
                @<Advance |p| to the end of the path and make |q| the previous knot@>
            }
        }
      DONE:
        free_number(dx);
        free_number(dy);
        free_number(xx);
        free_number(yy);
        free_number(z);
        free_number(d);
    }
}

@ @<Make |(dx,dy)| the final direction for the path segment from...@>=
if (q == mp_next_knot(p)) {
    set_number_from_subtraction(dx, p->x_coord, p->right_x);
    set_number_from_subtraction(dy, p->y_coord, p->right_y);
    if (number_zero(dx) && number_zero(dy)) {
        set_number_from_subtraction(dx, p->x_coord, q->left_x);
        set_number_from_subtraction(dy, p->y_coord, q->left_y);
    }
} else {
    set_number_from_subtraction(dx, p->x_coord, p->left_x);
    set_number_from_subtraction(dy, p->y_coord, p->left_y);
    if (number_zero(dx) && number_zero(dy)) {
        set_number_from_subtraction(dx, p->x_coord, q->right_x);
        set_number_from_subtraction(dy, p->y_coord, q->right_y);
    }
}
set_number_from_subtraction(dx, p->x_coord, q->x_coord);
set_number_from_subtraction(dy, p->y_coord, q->y_coord);

@ @<Normalize the direction |(dx,dy)| and find the pen offset |(xx,yy)|@>=
mp_number arg1, r;
new_fraction(r);
new_number(arg1);
make_fraction(r, dx, d);
number_clone(dx, r);
make_fraction(r, dy, d);
number_clone(dy, r);
free_number(r);
number_negated_clone(arg1, dy);
mp_find_offset(mp, &arg1, &dx, pp);
free_number(arg1);
number_clone(xx, mp->cur_x);
number_clone(yy, mp->cur_y);

@ @<Use |(dx,dy)| to generate a vertex of the square end cap and...@>=
mp_number r1, r2, arg1;
new_number(arg1);
new_fraction(r1);
new_fraction(r2);
mp_find_offset(mp, &dx, &dy, pp);
set_number_from_subtraction(arg1, xx, mp->cur_x);
take_fraction(r1, arg1, dx);
set_number_from_subtraction(arg1, yy, mp->cur_y);
take_fraction(r2, arg1, dy);
set_number_from_addition(d, r1, r2);
if ((number_negative(d) && (i == 1)) || (number_positive(d) && (i == 2))) {
    mp_confusion(mp, "box ends");
    @:this can't happen box ends}{\quad|box\_ends|@>
}
take_fraction(r1, d, dx);
set_number_from_addition(z, p->x_coord, mp->cur_x);
number_add(z, r1);
if (number_less(z, h->minx)) {
    number_clone(h->minx, z);
}
if (number_greater(z, h->maxx)) {
    number_clone(h->maxx, z);
}
take_fraction(r1, d, dy);
set_number_from_addition(z, p->y_coord, mp->cur_y);
number_add(z, r1);
if (number_less(z, h->miny)) {
    number_clone(h->miny, z);
}
if (number_greater(z, h->maxy)) {
    number_clone(h->maxy, z);
}
free_number(r1);
free_number(r2);
free_number(arg1);

@ @<Advance |p| to the end of the path and make |q| the previous knot@>=
do {
    q = p;
    p = mp_next_knot(p);
} while (mp_right_type(p) != mp_endpoint_knot);

@ The major difficulty in finding the bounding box of an edge structure is the
effect of clipping paths. We treat them conservatively by only clipping to the
clipping path's bounding box, but this still requires recursive calls to
|set_bbox| in order to find the bounding box of @^recursion@> the objects to be
clipped. Such calls are distinguished by the fact that the boolean parameter
|top_level| is false.

@c
void mp_set_bbox (MP mp, mp_edge_header_node h, int top_level)
{
    /*
        Wipe out any existing bounding box information if |bbtype(h)| is
        incompatible with |internal[mp_true_corners]|
    */
    switch (h->bbtype ) {
        case mp_no_bounds_code:
            break;
        case mp_bounds_set_code:
            if (number_positive(internal_value(mp_true_corners_internal))) {
                mp_init_bbox(mp, h);
            }
            break;
        case mp_bounds_unset_code:
            if (number_nonpositive(internal_value(mp_true_corners_internal))) {
                mp_init_bbox(mp, h);
            }
            break;
    }

    while (mp_link(mp_bblast(h)) != NULL) {
        mp_node p = mp_link(mp_bblast(h)); /* a graphical object being considered */
        mp_bblast(h) = p;
        switch (mp_type(p)) {
            case mp_stop_clip_node_type:
                if (top_level) {
                    mp_confusion(mp, "clip");
                    break;
                } else {
                    return;
                    @:this can't happen bbox}{\quad bbox@>
                }
            @<Other cases for updating the bounding box based on the type of object |p|@>
            default:
                break;
        }
    }
    if (! top_level) {
        mp_confusion(mp, "boundingbox");
    }
}

@ @<Declarations@>=
static void mp_set_bbox (MP mp, mp_edge_header_node h, int top_level);

@ @<Other cases for updating the bounding box...@>=
case mp_start_bounds_node_type:
    if (number_positive(internal_value(mp_true_corners_internal))) {
        h->bbtype = mp_bounds_unset_code;
    } else {
        h->bbtype = mp_bounds_set_code;
        mp_path_bbox(mp, mp_path_ptr((mp_start_node) p));
        mp_adjust_bbox(mp, h);
        @<Scan to the matching |mp_stop_bounds_node| node and update |p| and |mp_bblast(h)|@>
    }
    break;
case mp_stop_bounds_node_type:
    if (number_nonpositive (internal_value(mp_true_corners_internal))) {
        mp_confusion(mp, "bounds");
        @:this can't happen bbox2}{\quad bbox2@>
    }
    break;

@ @<Scan to the matching |mp_stop_bounds_node| node and update |p| and...@>=
{
    int lev = 1;
    while (lev != 0) {
        if (mp_link(p) == NULL) {
            mp_confusion(mp, "bounds");
            @:this can't happen bbox2}{\quad bbox2@>
        } else {
            p = mp_link(p);
            if (mp_type(p) == mp_start_bounds_node_type) {
                ++lev;
            } else if (mp_type(p) == mp_stop_bounds_node_type) {
                --lev;
            }
        }
    }
    mp_bblast(h) = p;
}

@ It saves a lot of grief here to be slightly conservative and not account for
omitted parts of dashed lines. We also don't worry about the material omitted
when using butt end caps. The basic computation is for round end caps and
|box_ends| augments it for square end caps.

@<Other cases for updating the bounding box...@>=
case mp_fill_node_type:
case mp_stroked_node_type:
    {
        mp_number x0a, y0a, x1a, y1a;
        mp_path_bbox(mp, mp_path_ptr((mp_shape_node) p));
        /* Stroked paths always have a pen */
        if (mp_pen_ptr((mp_shape_node) p) != NULL) {
            new_number_clone(x0a, mp_minx);
            new_number_clone(y0a, mp_miny);
            new_number_clone(x1a, mp_maxx);
            new_number_clone(y1a, mp_maxy);
            mp_pen_bbox(mp, mp_pen_ptr((mp_shape_node) p));
            number_add(mp_minx, x0a);
            number_add(mp_miny, y0a);
            number_add(mp_maxx, x1a);
            number_add(mp_maxy, y1a);
            free_number(x0a);
            free_number(y0a);
            free_number(x1a);
            free_number(y1a);
        }
        mp_adjust_bbox(mp, h);
        /* Stroked paths can be open, so: */
        if ((mp_left_type(mp_path_ptr((mp_shape_node) p)) == mp_endpoint_knot) && (((mp_shape_node) p)->linecap == 2)) {
            mp_box_ends(mp, mp_path_ptr((mp_shape_node) p), mp_pen_ptr((mp_shape_node) p), h);
        }
    }
    break;

@ This case involves a recursive call that advances |mp_bblast(h)| to the node of
type |mp_stop_clip_node| that matches |p|.

@<Other cases for updating the bounding box...@>=
case mp_start_clip_node_type:
    {
        mp_number sminx, sminy, smaxx, smaxy;
        /* for saving the bounding box during recursive calls */
        mp_number x0a, y0a, x1a, y1a;
        mp_path_bbox(mp, mp_path_ptr((mp_start_node) p));
        new_number_clone(x0a, mp_minx);
        new_number_clone(y0a, mp_miny);
        new_number_clone(x1a, mp_maxx);
        new_number_clone(y1a, mp_maxy);
        new_number_clone(sminx, h->minx);
        new_number_clone(sminy, h->miny);
        new_number_clone(smaxx, h->maxx);
        new_number_clone(smaxy, h->maxy);
        @<Reinitialize the bounding box in header |h| and call |set_bbox| recursively starting at |mp_link(p)|@>
        @<Clip the bounding box in |h| to the rectangle given by |x0a|, |x1a|, |y0a|, |y1a|@>
        number_clone(mp_minx, sminx);
        number_clone(mp_miny, sminy);
        number_clone(mp_maxx, smaxx);
        number_clone(mp_maxy, smaxy);
        mp_adjust_bbox(mp, h);
        free_number(sminx);
        free_number(sminy);
        free_number(smaxx);
        free_number(smaxy);
        free_number(x0a);
        free_number(y0a);
        free_number(x1a);
        free_number(y1a);
    }
    break;

@ @<Reinitialize the bounding box in header |h| and call |set_bbox|...@>=
set_number_to_inf(h->minx);
set_number_to_inf(h->miny);
set_number_to_negative_inf(h->maxx);
set_number_to_negative_inf(h->maxy);
mp_set_bbox(mp, h, 0);

@ @<Clip the bounding box in |h| to the rectangle given by |x0a|, |x1a|,...@>=
if (number_less(h->minx, x0a)) {
    number_clone(h->minx, x0a);
}
if (number_less(h->miny, y0a)) {
    number_clone(h->miny, y0a);
}
if (number_greater(h->maxx, x1a)) {
    number_clone(h->maxx, x1a);
}
if (number_greater(h->maxy, y1a)) {
    number_clone(h->maxy, y1a);
}

@* Finding an envelope.

When \MP\ has a path and a polygonal pen, it needs to express the desired shape
in terms of things \ps\ can understand. The present task is to compute a new path
that describes the region to be filled. It is convenient to define this as a two
step process where the first step is determining what offset to use for each
segment of the path.

@ Given a pointer |c| to a cyclic path, and a pointer~|h| to the first knot of a
pen polygon, the |offset_prep| routine changes the path into cubics that are
associated with particular pen offsets. Thus if the cubic between |p| and~|q| is
associated with the |k|th offset and the cubic between |q| and~|r| has offset |l|
then |mp_info(q) = zero_off + l - k|. (The constant |zero_off| is added to
because |l - k| could be negative.)

After overwriting the type information with offset differences, we no longer have
a true path so we refer to the knot list returned by |offset_prep| as an
\quote {envelope spec.} @^envelope spec@> Since an envelope spec only determines
relative changes in pen offsets, |offset_prep| sets a global variable
|spec_offset| to the relative change from |h| to the first offset.

@d zero_off 0 /* 16384 */ /* added to offset changes to make them positive */

@<Glob...@>=
int spec_offset;  /* number of pen edges between |h| and the initial offset */
int spec_padding; /* be nice */

@ The next function calculates $1/3 B'(t) = (-p + (3c_1 + (-3c_2 + q)))*t^2 + (2p
+ (-4c_1 + 2*c_2))t + (-p + c_1)$, for cubic curve |B(t)| given by
|p|,|c1|,|c2|,|q| and it's used for |t| near 0 and |t| near 1. We use double
mode, otherwise we have to take care of overflow.

@ @c
static mp_knot mp_offset_prep (MP mp, mp_knot c, mp_knot h)
{
    int n;                                 /* the number of vertices in the pen polygon */
    mp_knot c0, p, q, q0, r, w, ww;        /* for list manipulation */
    int k_needed;                          /* amount to be added to |mp_info(p)| when it is computed */
    mp_knot w0;                            /* a pointer to pen offset to use just before |p| */
    mp_number dxin, dyin;                  /* the direction into knot |p| */
    int turn_amt;                          /* change in pen offsets for the current cubic */
    mp_number max_coef;                    /* used while scaling */
    mp_number ss;
    mp_number x0, x1, x2, y0, y1, y2;      /* representatives of derivatives */
    mp_number t0, t1, t2;                  /* coefficients of polynomial for slope testing */
    mp_number du, dv, dx, dy;              /* for directions of the pen and the curve */
    mp_number dx0, dy0;                    /* initial direction for the first cubic in the curve */
    mp_number x0a, x1a,x2a, y0a, y1a, y2a; /* intermediate values */
    mp_number t;                           /* where the derivative passes through zero */
    mp_number s;                           /* a temporary value */
    mp_number dx_m;                        /* signal a pertubation of dx */
    mp_number dy_m;                        /* signal a pertubation of dx */
    mp_number dxin_m;                      /* signal a pertubation of dxin */
    mp_number u0, u1, v0, v1;              /* intermediate values for $d(t)$ calculation */
    int d_sign;                            /* sign of overall change in direction for this cubic */
    new_number(max_coef);
    new_number(dxin);
    new_number(dyin);
    new_number(dx0);
    new_number(dy0);
    new_number(x0);
    new_number(y0);
    new_number(x1);
    new_number(y1);
    new_number(x2);
    new_number(y2);
    new_number(du);
    new_number(dv);
    new_number(dx);
    new_number(dy);
    new_number(x0a);
    new_number(y0a);
    new_number(x1a);
    new_number(y1a);
    new_number(x2a);
    new_number(y2a);
    new_number(t0);
    new_number(t1);
    new_number(t2);
    new_number(u0);
    new_number(u1);
    new_number(v0);
    new_number(v1);
    new_number(dx_m);
    new_number(dy_m);
    new_number(dxin_m);
    new_fraction(ss);
    new_fraction(s);
    new_fraction(t);
    @<Initialize the pen size~|n|@>
    @<Initialize the incoming direction and pen offset at |c|@>
    p = c;
    c0 = c;
    k_needed = 0;
     do {
        q = mp_next_knot(p);
        @<Split the cubic between |p| and |q|, if necessary, into cubics associated with single offsets, after which |q| should point to the end of the final such cubic@>
      NOT_FOUND:
        @<Advance |p| to node |q|, removing any \quote {dead} cubics that might have been introduced by the splitting process@>
    } while (q != c);
    @<Fix the offset change in |mp_knot_info(c)| and set |c| to the return value of |offset_prep|@>
    free_number(ss);
    free_number(s);
    free_number(dxin);
    free_number(dyin);
    free_number(dx0);
    free_number(dy0);
    free_number(x0);
    free_number(y0);
    free_number(x1);
    free_number(y1);
    free_number(x2);
    free_number(y2);
    free_number(max_coef);
    free_number(du);
    free_number(dv);
    free_number(dx);
    free_number(dy);
    free_number(x0a);
    free_number(y0a);
    free_number(x1a);
    free_number(y1a);
    free_number(x2a);
    free_number(y2a);
    free_number(t0);
    free_number(t1);
    free_number(t2);
    free_number(u0);
    free_number(u1);
    free_number(v0);
    free_number(v1);
    free_number(dx_m);
    free_number(dy_m);
    free_number(dxin_m);
    free_number(t);
    return c;
}

@ We shall want to keep track of where certain knots on the cyclic path wind up
in the envelope spec. It doesn't suffice just to keep pointers to knot nodes
because some nodes are deleted while removing dead cubics. Thus |offset_prep|
updates the following pointers

@<Glob...@>=
mp_knot spec_p1;
mp_knot spec_p2; /* pointers to distinguished knots */

@ @<Set init...@>=
mp->spec_p1 = NULL;
mp->spec_p2 = NULL;

@ @<Initialize the pen size~|n|@>=
n = 0;
p = h;
do {
    ++n;
    p = mp_next_knot(p);
} while (p != h);

@ Since the true incoming direction isn't known yet, we just pick a direction
consistent with the pen offset~|h|. If this is wrong, it can be corrected later.

@<Initialize the incoming direction and pen offset at |c|@>=
{
    mp_knot hn = mp_next_knot(h);
    mp_knot hp = mp_prev_knot(h);
    set_number_from_subtraction(dxin, hn->x_coord, hp->x_coord);
    set_number_from_subtraction(dyin, hn->y_coord, hp->y_coord);
    if (number_zero(dxin) && number_zero(dyin)) {
        set_number_from_subtraction(dxin, hp->y_coord, h->y_coord);
        set_number_from_subtraction(dyin, h->x_coord, hp->x_coord);
    }
}
w0 = h;

@ We must be careful not to remove the only cubic in a cycle.

But we must also be careful for another reason. If the user-supplied path starts
with a set of degenerate cubics, the target node |q| can be collapsed to the
initial node |p| which might be the same as the initial node |c| of the curve.
This would cause the |offset_prep| routine to bail out too early, causing
distress later on. (See for example the testcase reported by Bogus||aw
Jackowski in tracker id 267, case 52c on Sarovar.)

@<Advance |p| to node |q|, removing any \quote {dead} cubics...@>=
q0 = q;
do {
    r = mp_next_knot(p);
    if (r != p && r != q
     && number_equal(p->x_coord, p->right_x)
     && number_equal(p->y_coord, p->right_y)
     && number_equal(p->x_coord, r->left_x)
     && number_equal(p->y_coord, r->left_y)
     && number_equal(p->x_coord, r->x_coord)
     && number_equal(p->y_coord, r->y_coord)) {
        @<Remove the cubic following |p| and update the data structures to merge |r| into |p|@>
    }
    p = r;
} while (p != q);
/* Check if we removed too much */
if ((q != q0) && (q != c || c == c0)) {
    q = mp_next_knot(q);
}

@ @<Remove the cubic following |p| and update the data structures...@>=
{
    k_needed = mp_knot_info(p) - zero_off;
    if (r == q) {
        q = p;
    } else {
        mp_knot_info(p) = k_needed + mp_knot_info(r);
        k_needed = 0;
    }
    if (r == c) {
        mp_knot_info(p) = mp_knot_info(c);
        c = p;
    }
    if (r == mp->spec_p1) {
        mp->spec_p1 = p;
    }
    if (r == mp->spec_p2) {
        mp->spec_p2 = p;
    }
    r = p;
    mp_remove_cubic(mp, p);
}

@ Not setting the |info| field of the newly created knot allows the splitting
routine to work for paths.

@<Declarations@>=
static void    mp_split_cubic      (MP mp, mp_knot p, mp_number *t);
static mp_knot mp_split_cubic_knot (MP mp, mp_knot p, mp_number *t);

@ @c
void mp_split_cubic (MP mp, mp_knot p, mp_number *t)
{
    /* splits the cubic after |p| */
    mp_number v;  /* an intermediate value */
    mp_knot q = mp_next_knot(p);
    mp_knot r = mp_new_knot(mp);
    mp_prev_knot(r) = p;
    mp_next_knot(p) = r;
    mp_prev_knot(q) = r;
    mp_next_knot(r) = q;
    mp_originator(r) = mp_program_code;
    mp_knotstate(r) = mp_regular_knot;
    mp_left_type(r) = mp_explicit_knot;
    mp_right_type(r) = mp_explicit_knot;
    new_number(v);
    set_number_from_of_the_way(v,          *t, p->right_x, q->left_x);
    set_number_from_of_the_way(p->right_x, *t, p->x_coord, p->right_x);
    set_number_from_of_the_way(q->left_x,  *t, q->left_x, q->x_coord);
    set_number_from_of_the_way(r->left_x,  *t, p->right_x, v);
    set_number_from_of_the_way(r->right_x, *t, v, q->left_x);
    set_number_from_of_the_way(r->x_coord, *t, r->left_x, r->right_x);
    set_number_from_of_the_way(v,          *t, p->right_y, q->left_y);
    set_number_from_of_the_way(p->right_y, *t, p->y_coord, p->right_y);
    set_number_from_of_the_way(q->left_y,  *t, q->left_y, q->y_coord);
    set_number_from_of_the_way(r->left_y,  *t, p->right_y, v);
    set_number_from_of_the_way(r->right_y, *t, v, q->left_y);
    set_number_from_of_the_way(r->y_coord, *t, r->left_y, r->right_y);
    free_number(v);
}

static mp_knot mp_split_cubic_knot (MP mp, mp_knot p, mp_number *t) /* can be less as we only need x y */
{
    mp_number v;
    mp_knot k = mp_new_knot(mp);
    mp_knot r = mp_copy_knot(mp, mp_next_knot(p));
    mp_knot l = mp_copy_knot(mp, p);
    mp_originator(k) = mp_program_code;
    mp_knotstate(k) = mp_regular_knot;
    mp_left_type(k) = mp_explicit_knot;
    mp_right_type(k) = mp_explicit_knot;
    new_number(v);
    set_number_from_of_the_way(v,          *t, l->right_x, r->left_x);
    set_number_from_of_the_way(l->right_x, *t, l->x_coord, l->right_x);
    set_number_from_of_the_way(r->left_x,  *t, r->left_x, r->x_coord);
    set_number_from_of_the_way(k->left_x,  *t, l->right_x, v);
    set_number_from_of_the_way(k->right_x, *t, v, r->left_x);
    set_number_from_of_the_way(k->x_coord, *t, k->left_x, k->right_x);
    set_number_from_of_the_way(v,          *t, l->right_y, r->left_y);
    set_number_from_of_the_way(l->right_y, *t, l->y_coord, l->right_y);
    set_number_from_of_the_way(r->left_y,  *t, r->left_y, r->y_coord);
    set_number_from_of_the_way(k->left_y,  *t, l->right_y, v);
    set_number_from_of_the_way(k->right_y, *t, v, r->left_y);
    set_number_from_of_the_way(k->y_coord, *t, k->left_y, k->right_y);
    free_number(v);
    mp_toss_knot(mp, l);
    mp_toss_knot(mp, r);
    return k;
}

@ This does not set |mp_knot_info(p)| or |mp_right_type(p)|.

@<Declarations@>=
static void mp_remove_cubic (MP mp, mp_knot p);

@ @c
void mp_remove_cubic (MP mp, mp_knot p)
{
    /* removes the dead cubic following~|p| */
    mp_knot q = mp_next_knot(p); /* the node that disappears */
    mp_prev_knot(q) = mp_next_knot(p);
    mp_next_knot(p) = mp_next_knot(q);
    number_clone(p->right_x, q->right_x);
    number_clone(p->right_y, q->right_y);
    /* was: mp_memory_free(q); */
    mp_toss_knot(mp, q);
}

@ Let $d\prec d'$ mean that the counter-clockwise angle from $d$ to~$d'$ is
strictly between zero and $180^\circ$. Then we can define $d\preceq d'$ to mean
that the angle could be zero or $180^\circ$. If $w_k=(u_k,v_k)$ is the $k$th pen
offset, the $k$th pen edge direction is defined by the formula
$$d_k=(u\k-u_k,\,v\k-v_k).$$ When listed by increasing $k$, these directions
occur in counter-clockwise order so that $d_k\preceq d\k$ for all~$k$. The goal
of |offset_prep| is to find an offset index~|k| to associate with each cubic,
such that the direction $d(t)$ of the cubic satisfies $$d_{k-1}\preceq
d(t)\preceq d_k\qquad\hbox{for $0\le t\le 1$.}\eqno(*)$$ We may have to split a
cubic into many pieces before each piece corresponds to a unique offset.

@<Split the cubic between |p| and |q|, if necessary, into cubics...@>=
mp_knot_info(p) = zero_off + k_needed;
k_needed = 0;
@<Prepare for derivative computations; |goto not_found| if the current cubic is dead@>
@<Find the initial direction |(dx,dy)|@>
@<Update |mp_knot_info(p)| and find the offset $w_k$ such that $d_{k-1}\preceq(|dx|,|dy|)\prec d_k$; also advance |w0| for the direction change at |p|@>
@<Find the final direction |(dxin,dyin)|@>
@<Decide on the net change in pen offsets and set |turn_amt|@>
@<Complete the offset splitting process@>
w0 = mp_pen_walk (mp, w0, turn_amt);

@ @<Declarations@>=
static mp_knot mp_pen_walk (MP mp, mp_knot w, int k);

@ @c
mp_knot mp_pen_walk (MP mp, mp_knot w, int k)
{
  /* walk |k| steps around a pen from |w| */
    (void) mp;
    while (k > 0) {
        w = mp_next_knot(w);
        --k;
    }
    while (k < 0) {
        w = mp_prev_knot(w);
        ++k;
    }
    return w;
}

@ The direction of a cubic $B(z_0,z_1,z_2,z_3;t)=\bigl(x(t),y(t)\bigr)$ can be
calculated from the quadratic polynomials
${1\over3}x'(t)=B(x_1-x_0,x_2-x_1,x_3-x_2;t)$ and
${1\over3}y'(t)=B(y_1-y_0,y_2-y_1,y_3-y_2;t)$.
Since we may be calculating directions from several cubics
split from the current one, it is desirable to do these calculations
without losing too much precision. \quote {Scaled up} values of the
derivatives, which will be less tainted by accumulated errors than
derivatives found from the cubics themselves, are maintained in
local variables |x0|, |x1|, and |x2|, representing $X_0=2^l(x_1-x_0)$,
$X_1=2^l(x_2-x_1)$, and $X_2=2^l(x_3-x_2)$; similarly |y0|, |y1|, and~|y2|
represent $Y_0=2^l(y_1-y_0)$, $Y_1=2^l(y_2-y_1)$, and $Y_2=2^l(y_3-y_2)$.

@ @<Prepare for derivative computations...@>=
set_number_from_subtraction(x0, p->right_x, p->x_coord);
set_number_from_subtraction(x2, q->x_coord, q->left_x);
set_number_from_subtraction(x1, q->left_x, p->right_x);
set_number_from_subtraction(y0, p->right_y, p->y_coord);
set_number_from_subtraction(y2, q->y_coord, q->left_y);
set_number_from_subtraction(y1, q->left_y, p->right_y);
{
	/* somewhat weird: these copies to absval */
    mp_number absval;
    new_number_abs(absval, x1);
    number_abs_clone(max_coef, x0);
    if (number_greater(absval, max_coef)) {
        number_clone(max_coef, absval);
    }
    number_abs_clone(absval, x2);
    if (number_greater(absval, max_coef)) {
        number_clone(max_coef, absval);
    }
    number_abs_clone(absval, y0);
    if (number_greater(absval, max_coef)) {
        number_clone(max_coef, absval);
    }
    number_abs_clone(absval, y1);
    if (number_greater(absval, max_coef)) {
        number_clone(max_coef, absval);
    }
    number_abs_clone(absval, y2);
    if (number_greater(absval, max_coef)) {
        number_clone(max_coef, absval);
    }
    free_number(absval);
    if (number_zero(max_coef)) {
        goto NOT_FOUND;
    }
}
while (number_less(max_coef, fraction_half_t)) {
    number_double(max_coef);
    number_double(x0);
    number_double(x1);
    number_double(x2);
    number_double(y0);
    number_double(y1);
    number_double(y2);
}

@ Let us first solve a special case of the problem: Suppose we know an index~$k$
such that either (i)~$d(t)\succeq d_{k-1}$ for all~$t$ and $d(0)\prec d_k$, or
(ii)~$d(t)\preceq d_k$ for all~$t$ and $d(0)\succ d_{k-1}$. Then, in a sense,
we're halfway done, since one of the two relations in $(*)$ is satisfied, and the
other couldn't be satisfied for any other value of~|k|. Actually, the conditions
can be relaxed somewhat since a relation such as

$d(t)\succeq d_{k-1}$ restricts $d(t)$ to a half plane when all that really
matters is whether $d(t)$ crosses the ray in the $d_{k-1}$ direction from the
origin. The condition for case~(i) becomes $d_{k-1}\preceq d(0)\prec d_k$ and
$d(t)$ never crosses the $d_{k-1}$ ray in the clockwise direction. Case~(ii) is
similar except $d(t)$ cannot cross the $d_k$ ray in the counterclockwise
direction.

The |fin_offset_prep| subroutine solves the stated subproblem. It has a parameter
called |rise| that is |1| in case~(i), |-1| in case~(ii). Parameters |x0| through
|y2| represent the derivative of the cubic following |p|. The |w| parameter
should point to offset~$w_k$ and |mp_info(p)| should already be set properly. The
|turn_amt| parameter gives the absolute value of the overall net change in pen
offsets.

@<Declarations@>=
static void mp_fin_offset_prep (MP mp, mp_knot p, mp_knot w, mp_number *x0, mp_number *x1, mp_number *x2, mp_number *y0, mp_number *y1, mp_number *y2, int rise, int turn_amt);

@ @c
void mp_fin_offset_prep (MP mp, mp_knot p, mp_knot w, mp_number *x0, mp_number *x1, mp_number *x2, mp_number *y0, mp_number *y1, mp_number *y2, int rise, int turn_amt)
{
    mp_number du, dv;     /* for slope calculation */
    mp_number t0, t1, t2; /* test coefficients */
    mp_number t;          /* place where the derivative passes a critical slope */
    mp_number s;          /* slope or reciprocal slope */
    mp_number v;          /* intermediate value for updating |x0..y2| */
    mp_knot q = mp_next_knot(p);
    new_number(du);
    new_number(dv);
    new_number(v);
    new_number(t0);
    new_number(t1);
    new_number(t2);
    new_fraction(s);
    new_fraction(t);
    while (1) {
        mp_knot ww = rise > 0 ? mp_next_knot(w) : mp_prev_knot(w);
        @<Compute (case 1) test coefficients |(t0,t1,t2)| for $d(t)$ versus $d_k$ or $d_{k-1}$@>
        crossing_point(t, t0, t1, t2);
        if (number_greaterequal(t, fraction_one_t)) {
            if (turn_amt > 0) {
                number_clone(t, fraction_one_t);
            } else {
                goto RETURN;
            }
        }
        @<Split the cubic at $t$, and split off another cubic if the derivative crosses back@>
        w = ww;
    }
  RETURN:
    free_number(s);
    free_number(t);
    free_number(du);
    free_number(dv);
    free_number(v);
    free_number(t0);
    free_number(t1);
    free_number(t2);
}

@ We want $B(|t0|,|t1|,|t2|;t)$ to be the dot product of $d(t)$ with a
$-90^\circ$ rotation of the vector from |w| to |ww|. This makes the resulting
function cross from positive to negative when $d_{k-1}\preceq d(t)\preceq d_k$
begins to fail.

@<Compute (case 1) test coefficients |(t0,t1,t2)| for $d(t)$ versus $d_k$ or $d_{k-1}$...@>=
{
    mp_number abs_du, abs_dv;
    new_number(abs_du);
    new_number(abs_dv);
    set_number_from_subtraction(du, ww->x_coord, w->x_coord);
    set_number_from_subtraction(dv, ww->y_coord, w->y_coord);
    number_abs_clone(abs_du, du);
    number_abs_clone(abs_dv, dv);
    if (number_greaterequal(abs_du, abs_dv)) {
        mp_number r1;
        new_fraction(r1);
        make_fraction(s, dv, du);
        take_fraction(r1, *x0, s);
        set_number_from_subtraction(t0, r1, *y0);
        take_fraction(r1, *x1, s);
        set_number_from_subtraction(t1, r1, *y1);
        take_fraction(r1, *x2, s);
        set_number_from_subtraction(t2, r1, *y2);
        if (number_negative(du)) {
            number_negate(t0);
            number_negate(t1);
            number_negate(t2);
        }
        free_number(r1);
    } else {
        mp_number r1;
        new_fraction(r1);
        make_fraction(s, du, dv);
        take_fraction(r1, *y0, s);
        set_number_from_subtraction(t0, *x0, r1);
        take_fraction(r1, *y1, s);
        set_number_from_subtraction(t1, *x1, r1);
        take_fraction(r1, *y2, s);
        set_number_from_subtraction(t2, *x2, r1);
        if (number_negative(dv)) {
            number_negate(t0);
            number_negate(t1);
            number_negate(t2);
        }
        free_number(r1);
    }
    free_number(abs_du);
    free_number(abs_dv);
    if (number_negative(t0)) {
        set_number_to_zero(t0); /* should be positive without rounding error */
    }
}

@ @<Compute (case 2) test coefficients |(t0,t1,t2)| for $d(t)$ versus $d_k$ or $d_{k-1}$...@>=
{
    mp_number abs_du, abs_dv;
    new_number(abs_du);
    new_number(abs_dv);
    set_number_from_subtraction(du, ww->x_coord, w->x_coord);
    set_number_from_subtraction(dv, ww->y_coord, w->y_coord);
    number_abs_clone(abs_du, du);
    number_abs_clone(abs_dv, dv);
    if (number_greaterequal(abs_du, abs_dv)) {
        mp_number r1;
        new_fraction(r1);
        make_fraction(s, dv, du);
        take_fraction(r1, x0, s);
        set_number_from_subtraction(t0, r1, y0);
        take_fraction(r1, x1, s);
        set_number_from_subtraction(t1, r1, y1);
        take_fraction(r1, x2, s);
        set_number_from_subtraction(t2, r1, y2);
        if (number_negative(du)) {
            number_negate(t0);
            number_negate(t1);
            number_negate(t2);
        }
        free_number(r1);
    } else {
        mp_number r1;
        new_fraction(r1);
        make_fraction(s, du, dv);
        take_fraction(r1, y0, s);
        set_number_from_subtraction(t0, x0, r1);
        take_fraction(r1, y1, s);
        set_number_from_subtraction(t1, x1, r1);
        take_fraction(r1, y2, s);
        set_number_from_subtraction(t2, x2, r1);
        if (number_negative(dv)) {
            number_negate(t0);
            number_negate(t1);
            number_negate(t2);
        }
        free_number(r1);
    }
    free_number(abs_du);
    free_number(abs_dv);
    if (number_negative(t0)) {
        set_number_to_zero(t0); /* should be positive without rounding error */
    }
}

@ The curve has crossed $d_k$ or $d_{k-1}$; its initial segment satisfies $(*)$,
and it might cross again and return towards $s_{k-1}$ or $s_k$, respectively,
yielding another solution of $(*)$.

@<Split the cubic at $t$, and split off another...@>=
{
    mp_split_cubic(mp, p, &t);
    p = mp_next_knot(p);
    mp_knot_info(p) = zero_off + rise;
    --turn_amt;
    set_number_from_of_the_way(v, t, *x0, *x1);
    set_number_from_of_the_way(*x1, t, *x1, *x2);
    set_number_from_of_the_way(*x0, t, v, *x1);
    set_number_from_of_the_way(v, t, *y0, *y1);
    set_number_from_of_the_way(*y1, t, *y1, *y2);
    set_number_from_of_the_way(*y0, t, v, *y1);
    if (turn_amt < 0) {
        mp_number arg1, arg2, arg3;
        new_number(arg1);
        new_number(arg2);
        new_number(arg3);
        set_number_from_of_the_way(t1, t, t1, t2);
        if (number_positive(t1)) {
            set_number_to_zero(t1); /* without rounding error, |t1| would be |<=0| */
        }
        number_negated_clone(arg2, t1);
        number_negated_clone(arg3, t2);
        crossing_point(t, arg1, arg2, arg3); /* arg1 is zero */
        free_number(arg1);
        free_number(arg2);
        free_number(arg3);
        if (number_greater(t, fraction_one_t)) {
            number_clone(t, fraction_one_t);
        }
        ++turn_amt;
        if (number_equal(t,fraction_one_t) && (mp_next_knot(p) != q)) {
            mp_knot_info(mp_next_knot(p)) = mp_knot_info(mp_next_knot(p)) - rise;
        } else {
            mp_split_cubic(mp, p, &t);
            mp_knot_info(mp_next_knot(p)) = zero_off - rise;
            set_number_from_of_the_way(v, t, *x1, *x2);
            set_number_from_of_the_way(*x1, t, *x0, *x1);
            set_number_from_of_the_way(*x2, t, *x1, v);
            set_number_from_of_the_way(v, t, *y1, *y2);
            set_number_from_of_the_way(*y1, t, *y0, *y1);
            set_number_from_of_the_way(*y2, t, *y1, v);
        }
    }
}

@ Now we must consider the general problem of |offset_prep|, when nothing is
known about a given cubic. We start by finding its direction in the vicinity of
|t=0|.

If $z'(t)=0$, the given cubic is numerically unstable but |offset_prep| has not
yet introduced any more numerical errors. Thus we can compute the true initial
direction for the given cubic, even if it is almost degenerate.

@<Find the initial direction |(dx,dy)|@>=
number_clone(dx_m, zero_t);
number_clone(dy_m, zero_t);
/* todo: just if else and test before assignment */
number_clone(dx, x0);
number_clone(dy, y0);
if (number_zero(dx) && number_zero(dy)) {
    number_clone(dx, x1);
    number_clone(dy, y1);
    if (number_zero(dx) && number_zero(dy)) {
        number_clone(dx, x2);
        number_clone(dy, y2);
    }
}
if (p == c) {
    number_clone(dx0, dx);
    number_clone(dy0, dy);
}

@ @<Find the final direction |(dxin,dyin)|@>=
number_clone(dxin, x2);
number_clone(dyin, y2);
if (number_zero(dxin) && number_zero(dyin)) {
    number_clone(dxin, x1);
    number_clone(dyin, y1);
    if (number_zero(dxin) && number_zero(dyin)) {
        number_clone(dxin, x0);
        number_clone(dyin, y0);
    }
}

@ The next step is to bracket the initial direction between consecutive edges of
the pen polygon. We must be careful to turn clockwise only if this makes the turn
less than $180^\circ$. (A $180^\circ$ turn must be counter-clockwise in order to
make |doublepath| envelopes come out @:double_path_}{|doublepath| primitive@>
right.) This code depends on |w0| being the offset for |(dxin,dyin)|.

@<Update |mp_knot_info(p)| and find the offset $w_k$ such that...@>=
{
    turn_amt = mp_get_turn_amt(mp, w0, &dx, &dy, ab_vs_cd(dy, dxin, dx, dyin) >= 0);
    w = mp_pen_walk(mp, w0, turn_amt);
    w0 = w;
    mp_knot_info(p) = mp_knot_info(p) + turn_amt;
}

@ Decide how many pen offsets to go away from |w| in order to find the offset for
|(dx,dy)|, going counterclockwise if |ccw| is |true|. This assumes that |w| is
the offset for some direction $(x',y')$ from which the angle to |(dx,dy)| in the
sense determined by |ccw| is less than or equal to $180^\circ$.

If the pen polygon has only two edges, they could both be parallel to |(dx,dy)|.
In this case, we must be careful to stop after crossing the first such edge in
order to avoid an infinite loop.

@<Declarations@>=
static int mp_get_turn_amt (MP mp, mp_knot w, mp_number *dx, mp_number *dy, int ccw);

@ @c
int mp_get_turn_amt (MP mp, mp_knot w, mp_number *dx, mp_number *dy, int ccw)
{
    int s = 0;      /* turn amount so far */
    mp_number arg1, arg2;
    new_number(arg1);
    new_number(arg2);
    if (ccw) {
        int t;
        mp_knot ww = mp_next_knot(w);
        do {
            set_number_from_subtraction(arg1, ww->x_coord, w->x_coord);
            set_number_from_subtraction(arg2, ww->y_coord, w->y_coord);
            t = ab_vs_cd(*dy, arg1, *dx, arg2);
            if (t < 0) {
                break;
            } else {
                ++s;
                w = ww;
                ww = mp_next_knot(ww);
            }
        } while (t > 0);
    } else {
        mp_knot ww = mp_prev_knot(w);
        set_number_from_subtraction(arg1, w->x_coord, ww->x_coord);
        set_number_from_subtraction(arg2, w->y_coord, ww->y_coord);
        while (ab_vs_cd(*dy, arg1, *dx, arg2) < 0) {
            --s;
            w = ww;
            ww = mp_prev_knot(ww);
            set_number_from_subtraction(arg1, w->x_coord, ww->x_coord);
            set_number_from_subtraction(arg2, w->y_coord, ww->y_coord);
        }
    }
    free_number(arg1);
    free_number(arg2);
    return s;
}

@ When we're all done, the final offset is |w0| and the final curve direction is
|(dxin,dyin)|. With this knowledge of the incoming direction at |c|, we can
correct |mp_info(c)| which was erroneously based on an incoming offset of~|h|.

@<Fix the offset change in |mp_knot_info(c)| and set |c| to the return value of...@>=
mp->spec_offset = mp_knot_info(c) - zero_off;
if (mp_next_knot(c) == c) {
    mp_knot_info(c) = zero_off + n;
} else {
    mp_knot_info(c) += k_needed;
    while (w0 != h) {
        mp_knot_info(c) += 1;
        w0 = mp_next_knot(w0);
    }
    while (mp_knot_info(c) <= zero_off - n) {
        mp_knot_info(c) += n;
    }
    while (mp_knot_info(c) > zero_off) {
        mp_knot_info(c) -= n;
    }
    ;
    if ((mp_knot_info(c) != zero_off) && ab_vs_cd(dy0, dxin, dx0, dyin) >= 0) {
        mp_knot_info(c) += n;
    }
}

@ Finally we want to reduce the general problem to situations that
|fin_offset_prep| can handle. We split the cubic into at most three parts with
respect to $d_{k-1}$, and apply |fin_offset_prep| to each part.

@<Complete the offset splitting process@>=
ww = mp_prev_knot(w);
@<Compute (case 2) test coefficients |(t0,t1,t2)| for $d(t)$ versus $d_k$ or $d_{k-1}$@>
@<Find the first |t| where $d(t)$ crosses $d_{k-1}$ or set |t:=fraction_one+1|@>
if (number_greater(t, fraction_one_t)) {
    mp_fin_offset_prep(mp, p, w, &x0, &x1, &x2, &y0, &y1, &y2, 1, turn_amt);
} else {
    mp_split_cubic(mp, p, &t);
    r = mp_next_knot(p);
    set_number_from_of_the_way(x1a, t, x0, x1);
    set_number_from_of_the_way(x1, t, x1, x2);
    set_number_from_of_the_way(x2a, t, x1a, x1);
    set_number_from_of_the_way(y1a, t, y0, y1);
    set_number_from_of_the_way(y1, t, y1, y2);
    set_number_from_of_the_way(y2a, t, y1a, y1);
    mp_fin_offset_prep (mp, p, w, &x0, &x1a, &x2a, &y0, &y1a, &y2a, 1, 0);
    number_clone(x0, x2a);
    number_clone(y0, y2a);
    mp_knot_info(r) = zero_off - 1;
    if (turn_amt >= 0) {
        mp_number arg1, arg2, arg3;
        new_number(arg1);
        new_number(arg2);
        new_number(arg3);
        set_number_from_of_the_way(t1, t, t1, t2);
        if (number_positive(t1)) {
            set_number_to_zero(t1);
        }
        number_negated_clone(arg2, t1);
        number_negated_clone(arg3, t2);
        crossing_point(t, arg1, arg2, arg3);
        free_number(arg1);
        free_number(arg2);
        free_number(arg3);
        if (number_greater(t, fraction_one_t)) {
            number_clone(t, fraction_one_t);
        }
        @<Split off another rising cubic for |fin_offset_prep|@>
        mp_fin_offset_prep(mp, r, ww, &x0, &x1, &x2, &y0, &y1, &y2, -1, 0);
    } else {
        mp_fin_offset_prep(mp, r, ww, &x0, &x1, &x2, &y0, &y1, &y2, -1, (-1 - turn_amt));
    }
}

@ @<Split off another rising cubic for |fin_offset_prep|@>=
mp_split_cubic(mp, r, &t);
mp_knot_info(mp_next_knot(r)) = zero_off + 1;
set_number_from_of_the_way(x1a, t, x1, x2);
set_number_from_of_the_way(x1,  t, x0, x1);
set_number_from_of_the_way(x0a, t, x1, x1a);
set_number_from_of_the_way(y1a, t, y1, y2);
set_number_from_of_the_way(y1,  t, y0, y1);
set_number_from_of_the_way(y0a, t, y1, y1a);
mp_fin_offset_prep (mp, mp_next_knot(r), w, &x0a, &x1a, &x2, &y0a, &y1a, &y2, 1, turn_amt);
number_clone(x2, x0a);
number_clone(y2, y0a);

@ At this point, the direction of the incoming pen edge is |(-du,-dv)|. When the
component of $d(t)$ perpendicular to |(-du,-dv)| crosses zero, we need to decide
whether the directions are parallel or antiparallel. We can test this by finding
the dot product of $d(t)$ and |(-du,-dv)|, but this should be avoided when the
value of |turn_amt| already determines the answer. If |t2<0|, there is one
crossing and it is antiparallel only if |turn_amt>=0|. If |turn_amt<0|, there
should always be at least one crossing and the first crossing cannot be
antiparallel.

@<Find the first |t| where $d(t)$ crosses $d_{k-1}$ or set...@>=
crossing_point(t, t0, t1, t2);
if (turn_amt >= 0) {
    if (number_negative(t2)) {
        number_clone(t, fraction_one_t);
        number_add_scaled(t, 1);
    } else {
        mp_number tmp, arg1, r1;
        new_fraction(r1);
        new_number(tmp);
        new_number(arg1);
        set_number_from_of_the_way(u0, t, x0, x1);
        set_number_from_of_the_way(u1, t, x1, x2);
        set_number_from_of_the_way(tmp, t, u0, u1);
        number_negated_clone(arg1, du);
        take_fraction(ss, arg1, tmp);
        set_number_from_of_the_way(v0, t, y0, y1);
        set_number_from_of_the_way(v1, t, y1, y2);
        set_number_from_of_the_way(tmp, t, v0, v1);
        number_negated_clone(arg1, dv);
        take_fraction(r1, arg1, tmp);
        number_add(ss, r1);
        free_number(tmp);
        if (number_negative(ss)) {
            number_clone(t, fraction_one_t);
            number_add_scaled(t, 1);
        }
        free_number(arg1);
        free_number(r1);
    }
} else if (number_greater(t, fraction_one_t)) {
    number_clone(t, fraction_one_t);
}

@ If the cubic almost has a cusp, it is a numerically ill-conditioned problem to
decide which way it loops around but that's OK as long we're consistent. To make
|doublepath| envelopes work properly, reversing the path should always change
the sign of |turn_amt|.

@<Decide on the net change in pen offsets and set |turn_amt|@>=
{
    int sign = ab_vs_cd(dx, dyin, dxin, dy);
    if (sign < 0) {
        d_sign = -1;
    } else if (sign == 0) {
        d_sign = 0;
    } else {
        d_sign = 1;
    }
}
if (d_sign == 0) {
    @<Check rotation direction based on node position@>
}
if (d_sign == 0) {
    if (number_zero(dx)) {
        d_sign = number_positive(dy) ? 1 : -1;
    } else {
        d_sign = number_positive(dx) ? 1 : -1;
    }
}
@<Make |ss| negative if and only if the total change in direction is more than $180^\circ$@>
turn_amt = mp_get_turn_amt(mp, w, &dxin, &dyin, (d_sign > 0));
if (number_negative(ss)) {
    turn_amt = turn_amt - d_sign * n;
}

@ We check rotation direction by looking at the vector connecting the current
node with the next. If its angle with incoming and outgoing tangents has the same
sign, we pick this as |d_sign|, since it means we have a flex, not a cusp.
Otherwise we proceed to the cusp code.

@<Check rotation direction based on node position@>=
{
    int t;
    set_number_from_subtraction(u0, q->x_coord, p->x_coord);
    set_number_from_subtraction(u1, q->y_coord, p->y_coord);
    t = ab_vs_cd(dx, u1, u0, dy) + ab_vs_cd(u0, dyin, dxin, u1);
 //   number_half(t);
    if (t < 0) {
        d_sign = -1;
    } else if (t == 0) {
        d_sign = 0;
    } else {
        d_sign = 1;
    }
}

@ In order to be invariant under path reversal, the result of this computation
should not change when |x0|, |y0|, $\ldots$ are all negated and |(x0,y0)| is then
swapped with |(x2,y2)|. We make use of the identities |take_fraction(-a,-b) =
take_fraction(a,b)| and |t_of_the_way(-a,-b) = - (t_of_the_way(a,b))|.

@<Make |ss| negative if and only if the total change in direction is...@>=
{
    mp_number r1, r2, arg1;
    new_number(arg1);
    new_fraction(r1);
    new_fraction(r2);
    take_fraction(r1, x0, y2);
    take_fraction(r2, x2, y0);
    number_half(r1);
    number_half(r2);
    set_number_from_subtraction(t0, r1, r2);
    set_number_from_addition(arg1, y0, y2);
    take_fraction(r1, x1, arg1);
    set_number_from_addition(arg1, x0, x2);
    /*|take_fraction(r1, y1, arg1);|*//* The old one, is it correct ?*/
    take_fraction(r2, y1, arg1);
    number_half(r1);
    number_half(r2);
    set_number_from_subtraction(t1, r1, r2);
    free_number(arg1);
    free_number(r1);
    free_number(r2);
}
if (number_zero(t0)) {
    set_number_from_scaled(t0, d_sign); /* path reversal always negates |d_sign| */
}
if (number_positive(t0)) {
    mp_number arg3;
    new_number(arg3);
    number_negated_clone(arg3, t0);
    crossing_point(t, t0, t1, arg3);
    free_number(arg3);
    set_number_from_of_the_way(u0, t, x0, x1);
    set_number_from_of_the_way(u1, t, x1, x2);
    set_number_from_of_the_way(v0, t, y0, y1);
    set_number_from_of_the_way(v1, t, y1, y2);
} else {
    mp_number arg1;
    new_number(arg1);
    number_negated_clone(arg1, t0);
    crossing_point(t, arg1, t1, t0);
    free_number(arg1);
    set_number_from_of_the_way(u0, t, x2, x1);
    set_number_from_of_the_way(u1, t, x1, x0);
    set_number_from_of_the_way(v0, t, y2, y1);
    set_number_from_of_the_way(v1, t, y1, y0);
}
{
    mp_number tmp1, tmp2, r1, r2, arg1;
    new_fraction(r1);
    new_fraction(r2);
    new_number(arg1);
    new_number(tmp1);
    new_number(tmp2);
    set_number_from_of_the_way(tmp1, t, u0, u1);
    set_number_from_of_the_way(tmp2, t, v0, v1);
    set_number_from_addition(arg1, x0, x2);
    take_fraction(r1, arg1, tmp1);
    set_number_from_addition(arg1, y0, y2);
    take_fraction(r2, arg1, tmp2);
    set_number_from_addition(ss, r1, r2);
    free_number(arg1);
    free_number(r1);
    free_number(r2);
    free_number(tmp1);
    free_number(tmp2);
}

@ Here's a routine that prints an envelope spec in symbolic form. It assumes that
the |cur_pen| has not been walked around to the first offset.

@c
static void mp_print_spec (MP mp, mp_knot cur_spec, mp_knot cur_pen, const char *s)
{
    mp_knot w;            /* the current pen offset */
    mp_knot p = cur_spec; /* list traversal */
    mp_print_diagnostic(mp, "Envelope spec", s, 1);
    w = mp_pen_walk(mp, cur_pen, mp->spec_offset);
    mp_print_ln(mp);
    mp_print_two(mp, &(cur_spec->x_coord), &(cur_spec->y_coord));
    mp_print_str(mp, " % beginning with offset ");
    mp_print_two(mp, &(w->x_coord), &(w->y_coord));
    do {
        while (1) {
            mp_knot q = mp_next_knot(p);
            @<Print the cubic between |p| and |q|@>
            p = q;
            if ((p == cur_spec) || (mp_knot_info(p) != zero_off)) {
                break;
            }
        }
        if (mp_knot_info(p) != zero_off) {
            @<Update |w| as indicated by |mp_knot_info(p)| and print an explanation@>
        }
    } while (p != cur_spec);
    mp_print_nl(mp, " & cycle");
    mp_end_diagnostic(mp, 1);
}

@ @<Update |w| as indicated by |mp_knot_info(p)| and print an explanation@>=
w = mp_pen_walk (mp, w, (mp_knot_info(p) - zero_off));
mp_print_str(mp, " % ");
if (mp_knot_info(p) > zero_off) {
    mp_print_str(mp, "counter");
}
mp_print_str(mp, "clockwise to offset ");
mp_print_two(mp, &(w->x_coord), &(w->y_coord));

@ @<Print the cubic between |p| and |q|@>=
mp_print_nl(mp, " .. controls ");
mp_print_two(mp, &(p->right_x), &(p->right_y));
mp_print_str(mp, " and ");
mp_print_two(mp, &(q->left_x), &(q->left_y));
mp_print_nl(mp, " .. ");
mp_print_two(mp, &(q->x_coord), &(q->y_coord));

@ Once we have an envelope spec, the remaining task to construct the actual
envelope by offsetting each cubic as determined by the |info| fields in the
knots. First we use |offset_prep| to convert the |c| into an envelope spec. Then
we add the offsets so that |c| becomes a cyclic path that represents the
envelope.

The |linejoin| and |miterlimit| parameters control the treatment of points where the
pen offset changes, and |linecap| controls the endpoints of a |doublepath|. The
endpoints are easily located because |c| is given in undoubled form and then
doubled in this procedure. We use |spec_p1| and |spec_p2| to keep track of the
endpoints and treat them like very sharp corners. Butt end caps are treated like
beveled joins; round end caps are treated like round joins; and square end caps
are achieved by setting |join_type:=3|.

None of these parameters apply to inside joins where the convolution tracing has
retrograde lines. In such cases we use a simple connect-the-endpoints approach
that is achieved by setting |join_type:=2|.

@c
static mp_knot mp_make_envelope (MP mp, mp_knot c, mp_knot h, int linejoin, int linecap, mp_number *miterlimit)
{
    mp_knot p, q, r, q0; /* for manipulating the path */
    mp_knot w, w0;       /* the pen knot for the current offset */
    int k, k0;           /* controls pen edge insertion */
    mp_number qx, qy;    /* unshifted coordinates of |q| */
    mp_fraction dxin, dyin, dxout, dyout; /* directions at |q| when square or mitered */
    int join_type = 0;   /* codes |0..3| for mitered, round, beveled, or square */
    @<Other local variables for |make_envelope|@>
    new_number(max_ht);
    new_number(tmp);
    new_fraction(dxin);
    new_fraction(dyin);
    new_fraction(dxout);
    new_fraction(dyout);
    mp->spec_p1 = NULL;
    mp->spec_p2 = NULL;
    new_number(qx);
    new_number(qy);
    @<If endpoint, double the path |c|, and set |spec_p1| and |spec_p2|@>
    @<Use |offset_prep| to compute the envelope spec then walk |h| around to the initial offset@>
    w = h;
    p = c;
    do {
        q = mp_next_knot(p);
        q0 = q;
        number_clone(qx, q->x_coord);
        number_clone(qy, q->y_coord);
        k = mp_knot_info(q);
        k0 = k;
        w0 = w;
        if (k != zero_off) {
            @<Set |join_type| to indicate how to handle offset changes at~|q|@>
        }
        @<Add offset |w| to the cubic from |p| to |q|@>
        while (k != zero_off) {
            @<Step |w| and move |k| one step closer to |zero_off|@>
            if ((join_type == 1) || (k == zero_off)) {
                mp_number xtot, ytot;
                new_number(xtot);
                new_number(ytot);
                set_number_from_addition(xtot, qx, w->x_coord);
                set_number_from_addition(ytot, qy, w->y_coord);
                q = mp_insert_knot(mp, q, &xtot, &ytot);
                free_number(xtot);
                free_number(ytot);
            }
        }
        if (q != mp_next_knot(p)) {
            @<Set |p=mp_link(p)| and add knots between |p| and |q| as required by |join_type|@>
        }
        p = q;
    } while (q0 != c);
    free_number(max_ht);
    free_number(tmp);
    free_number(qx);
    free_number(qy);
    free_number(dxin);
    free_number(dyin);
    free_number(dxout);
    free_number(dyout);
    return c;
}

@ @<Use |offset_prep| to compute the envelope spec then walk |h| around to...@>=
c = mp_offset_prep (mp, c, h);
if (number_positive(internal_value(mp_tracing_specs_internal))) {
    mp_print_spec(mp, c, h, "");
}
h = mp_pen_walk (mp, h, mp->spec_offset);

@ Mitered and squared-off joins depend on path directions that are difficult to
compute for degenerate cubics. The envelope spec computed by |offset_prep| can
have degenerate cubics only if the entire cycle collapses to a single degenerate
cubic. Setting |join_type:=2| in this case makes the computed envelope degenerate
as well.

@<Set |join_type| to indicate how to handle offset changes at~|q|@>=
if (k < zero_off) {
    join_type = 2; /* mp_beveled_linejoin_code */
} else {
    if ((q != mp->spec_p1) && (q != mp->spec_p2)) {
        join_type = linejoin;
    } else if (linecap == mp_squared_linecap_code) {
        join_type = 3; /*  mp_weird_linejoin_code */
    } else {
        join_type = 2 - linecap; /* mp_beveled_linejoin_code - linecap */
    }
    if ((join_type == 0) || (join_type == 3)) { /* mp_mitered_linejoin_code || mp_weird_linejoin_code */
        @<Set the incoming and outgoing directions at |q|; in case of degeneracy set |join_type:=2|@>
        if (join_type == 0) { /* mp_mitered_linejoin_code */
            @<If |miterlimit| is less than the secant of half the angle at |q| then set |join_type:=2|@>
        }
    }
}

@ @<If |miterlimit| is less than the secant of half the angle at |q|...@>=
mp_number r1, r2;
new_fraction(r1);
new_fraction(r2);
take_fraction(r1, dxin, dxout);
take_fraction(r2, dyin, dyout);
number_add(r1, r2);
number_half(r1);
number_add(r1, fraction_half_t);
take_fraction(tmp, *miterlimit, r1);
if (number_less(tmp, unity_t)) {
    mp_number ret;
    new_number(ret);
    take_scaled(ret, *miterlimit, tmp);
    if (number_less(ret, unity_t)) {
        join_type = 2;
    }
    free_number(ret);
}
free_number(r1);
free_number(r2);

@ @<Other local variables for |make_envelope|@>=
mp_number tmp; /* a temporary value */

@ The coordinates of |p| have already been shifted unless |p| is the first knot
in which case they get shifted at the very end.

@<Add offset |w| to the cubic from |p| to |q|@>=
number_add(p->right_x, w->x_coord);
number_add(p->right_y, w->y_coord);
number_add(q->left_x,  w->x_coord);
number_add(q->left_y,  w->y_coord);
number_add(q->x_coord, w->x_coord);
number_add(q->y_coord, w->y_coord);
mp_left_type(q) = mp_explicit_knot;
mp_right_type(q) = mp_explicit_knot;

@ @<Step |w| and move |k| one step closer to |zero_off|@>=
if (k > zero_off) {
    w = mp_next_knot(w);
    --k;
} else {
    w = mp_prev_knot(w);
    ++k;
}

@ The cubic from |q| to the new knot at |(x,y)| becomes a line segment and the
|mp_right_x| and |mp_right_y| fields of |r| are set from |q|. This is done in
case the cubic containing these control points is \quote {yet to be examined.}

@<Declarations@>=
static mp_knot mp_insert_knot (MP mp, mp_knot q, mp_number *x, mp_number *y);

@ @c
mp_knot mp_insert_knot (MP mp, mp_knot q, mp_number *x, mp_number *y)
{
    /* returns the inserted knot */
    mp_knot r = mp_new_knot(mp);
    mp_knot n = mp_next_knot(q);
    mp_next_knot(r) = n;
    mp_prev_knot(n) = r;
    mp_prev_knot(r) = q;
    mp_next_knot(q) = r;
    number_clone(r->right_x, q->right_x);
    number_clone(r->right_y, q->right_y);
    number_clone(r->x_coord, *x);
    number_clone(r->y_coord, *y);
    number_clone(q->right_x, q->x_coord);
    number_clone(q->right_y, q->y_coord);
    number_clone(r->left_x, r->x_coord);
    number_clone(r->left_y, r->y_coord);
    mp_left_type(r) = mp_explicit_knot;
    mp_right_type(r) = mp_explicit_knot;
    mp_originator(r) = mp_program_code;
    mp_knotstate(r) = mp_regular_knot;
    return r;
}

@ After setting |p:=mp_link(p)|, either |join_type=1| or |q=mp_link(p)|.

@<Set |p=mp_link(p)| and add knots between |p| and |q| as...@>=
p = mp_next_knot(p);
if ((join_type == 0) || (join_type == 3)) {
    if (join_type == 0) {
        @<Insert a new knot |r| between |p| and |q| as required for a mitered join@>
    } else {
        @<Make |r| the last of two knots inserted between |p| and |q| to form a squared join@>
    }
    if (r != NULL) {
        number_clone(r->right_x, r->x_coord);
        number_clone(r->right_y, r->y_coord);
    }
}

@ For very small angles, adding a knot is unnecessary and would cause numerical
problems, so we just set |r:=NULL| in that case.

@d near_zero_angle_k mp->math->md_near_zero_angle_t

@<Insert a new knot |r| between |p| and |q| as required for a mitered join@>=
mp_number det; /* a determinant used for mitered join calculations */
mp_number absdet;
mp_number r1, r2;
new_fraction(r1);
new_fraction(r2);
new_fraction(det);
new_fraction(absdet);
take_fraction(r1, dyout, dxin);
take_fraction(r2, dxout, dyin);
set_number_from_subtraction(det, r1, r2);
number_abs_clone(absdet, det);
if (number_less(absdet, near_zero_angle_k)) {
    r = NULL;                                     /* sine $<10^{-4}$ */
} else {
    mp_number xtot, ytot, xsub, ysub;
    new_fraction(xsub);
    new_fraction(ysub);
    new_number(xtot);
    new_number(ytot);
    set_number_from_subtraction(tmp, q->x_coord, p->x_coord);
    take_fraction(r1, tmp, dyout);
    set_number_from_subtraction(tmp, q->y_coord, p->y_coord);
    take_fraction(r2, tmp, dxout);
    set_number_from_subtraction(tmp, r1, r2);
    make_fraction(r1, tmp, det);
    number_clone(tmp, r1);
    take_fraction(xsub, tmp, dxin);
    take_fraction(ysub, tmp, dyin);
    set_number_from_addition(xtot, p->x_coord, xsub);
    set_number_from_addition(ytot, p->y_coord, ysub);
    r = mp_insert_knot(mp, p, &xtot, &ytot);
    free_number(xtot);
    free_number(ytot);
    free_number(xsub);
    free_number(ysub);
}
free_number(r1);
free_number(r2);
free_number(det);
free_number(absdet);

@ @<Make |r| the last of two knots inserted between |p| and |q| to form a...@>=
mp_number ht_x, ht_y;         /* perpendicular to the segment from |p| to |q| */
mp_number ht_x_abs, ht_y_abs; /* absolutes */
mp_number xtot, ytot, xsub, ysub;
new_fraction(xsub);
new_fraction(ysub);
new_number(xtot);
new_number(ytot);
new_fraction(ht_x);
new_fraction(ht_y);
new_fraction(ht_x_abs);
new_fraction(ht_y_abs);
set_number_from_subtraction(ht_x, w->y_coord, w0->y_coord);
set_number_from_subtraction(ht_y, w0->x_coord, w->x_coord);
number_abs_clone(ht_x_abs, ht_x);
number_abs_clone(ht_y_abs, ht_y);
while (number_less(ht_x_abs, fraction_half_t) && number_less(ht_y_abs, fraction_half_t)) {
    number_double(ht_x);
    number_double(ht_y);
    number_abs_clone(ht_x_abs, ht_x);
    number_abs_clone(ht_y_abs, ht_y);
}
@<Scan the pen polygon between |w0| and |w| and make |max_ht| the range dot product with |(ht_x,ht_y)|@>
{
    mp_number    r1 ,r2;
    new_fraction(r1);
    new_fraction(r2);
    take_fraction(r1, dxin, ht_x);
    take_fraction(r2, dyin, ht_y);
    number_add(r1, r2);
    make_fraction(tmp, max_ht, r1);
    free_number(r1);
    free_number(r2);
}
take_fraction(xsub, tmp, dxin);
take_fraction(ysub, tmp, dyin);
set_number_from_addition(xtot, p->x_coord, xsub);
set_number_from_addition(ytot, p->y_coord, ysub);
r = mp_insert_knot(mp, p, &xtot, &ytot);
{
    mp_number r1 ,r2;
    new_fraction(r1);
    new_fraction(r2);
    take_fraction(r1, dxout, ht_x);
    take_fraction(r2, dyout, ht_y);
    number_add(r1, r2);
    make_fraction(tmp, max_ht, r1);
    free_number(r1);
    free_number(r2);
}
take_fraction(xsub, tmp, dxout);
take_fraction(ysub, tmp, dyout);
set_number_from_addition(xtot, q->x_coord, xsub);
set_number_from_addition(ytot, q->y_coord, ysub);
r = mp_insert_knot(mp, r, &xtot, &ytot);
free_number(xsub);
free_number(ysub);
free_number(xtot);
free_number(ytot);
free_number(ht_x);
free_number(ht_y);
free_number(ht_x_abs);
free_number(ht_y_abs);

@ @<Other local variables for |make_envelope|@>=
mp_number max_ht; /* maximum height of the pen polygon above the |w0|-|w| line */
int kk;           /* keeps track of the pen vertices being scanned */
mp_knot ww;       /* the pen vertex being tested */

@ The dot product of the vector from |w0| to |ww| with |(ht_x,ht_y)| ranges
from zero to |max_ht|.

@<Scan the pen polygon between |w0| and |w| and make |max_ht| the range...@>=
set_number_to_zero(max_ht);
kk = zero_off;
ww = w;
while (1) {
    @<Step |ww| and move |kk| one step closer to |k0|@>
    if (kk == k0) {
        break;
    } else {
        mp_number r1, r2;
        new_fraction(r1);
        new_fraction(r2);
        set_number_from_subtraction(tmp, ww->x_coord, w0->x_coord);
        take_fraction(r1, tmp, ht_x);
        set_number_from_subtraction(tmp, ww->y_coord, w0->y_coord);
        take_fraction(r2, tmp, ht_y);
        set_number_from_addition(tmp, r1,    r2);
        free_number(r1);
        free_number(r2);
        if (number_greater(tmp, max_ht)) {
            number_clone(max_ht, tmp);
        }
    }
}

@ @<Step |ww| and move |kk| one step closer to |k0|@>=
if (kk > k0) {
    ww = mp_next_knot(ww);
    --kk;
} else {
    ww = mp_prev_knot(ww);
    ++kk;
}

@ @<If endpoint, double the path |c|, and set |spec_p1| and |spec_p2|@>=
if (mp_left_type(c) == mp_endpoint_knot) {
    mp->spec_p1 = mp_htap_ypoc(mp, c);
    mp->spec_p2 = mp->path_tail;
    mp_originator(mp->spec_p1) = mp_program_code;
    mp_knotstate(mp->spec_p1) = mp_regular_knot;
    mp_prev_knot(mp->spec_p1) = mp_next_knot(mp->spec_p2);
    mp_next_knot(mp->spec_p2) = mp_next_knot(mp->spec_p1);
    mp_prev_knot(c) = mp->spec_p1;
    mp_next_knot(mp->spec_p1) = c;
    mp_remove_cubic(mp, mp->spec_p1);
    c = mp->spec_p1;
    if (c != mp_next_knot(c)) {
        mp_originator(mp->spec_p2) = mp_program_code;
        mp_knotstate(mp->spec_p2) = mp_regular_knot;
        mp_remove_cubic(mp, mp->spec_p2);
    } else {
        @<Make |c| look like a cycle of length one@>
    }
}

@ @<Make |c| look like a cycle of length one@>=
mp_left_type(c) = mp_explicit_knot;
mp_right_type(c) = mp_explicit_knot;
number_clone(c->left_x, c->x_coord);
number_clone(c->left_y, c->y_coord);
number_clone(c->right_x, c->x_coord);
number_clone(c->right_y, c->y_coord);

@ In degenerate situations we might have to look at the knot preceding~|q|. That
knot is |p| but if |p<>c|, its coordinates have already been offset by |w|.

@<Set the incoming and outgoing directions at |q|; in case of...@>=
set_number_from_subtraction(dxin, q->x_coord, q->left_x);
set_number_from_subtraction(dyin, q->y_coord, q->left_y);
if (number_zero(dxin) && number_zero(dyin)) {
    set_number_from_subtraction(dxin, q->x_coord, p->right_x);
    set_number_from_subtraction(dyin, q->y_coord, p->right_y);
    if (number_zero(dxin) && number_zero(dyin)) {
        set_number_from_subtraction(dxin, q->x_coord, p->x_coord);
        set_number_from_subtraction(dyin, q->y_coord, p->y_coord);
        if (p != c) {
            /* the coordinates of |p| have been offset by |w| */
            number_add(dxin, w->x_coord);
            number_add(dyin, w->y_coord);
        }
    }
}
pyth_add(tmp, dxin, dyin);
if (number_zero(tmp)) {
    join_type = 2;
} else {
    mp_number r1;
    new_fraction(r1);
    make_fraction(r1, dxin, tmp);
    number_clone(dxin, r1);
    make_fraction(r1, dyin, tmp);
    number_clone(dyin, r1);
    free_number(r1);
    @<Set the outgoing direction at |q|@>
}

@ If |q=c| then the coordinates of |r| and the control points between |q| and~|r|
have already been offset by |h|.

@<Set the outgoing direction at |q|@>=
set_number_from_subtraction(dxout, q->right_x, q->x_coord);
set_number_from_subtraction(dyout, q->right_y, q->y_coord);
if (number_zero(dxout) && number_zero(dyout)) {
    r = mp_next_knot(q);
    set_number_from_subtraction(dxout, r->left_x, q->x_coord);
    set_number_from_subtraction(dyout, r->left_y, q->y_coord);
    if (number_zero(dxout) && number_zero(dyout)) {
        set_number_from_subtraction(dxout, r->x_coord, q->x_coord);
        set_number_from_subtraction(dyout, r->y_coord, q->y_coord);
    }
}
if (q == c) {
    number_subtract(dxout, h->x_coord);
    number_subtract(dyout, h->y_coord);
}
pyth_add(tmp, dxout, dyout);
if (number_zero(tmp)) {
    /* |mp_confusion(mp, "degenerate spec");| */
    @:this can't happen degerate spec}{\quad degenerate spec@>
    /*

        But apparently, it actually can happen. The test case is this:

          path p;
          linejoin := mitered;
          p:= (10,0)..(0,10)..(-10,0)..(0,-10)..cycle;
          addto currentpicture contour p withpen pensquare;

        The reason for failure here is the addition of |r != q| in revision
        1757 in \quote {Advance |p| to node |q|, removing any ``dead} cubics'',
        which itself was needed to fix a bug with disappearing knots in a
        path that was rotated exactly 45 degrees (luatex.org bug 530).
     */
} else {
    mp_number r1;
    new_fraction(r1);
    make_fraction(r1, dxout, tmp);
    number_clone(dxout, r1);
    make_fraction(r1, dyout, tmp);
    number_clone(dyout, r1);
    free_number(r1);
}

@* Direction and intersection times.

A path of length $n$ is defined parametrically by functions $x(t)$ and $y(t)$,
for |0<=t<=n|; we can regard $t$ as the \quote {time} at which the path reaches the
point $\bigl(x(t),y(t)\bigr)$. In this section of the program we shall consider
operations that determine special times associated with given paths: the first
time that a path travels in a given direction, and a pair of times at which two
paths cross each other.

@ Let's start with the easier task. The function |find_direction_time| is given a
direction |(x,y)| and a path starting at~|h|. If the path never travels in
direction |(x,y)|, the direction time will be~|-1|; otherwise it will be
nonnegative.

Certain anomalous cases can arise: If |(x,y)=(0,0)|, so that the given direction
is undefined, the direction time will be~0. If $\bigl(x'(t), y'(t)\bigr)=(0,0)$,
so that the path direction is undefined, it will be assumed to match any given
direction at time~|t|.

The routine solves this problem in nondegenerate cases by rotating the path and
the given direction so that |(x,y)=(1,0)|; i.e., the main task will be to find
when a given path first travels \quote {due east.}

@c
static void mp_find_direction_time (MP mp, mp_number *ret, mp_number *x_orig, mp_number *y_orig, mp_knot h)
{
    mp_number max;          /* $\max\bigl(\vert x\vert,\vert y\vert\bigr)$ */
    mp_knot p, q;           /* for list traversal */
    mp_number n;            /* the direction time at knot |p| */
    mp_number tt;           /* the direction time within a cubic */
    mp_number abs_x, abs_y; /* Other local variables for |find_direction_time| */
    mp_number x1, x2, x3, y1, y2, y3; /* multiples of rotated derivatives */
    mp_number phi;          /* angles of exit and entry at a knot */
    mp_number t;            /* temp storage */
    mp_number x, y;
    new_number(max);
    new_number(x1);
    new_number(x2);
    new_number(x3);
    new_number(y1);
    new_number(y2);
    new_number(y3);
    new_fraction(t);
    new_angle(phi);
    set_number_to_zero(*ret); /* just in case */
    new_number(x);
    new_number(y);
    new_number(abs_x);
    new_number(abs_y);
    new_number(n);
    new_fraction(tt);
    number_clone(x, *x_orig);
    number_clone(y, *y_orig);
    number_abs_clone(abs_x, *x_orig);
    number_abs_clone(abs_y, *y_orig);
    /*
        Normalize the given direction for better accuracy; but |return| with zero
        result if it's zero
    */
    if (number_less(abs_x, abs_y)) {
        mp_number r1;
        new_fraction(r1);
        make_fraction(r1, x, abs_y);
        number_clone(x, r1);
        free_number(r1);
        if (number_positive(y)) {
            number_clone(y, fraction_one_t);
        } else {
            number_negated_clone(y, fraction_one_t);
        }
    } else if (number_zero(x)) {
        goto FREE;
    } else {
        mp_number r1;
        new_fraction(r1);
        make_fraction(r1, y, abs_x);
        number_clone(y, r1);
        free_number(r1);
        if (number_positive(x)) {
            number_clone(x, fraction_one_t);
        } else {
            number_negated_clone(x, fraction_one_t);
        }
    }
    p = h;
    while (1) {
        if (mp_right_type(p) == mp_endpoint_knot) {
            break;
        } else {
            q = mp_next_knot(p);
            @<Rotate the cubic between |p| and |q|; then |goto found| if the rotated cubic travels due east at some time |tt|; but |break| if an entire cyclic path has been traversed@>
            p = q;
            number_add(n, unity_t);
        }
    }
    set_number_to_unity(*ret);
    number_negate(*ret);
    goto FREE;
  FOUND:
    set_number_from_addition(*ret, n, tt);
    goto FREE;
  FREE:
    free_number(x);
    free_number(y);
    free_number(abs_x);
    free_number(abs_y);
    /* Free local variables for |find_direction_time| */
    free_number(x1);
    free_number(x2);
    free_number(x3);
    free_number(y1);
    free_number(y2);
    free_number(y3);
    free_number(t);
    free_number(phi);
    free_number(n);
    free_number(max);
    free_number(tt);
}

@ Since we're interested in the tangent directions, we work with the derivative
$${1\over3}B'(x_0,x_1,x_2,x_3;t)= B(x_1-x_0,x_2-x_1,x_3-x_2;t)$$ instead of
$B(x_0,x_1,x_2,x_3;t)$ itself. The derived coefficients are also scale-d up in
order to achieve better accuracy.

The given path may turn abruptly at a knot, and it might pass the critical
tangent direction at such a time. Therefore we remember the direction |phi| in
which the previous rotated cubic was traveling. (The value of |phi| will be
undefined on the first cubic, i.e., when |n=0|.)

@<Rotate the cubic between |p| and |q|; then...@>=
set_number_to_zero(tt);
/*
    Set local variables |x1,x2,x3| and |y1,y2,y3| to multiples of the control
    points of the rotated derivatives.
*/
{
    mp_number absval;
    new_number(absval);
    set_number_from_subtraction(x1, p->right_x, p->x_coord);
    set_number_from_subtraction(x2, q->left_x,  p->right_x);
    set_number_from_subtraction(x3, q->x_coord, q->left_x);
    set_number_from_subtraction(y1, p->right_y, p->y_coord);
    set_number_from_subtraction(y2, q->left_y,  p->right_y);
    set_number_from_subtraction(y3, q->y_coord, q->left_y);
    number_abs_clone(absval, x2);
    number_abs_clone(max, x1);
    if (number_greater(absval, max)) {
        number_clone(max, absval);
    }
    number_abs_clone(absval, x3);
    if (number_greater(absval, max)) {
        number_clone(max, absval);
    }
    number_abs_clone(absval, y1);
    if (number_greater(absval, max)) {
        number_clone(max, absval);
    }
    number_abs_clone(absval, y2);
    if (number_greater(absval, max)) {
        number_clone(max, absval);
    }
    number_abs_clone(absval, y3);
    if (number_greater(absval, max)) {
        number_clone(max, absval);
    }
    free_number(absval);
    if (number_zero(max)) {
        goto FOUND;
    }
    while (number_less(max, fraction_half_t)) {
        number_double(max);
        number_double(x1);
        number_double(x2);
        number_double(x3);
        number_double(y1);
        number_double(y2);
        number_double(y3);
    }
    number_clone(t, x1);
    {
         mp_number r1, r2;
         new_fraction(r1);
         new_fraction(r2);
         take_fraction(r1, x1, x);
         take_fraction(r2, y1, y);
         set_number_from_addition(x1, r1, r2);
         take_fraction(r1, y1, x);
         take_fraction(r2, t, y);
         set_number_from_subtraction(y1, r1, r2);
         number_clone(t, x2);
         take_fraction(r1, x2, x);
         take_fraction(r2, y2, y);
         set_number_from_addition(x2, r1, r2);
         take_fraction(r1, y2, x);
         take_fraction(r2, t, y);
         set_number_from_subtraction(y2, r1, r2);
         number_clone(t, x3);
         take_fraction(r1, x3 ,x);
         take_fraction(r2, y3, y);
         set_number_from_addition(x3, r1, r2);
         take_fraction(r1, y3, x);
         take_fraction(r2, t, y);
         set_number_from_subtraction(y3, r1, r2);
         free_number(r1);
         free_number(r2);
    }
}
if (number_zero(y1) && (number_zero(x1) || number_positive(x1))) {
    goto FOUND;
}
if (number_positive(n)) {
    /* Exit to |found| if an eastward direction occurs at knot |p| */
    mp_number theta;
    mp_number tmp;
    new_angle(theta);
    n_arg(theta, x1, y1);
    new_angle(tmp);
    set_number_from_subtraction(tmp, theta, one_eighty_deg_t);
    if (number_nonnegative(theta) && number_nonpositive(phi) && number_greaterequal(phi, tmp)) {
        free_number(tmp);
        free_number(theta);
        goto FOUND;
    }
    set_number_from_addition(tmp, theta, one_eighty_deg_t);
    if (number_nonpositive(theta) && number_nonnegative(phi) && number_lessequal(phi, tmp)) {
        free_number(tmp);
        free_number(theta);
        goto FOUND;
    }
    free_number(tmp);
    free_number(theta);
    if (p == h) {
        break;
    }
}
if (number_nonzero(x3) || number_nonzero(y3)) {
    n_arg(phi, x3, y3);
}
/*
    Exit to |found| if the curve whose derivatives are specified by
    |x1,x2,x3,y1,y2,y3| travels eastward at some time~|tt|. In this step we
    want to use the |crossing_point| routine to find the roots of the
    quadratic equation $B(y_1,y_2,y_3;t)=0$. Several complications arise: If
    the quadratic equation has a double root, the curve never crosses zero,
    and |crossing_point| will find nothing; this case occurs iff
    $y_1y_3=y_2^2$ and $y_1y_2<0$. If the quadratic equation has simple
    roots, or only one root, we may have to negate it so that
    $B(y_1,y_2,y_3;t)$ crosses from positive to negative at its first root.
    And finally, we need to do special things if $B(y_1,y_2,y_3;t)$ is
    identically zero.
*/
if (number_negative(x1) && number_negative(x2) && number_negative(x3)) {
    goto DONE;
}
{
    if (ab_vs_cd(y1, y3, y2, y2) == 0) {
        /*
             Handle the test for eastward directions when $y_1y_3=y_2^2$; either |goto
             found| or |goto done|.
        */
        {
            if (ab_vs_cd(y1, y2, zero_t, zero_t) < 0) {
                mp_number tmp, arg2;
                new_number(tmp);
                new_number(arg2);
                set_number_from_subtraction(arg2, y1, y2);
                make_fraction(t, y1, arg2);
                free_number(arg2);
                set_number_from_of_the_way(x1, t, x1, x2);
                set_number_from_of_the_way(x2, t, x2, x3);
                set_number_from_of_the_way(tmp, t, x1, x2);
                if (number_zero(tmp) || number_positive(tmp)) {
                    free_number(tmp);
                    number_clone(tt, t);
                    fraction_to_round_scaled(tt);
                    goto FOUND;
                } else {
                    free_number(tmp);
                }
            } else if (number_zero(y3)) {
                if (number_zero(y1)) {
                    /*
                         Exit to |found| if the derivative $B(x_1,x_2,x_3;t)$ becomes |>=0| At
                         this point we know that the derivative of |y(t)| is identically zero,
                         and that |x1<0|; but either |x2>=0| or |x3>=0|, so there's some hope of
                         traveling east.
                    */
                    {
                        mp_number arg1, arg2, arg3;
                        new_number(arg1);
                        new_number(arg2);
                        new_number(arg3);
                        number_negated_clone(arg1, x1);
                        number_negated_clone(arg2, x2);
                        number_negated_clone(arg3, x3);
                        crossing_point(t, arg1, arg2, arg3);
                        free_number(arg1);
                        free_number(arg2);
                        free_number(arg3);
                        if (number_lessequal(t, fraction_one_t)) {
                            number_clone(tt, t);
                            fraction_to_round_scaled(tt);
                            goto FOUND;
                        } else if (ab_vs_cd(x1, x3, x2, x2) <= 0) {
                            mp_number arg2;
                            new_number(arg2);
                            set_number_from_subtraction(arg2, x1, x2);
                            make_fraction(t, x1, arg2);
                            free_number(arg2);
                            number_clone(tt, t);
                            fraction_to_round_scaled(tt);
                            goto FOUND;
                        }
                    }
                } else if (number_zero(x3) || number_positive(x3)) {
                    set_number_to_unity(tt);
                    goto FOUND;
                }
            }
            goto DONE;
        }
    }
}
if (number_zero(y1) || number_negative(y1)) {
    if (number_negative(y1)) {
        number_negate(y1);
        number_negate(y2);
        number_negate(y3);
    } else if (number_positive(y2)) {
        number_negate(y2);
        number_negate(y3);
    }
}
/*
    Check the places where $B(y_1,y_2,y_3;t)=0$ to see if $B(x_1,x_2,x_3;t)\ge0$
    The quadratic polynomial $B(y_1,y_2,y_3;t)$ begins |>=0| and has at most two
    roots, because we know that it isn't identically zero.

    It must be admitted that the |crossing_point| routine is not perfectly
    accurate; rounding errors might cause it to find a root when $y_1y_3>y_2^2$, or
    to miss the roots when $y_1y_3<y_2^2$. The rotation process is itself subject
    to rounding errors. Yet this code optimistically tries to do the right thing.
*/
crossing_point(t, y1, y2, y3);
if (number_greater(t, fraction_one_t)) {
    goto DONE;
}
set_number_from_of_the_way(y2, t, y2, y3);
set_number_from_of_the_way(x1, t, x1, x2);
set_number_from_of_the_way(x2, t, x2, x3);
set_number_from_of_the_way(x1, t, x1, x2);
if (number_zero(x1) || number_positive(x1)) {
    number_clone(tt, t);
    fraction_to_round_scaled(tt);
    goto FOUND;
}
if (number_positive(y2)) {
    set_number_to_zero(y2);
}
number_clone(tt, t);
{
    mp_number arg1, arg2, arg3;
    new_number(arg1);
    new_number(arg2);
    new_number(arg3);
    number_negated_clone(arg2, y2);
    number_negated_clone(arg3, y3);
    crossing_point(t, arg1, arg2, arg3);
    free_number(arg1);
    free_number(arg2);
    free_number(arg3);
}
if (number_greater(t, fraction_one_t)) {
    goto DONE;
} else {
    mp_number tmp;
    new_number(tmp);
    set_number_from_of_the_way(x1, t, x1, x2);
    set_number_from_of_the_way(x2, t, x2, x3);
    set_number_from_of_the_way(tmp, t, x1, x2);
    if (number_nonnegative(tmp)) {
        free_number(tmp);
        set_number_from_of_the_way(t, t, tt, fraction_one_t);
        number_clone(tt, t);
        fraction_to_round_scaled(tt);
        goto FOUND;
    }
    free_number(tmp);
}
DONE:

@ The intersection of two cubics can be found by an interesting variant of the
general bisection scheme described in the introduction to |crossing_point|.\
Given $w(t)=B(w_0,w_1,w_2,w_3;t)$ and $z(t)=B(z_0,z_1,z_2,z_3;t)$, we wish to
find a pair of times $(t_1,t_2)$ such that $w(t_1)=z(t_2)$, if an intersection
exists. First we find the smallest rectangle that encloses the points
$\{w_0,w_1,w_2,w_3\}$ and check that it overlaps the smallest rectangle that
encloses $\{z_0,z_1,z_2,z_3\}$; if not, the cubics certainly don't intersect. But
if the rectangles do overlap, we bisect the intervals, getting new cubics $w'$
and~$w''$, $z'$~and~$z''$; the intersection routine first tries for an
intersection between $w'$ and~$z'$, then (if unsuccessful) between $w'$
and~$z''$, then (if still unsuccessful) between $w''$ and~$z'$, finally (if
thrice unsuccessful) between $w''$ and~$z''$. After $l$~successful levels of
bisection we will have determined the intersection times $t_1$ and~$t_2$ to
$l$~bits of accuracy.

\def\submin{_{\rm min}} \def\submax{_{\rm max}}

As before, it is better to work with the numbers $W_k=2^l(w_k-w_{k-1})$ and
$Z_k=2^l(z_k-z_{k-1})$ rather than the coefficients $w_k$ and $z_k$ themselves.
We also need one other quantity, $\Delta=2^l(w_0-z_0)$, to determine when the
enclosing rectangles overlap. Here's why: The $x$~coordinates of~$w(t)$ are
between $u\submin$ and $u\submax$, and the $x$~coordinates of~$z(t)$ are between
$x\submin$ and $x\submax$, if we write $w_k=(u_k,v_k)$ and $z_k=(x_k,y_k)$ and
$u\submin= \min(u_0,u_1,u_2,u_3)$, etc. These intervals of $x$~coordinates
overlap if and only if $u\submin\L x\submax$ and $x\submin\L u\submax$. Letting

$$
    U\submin=\min(0,U_1,U_1+U_2,U_1+U_2+U_3),\;
    U\submax=\max(0,U_1,U_1+U_2,U_1+U_2+U_3),
$$

we have $2^lu\submin=2^lu_0+U\submin$, etc.; the condition for overlap reduces to

$$
    X\submin-U\submax\L 2^l(u_0-x_0)\L X\submax-U\submin.
$$

Thus we want to maintain the quantity $2^l(u_0-x_0)$; similarly, the quantity
$2^l(v_0-y_0)$ accounts for the $y$~coordinates. The coordinates of
$\Delta=2^l(w_0-z_0)$ must stay bounded as $l$ increases, because of the overlap
condition; i.e., we know that $X\submin$, $X\submax$, and their relatives are
bounded, hence $X\submax- U\submin$ and $X\submin-U\submax$ are bounded.

@ Incidentally, if the given cubics intersect more than once, the process just
sketched will not necessarily find the lexicographically smallest pair
$(t_1,t_2)$. The solution actually obtained will be smallest in \quote {shuffled
order}; i.e., if $t_1=(.a_1a_2\ldots a_{16})_2$ and $t_2=(.b_1b_2\ldots
b_{16})_2$, then we will minimize $a_1b_1a_2b_2\ldots a_{16}b_{16}$, not
$a_1a_2\ldots a_{16}b_1b_2\ldots b_{16}$. Shuffled order agrees with
lexicographic order if all pairs of solutions $(t_1,t_2)$ and $(t_1',t_2')$ have
the property that $t_1<t_1'$ iff $t_2<t_2'$; but in general, lexicographic order
can be quite different, and the bisection algorithm would be substantially less
efficient if it were constrained by lexicographic order.

For example, suppose that an overlap has been found for $l=3$ and $(t_1,t_2)=
(.101,.011)$ in binary, but that no overlap is produced by either of the
alternatives $(.1010,.0110)$, $(.1010,.0111)$ at level~4. Then there is probably
an intersection in one of the subintervals $(.1011,.011x)$; but lexicographic
order would require us to explore $(.1010,.1xxx)$ and $(.1011,.00xx)$ and
$(.1011,.010x)$ first. We wouldn't want to store all of the subdivision data for
the second path, so the subdivisions would have to be regenerated many times.
Such inefficiencies would be associated with every `1' in the binary
representation of~$t_1$.

@ The subdivision process introduces rounding errors, hence we need to make a
more liberal test for overlap. It is not hard to show that the computed values of
$U_i$ differ from the truth by at most~$l$, on level~$l$, hence $U\submin$ and
$U\submax$ will be at most $3l$ in error. If $\beta$ is an upper bound on the
absolute error in the computed components of $\Delta=(|delx|,|dely|)$ on
level~$l$, we will replace the test `$X\submin-U\submax\L|delx|$' by the more
liberal test `$X\submin-U\submax\L|delx|+|tol|$', where $|tol|=6l+\beta$.

More accuracy is obtained if we try the algorithm first with |tol=0|; the more
liberal tolerance is used only if an exact approach fails. It is convenient to do
this double-take by letting `3' in the preceding paragraph be a parameter, which
is first 0, then 3.

@<Glob...@>=
unsigned int tol_step;  /* either 0 or 3, usually */

@ We shall use an explicit stack to implement the recursive bisection
method described above. The |bisect_stack| array will contain numerous 5-word
packets like $(U_1,U_2,U_3,U\submin,U\submax)$, as well as 20-word packets
comprising the 5-word packets for $U$, $V$, $X$, and~$Y$.

The following macros define the allocation of stack positions to
the quantities needed for bisection-intersection.

@d stack_1(A)   mp->bisect_stack[(A)]   /* $U_1$, $V_1$, $X_1$, or $Y_1$ */
@d stack_2(A)   mp->bisect_stack[(A)+1] /* $U_2$, $V_2$, $X_2$, or $Y_2$ */
@d stack_3(A)   mp->bisect_stack[(A)+2] /* $U_3$, $V_3$, $X_3$, or $Y_3$ */
@d stack_min(A) mp->bisect_stack[(A)+3] /* $U\submin$, $V\submin$, $X\submin$, or $Y\submin$ */
@d stack_max(A) mp->bisect_stack[(A)+4] /* $U\submax$, $V\submax$, $X\submax$, or $Y\submax$ */

@d int_packets  20 /* number of words to represent $U_k$, $V_k$, $X_k$, and $Y_k$ */

@d u_packet(A) ((A)- 5)
@d v_packet(A) ((A)-10)
@d x_packet(A) ((A)-15)
@d y_packet(A) ((A)-20)

@d l_packets (mp->bisect_ptr-int_packets)
@d r_packets mp->bisect_ptr

@d ul_packet u_packet(l_packets) /* base of $U'_k$ variables */
@d vl_packet v_packet(l_packets) /* base of $V'_k$ variables */
@d xl_packet x_packet(l_packets) /* base of $X'_k$ variables */
@d yl_packet y_packet(l_packets) /* base of $Y'_k$ variables */
@d ur_packet u_packet(r_packets) /* base of $U''_k$ variables */
@d vr_packet v_packet(r_packets) /* base of $V''_k$ variables */
@d xr_packet x_packet(r_packets) /* base of $X''_k$ variables */
@d yr_packet y_packet(r_packets) /* base of $Y''_k$ variables */

@d u1l stack_1(ul_packet) /* $U'_1$ */
@d u2l stack_2(ul_packet) /* $U'_2$ */
@d u3l stack_3(ul_packet) /* $U'_3$ */
@d v1l stack_1(vl_packet) /* $V'_1$ */
@d v2l stack_2(vl_packet) /* $V'_2$ */
@d v3l stack_3(vl_packet) /* $V'_3$ */
@d x1l stack_1(xl_packet) /* $X'_1$ */
@d x2l stack_2(xl_packet) /* $X'_2$ */
@d x3l stack_3(xl_packet) /* $X'_3$ */
@d y1l stack_1(yl_packet) /* $Y'_1$ */
@d y2l stack_2(yl_packet) /* $Y'_2$ */
@d y3l stack_3(yl_packet) /* $Y'_3$ */
@d u1r stack_1(ur_packet) /* $U''_1$ */
@d u2r stack_2(ur_packet) /* $U''_2$ */
@d u3r stack_3(ur_packet) /* $U''_3$ */
@d v1r stack_1(vr_packet) /* $V''_1$ */
@d v2r stack_2(vr_packet) /* $V''_2$ */
@d v3r stack_3(vr_packet) /* $V''_3$ */
@d x1r stack_1(xr_packet) /* $X''_1$ */
@d x2r stack_2(xr_packet) /* $X''_2$ */
@d x3r stack_3(xr_packet) /* $X''_3$ */
@d y1r stack_1(yr_packet) /* $Y''_1$ */
@d y2r stack_2(yr_packet) /* $Y''_2$ */
@d y3r stack_3(yr_packet) /* $Y''_3$ */

@d stack_dx  mp->bisect_stack[mp->bisect_ptr]   /* stacked value of |delx| */
@d stack_dy  mp->bisect_stack[mp->bisect_ptr+1] /* stacked value of |dely| */
@d stack_tol mp->bisect_stack[mp->bisect_ptr+2] /* stacked value of |tol| */
@d stack_uv  mp->bisect_stack[mp->bisect_ptr+3] /* stacked value of |uv| */
@d stack_xy  mp->bisect_stack[mp->bisect_ptr+4] /* stacked value of |xy| */

@d int_increment (int_packets+int_packets+5) /* number of stack words per level */

@<Glob...@>=
mp_number *bisect_stack;
int bisect_ptr;

@ @<Allocate or initialize ...@>=
mp->bisect_stack = mp_memory_allocate((size_t) (bistack_size + 1) * sizeof(mp_number));
for (int i=0; i<bistack_size + 1; i++) {
    new_number(mp->bisect_stack[i]);
}

@ @<Dealloc variables@>=
for (int i=0; i<bistack_size + 1; i++) {
    free_number(mp->bisect_stack[i]);
}
mp_memory_free(mp->bisect_stack);

@ Computation of the min and max is a tedious but fairly fast sequence of
instructions; exactly four comparisons are made in each branch.

@<Declarations...@>=
static void mp_set_min_max (MP mp, int v);

@ This was a macro but a function is way more efficient here. @c
void mp_set_min_max (MP mp, int v)
{
    if (number_negative(stack_1(v))) {
        if (number_nonnegative (stack_3(v))) {
            if (number_negative(stack_2(v))) {
                set_number_from_addition(stack_min(v), stack_1(v), stack_2(v));
            } else {
                number_clone(stack_min(v), stack_1(v));
            }
            set_number_from_addition(stack_max(v), stack_1(v), stack_2(v));
            number_add(stack_max(v), stack_3(v));
            if (number_negative(stack_max(v))) {
                set_number_to_zero(stack_max(v));
            }
        } else {
            set_number_from_addition(stack_min(v), stack_1(v), stack_2(v));
            number_add(stack_min(v), stack_3(v));
            if (number_greater(stack_min(v), stack_1(v))) {
                number_clone(stack_min(v), stack_1(v));
            }
            set_number_from_addition(stack_max(v), stack_1(v), stack_2(v));
            if (number_negative(stack_max(v))) {
                set_number_to_zero(stack_max(v));
            }
        }
    } else if (number_nonpositive(stack_3(v))) {
        if (number_positive(stack_2(v))) {
            set_number_from_addition(stack_max(v), stack_1(v), stack_2(v));
        } else {
            number_clone(stack_max(v), stack_1(v));
        }
        set_number_from_addition(stack_min(v), stack_1(v), stack_2(v));
        number_add(stack_min(v), stack_3(v));
        if (number_positive(stack_min(v))) {
            set_number_to_zero(stack_min(v));
        }
    } else  {
        set_number_from_addition(stack_max(v), stack_1(v), stack_2(v));
        number_add(stack_max(v), stack_3(v));
        if (number_less(stack_max(v), stack_1(v))) {
            number_clone(stack_max(v), stack_1(v));
        }
        set_number_from_addition(stack_min(v), stack_1(v), stack_2(v));
        if (number_positive(stack_min(v))) {
            set_number_to_zero(stack_min(v));
        }
    }
}

@ It's convenient to keep the current values of $l$, $t_1$, and $t_2$ in the
integer form $2^l+2^lt_1$ and $2^l+2^lt_2$. The |cubic_intersection| routine uses
global variables |cur_t| and |cur_tt| for this purpose; after successful
completion, |cur_t| and |cur_tt| will contain |unity| plus the |scaled| values of
$t_1$ and~$t_2$.

The values of |cur_t| and |cur_tt| will be set to zero if |cubic_intersection|
finds no intersection. The routine gives up and gives an approximate answer if it
has backtracked more than 5000 times (otherwise there are cases where several
minutes of fruitless computation would be possible).

@d max_patience 5000

@<Glob...@>=
mp_number cur_t;
mp_number cur_tt;   /* controls and results of |cubic_intersection| */
int time_to_go; /* this many backtracks before giving up */
mp_number max_t;    /* maximum of $2^{l+1}$ so far achieved */

@ @<Initialize table ...@>=
new_number(mp->cur_t);
new_number(mp->cur_tt);
new_number(mp->max_t);

@ @<Dealloc ...@>=
free_number(mp->cur_t);
free_number(mp->cur_tt);
free_number(mp->max_t);

@ The given cubics $B(w_0,w_1,w_2,w_3;t)$ and
$B(z_0,z_1,z_2,z_3;t)$ are specified in adjacent knot nodes |(p,mp_link(p))|
and |(pp,mp_link(pp))|, respectively.

@d half(A) ((A)/2)

@c
static int mp_cubic_intersection(MP mp, mp_knot p, mp_knot pp, int run)
{
    mp_knot q, qq;                   /* |mp_link(p)|, |mp_link(pp)| */
    mp_number x_two_t;               /* increment bit precision */
    mp_number x_two_t_low_precision; /* check for low precision */
    mp->time_to_go = max_patience;
    set_number_from_scaled(mp->max_t, 2);
    new_number_clone(x_two_t, two_t);
    new_number(x_two_t_low_precision);
    /* added 2 bit of precision */
    number_double(x_two_t);
    number_double(x_two_t);
    set_number_from_double(x_two_t_low_precision, -0.5);
    number_add(x_two_t_low_precision, x_two_t);
    @<Initialize for intersections at level zero@>
  CONTINUE:
    while (1) {
        /*
            When we are in arbitrary precision math, low precisions can lead to
            acces locations beyond the |stack_size|: in this case we say that
            there is no intersection.
        */
        if (((x_packet (mp->xy))+4)>bistack_size
         || ((u_packet (mp->uv))+4)>bistack_size
         || ((y_packet (mp->xy))+4)>bistack_size
         || ((v_packet (mp->uv))+4)>bistack_size){
            set_number_from_scaled(mp->cur_t,1);
            set_number_from_scaled(mp->cur_tt,1);
            goto NOT_FOUND;
        }
        /*
            Also, low precision can lead to wrong result in comparing so we check
            that the level of bisection stay low, and later we will also check
            that the bisection level are safe from approximations.
        */
        if (number_greater(mp->max_t, x_two_t)){
            set_number_from_scaled(mp->cur_t,1);
            set_number_from_scaled(mp->cur_tt,1);
            goto NOT_FOUND;
        }
        if (number_to_scaled(mp->delx) - mp->tol <= number_to_scaled(stack_max (x_packet (mp->xy))) - number_to_scaled(stack_min (u_packet (mp->uv)))) {
            if (number_to_scaled(mp->delx) + mp->tol >= number_to_scaled(stack_min (x_packet (mp->xy))) - number_to_scaled(stack_max (u_packet (mp->uv)))) {
                if (number_to_scaled(mp->dely) - mp->tol <= number_to_scaled(stack_max (y_packet (mp->xy))) - number_to_scaled(stack_min (v_packet (mp->uv)))) {
                    if (number_to_scaled(mp->dely) + mp->tol >= number_to_scaled(stack_min (y_packet (mp->xy))) - number_to_scaled(stack_max (v_packet (mp->uv)))) {
                        if (number_to_scaled(mp->cur_t) >= number_to_scaled(mp->max_t)) {
                            if (number_equal(mp->max_t, x_two_t) || number_greater(mp->max_t, x_two_t_low_precision)) {
                                if (run == 1) {
                                    /* we've done 17+2 bisections, first restore values due bit precision */
                                    number_divide_int(mp->cur_t,1<<2);
                                    number_divide_int(mp->cur_tt,1<<2);
                                    set_number_from_scaled(mp->cur_t, ((number_to_scaled(mp->cur_t) + 1)/2));
                                    set_number_from_scaled(mp->cur_tt, ((number_to_scaled(mp->cur_tt) + 1)/2));
free_number(x_two_t);
free_number(x_two_t_low_precision);
                                    return 1;
                                } else {
                                    run--;
                                    goto NOT_FOUND;
                                }
                            }
                            number_double(mp->max_t);
                            number_clone(mp->appr_t, mp->cur_t);
                            number_clone(mp->appr_tt, mp->cur_tt);
                        }
                        @<Subdivide for a new level of intersection@>
                        goto CONTINUE;
                    }
                }
            }
        }
        if (mp->time_to_go > 0) {
            --mp->time_to_go;
        } else {
            /* we have added 2 bit of precision */
            number_divide_int(mp->appr_t, 1<<2);
            number_divide_int(mp->appr_tt, 1<<2);
            while (number_less(mp->appr_t, unity_t)) {
                number_double(mp->appr_t);
                number_double(mp->appr_tt);
            }
            number_clone(mp->cur_t, mp->appr_t);
            number_clone(mp->cur_tt, mp->appr_tt);
free_number(x_two_t);
free_number(x_two_t_low_precision);
            return 2;
        }
      NOT_FOUND:
        /* Advance to the next pair |(cur_t,cur_tt)| */
        if (odd(number_to_scaled(mp->cur_tt))) {
     // if (number_odd(mp->cur_tt)) {
            if (odd(number_to_scaled(mp->cur_t))) {
         // if (number_odd(mp->cur_t)) {
                /* Descend to the previous level and |goto not_found| */
                set_number_from_scaled(mp->cur_t, half (number_to_scaled(mp->cur_t)));
                set_number_from_scaled(mp->cur_tt, half (number_to_scaled(mp->cur_tt)));
                if (number_to_scaled(mp->cur_t) == 0) {
free_number(x_two_t);
free_number(x_two_t_low_precision);
                    return 3;
                } else {
                    mp->bisect_ptr -= int_increment;
                    mp->three_l -= (int) mp->tol_step;
                    number_clone(mp->delx, stack_dx);
                    number_clone(mp->dely, stack_dy);
                    mp->tol = number_to_scaled(stack_tol);
                    mp->uv = number_to_scaled(stack_uv);
                    mp->xy = number_to_scaled(stack_xy);
                    goto NOT_FOUND;
                }
            } else {
                set_number_from_scaled(mp->cur_t, number_to_scaled(mp->cur_t) + 1);
                number_add(mp->delx, stack_1(u_packet (mp->uv)));
                number_add(mp->delx, stack_2(u_packet (mp->uv)));
                number_add(mp->delx, stack_3(u_packet (mp->uv)));
                number_add(mp->dely, stack_1(v_packet (mp->uv)));
                number_add(mp->dely, stack_2(v_packet (mp->uv)));
                number_add(mp->dely, stack_3(v_packet (mp->uv)));
                mp->uv = mp->uv + int_packets; /* switch from |l_packets| to |r_packets| */
                set_number_from_scaled(mp->cur_tt, number_to_scaled(mp->cur_tt) - 1);
                mp->xy = mp->xy - int_packets;
                number_add(mp->delx, stack_1(x_packet (mp->xy)));
                number_add(mp->delx, stack_2(x_packet (mp->xy)));
                number_add(mp->delx, stack_3(x_packet (mp->xy)));
                number_add(mp->dely, stack_1(y_packet (mp->xy)));
                number_add(mp->dely, stack_2(y_packet (mp->xy)));
                number_add(mp->dely, stack_3(y_packet (mp->xy)));
            }
        } else {
            set_number_from_scaled(mp->cur_tt, number_to_scaled(mp->cur_tt) + 1);
            mp->tol = mp->tol + mp->three_l;
            number_subtract(mp->delx, stack_1(x_packet (mp->xy)));
            number_subtract(mp->delx, stack_2(x_packet (mp->xy)));
            number_subtract(mp->delx, stack_3(x_packet (mp->xy)));
            number_subtract(mp->dely, stack_1(y_packet (mp->xy)));
            number_subtract(mp->dely, stack_2(y_packet (mp->xy)));
            number_subtract(mp->dely, stack_3(y_packet (mp->xy)));
            mp->xy = mp->xy + int_packets; /* switch from |l_packets| to |r_packets| */
        }
    }
free_number(x_two_t);
free_number(x_two_t_low_precision);
}

@ The following variables are global, although they are used only by
|cubic_intersection|, because it is necessary on some machines to split
|cubic_intersection| up into two procedures.

@<Glob...@>=
mp_number delx;
mp_number dely;    /* the components of $\Delta=2^l(w_0-z_0)$ */
int       tol;     /* bound on the uncertainty in the overlap test */
int       uv;
int       xy;      /* pointers to the current packets of interest */
int       three_l; /* |tol_step| times the bisection level */
mp_number appr_t;
mp_number appr_tt; /* best approximations known to the answers */

@ @<Initialize table ...@>=
new_number(mp->delx);
new_number(mp->dely);
new_number(mp->appr_t);
new_number(mp->appr_tt);

@ @<Dealloc...@>=
free_number(mp->delx);
free_number(mp->dely);
free_number(mp->appr_t);
free_number(mp->appr_tt);

@ We shall assume that the coordinates are sufficiently non-extreme that
integer overflow will not occur.
@^overflow in arithmetic@>

@<Initialize for intersections at level zero@>=
q = mp_next_knot(p);
qq = mp_next_knot(pp);
mp->bisect_ptr = int_packets;
set_number_from_subtraction(u1r, p->right_x, p->x_coord);
set_number_from_subtraction(u2r, q->left_x, p->right_x);
set_number_from_subtraction(u3r, q->x_coord, q->left_x);
mp_set_min_max(mp, ur_packet);
set_number_from_subtraction(v1r, p->right_y, p->y_coord);
set_number_from_subtraction(v2r, q->left_y, p->right_y);
set_number_from_subtraction(v3r, q->y_coord, q->left_y);
mp_set_min_max(mp, vr_packet);
set_number_from_subtraction(x1r, pp->right_x, pp->x_coord);
set_number_from_subtraction(x2r, qq->left_x, pp->right_x);
set_number_from_subtraction(x3r, qq->x_coord, qq->left_x);
mp_set_min_max(mp, xr_packet);
set_number_from_subtraction(y1r, pp->right_y, pp->y_coord);
set_number_from_subtraction(y2r, qq->left_y, pp->right_y);
set_number_from_subtraction(y3r, qq->y_coord, qq->left_y);
mp_set_min_max(mp, yr_packet);
set_number_from_subtraction(mp->delx, p->x_coord, pp->x_coord);
set_number_from_subtraction(mp->dely, p->y_coord, pp->y_coord);
mp->tol = 0;
mp->uv = r_packets;
mp->xy = r_packets;
mp->three_l = 0;
set_number_from_scaled(mp->cur_t, 1);
set_number_from_scaled(mp->cur_tt, 1);

@ @<Subdivide for a new level of intersection@>=
number_clone(stack_dx, mp->delx);
number_clone(stack_dy, mp->dely);
set_number_from_scaled(stack_tol, mp->tol);
set_number_from_scaled(stack_uv, mp->uv);
set_number_from_scaled(stack_xy, mp->xy);
mp->bisect_ptr = mp->bisect_ptr + int_increment;
number_double(mp->cur_t);
number_double(mp->cur_tt);
number_clone(u1l, stack_1(u_packet (mp->uv)));
number_clone(u3r, stack_3(u_packet (mp->uv)));
set_number_half_from_addition(u2l, u1l, stack_2(u_packet(mp->uv)));
set_number_half_from_addition(u2r, u3r, stack_2(u_packet(mp->uv)));
set_number_half_from_addition(u3l, u2l, u2r);
number_clone(u1r, u3l);
mp_set_min_max(mp, ul_packet);
mp_set_min_max(mp, ur_packet);
number_clone(v1l, stack_1(v_packet (mp->uv)));
number_clone(v3r, stack_3(v_packet (mp->uv)));
set_number_half_from_addition(v2l, v1l, stack_2(v_packet(mp->uv)));
set_number_half_from_addition(v2r, v3r, stack_2(v_packet(mp->uv)));
set_number_half_from_addition(v3l, v2l, v2r);
number_clone(v1r, v3l);
mp_set_min_max(mp, vl_packet);
mp_set_min_max(mp, vr_packet);
number_clone(x1l, stack_1(x_packet (mp->xy)));
number_clone(x3r, stack_3(x_packet (mp->xy)));
set_number_half_from_addition(x2l, x1l, stack_2(x_packet(mp->xy)));
set_number_half_from_addition(x2r, x3r, stack_2(x_packet(mp->xy)));
set_number_half_from_addition(x3l, x2l, x2r);
number_clone(x1r, x3l);
mp_set_min_max(mp, xl_packet);
mp_set_min_max(mp, xr_packet);
number_clone(y1l, stack_1(y_packet (mp->xy)));
number_clone(y3r, stack_3(y_packet (mp->xy)));
set_number_half_from_addition(y2l, y1l, stack_2(y_packet(mp->xy)));
set_number_half_from_addition(y2r, y3r, stack_2(y_packet(mp->xy)));
set_number_half_from_addition(y3l, y2l, y2r);
number_clone(y1r, y3l);
mp_set_min_max(mp, yl_packet);
mp_set_min_max(mp, yr_packet);
mp->uv = l_packets;
mp->xy = l_packets;
number_double(mp->delx);
number_double(mp->dely);
mp->tol = mp->tol - mp->three_l + (int) mp->tol_step;
mp->tol += mp->tol;
mp->three_l = mp->three_l + (int) mp->tol_step;

@ The |path_intersection| procedure is much simpler. It invokes
|cubic_intersection| in lexicographic order until finding a pair of cubics that
intersect. The final intersection times are placed in |cur_t| and~|cur_tt|.

@d intersection_run_shift 8

@c
static mp_knot mp_path_intersection_add(MP mp, mp_knot list, mp_knot *last, mp_number *t, mp_number *tt)
{
    int a = number_to_scaled(*t) >> intersection_run_shift;
    int aa = number_to_scaled(*tt) >> intersection_run_shift;
    int b =  (list ? number_to_scaled((*last)->x_coord) : -1) >> intersection_run_shift ;
    int bb = (list ? number_to_scaled((*last)->y_coord) : -1) >> intersection_run_shift ;
    if (a == b && aa == bb) {
        /* ignore */
    } else {
        /* todo: just the point as we have it */
        mp_knot k = mp_new_knot(mp);
        mp_left_type(k) = mp_explicit_knot;
        mp_right_type(k) = mp_explicit_knot;
        number_clone(k->x_coord, *t);
        number_clone(k->y_coord, *tt);
        if (list) {
            mp_prev_knot(k) = *last;
            mp_next_knot(*last) = k;
            mp_prev_knot(list) = k;
            mp_next_knot(k) = list;
        } else {
            list = k;
            mp_prev_knot(k) = k;
            mp_next_knot(k) = k;
        }
        *last = k;
    }
    return list;
}

@c
static mp_knot mp_path_intersection(MP mp, mp_knot h, mp_knot hh, int path, mp_knot *last)
{
    mp_number n, nn; /* integer parts of intersection times, minus |unity| */
    int done = 0;
    mp_knot list = NULL;
    mp_knot l = NULL;
    mp_knot ll = NULL;
    if (last) {
        *last = NULL;
    }
    @<Change one-point paths into dead cycles@>
    new_number(n);
    new_number(nn);
    mp->tol_step = 0;
    do {
        mp_knot p, pp;   /* link registers that traverse the given paths */
        int t = -1;
        int tt = -1;
     // set_number_to_unity(n);
     // number_negate(n);
        number_negated_clone(n, unity_t);
        p = h;
        do {
            if (mp_right_type(p) != mp_endpoint_knot) {
             // set_number_to_unity(nn);
             // number_negate(nn);
                number_negated_clone(nn, unity_t);
                pp = hh;
                do {
                    if (mp_right_type(pp) != mp_endpoint_knot) {
                        int run = 0;
                        int retrials = 0;
                      RETRY:
                        ++run;
                        mp_cubic_intersection(mp, p, pp, run);
                        if (number_positive(mp->cur_t)) {
                            number_add(mp->cur_t, n);
                            number_add(mp->cur_tt, nn);
                            done = 1;
                            if (path) {
                                list = mp_path_intersection_add(mp, list, last, &(mp->cur_t), &(mp->cur_tt));
                                if (t == number_to_scaled(mp->cur_t) && tt == number_to_scaled(mp->cur_tt)) {
                                    if (retrials == 8) { /* is 8 okay? */
                                        break;
                                    } else {
                                        retrials += 1;
                                        goto RETRY;
                                    }
                                } else {
                                    retrials = 0;
                                    t = number_to_scaled(mp->cur_t);
                                    tt = number_to_scaled(mp->cur_tt);
                                    goto RETRY;
                                }
                            } else {
                                goto DONE;
                            }
                        }
                    }
                    number_add(nn, unity_t);
                    ll = pp;
                    pp = mp_next_knot(pp);
                } while (pp != hh);
            }
            number_add(n, unity_t);
            l = p;
            p = mp_next_knot(p);
        } while (p != h);
        mp->tol_step = mp->tol_step + 3;
        if (done) {
            goto DONE; /* when we do all points */
        }
    } while (mp->tol_step <= 3);
  DONE:
    if (path && l && ll && number_equal(l->x_coord, ll->x_coord) && number_equal(l->y_coord, ll->y_coord)) {
        list = mp_path_intersection_add(mp, list, last, &n, &nn);
    }
    if (! done) {
        number_negated_clone(mp->cur_t, unity_t);
        number_negated_clone(mp->cur_tt, unity_t);
        if (path && ! list) {
            mp_knot k = mp_new_knot(mp);
            number_clone(k->x_coord, mp->cur_t);
            number_clone(k->y_coord, mp->cur_tt);
            mp_prev_knot(k) = k;
            mp_next_knot(k) = k;
            list = k;
            if (last) {
                *last = k;
            }
        }
    }
    free_number(n);
    free_number(nn);
    return list;
}

@ @<Change one-point paths...@>=
if (mp_right_type(h) == mp_endpoint_knot) {
    number_clone(h->right_x, h->x_coord);
    number_clone(h->left_x, h->x_coord);
    number_clone(h->right_y, h->y_coord);
    number_clone(h->left_y, h->y_coord);
    mp_right_type(h) = mp_explicit_knot;
}
if (mp_right_type(hh) == mp_endpoint_knot) {
    number_clone(hh->right_x, hh->x_coord);
    number_clone(hh->left_x, hh->x_coord);
    number_clone(hh->right_y, hh->y_coord);
    number_clone(hh->left_y, hh->y_coord);
    mp_right_type(hh) = mp_explicit_knot;
}

@* Dynamic linear equations.

\MP\ users define variables implicitly by stating equations that should be
satisfied; the computer is supposed to be smart enough to solve those equations.
And indeed, the computer tries valiantly to do so, by distinguishing five
different types of numeric values:

\smallskip\hang |type(p)=mp_known| is the nice case, when |value(p)| is the
|scaled| value of the variable whose address is~|p|.

\smallskip\hang |type(p)=mp_dependent| means that |value(p)| is not present, but
|mp_get_dep_list(p)| points to a {\sl dependency list} that expresses the value of
variable~|p| as a |scaled| number plus a sum of independent variables with
|fraction| coefficients.

\smallskip\hang |type(p)=mp_independent| means that |mp_get_indep_value(p)=s|, where
|s>0| is a \quote {serial number} reflecting the time this variable was first used in
an equation; and there is an extra field |mp_get_indep_scale(p)=m|, with |0<=m<64|, each
dependent variable that refers to this one is actually referring to the future
value of this variable times~$2^m$. (Usually |m=0|, but higher degrees of scaling
are sometimes needed to keep the coefficients in dependency lists from getting
too large. The value of~|m| will always be even.)

\smallskip\hang |type(p)=mp_numeric_type| means that variable |p| hasn't appeared
in an equation before, but it has been explicitly declared to be numeric.

\smallskip\hang |type(p)=undefined| means that variable |p| hasn't appeared
before.

\smallskip\noindent We have actually discussed these five types in the reverse
order of their history during a computation: Once |known|, a variable never again
becomes |dependent|; once |dependent|, it almost never again becomes
|mp_independent|; once |mp_independent|, it never again becomes
|mp_numeric_type|; and once |mp_numeric_type|, it never again becomes |undefined|
(except of course when the user specifically decides to scrap the old value and
start again). A backward step may, however, take place: Sometimes a |dependent|
variable becomes |mp_independent| again, when one of the independent variables it
depends on is reverting to |undefined|.

@d mp_get_indep_scale(A)   ((mp_value_node) (A))->data.indep.scale
@d mp_set_indep_scale(A,B) ((mp_value_node) (A))->data.indep.scale = (B)
@d mp_get_indep_value(A)   ((mp_value_node) (A))->data.indep.serial
@d mp_set_indep_value(A,B) ((mp_value_node) (A))->data.indep.serial = (B)

@c
static void mp_new_indep (MP mp, mp_node p)
{
    (void) mp;
    /* create a new independent variable */
    if (mp->serial_no >= max_integer) {
        mp_fatal_error(mp, "Variable instance identifiers exhausted");
    }
    mp_type(p) = mp_independent_type;
    mp->serial_no = mp->serial_no + 1;
    mp_set_indep_scale(p, 0);
    mp_set_indep_value(p, mp->serial_no);
}

@ @<Declarations@>=
static void mp_new_indep (MP mp, mp_node p);

@ @<Glob...@>=
int serial_no; /* the most recent serial number */

@ But how are dependency lists represented? It's simple: The linear combination
$\alpha_1v_1+\cdots+\alpha_kv_k+\beta$ appears in |k+1| value nodes. If
|q=mp_get_dep_list(p)| points to this list, and if |k>0|, then |mp_get_dep_value(q)=
@t$\alpha_1$@>| (which is a |fraction|); |mp_get_dep_info(q)| points to the location of
$\alpha_1$; and |mp_link(p)| points to the dependency list
$\alpha_2v_2+\cdots+\alpha_kv_k+\beta$. On the other hand if |k=0|, then
|mp_get_dep_value(q)=@t$\beta$@>| (which is |scaled|) and |mp_get_dep_info(q)=NULL|. The
independent variables $v_1$, \dots,~$v_k$ have been sorted so that they appear in
decreasing order of their |value| fields (i.e., of their serial numbers). \ (It
is convenient to use decreasing order, since |value(NULL)=0|. If the independent
variables were not sorted by serial number but by some other criterion, such as
their location in |mem|, the equation-solving mechanism would be too
system-dependent, because the ordering can affect the computed results.)

The |link| field in the node that contains the constant term $\beta$ is called
the {\sl final link} of the dependency list. \MP\ maintains a doubly-linked
master list of all dependency lists, in terms of a permanently allocated node in
|mem| called |dep_head|. If there are no dependencies, we have
|mp_link(dep_head)=dep_head| and |mp_get_prev_dep(dep_head)=dep_head|; otherwise
|mp_link(dep_head)| points to the first dependent variable, say~|p|, and
|mp_get_prev_dep(p)=dep_head|. We have |type(p)=mp_dependent|, and |mp_get_dep_list(p)| points
to its dependency list. If the final link of that dependency list occurs in
location~|q|, then |mp_link(q)| points to the next dependent variable (say~|r|);
and we have |mp_get_prev_dep(r)=q|, etc.

Dependency nodes sometimes mutate into value nodes and vice versa, so their
structures have to match.

@d mp_get_dep_value(A)   ((mp_value_node) (A))->data.n
@d mp_get_dep_list(A)    ((mp_value_node) (A))->attr_head   /* half of the |value| field in a |dependent| variable */
@d mp_get_prev_dep(A)    ((mp_value_node) (A))->subscr_head /* the other half; makes a doubly linked list */
@d mp_get_dep_info(A)    do_get_dep_info(mp, (A))

@d mp_set_dep_value(A,B) do_set_dep_value(mp,(A),&(B))
@d mp_set_dep_list(A,B)  ((mp_value_node) (A))->attr_head = (mp_node) (B)
@d mp_set_prev_dep(A,B)  ((mp_value_node) (A))->subscr_head = (mp_node) (B)
@d mp_set_dep_info(A,B)  ((mp_value_node) (A))->parent = (mp_node) (B)

@c
inline static mp_node do_get_dep_info (MP mp, mp_value_node p)
{
    (void) mp;
    mp_node d;
    d = p->parent; /* half of the |value| field in a |dependent| variable */
    return d;
}

inline static void do_set_dep_value (MP mp, mp_value_node p, mp_number *q)
{
    number_clone(p->data.n, *q); /* half of the |value| field in a |dependent| variable */
    p->attr_head = NULL;
    p->subscr_head = NULL;
}

@ @<Declarations...@>=
inline static mp_node do_get_dep_info  (MP mp, mp_value_node p);
inline static void    do_set_dep_value (MP mp, mp_value_node p, mp_number *q);

@ @c
static mp_value_node mp_get_dep_node (MP mp)
{
    mp_value_node p = (mp_value_node) mp_new_value_node(mp);
    mp_type(p) = mp_dep_node_type;
    return p;
}

static void mp_free_dep_node (MP mp, mp_value_node p)
{
    mp_free_value_node(mp, (mp_node) p);
}

@ @<Declarations...@>=
static void mp_free_dep_node (MP mp, mp_value_node p);

@ @<Initialize table entries@>=
mp->serial_no = 0;
mp->dep_head  = mp_get_dep_node(mp);

mp_set_link(mp->dep_head, mp->dep_head);
mp_set_prev_dep(mp->dep_head, mp->dep_head);
mp_set_dep_info(mp->dep_head, NULL);
mp_set_dep_list(mp->dep_head, NULL);

@ @<Free table entries@>=
mp_free_dep_node(mp, mp->dep_head);

@ Actually the description above contains a little white lie. There's another
kind of variable called |mp_proto_dependent|, which is just like a |dependent|
one except that the $\alpha$ coefficients in its dependency list are |scaled|
instead of being fractions. Proto-dependency lists are mixed with dependency
lists in the nodes reachable from |dep_head|.

@ Here is a procedure that prints a dependency list in symbolic form. The second
parameter should be either |dependent| or |mp_proto_dependent|, to indicate the
scaling of the coefficients.

@<Declarations@>=
static void mp_print_dependency (MP mp, mp_value_node p, int t);

@ @c
void mp_print_dependency (MP mp, mp_value_node p, int t)
{
    mp_number v; /* a coefficient */
    mp_node q;
    mp_value_node pp = p;
    new_number(v);
    while (1) {
        number_abs_clone(v, mp_get_dep_value(p));
        q = mp_get_dep_info(p);
        if (q == NULL) {
            /* the constant term */
            if (number_nonzero(v) || (p == pp)) {
                if (number_positive(mp_get_dep_value(p)) && p != pp) {
                    mp_print_chr(mp, '+');
                }
                print_number(mp_get_dep_value(p));
            }
            return;
        }
        /* Print the coefficient, unless it's $\pm1.0$ */
        if (number_negative(mp_get_dep_value(p))) {
            mp_print_chr(mp, '-');
        } else if (p != pp) {
            mp_print_chr(mp, '+');
        }
        if (t == mp_dependent_type) {
            fraction_to_round_scaled(v);
        }
        if (! number_equal(v, unity_t)) {
            print_number(v);
        }
        if (mp_type(q) != mp_independent_type) {
            mp_confusion(mp, "dependency");
        } else {
            mp_print_variable_name(mp, q);
            set_number_from_scaled(v, mp_get_indep_scale(q));
            while (number_positive(v)) {
                mp_print_str(mp, "*4");
                number_add_scaled(v, -2);
            }
            p = (mp_value_node) mp_link(p);
        }
    }
}

@ The maximum absolute value of a coefficient in a given dependency list is
returned by the following simple function.

@c
static void mp_max_coef (MP mp, mp_number *x, mp_value_node p)
{
    mp_number(absv);
    new_number(absv);
    set_number_to_zero(*x);
    while (mp_get_dep_info(p) != NULL) {
        number_abs_clone(absv, mp_get_dep_value(p));
        if (number_greater(absv, *x)) {
            number_clone(*x, absv);
        }
        p = (mp_value_node) mp_link(p);
    }
    free_number(absv);
}

@ One of the main operations needed on dependency lists is to add a multiple of
one list to the other; we call this |p_plus_fq|, where |p| and~|q| point to
dependency lists and |f| is a fraction.

If the coefficient of any independent variable becomes |coef_bound| or more, in
absolute value, this procedure changes the type of that variable to
|independent_needing_fix|, and sets the global variable |fix_needed| to~|true|.
The value of $|coef_bound|=\mu$ is chosen so that $\mu^2+\mu<8$; this means that
the numbers we deal with won't get too large. (Instead of the \quote {optimum}
$\mu=(\sqrt{33}-1)/2\approx 2.3723$, the safer value 7/3 is taken as the
threshold.)

The changes mentioned in the preceding paragraph are actually done only if the
global variable |watch_coefs| is |true|. But it usually is; in fact, it is
|false| only when \MP\ is making a dependency list that will soon be equated to
zero.

Several procedures that act on dependency lists, including |p_plus_fq|, set the
global variable |dep_final| to the final (constant term) node of the dependency
list that they produce.

@d independent_needing_fix 0

@<Glob...@>=
int           fix_needed;  /* does at least one |independent| variable need scaling? */
int           watch_coefs; /* should we scale coefficients that exceed |coef_bound|? */
mp_value_node dep_final;   /* location of the constant term and final link */

@ @<Set init...@>=
mp->fix_needed  = 0;
mp->watch_coefs = 1;

@ The |p_plus_fq| procedure has a fourth parameter, |t|, that should be set to
|mp_proto_dependent| if |p| is a proto-dependency list. In this case |f| will be
|scaled|, not a |fraction|. Similarly, the fifth parameter~|tt| should be
|mp_proto_dependent| if |q| is a proto-dependency list.

List |q| is unchanged by the operation; but list |p| is totally destroyed.

The final link of the dependency list or proto-dependency list returned by
|p_plus_fq| is the same as the original final link of~|p|. Indeed, the constant
term of the result will be located in the same |mem| location as the original
constant term of~|p|.

Coefficients of the result are assumed to be zero if they are less than a certain
threshold. This compensates for inevitable rounding errors, and tends to make
more variables |known|. The threshold is approximately $10^{-5}$ in the case of
normal dependency lists, $10^{-4}$ for proto-dependencies.

@d fraction_threshold_k      mp->math->md_fraction_threshold_t
@d half_fraction_threshold_k mp->math->md_half_fraction_threshold_t
@d scaled_threshold_k        mp->math->md_scaled_threshold_t
@d half_scaled_threshold_k   mp->math->md_half_scaled_threshold_t

@<Declarations@>=
static mp_value_node mp_p_plus_fq (MP mp, mp_value_node p, mp_number *f, mp_value_node q, mp_variable_type t, mp_variable_type tt);

@ @c
static mp_value_node mp_p_plus_fq (MP mp,
    mp_value_node p, mp_number *f,
    mp_value_node q, mp_variable_type t,
    mp_variable_type tt
)
{
    mp_node pp, qq;           /* |mp_get_dep_info(p)| and |mp_get_dep_info(q)|, respectively */
    mp_value_node r, s;       /* for list manipulation */
    mp_number threshold;      /* defines a neighborhood of zero */
    mp_number half_threshold;
    mp_number v, vv;          /* temporary registers */
    new_number(v);
    new_number(vv);
    if (t == mp_dependent_type) {
        new_number_clone(threshold, fraction_threshold_k);
        new_number_clone(half_threshold, half_fraction_threshold_k);
    } else {
        new_number_clone(threshold, scaled_threshold_k);
        new_number_clone(half_threshold, half_scaled_threshold_k);
    }
    r = (mp_value_node) mp->temp_head;
    pp = mp_get_dep_info(p);
    qq = mp_get_dep_info(q);
    while (1) {
        if (pp == qq) {
            if (pp == NULL) {
                break;
            } else {
                /*
                    Contribute a term from |p|, plus |f| times the corresponding
                    term from |q|
                */
                mp_number r1;
                mp_number absv;
                new_fraction(r1);
                new_number(absv);
                if (tt == mp_dependent_type) {
                    take_fraction(r1, *f, mp_get_dep_value(q));
                } else {
                    take_scaled(r1, *f, mp_get_dep_value(q));
                }
                set_number_from_addition(v, mp_get_dep_value(p), r1);
                free_number(r1);
                mp_set_dep_value(p, v);
                s = p;
                p = (mp_value_node) mp_link(p);
                number_abs_clone(absv, v);
                if (number_less(absv, threshold)) {
                    mp_free_dep_node(mp, s);
                } else {
                    if (number_greaterequal(absv, coef_bound_k) && mp->watch_coefs) {
                        mp_type(qq) = independent_needing_fix;
                        /*
                            If we set this , then we can drop |(mp_type(pp) ==
                            independent_needing_fix && mp->fix_needed)| later
                            |set_number_from_scaled(mp_get_value_number(qq),
                            mp_get_indep_value(qq));|
                        */
                        mp->fix_needed = 1;
                    }
                    mp_set_link(r, s);
                    r = s;
                }
                free_number(absv);
                pp = mp_get_dep_info(p);
                q = (mp_value_node) mp_link(q);
                qq = mp_get_dep_info(q);
            }
        } else {
            if (pp == NULL) {
                set_number_to_negative_inf(v);
            } else if (mp_type(pp) == mp_independent_type || (mp_type(pp) == independent_needing_fix && mp->fix_needed)) {
                set_number_from_scaled(v, mp_get_indep_value(pp));
            } else {
                number_clone(v, mp_get_value_number(pp));
            }
            if (qq == NULL) {
                set_number_to_negative_inf(vv);
            } else if (mp_type(qq) == mp_independent_type || (mp_type(qq) == independent_needing_fix && mp->fix_needed)) {
                set_number_from_scaled(vv, mp_get_indep_value(qq));
            } else {
                number_clone(vv, mp_get_value_number(qq));
            }
            if (number_less(v, vv)) {
                /* Contribute a term from |q|, multiplied by~|f| */
                mp_number absv;
                {
                    mp_number r1;
                    mp_number arg1, arg2;
                    new_fraction(r1);
                    new_number_clone(arg1, *f);
                    new_number_clone(arg2, mp_get_dep_value(q));
                    if (tt == mp_dependent_type) {
                        take_fraction(r1, arg1, arg2);
                    } else {
                        take_scaled(r1, arg1, arg2);
                    }
                    number_clone(v, r1);
                    free_number(r1);
                    free_number(arg1);
                    free_number(arg2);
                }
                new_number_abs(absv, v);
                if (number_greater(absv, half_threshold)) {
                    s = mp_get_dep_node(mp);
                    mp_set_dep_info(s, qq);
                    mp_set_dep_value(s, v);
                    if (number_greaterequal(absv, coef_bound_k) && mp->watch_coefs) {
                        mp_type(qq) = independent_needing_fix;
                        mp->fix_needed = 1;
                    }
                    mp_set_link(r, s);
                    r = s;
                }
                q = (mp_value_node) mp_link(q);
                qq = mp_get_dep_info(q);
                free_number(absv);
            } else {
                mp_set_link(r, p);
                r = p;
                p = (mp_value_node) mp_link(p);
                pp = mp_get_dep_info(p);
            }
        }
    }
    {
        mp_number r1;
        mp_number arg1, arg2;
        new_fraction(r1);
        new_number(arg1);
        new_number(arg2);
        number_clone(arg1, mp_get_dep_value(q));
        number_clone(arg2, *f);
        if (t == mp_dependent_type) {
            take_fraction(r1, arg1, arg2);
        } else {
            take_scaled(r1, arg1, arg2);
        }
        slow_add(arg1, mp_get_dep_value(p), r1);
        mp_set_dep_value(p, arg1);
        free_number(r1);
        free_number(arg1);
        free_number(arg2);
    }
    mp_set_link(r, p);
    mp->dep_final = p;
    free_number(threshold);
    free_number(half_threshold);
    free_number(v);
    free_number(vv);
    return (mp_value_node) mp_link(mp->temp_head);
}

@ It is convenient to have another subroutine for the special case of |p_plus_fq|
when |f=1.0|. In this routine lists |p| and |q| are both of the same type~|t|
(either |dependent| or |mp_proto_dependent|).

@c
static mp_value_node mp_p_plus_q (MP mp, mp_value_node p, mp_value_node q, mp_variable_type t)
{
    mp_node pp, qq;      /* |mp_get_dep_info(p)| and |mp_get_dep_info(q)|, respectively */
    mp_value_node s;     /* for list manipulation */
    mp_value_node r;     /* for list manipulation */
    mp_number threshold; /* defines a neighborhood of zero */
    mp_number v, vv;     /* temporary register */
    new_number(v);
    new_number(vv);
    new_number(threshold);
    if (t == mp_dependent_type) {
        number_clone(threshold, fraction_threshold_k);
    } else {
        number_clone(threshold, scaled_threshold_k);
    }
    r = (mp_value_node) mp->temp_head;
    pp = mp_get_dep_info(p);
    qq = mp_get_dep_info(q);
    while (1) {
        if (pp == qq) {
            if (pp == NULL) {
                break;
            } else {
                /* Contribute a term from |p|, plus the corresponding term from |q| */
                mp_number test;
                new_number(test);
                set_number_from_addition(v, mp_get_dep_value(p), mp_get_dep_value(q));
                mp_set_dep_value(p, v);
                s = p;
                p = (mp_value_node) mp_link(p);
                pp = mp_get_dep_info(p);
                number_abs_clone(test, v);
                if (number_less(test, threshold)) {
                    mp_free_dep_node(mp, s);
                } else {
                    if (number_greaterequal(test, coef_bound_k) && mp->watch_coefs) {
                        mp_type(qq) = independent_needing_fix;
                        /*
                            If we set this , then we can drop |(mp_type(pp) ==
                            independent_needing_fix && mp->fix_needed)| later
                            |set_number_from_scaled(mp_get_value_number(qq),
                            mp_get_indep_value(qq));|
                        */
                        mp->fix_needed = 1;
                    }
                    mp_set_link(r, s);
                    r = s;
                }
                free_number(test);
                q = (mp_value_node) mp_link(q);
                qq = mp_get_dep_info(q);
            }

        } else {
            if (pp == NULL) {
                set_number_to_zero(v);
            } else if (mp_type(pp) == mp_independent_type || (mp_type(pp) == independent_needing_fix && mp->fix_needed)) {
                set_number_from_scaled(v, mp_get_indep_value(pp));
            } else {
                number_clone(v, mp_get_value_number(pp));
            }
            if (qq == NULL) {
                set_number_to_zero(vv);
            } else if (mp_type(qq) == mp_independent_type || (mp_type(qq) == independent_needing_fix && mp->fix_needed)) {
                set_number_from_scaled(vv, mp_get_indep_value(qq));
            } else {
                number_clone(vv, mp_get_value_number(qq));
            }
            if (number_less(v, vv)) {
                s = mp_get_dep_node(mp);
                mp_set_dep_info(s, qq);
                mp_set_dep_value(s, mp_get_dep_value(q));
                q = (mp_value_node) mp_link(q);
                qq = mp_get_dep_info(q);
                mp_set_link(r, s);
                r = s;
            } else {
                mp_set_link(r, p);
                r = p;
                p = (mp_value_node) mp_link(p);
                pp = mp_get_dep_info(p);
            }
        }
    }
    {
        mp_number r1;
        new_number(r1);
        slow_add(r1, mp_get_dep_value(p), mp_get_dep_value(q));
        mp_set_dep_value(p, r1);
        free_number(r1);
    }
    mp_set_link(r, p);
    mp->dep_final = p;
    free_number(v);
    free_number(vv);
    free_number(threshold);
    return (mp_value_node) mp_link(mp->temp_head);
}

@ A somewhat simpler routine will multiply a dependency list by a given
constant~|v|. The constant is either a |fraction| less than |fraction_one|, or it
is |scaled|. In the latter case we might be forced to convert a dependency list
to a proto-dependency list. Parameters |t0| and |t1| are the list types before
and after; they should agree unless |t0=mp_dependent| and |t1=mp_proto_dependent|
and |v_is_scaled=true|.

@c
static mp_value_node mp_p_times_v (MP mp, mp_value_node p, mp_number *v, int t0, int t1, int v_is_scaled)
{
    mp_value_node r, s; /* for list manipulation */
    mp_number w;        /* tentative coefficient */
    mp_number threshold;
    int scaling_down = (t0 != t1) ? 1 : (! v_is_scaled);
    new_number(threshold);
    new_number(w);
    if (t1 == mp_dependent_type) {
        number_clone(threshold, half_fraction_threshold_k);
    } else {
        number_clone(threshold, half_scaled_threshold_k);
    }
    r = (mp_value_node) mp->temp_head;
    while (mp_get_dep_info(p) != NULL) {
        mp_number test;
        new_number(test);
        if (scaling_down) {
            take_fraction(w, *v, mp_get_dep_value(p));
        } else {
            take_scaled(w, *v, mp_get_dep_value(p));
        }
        number_abs_clone(test, w);
        if (number_lessequal(test, threshold)) {
            s = (mp_value_node) mp_link(p);
            mp_free_dep_node(mp, p);
            p = s;
        } else {
            if (number_greaterequal(test, coef_bound_k)) {
                mp->fix_needed = 1;
                mp_type(mp_get_dep_info(p)) = independent_needing_fix;
            }
            mp_set_link(r, p);
            r = p;
            mp_set_dep_value(p, w);
            p = (mp_value_node) mp_link(p);
        }
        free_number(test);
    }
    mp_set_link(r, p);
    {
        mp_number r1;
        new_number(r1);
        if (v_is_scaled) {
            take_scaled(r1, mp_get_dep_value(p), *v);
        } else {
            take_fraction(r1, mp_get_dep_value(p), *v);
        }
        mp_set_dep_value(p, r1);
        free_number(r1);
    }
    free_number(w);
    free_number(threshold);
    return (mp_value_node) mp_link(mp->temp_head);
}

@ Similarly, we sometimes need to divide a dependency list by a given |scaled|
constant.

@<Declarations@>=
static mp_value_node mp_p_over_v (MP mp, mp_value_node p, mp_number *v, int t0, int t1);

@ @d p_over_v_threshold_k mp->math->md_p_over_v_threshold_t

@ @c
mp_value_node mp_p_over_v (MP mp, mp_value_node p, mp_number *v_orig, int t0, int t1)
{
    mp_value_node r, s; /* for list manipulation */
    mp_number w;        /* tentative coefficient */
    mp_number threshold;
    mp_number v;
    int scaling_down = (t0 != t1);
    new_number(w);
    new_number(threshold);
    new_number_clone(v, *v_orig);
    if (t1 == mp_dependent_type) {
        number_clone(threshold, half_fraction_threshold_k);
    } else {
        number_clone(threshold, half_scaled_threshold_k);
    }
    r = (mp_value_node) mp->temp_head;
    while (mp_get_dep_info(p) != NULL) {
        if (scaling_down) {
            mp_number x, absv;
            new_number_abs(absv, v);
            if (number_less(absv, p_over_v_threshold_k)) {
                new_number_clone(x, v);
                convert_scaled_to_fraction(x);
                make_scaled(w, mp_get_dep_value(p), x);
            } else {
                new_number_clone(x, mp_get_dep_value(p));
                fraction_to_round_scaled(x);
                make_scaled(w, x, v);
            }
            free_number(x);
            free_number(absv);
        } else {
            make_scaled(w, mp_get_dep_value(p), v);
        }
        {
            mp_number test;
            new_number(test);
            number_abs_clone(test, w);
            if (number_lessequal(test, threshold)) {
                s = (mp_value_node) mp_link(p);
                mp_free_dep_node(mp, p);
                p = s;
            } else {
                if (number_greaterequal(test, coef_bound_k)) {
                    mp->fix_needed = 1;
                    mp_type(mp_get_dep_info(p)) = independent_needing_fix;
                }
                mp_set_link(r, p);
                r = p;
                mp_set_dep_value(p, w);
                p = (mp_value_node) mp_link(p);
            }
            free_number(test);
        }
    }
    mp_set_link(r, p);
    {
        mp_number ret;
        new_number(ret);
        make_scaled(ret, mp_get_dep_value(p), v);
        mp_set_dep_value(p, ret);
        free_number(ret);
    }
    free_number(v);
    free_number(w);
    free_number(threshold);
    return (mp_value_node) mp_link(mp->temp_head);
}

@ Here's another utility routine for dependency lists. When an independent
variable becomes dependent, we want to remove it from all existing dependencies.
The |p_with_x_becoming_q| function computes the dependency list of~|p| after
variable~|x| has been replaced by~|q|.

This procedure has basically the same calling conventions as |p_plus_fq|:
List~|q| is unchanged; list~|p| is destroyed; the constant node and the final
link are inherited from~|p|; and the fourth parameter tells whether or not |p| is
|mp_proto_dependent|. However, the global variable |dep_final| is not altered if
|x| does not occur in list~|p|.

@c
static mp_value_node mp_p_with_x_becoming_q (MP mp, mp_value_node p, mp_node x, mp_node q, int t)
{
    mp_value_node s = p;
    mp_value_node r = (mp_value_node) mp->temp_head;
    int sx = mp_get_indep_value(x); /* serial number of |x| */
    while (mp_get_dep_info(s) != NULL && mp_get_indep_value(mp_get_dep_info(s)) > sx) {
        r = s;
        s = (mp_value_node) mp_link(s);
    }
    if (mp_get_dep_info(s) == NULL || mp_get_dep_info(s) != x) {
        return p;
    } else {
        mp_value_node ret;
        mp_number v1;
        mp_set_link(mp->temp_head, p);
        mp_set_link(r, mp_link(s));
        new_number_clone(v1, mp_get_dep_value(s));
        mp_free_dep_node(mp, s);
        ret = mp_p_plus_fq(mp, (mp_value_node) mp_link(mp->temp_head), &v1, (mp_value_node) q, t, mp_dependent_type);
        free_number(v1);
        return ret;
    }
}

@ Here's a simple procedure that reports an error when a variable has just
received a known value that's out of the required range.

@<Declarations@>=
static void mp_val_too_big (MP mp, mp_number *x);

@ @c
static void mp_val_too_big (MP mp, mp_number *x)
{
    if (number_positive(internal_value(mp_warning_check_internal))) {
        char msg[256];
        mp_snprintf(msg, 256, "Value is too large (%s)", number_tostring(*x));
        mp_error(
            mp,
            msg,
            "The equation I just processed has given some variable a value outside of the\n"
            "safetyp range. Continue and I'll try to cope with that big value; but it might be\n"
            "dangerous. (Set 'warningcheck := 0' to suppress this message.)"
        );
    }
}

@ When a dependent variable becomes known, the following routine removes its
dependency list. Here |p| points to the variable, and |q| points to the
dependency list (which is one node long).

@<Declarations@>=
static void mp_make_known (MP mp, mp_value_node p, mp_value_node q);

@ @c
void mp_make_known (MP mp, mp_value_node p, mp_value_node q)
{
    mp_variable_type t = mp_type(p); /* the previous type */
    mp_number absp;
    new_number(absp);
    mp_set_prev_dep(mp_link(q), mp_get_prev_dep(p));
    mp_set_link(mp_get_prev_dep(p), mp_link(q));
    mp_type(p) = mp_known_type;
    mp_set_value_number(p, mp_get_dep_value(q));
    mp_free_dep_node(mp, q);
    number_abs_clone(absp, mp_get_value_number(p));
    if (number_greaterequal(absp, warning_limit_t)) {
        mp_val_too_big (mp, &(mp_get_value_number(p)));
    }
    if ((number_positive(internal_value(mp_tracing_equations_internal))) && mp_interesting(mp, (mp_node) p)) {
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "#### ");
        mp_print_variable_name(mp, (mp_node) p);
        mp_print_chr(mp, '=');
        print_number(mp_get_value_number(p));
        mp_end_diagnostic(mp, 0);
    }
    if (cur_exp_node == (mp_node) p && mp->cur_exp.type == t) {
        mp->cur_exp.type = mp_known_type;
        mp_set_cur_exp_value_number(mp, &(mp_get_value_number(p)));
        mp_free_value_node(mp, (mp_node) p);
    }
    free_number(absp);
}

@ The |fix_dependencies| routine is called into action when |fix_needed|
has been triggered. The program keeps a list~|s| of independent variables
whose coefficients must be divided by~4.

In unusual cases, this fixup process might reduce one or more coefficients
to zero, so that a variable will become known more or less by default.

@<Declarations@>=
static void mp_fix_dependencies (MP mp);

@ @d independent_being_fixed 1 /* this variable already appears in |s| */

@ @c
static void mp_fix_dependencies (MP mp)
{
    mp_value_node r = (mp_value_node) mp_link(mp->dep_head);
    mp_value_node s = NULL;
    while (r != mp->dep_head) {
        /*
            Run through the dependency list for variable |t|, fixing all nodes,
            and ending with final link~|q|
        */
        mp_value_node t = r;
        mp_value_node q;
        while (1) {
            mp_node x;
            if (t == r) {
                q = (mp_value_node) mp_get_dep_list(t);
            } else {
                q = (mp_value_node) mp_link(r);
            }
            x = mp_get_dep_info(q);
            if (x == NULL) {
                break;
            } else if (mp_type(x) <= independent_being_fixed) {
                if (mp_type(x) < independent_being_fixed) {
                    mp_value_node p = mp_get_dep_node(mp);
                    mp_set_link(p, s);
                    s = p;
                    mp_set_dep_info(s, x);
                    mp_type(x) = independent_being_fixed;
                }
                mp_set_dep_value(q, mp_get_dep_value(q));
                number_divide_int(mp_get_dep_value(q), 4);
                if (number_zero(mp_get_dep_value(q))) {
                    mp_set_link(r, mp_link(q));
                    mp_free_dep_node(mp, q);
                    q = r;
                }
            }
            r = q;
        }
        r = (mp_value_node) mp_link(q);
        if (q == (mp_value_node) mp_get_dep_list(t)) {
            mp_make_known(mp, t, q);
        }
    }
    while (s != NULL) {
        mp_value_node p = (mp_value_node) mp_link(s);
        mp_node x = mp_get_dep_info(s);
        mp_free_dep_node(mp, s);
        s = p;
        mp_type(x) = mp_independent_type;
        mp_set_indep_scale(x, mp_get_indep_scale(x) + 2);
    }
    mp->fix_needed = 0;
}

@ The |new_dep| routine installs a dependency list~|p| based on the value
node~|q|, linking it into the list of all known dependencies. It replaces |q|
with the new dependency node. We assume that |dep_final| points to the final node
of list~|p|.

@c
static void mp_new_dep (MP mp, mp_node q, mp_variable_type newtype, mp_value_node p)
{
    mp_node r; /* what used to be the first dependency */
    mp_type(q) = newtype;
    mp_set_dep_list(q, p);
    mp_set_prev_dep(q, (mp_node) mp->dep_head);
    r = mp_link(mp->dep_head);
    mp_set_link(mp->dep_final, r);
    mp_set_prev_dep(r, (mp_node) mp->dep_final);
    mp_set_link(mp->dep_head, q);
}

@ Here is one of the ways a dependency list gets started.
The |const_dependency| routine produces a list that has nothing but
a constant term.

@c
static mp_value_node mp_const_dependency (MP mp, mp_number *v)
{
    mp->dep_final = mp_get_dep_node(mp);
    mp_set_dep_value(mp->dep_final, *v);
    mp_set_dep_info(mp->dep_final, NULL);
    return mp->dep_final;
}

@ And here's a more interesting way to start a dependency list from scratch: The
parameter to |single_dependency| is the location of an independent variable~|x|,
and the result is the simple dependency list |x+0|.

In the unlikely event that the given independent variable has been doubled so
often that we can't refer to it with a nonzero coefficient, |single_dependency|
returns the simple list `0'. This case can be recognized by testing that the
returned list pointer is equal to |dep_final|.

@d two_to_the(A) (1<<(unsigned)(A))

@ @c
static mp_value_node mp_single_dependency (MP mp, mp_node p)
{
    mp_value_node q; /* the new dependency list */
    int m = mp_get_indep_scale(p); /* the number of doublings */
    if (m > 28) {
        q = mp_const_dependency(mp, &zero_t);
    } else {
        mp_value_node rr;
        q = mp_get_dep_node(mp);
        mp_set_dep_value(q, zero_t);
        set_number_from_scaled(mp_get_dep_value(q), (int) two_to_the(28 - m));
        mp_set_dep_info(q, p);
        rr = mp_const_dependency(mp, &zero_t);
        mp_set_link(q, rr);
    }
    return q;
}

@ We sometimes need to make an exact copy of a dependency list.

@c
static mp_value_node mp_copy_dep_list (MP mp, mp_value_node p)
{
    mp_value_node q = mp_get_dep_node(mp); /* the new dependency list */
    mp->dep_final = q;
    while (1) {
        mp_set_dep_info(mp->dep_final, mp_get_dep_info(p));
        mp_set_dep_value(mp->dep_final, mp_get_dep_value(p));
        if (mp_get_dep_info(mp->dep_final) == NULL) {
            break;
        } else {
            mp_set_link(mp->dep_final, mp_get_dep_node(mp));
            mp->dep_final = (mp_value_node) mp_link(mp->dep_final);
            p = (mp_value_node) mp_link(p);
        }
    }
    return q;
}

@ But how do variables normally become known? Ah, now we get to the heart of the
equation-solving mechanism. The |linear_eq| procedure is given a |dependent| or
|mp_proto_dependent| list,~|p|, in which at least one independent variable
appears. It equates this list to zero, by choosing an independent variable with
the largest coefficient and making it dependent on the others. The newly
dependent variable is eliminated from all current dependencies, thereby possibly
making other dependent variables known.

The given list |p| is, of course, totally destroyed by all this processing.

@c
static mp_value_node find_node_with_largest_coefficient (MP mp, mp_value_node p, mp_number *v);

static void display_new_dependency (MP mp, mp_value_node p, mp_node x, int n);

static void change_to_known (MP mp, mp_value_node p, mp_node x, mp_value_node final_node, int n);

static mp_value_node divide_p_by_minusv_removing_q (MP mp,
    mp_value_node p, mp_value_node q,
    mp_value_node *final_node, mp_number *v, int t
);

static mp_value_node divide_p_by_2_n (MP mp, mp_value_node p, int n);

static void mp_linear_eq (MP mp, mp_value_node p, int t)
{
    mp_value_node r;          /* for link manipulation */
    mp_node x;                /* the variable that loses its independence */
    int n;                    /* the number of times |x| had been halved */
    mp_number v;              /* the coefficient of |x| in list |p| */
    mp_value_node prev_r;     /* lags one step behind |r| */
    mp_value_node final_node; /* the constant term of the new dependency list */
    mp_value_node qq;
    new_number(v);
    qq = find_node_with_largest_coefficient(mp, p, &v);
    x = mp_get_dep_info(qq);
    n = mp_get_indep_scale(x);
    p = divide_p_by_minusv_removing_q(mp, p, qq, &final_node, &v, t);
    if (number_positive(internal_value(mp_tracing_equations_internal))) {
        display_new_dependency(mp, p, (mp_node) x, n);
    }
    prev_r = (mp_value_node) mp->dep_head;
    r = (mp_value_node) mp_link(mp->dep_head);
    while (r != mp->dep_head) {
        mp_value_node s = (mp_value_node) mp_get_dep_list(r);
        mp_value_node q = mp_p_with_x_becoming_q(mp, s, x, (mp_node) p, mp_type(r));
        if (mp_get_dep_info(q) == NULL) {
            mp_make_known(mp, r, q);
        } else {
            mp_set_dep_list(r, q);
            do {
                q = (mp_value_node) mp_link(q);
            } while (mp_get_dep_info(q) != NULL);
            prev_r = q;
        }
        r = (mp_value_node) mp_link(prev_r);
    }
    if (n > 0) {
        p = divide_p_by_2_n(mp, p, n);
    }
    change_to_known(mp, p, (mp_node) x, final_node, n);
    if (mp->fix_needed) {
        mp_fix_dependencies(mp);
    }
    free_number(v);
}

@ @c
static mp_value_node find_node_with_largest_coefficient (MP mp, mp_value_node p, mp_number *v)
{
    mp_number vabs; /* its absolute value of v*/
    mp_number rabs; /* the absolute value of |mp_get_dep_value(r)| */
    mp_value_node q = p;
    mp_value_node r = (mp_value_node) mp_link(p);
    new_number(vabs);
    new_number(rabs);
    number_clone(*v, mp_get_dep_value(q));
    while (mp_get_dep_info(r) != NULL) {
        number_abs_clone(vabs, *v);
        number_abs_clone(rabs, mp_get_dep_value(r));
        if (number_greater(rabs, vabs)) {
            q = r;
            number_clone(*v, mp_get_dep_value(r));
        }
        r = (mp_value_node) mp_link(r);
    }
    free_number(vabs);
    free_number(rabs);
    return q;
}

@ Here we want to change the coefficients from |scaled| to |fraction|, except in
the constant term. In the common case of a trivial equation like |x=3.14|, we
will have |v=-fraction_one|, |q=p|, and |t=mp_dependent|.

@c
static mp_value_node divide_p_by_minusv_removing_q (MP mp,
    mp_value_node p, mp_value_node q,
    mp_value_node *final_node, mp_number *v, int t
)
{
    mp_value_node r = p; /* for link manipulation */
    mp_value_node s = (mp_value_node) mp->temp_head;
    mp_set_link(s, p);
    do {
        if (r == q) {
            mp_set_link(s, mp_link(r));
            mp_free_dep_node(mp, r);
        } else {
            mp_number w; /* a tentative coefficient */
            mp_number absw;
            new_number(w);
            new_number(absw);
            make_fraction(w, mp_get_dep_value(r), *v);
            number_abs_clone(absw, w);
            if (number_lessequal(absw, half_fraction_threshold_k)) {
                mp_set_link(s, mp_link(r));
                mp_free_dep_node(mp, r);
            } else {
                number_negate(w);
                mp_set_dep_value(r, w);
                s = r;
            }
            free_number(w);
            free_number(absw);
        }
        r = (mp_value_node) mp_link(s);
    } while (mp_get_dep_info(r) != NULL);
    if (t == mp_proto_dependent_type) {
        mp_number ret;
        new_number(ret);
        make_scaled(ret, mp_get_dep_value(r), *v);
        number_negate(ret);
        mp_set_dep_value(r, ret);
        free_number(ret);
    } else if (number_to_scaled(*v) != -number_to_scaled(fraction_one_t)) {
        mp_number ret;
        new_fraction(ret);
        make_fraction(ret, mp_get_dep_value(r), *v);
        number_negate(ret);
        mp_set_dep_value(r, ret);
        free_number(ret);
    }
    *final_node = r;
    return (mp_value_node) mp_link(mp->temp_head);
}

@ @c
static void display_new_dependency (MP mp, mp_value_node p, mp_node x, int n)
{
    if (mp_interesting(mp, x)) {
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "## ");
        mp_print_variable_name(mp, x);
        while (n > 0) {
            mp_print_str(mp, "*4");
            n = n - 2;
        }
        mp_print_chr(mp, '=');
        mp_print_dependency(mp, p, mp_dependent_type);
        mp_end_diagnostic(mp, 0);
    }
}

@ The |n > 0| test is repeated here because it is of vital importance to the
function's functioning.

@c
static mp_value_node divide_p_by_2_n (MP mp, mp_value_node p, int n)
{
    mp_value_node pp = NULL;
    if (n > 0) {
        /* Divide list |p| by $2^n$ */
        mp_value_node r;
        mp_value_node s;
        mp_number absw;
        mp_number w; /* a tentative coefficient */
        new_number(w);
        new_number(absw);
        s = (mp_value_node) mp->temp_head;
        mp_set_link(mp->temp_head, p);
        r = p;
        do {
            if (n > 30) {
                set_number_to_zero(w);
            } else {
                number_clone(w, mp_get_dep_value(r));
                number_divide_int(w, two_to_the(n));
            }
            number_abs_clone(absw, w);
            if (number_lessequal(absw, half_fraction_threshold_k) && (mp_get_dep_info(r) != NULL)) {
                mp_set_link(s, mp_link(r));
                mp_free_dep_node(mp, r);
            } else {
                mp_set_dep_value(r, w);
                s = r;
            }
            r = (mp_value_node) mp_link(s);
        } while (mp_get_dep_info(s) != NULL);
        pp = (mp_value_node) mp_link(mp->temp_head);
        free_number(absw);
        free_number(w);
    }
    return pp;
}

@ @c
static void change_to_known (MP mp, mp_value_node p, mp_node x, mp_value_node final_node, int n)
{
    (void) n;
    if (mp_get_dep_info(p) == NULL) {
        mp_number absx;
        mp_type(x) = mp_known_type;
        mp_set_value_number(x, mp_get_dep_value(p));
        new_number_abs(absx, mp_get_value_number(x));
        if (number_greaterequal(absx, warning_limit_t)) {
            mp_val_too_big(mp, &(mp_get_value_number(x)));
        }
        free_number(absx);
        mp_free_dep_node(mp, p);
        if (cur_exp_node == x && mp->cur_exp.type == mp_independent_type) {
            mp_set_cur_exp_value_number(mp, &(mp_get_value_number(x)));
            mp->cur_exp.type = mp_known_type;
            mp_free_value_node(mp, x);
        }
    } else {
        mp->dep_final = final_node;
        mp_new_dep(mp, x, mp_dependent_type, p);
        if (cur_exp_node == x && mp->cur_exp.type == mp_independent_type) {
            mp->cur_exp.type = mp_dependent_type;
        }
    }
}

@* Dynamic nonlinear equations.

Variables of numeric type are maintained by the general scheme of independent,
dependent, and known values that we have just studied; and the components of pair
and transform variables are handled in the same way. But \MP\ also has five other
types of values: |boolean|, |string|, |pen|, |path|, and |picture|;
what about them?

Equations are allowed between nonlinear quantities, but only in a simple form.
Two variables that haven't yet been assigned values are either equal to each
other, or they're not.

Before a boolean variable has received a value, its type is |mp_unknown_boolean|;
similarly, there are variables whose type is |mp_unknown_string|,
|mp_unknown_pen|, |mp_unknown_path|, and |mp_unknown_picture|. In such cases the
value is either |NULL| (which means that no other variables are equivalent to
this one), or it points to another variable of the same undefined type. The
pointers in the latter case form a cycle of nodes, which we shall call a
\quote {ring.} Rings of undefined variables may include capsules, which arise as
intermediate results within expressions or as |expr| parameters to macros.

When one member of a ring receives a value, the same value is given to all the
other members. In the case of paths and pictures, this implies making separate
copies of a potentially large data structure; users should restrain their
enthusiasm for such generality, unless they have lots and lots of memory space.

@ The following procedure is called when a capsule node is being added to a ring
(e.g., when an unknown variable is mentioned in an expression).

@c
static mp_node mp_new_ring_entry (MP mp, mp_node p)
{
    mp_node q = mp_new_value_node(mp); /* the new capsule node */
    mp_name_type(q) = mp_capsule_operation;
    mp_type(q) = mp_type(p);
    if (mp_get_value_node(p) == NULL) {
        mp_set_value_node(q, p);
    } else {
        mp_set_value_node(q, mp_get_value_node(p));
    }
    mp_set_value_node(p, q);
    return q;
}

@ Conversely, we might delete a capsule or a variable before it becomes known.
The following procedure simply detaches a quantity from its ring, without
recycling the storage.

@<Declarations@>=
static void mp_ring_delete (MP mp, mp_node p);

@ @c
void mp_ring_delete (MP mp, mp_node p)
{
    (void) mp;
    mp_node q = mp_get_value_node(p);
    if (q != NULL && q != p) {
        while (mp_get_value_node(q) != p) {
            q = mp_get_value_node(q);
        }
        mp_set_value_node(q, mp_get_value_node(p));
    }
}

@ Eventually there might be an equation that assigns values to all of the
variables in a ring. The |nonlinear_eq| subroutine does the necessary propagation
of values.

If the parameter |flush_p| is |true|, node |p| itself needn't receive a value, it
will soon be recycled.

@c
static void mp_nonlinear_eq (MP mp, mp_value v, mp_node p, int flush_p)
{
    mp_variable_type t = mp_type(p) - unknown_tag; /* the type of ring |p| */
    mp_node q = mp_get_value_node(p);
    if (flush_p) {
        mp_type(p) = mp_vacuous_type;
    } else {
        p = q;
    }
    do {
        mp_node r = mp_get_value_node(q);
        mp_type(q) = t;
        switch (t) {
            case mp_boolean_type:
                mp_set_value_number(q, v.data.n);
                break;
            case mp_string_type:
                mp_set_value_str(q, v.data.str);
                add_str_ref(v.data.str);
                break;
            case mp_pen_type:
            case mp_nep_type:
                mp_set_value_knot(q, mp_copy_pen(mp, v.data.p));
                break;
            case mp_path_type:
                mp_set_value_knot(q, mp_copy_path(mp, v.data.p));
                break;
            case mp_picture_type:
                mp_set_value_node(q, v.data.node);
                mp_add_edge_ref(mp, v.data.node);
                break;
            default:
                break;
        }
        /* there ain't no more cases */
        q = r;
    } while (q != p);
}

@ If two members of rings are equated, and if they have the same type, the
|ring_merge| procedure is called on to make them equivalent.

@c
static void mp_ring_merge (MP mp, mp_node p, mp_node q)
{
    mp_node r = mp_get_value_node(p); /* traverses one list */
    while (r != p) {
        if (r == q) {
            mp_exclaim_redundant_equation(mp);
            return;
        } else {
            r = mp_get_value_node(r);
        }
    }
    r = mp_get_value_node(p);
    mp_set_value_node(p, mp_get_value_node(q));
    mp_set_value_node(q, r);
}

@ @c
static void mp_exclaim_redundant_equation (MP mp)
{
    mp_back_error(
        mp,
        "Redundant equation",
        "I already knew that this equation was true. But perhaps no harm has been done;\n"
        "let's continue."
    );
    mp_get_x_next(mp);
}

@ @<Declarations@>=
static void mp_exclaim_redundant_equation (MP mp);

@* Introduction to the syntactic routines.

Let's pause a moment now and try to look at the Big Picture. The \MP\ program
consists of three main parts: syntactic routines, semantic routines, and output
routines. The chief purpose of the syntactic routines is to deliver the user's
input to the semantic routines, while parsing expressions and locating operators
and operands. The semantic routines act as an interpreter responding to these
operators, which may be regarded as commands. And the output routines are
periodically called on to produce compact font descriptions that can be used for
typesetting or for making interim proof drawings. We have discussed the basic
data structures and many of the details of semantic operations, so we are good
and ready to plunge into the part of \MP\ that actually controls the activities.

Our current goal is to come to grips with the |get_next| procedure, which is the
keystone of \MP's input mechanism. Each call of |get_next| sets the value of
three variables |cur_cmd|, |cur_mod|, and |cur_sym|, representing the next input
token.

$$
\vbox{\halign{#\hfil\cr
  \hbox{|cur_cmd| denotes a command code from the long list of codes given
        earlier;}\cr
  \hbox{|cur_mod| denotes a modifier or operand of the command code;}\cr
  \hbox{|cur_sym| is the hash address of the symbolic token that was just
        scanned,}\cr
  \hbox{\qquad or zero in the case of a numeric or string or capsule
        token.}\cr}}
$$

Underlying this external behavior of |get_next| is all the machinery necessary to
convert from character files to tokens. At a given time we may be only partially
finished with the reading of several files (for which |input| was specified),
and partially finished with the expansion of some user-defined macros and/or some
macro parameters, and partially finished reading some text that the user has
inserted online, and so on. When reading a character file, the characters must be
converted to tokens; comments and blank spaces must be removed, numeric and
string tokens must be evaluated.

To handle these situations, which might all be present simultaneously, \MP\ uses
various stacks that hold information about the incomplete activities, and there
is a finite state control for each level of the input mechanism. These stacks
record the current state of an implicitly recursive process, but the |get_next|
procedure is not recursive.

@d cur_cmd               mp->cur_mod_->command
@d cur_mod               number_to_scaled(mp->cur_mod_->data.n)
@d cur_mod_number        mp->cur_mod_->data.n
@d cur_mod_node          mp->cur_mod_->data.node
@d cur_mod_str           mp->cur_mod_->data.str
@d cur_sym               mp->cur_mod_->data.sym
@d cur_sym_mod           mp->cur_mod_->name_type

@d set_cur_cmd(A)        mp->cur_mod_->command = (A)
@d set_cur_mod(A)        set_number_from_scaled(mp->cur_mod_->data.n, (A))
@d set_cur_mod_number(A) number_clone(mp->cur_mod_->data.n, (A))
@d set_cur_mod_node(A)   mp->cur_mod_->data.node = (A)
@d set_cur_mod_str(A)    mp->cur_mod_->data.str = (A)
@d set_cur_sym(A)        mp->cur_mod_->data.sym = (A)
@d set_cur_sym_mod(A)    mp->cur_mod_->name_type = (A)

@<Glob...@>=
mp_node cur_mod_; /* current command, symbol, and its operands */

@ @<Initialize table...@>=
mp->cur_mod_ = mp_new_symbolic_node(mp);

@ @<Free table...@>=
mp_free_symbolic_node(mp, mp->cur_mod_);

@ The |print_cmd_mod| routine prints a symbolic interpretation of a command code
and its modifier. It consists of a rather tedious sequence of print commands, and
most of it is essentially an inverse to the |primitive| routine that enters a
\MP\ primitive into |hash| and |eqtb|. Therefore almost all of this procedure
appears elsewhere in the program, together with the corresponding |primitive|
calls.

@<Declarations@>=
static const char *mp_cmd_mod_string (MP mp, int c, int m);
static void        mp_print_cmd_mod  (MP mp, int c, int m);

@ @c
const char *mp_cmd_mod_string (MP mp, int c, int m)
{
    switch (c) {
        @<Cases of |print_cmd_mod| for symbolic printing of primitives@>
    }
    return "[unknown command code!]";
}

void mp_print_cmd_mod (MP mp, int c, int m)
{
    mp_print_str(mp, mp_cmd_mod_string(mp, c, m));
}

@ Here is a procedure that displays a given command in braces, in the
user's transcript file.

@c
static void mp_show_cmd_mod (MP mp, int c, int m)
{
    mp_begin_diagnostic(mp);
    mp_print_nl(mp, "{");
    switch (c) {
        case mp_primary_def_command:
        case mp_secondary_def_command:
        case mp_tertiary_def_command:
            mp_print_cmd_mod(mp, mp_macro_def_command, c);
            mp_print_str(mp, "'d macro:");
            mp_print_ln(mp);
            mp_show_token_list(mp, mp_link(mp_link(cur_mod_node)),0);
            break;
        default:
            mp_print_cmd_mod(mp, c, m);
            break;
    }
    mp_print_chr(mp, '}');
    mp_end_diagnostic(mp, 0);
}

@* Input stacks and states.

The state of \MP's input mechanism appears in the input stack, whose entries are
records with five fields, called |index|, |start|, |loc|, |limit|, and |name|.
The top element of this stack is maintained in a global variable for which no
subscripting needs to be done; the other elements of the stack appear in an
array. Hence the stack is declared thus:

@<Types...@>=
typedef struct mp_in_state_record {
    int       start_field;
    int       loc_field;
    int       limit_field;
    int       index_field;
    mp_node   nstart_field;
    mp_node   nloc_field;
    mp_string name_field;
} mp_in_state_record;

@ @<Glob...@>=
mp_in_state_record *input_stack;
int                 input_ptr;    /* first unused location of |input_stack| */
int                 max_in_stack; /* largest value of |input_ptr| when pushing */
mp_in_state_record  cur_input;    /* the \quote {top} input state */
int                 stack_size;   /* maximum number of simultaneous input sources */

@ @<Allocate or initialize ...@>=
mp->stack_size = 16;
mp->input_stack = mp_memory_allocate((size_t) (mp->stack_size + 1) * sizeof(mp_in_state_record));

@ @<Dealloc variables@>=
mp_memory_free(mp->input_stack);

@ We've already defined the special variable |loc==cur_input.loc_field| in our
discussion of basic input-output routines. The other components of |cur_input|
are defined in the same way:

@d iindex mp->cur_input.index_field /* reference for buffer information */
@d start  mp->cur_input.start_field /* starting position in |buffer| */
@d limit  mp->cur_input.limit_field /* end of current line in |buffer| */
@d name   mp->cur_input.name_field  /* name of the current file */

@ Let's look more closely now at the five control variables
(|index|,~|start|,~|loc|,~|limit|,~|name|), assuming that \MP\ is reading a line
of characters that have been input from some file or from the user's terminal.
There is an array called |buffer| that acts as a stack of all lines of characters
that are currently being read from files, including all lines on subsidiary
levels of the input stack that are not yet completed. \MP\ will return to the
other lines when it is finished with the present input file.

(Incidentally, on a machine with byte-oriented addressing, it would be
appropriate to combine |buffer| with the |str_pool| array, letting the buffer
entries grow downward from the top of the string pool and checking that these two
tables don't bump into each other.)

The line we are currently working on begins in position |start| of the buffer;
the next character we are about to read is |buffer[loc]|; and |limit| is the
location of the last character present. We always have |loc<=limit|. For
convenience, |buffer[limit]| has been set to |"%"|, so that the end of a line is
easily sensed.

The |name| variable is a string number that designates the name of the current
file, if we are reading an ordinary text file. Special codes
|is_term..max_spec_src| indicate other sources of input text.

@d is_term    (mp_string) 0 /* |name| value when reading from the terminal for normal input */
@d is_read    (mp_string) 1 /* |name| value when executing a |readstring| or |readfrom| */
@d is_scantok (mp_string) 2 /* |name| value when reading text generated by |scantokens| */

@d max_spec_src is_scantok

@ Additional information about the current line is available via the |index|
variable, which counts how many lines of characters are present in the buffer
below the current level. We have |index=0| when reading from the terminal and
prompting the user for each line; then if the user types, e.g., |input figs|,
we will have |index=1| while reading the file |figs.mp|. However, it does not
follow that |index| is the same as the input stack pointer, since many of the
levels on the input stack may come from token lists.

The global variable |in_open| is equal to the highest |index| value excluding
token-list input levels. Thus, the number of partially read lines in the buffer
is |in_open+1| and we have |in_open>=index| when we are not reading a token list.

If we are not currently reading from the terminal, we are reading from the file
variable |input_file[index]|. We use the notation |terminal_input| as a
convenient abbreviation for |name=is_term|, and |cur_file| as an abbreviation for
|input_file[index]|.

When \MP\ is not reading from the terminal, the global variable |line| contains
the line number in the current file, for use in error messages. More precisely,
|line| is a macro for |line_stack[index]| and the |line_stack| array gives the
line number for each file in the |input_file| array.

If more information about the input state is needed, it can be included in small
arrays like those shown here. For example, the current page or segment number in
the input file might be put into a variable |page|, that is really a macro for
the current entry in `\ignorespaces|page_stack:array[0..max_in_open] of
integer|\unskip' by analogy with |line_stack|. @^system dependencies@>

@d terminal_input (name == is_term)      /* are we reading from the terminal? */
@d cur_file       mp->input_file[iindex] /* the current |void *| variable */
@d line           mp->line_stack[iindex] /* current line number in the current source file */

@<Glob...@>=
int            in_open;     /* the number of lines in the buffer, less one */
int            in_open_max; /* highest value of |in_open| ever seen */
unsigned int   open_parens; /* the number of open text files */
void         **input_file;
int           *line_stack;  /* the line number for each file */

@ @<Declarations@>=
static void mp_reallocate_input_stack (MP mp, int newsize);

@ @c
static void mp_reallocate_input_stack (MP mp, int newsize)
{
    int n = newsize + 1;
    mp->input_file = mp_memory_reallocate(mp->input_file, (size_t) (n + 1) * sizeof(void *));
    mp->line_stack = mp_memory_reallocate(mp->line_stack, (size_t) (n + 1) * sizeof(int));
    for (int k = mp->max_in_open; k <= n; k++) {
        mp->input_file[k] = NULL;
        mp->line_stack[k] = 0;
    }
    mp->max_in_open = newsize;
}

@ This has to be more than |file_bottom|, so:
@<Allocate or ...@>=
mp_reallocate_input_stack(mp, mp_file_bottom_text + 4);

@ @<Dealloc variables@>=
mp_memory_free(mp->input_file);
mp_memory_free(mp->line_stack);

@ However, all this discussion about input state really applies only to the case
that we are inputting from a file. There is another important case, namely when
we are currently getting input from a token list. In this case
|iindex>max_in_open|, and the conventions about the other state variables are
different:

\yskip\hang|nloc| is a pointer to the current node in the token list, i.e., the
node that will be read next. If |nloc=NULL|, the token list has been fully read.

\yskip\hang|start| points to the first node of the token list; this node may or
may not contain a reference count, depending on the type of token list involved.

\yskip\hang|token_type|, which takes the place of |iindex| in the discussion
above, is a code number that explains what kind of token list is being scanned.

\yskip\hang|name| points to the |eqtb| address of the control sequence being
expanded, if the current token list is a macro not defined by |vardef|. Macros
defined by |vardef| have |name=NULL|; their name can be deduced by looking at
their first two parameters.

\yskip\hang|param_start|, which takes the place of |limit|, tells where the
parameters of the current macro or loop text begin in the |param_stack|.

\yskip\noindent The |token_type| can take several values, depending on where the
current token list came from:

\yskip \indent|forever_text|, if the token list being scanned is the body of a
|forever| loop;

\indent|loop_text|, if the token list being scanned is the body of a |for| or
|forsuffixes| loop;

\indent|parameter|, if a |text| or |suffix| parameter is being scanned;

\indent|backed_up|, if the token list being scanned has been inserted as `to be
read again'.

\indent|inserted|, if the token list being scanned has been inserted as part of
error recovery;

\indent|macro|, if the expansion of a user-defined symbolic token is being
scanned.

\yskip\noindent The token list begins with a reference count if and only if
|token_type= macro|. @^reference counts@>

@d nloc   mp->cur_input.nloc_field   /* location of next node node */
@d nstart mp->cur_input.nstart_field /* location of next node node */

@d token_type  iindex                  /* type of current token list */
@d token_state (iindex<=mp_macro_text) /* are we scanning a token list? */
@d file_state  (iindex>mp_macro_text)  /* are we scanning a file line? */
@d param_start limit                   /* base of macro parameters in |param_stack| */


@ @<Enumeration types@>=
typedef enum mp_text_codes {
    mp_forever_text,     /* |token_type| code for loop texts */
    mp_loop_text,        /* |token_type| code for loop texts */
    mp_parameter_text,   /* |token_type| code for parameter texts */
    mp_backed_up_text,   /* |token_type| code for texts to be reread */
    mp_inserted_text,    /* |token_type| code for inserted texts */
    mp_macro_text,       /* |token_type| code for macro replacement texts */
    mp_file_bottom_text, /* lowest file code */
} mp_text_codes;

@ The |param_stack| is an auxiliary array used to hold pointers to the token
lists for parameters at the current level and subsidiary levels of input. This
stack grows at a different rate from the others, and is dynamically reallocated
when needed.

@<Glob...@>=
mp_node *param_stack;     /* token list pointers for parameters */
int      param_ptr;       /* first unused entry in |param_stack| */
int      max_param_stack; /* largest value of |param_ptr| */

@ @<Allocate or initialize ...@>=
mp->param_stack = mp_memory_allocate((size_t) (mp->param_size + 1) * sizeof(mp_node));

@ @c
static void mp_check_param_size (MP mp, int k)
{
    while (k >= mp->param_size) {
        mp->param_stack = mp_memory_reallocate(mp->param_stack, (size_t) ((k + k / 4) + 1) * sizeof(mp_node));
        mp->param_size = k + k / 4;
    }
}

@ @<Dealloc variables@>=
mp_memory_free(mp->param_stack);

@ Notice that the |line| isn't valid when |token_state| is true because it
depends on |iindex|. If we really need to know the line number for the topmost
file in the iindex stack we use the following function. If a page number or other
information is needed, this routine should be modified to compute it as well.
@^system dependencies@>

@<Declarations@>=
static int mp_true_line (MP mp);

@ @c
int mp_true_line (MP mp)
{
    int k; /* an index into the input stack */
    if (file_state && (name > max_spec_src)) {
        return line;
    } else {
        k = mp->input_ptr;
        while ((k > 0) && ((mp->input_stack[(k - 1)].index_field <  mp_file_bottom_text)
                        || (mp->input_stack[(k - 1)].name_field  <= max_spec_src))) {
            --k;
        }
        return (k > 0 ? mp->line_stack[(k - 1) + mp_file_bottom_text] : 0);
    }
}

@ Thus, the \quote {current input state} can be very complicated indeed; there can be
many levels and each level can arise in a variety of ways. The |show_context|
procedure, which is used by \MP's error-reporting routine to print out the
current input state on all levels down to the most recent line of characters from
an input file, illustrates most of these conventions. The global variable
|file_ptr| contains the lowest level that was displayed by this procedure.

@<Glob...@>=
int file_ptr; /* shallowest level shown by |show_context| */

@ The status at each level is indicated by printing two lines, where the first
line indicates what was read so far and the second line shows what remains to be
read. Non-current input levels whose |token_type| is |backed_up| are shown only if
they have not been fully read.

@c
void mp_show_context (MP mp)
{
    /* prints where the scanner is */
    mp->file_ptr = mp->input_ptr;
    mp->input_stack[mp->file_ptr] = mp->cur_input;
    /* store current state */
    while (1) {
        /* enter into the context */
        mp->cur_input = mp->input_stack[mp->file_ptr];
        @<Display the current context@>
        if (file_state && (name > max_spec_src || mp->file_ptr == 0)) {
            break;
        } else {
            --mp->file_ptr;
        }
    }
    /* restore original state */
    mp->cur_input = mp->input_stack[mp->input_ptr];
}

@ @<Display the current context@>=
/* we omit backed-up token lists that have already been read */
if ((mp->file_ptr == mp->input_ptr) || file_state || (token_type != mp_backed_up_text) || (nloc != NULL)) {
    if (file_state) {
        @<Print location of current line@>
        if (limit > 0) {
            for (int i = start; i <= limit - 1; i++) {
                mp_print_chr(mp, mp->buffer[i]);
            }
        }
    } else {
        @<Print type of token list@>
        if (token_type == mp_macro_text) {
            mp_show_macro(mp, nstart, nloc);
        } else if (mp->show_mode) {
            mp_show_token_list_space(mp, nstart, nloc);
        } else {
            mp_show_token_list(mp, nstart, nloc);
        }
    }
}

@ This routine should be changed, if necessary, to give the best possible
indication of where the current line resides in the input file. For example, on
some systems it is best to print both a page and line number. @^system
dependencies@>

@<Print location of current line@>=
if (name > max_spec_src) {
 /* mp_print_nl(mp, "l."); */
    mp_print_nl(mp, "<line ");
    mp_print_int(mp, mp_true_line(mp));
    mp_print_chr(mp, '>');
} else if (terminal_input) {
    if (mp->file_ptr == 0) {
        mp_print_nl(mp, "<direct>");
    } else {
        mp_print_nl(mp, "<insert>");
    }
} else if (name == is_scantok) {
    mp_print_nl(mp, "<scantokens>");
} else {
    mp_print_nl(mp, "<read>");
}
mp_print_chr(mp, ' ');

@ Can't use case statement here because the |token_type| is not a constant
expression.

@<Print type of token list@>=
{
    switch (token_type) {
        case mp_forever_text:
            mp_print_nl(mp, "<forever> ");
            break;
        case mp_loop_text:
            @<Print the current loop value@>
            break;
        case mp_parameter_text:
            mp_print_nl(mp, "<argument> ");
            break;
        case mp_backed_up_text:
            mp_print_nl(mp, nloc == NULL ? "<recently read> " : "<to be read again> ");
            break;
        case mp_inserted_text:
            mp_print_nl(mp, "<inserted text> ");
            break;
        case mp_macro_text:
            mp_print_nl(mp, "<macro> ");
         // mp_print_ln(mp);
            if (name != NULL) {
                mp_print_mp_str(mp, name);
            } else {
                @<Print the name of a |vardef|'d macro@>
            }
        //  mp_print_str(mp, "->");
            mp_print_str(mp, " -> ");
            break;
        default:
            mp_print_nl(mp, "?"); /* this should never happen */
            @.?\relax@>
            break;
    }
}

@ The parameter that corresponds to a loop text is either a token list (in the
case of |forsuffixes|) or a \quote {capsule} (in the case of |for|). We'll discuss
capsules later; for now, all we need to know is that the |link| field in a
capsule parameter is |void| and that |print_exp(p,0)| displays the value of
capsule~|p| in abbreviated form.

@<Print the current loop value@>=
{
    mp_node pp = mp->param_stack[param_start];
    mp_print_nl(mp, "<for(");
    if (pp != NULL) {
        if (mp_link(pp) == MP_VOID) {
            mp_print_exp(mp, pp, 0); /* we're in a |for| loop */
        } else {
            mp_show_token_list(mp, pp, NULL);
        }
    }
    mp_print_str(mp, ")> ");
}

@ The first two parameters of a macro defined by |vardef| will be token
lists representing the macro's prefix and \quote {at point.} By putting these
together, we get the macro's full name.

@<Print the name of a |vardef|'d macro@>=
{
    mp_node pp = mp->param_stack[param_start];
    if (pp == NULL) {
        mp_show_token_list(mp, mp->param_stack[param_start + 1], NULL);
    } else {
        mp_node qq = pp;
        while (mp_link(qq) != NULL) {
            qq = mp_link(qq);
        }
        mp_link(qq) = mp->param_stack[param_start + 1];
        mp_show_token_list(mp, pp, NULL);
        mp_link(qq) = NULL;
    }
}

@* Maintaining the input stacks.

The following subroutines change the input status in commonly needed ways.

First comes |mp_push_input|, which stores the current state and creates a
new level (having, initially, the same properties as the old). We could have
a maximum depth here.

@<Declarations@>=
static void mp_push_input (MP mp);

@ @c
void mp_push_input (MP mp)
{
    if (mp->input_ptr > mp->max_in_stack) {
        mp->max_in_stack = mp->input_ptr;
        if (mp->input_ptr == mp->stack_size) {
            int l = (mp->stack_size + (mp->stack_size/4));
            if (l > 1000) {
                mp_fatal_error(mp, "job aborted, more than 1000 input levels");
            } else {
                mp_in_state_record *s = mp_memory_reallocate(mp->input_stack, (size_t) (l + 1) * sizeof(mp_in_state_record));
                if (s) {
                    mp->input_stack = s;
                    mp->stack_size = l;
                } else {
                    mp_fatal_error(mp, "job aborted, out of memory");
                }
            }
        }
    }
    mp->input_stack[mp->input_ptr] = mp->cur_input;
    ++mp->input_ptr;
}

@ And of course what goes up must come down.

@<Declarations@>=
static void mp_pop_input (MP mp);

@ @c

void mp_pop_input (MP mp)
{
    --mp->input_ptr;
    mp->cur_input = mp->input_stack[mp->input_ptr];
}

@ Here is a procedure that starts a new level of token-list input, given a token
list |p| and its type |t|. If |t=macro|, the calling routine should set |name|,
reset~|loc|, and increase the macro's reference count.

@c
static void mp_begin_token_list (MP mp, mp_node p, int t)
{
    mp_push_input(mp);
    nstart = p;
    token_type = t;
    param_start = mp->param_ptr;
    nloc = p;
}

@ When a token list has been fully scanned, the following computations should be
done as we leave that level of input. @^inner loop@>

@c
static void mp_end_token_list (MP mp)
{
    /* leave a token-list input level */
    if (token_type >= mp_backed_up_text) {
        /* token list to be deleted */
        if (token_type <= mp_inserted_text) {
            mp_flush_token_list(mp, nstart);
            goto DONE;
        } else {
            /* update reference count */
            mp_delete_mac_ref(mp, nstart);
        }
    }
    while (mp->param_ptr > param_start) {
        /* parameters must be flushed */
        mp_node p; /* temporary register */
        --mp->param_ptr;
        p = mp->param_stack[mp->param_ptr];
        if (p != NULL) {
            if (mp_link(p) == MP_VOID) {
                /* it's an |expr| parameter */
                mp_recycle_value(mp, p);
                mp_free_value_node(mp, p);
            } else {
                /* it's a |suffix| or |text| parameter */
                mp_flush_token_list(mp, p);
            }
        }
    }
  DONE:
    mp_pop_input(mp);
}

@ The contents of |cur_cmd, cur_mod, cur_sym| are placed into an equivalent
token by the |cur_tok| routine.
@^inner loop@>

@c
@<Declare the procedure called |make_exp_copy|@>
static mp_node mp_cur_tok (MP mp)
{
    mp_node p; /* a new token node */
    if (cur_sym == NULL && (cur_sym_mod == 0 || cur_sym_mod == mp_normal_operation)) {
        if (cur_cmd == mp_capsule_command) {
            mp_number save_exp_num;          /* possible |cur_exp| numerical to be restored */
            mp_value save_exp = mp->cur_exp; /* |cur_exp| to be restored */
            new_number(save_exp_num);
            number_clone(save_exp_num, cur_exp_value_number);
            mp_make_exp_copy(mp, cur_mod_node);
            p = mp_stash_cur_exp(mp);
            mp_link(p) = NULL;
            mp->cur_exp = save_exp;
            number_clone(mp->cur_exp.data.n, save_exp_num);
            free_number(save_exp_num);
        } else {
            p = mp_new_token_node(mp);
            mp_name_type(p) = mp_token_operation;
            if (cur_cmd == mp_numeric_command) {
                mp_set_value_number(p, cur_mod_number);
                mp_type(p) = mp_known_type;
            } else {
                mp_set_value_str(p, cur_mod_str);
                mp_type(p) = mp_string_type;
            }
        }
    } else {
        p = mp_new_symbolic_node(mp);
        mp_set_sym_sym(p, cur_sym);
        mp_name_type(p) = cur_sym_mod;
    }
    return p;
}

@ Sometimes \MP\ has read too far and wants to \quote {unscan} what it has seen. The
|back_input| procedure takes care of this by putting the token just scanned back
into the input stream, ready to be read again. If |cur_sym<>0|, the values of
|cur_cmd| and |cur_mod| are irrelevant.

@<Declarations@>=
static void mp_back_input (MP mp);

@ @c
void mp_back_input (MP mp)
{
    /* undoes one token of input */
    mp_node p = mp_cur_tok(mp); /* a token list of length one */
    /* conserve stack space */
    while (token_state && (nloc == NULL)) {
        mp_end_token_list(mp);
    }
    mp_begin_token_list(mp, p, mp_backed_up_text);
}

@ The |back_error| routine is used when we want to restore or replace an
offending token just before issuing an error message.

@<Declarations@>=
static void mp_back_error (MP mp, const char *msg, const char *hlp) ;

@ @c
static void mp_back_error (MP mp, const char *msg, const char *hlp)
{
    /* back up one token and call |error| */
    mp_back_input(mp);
    mp_error(mp, msg, hlp);
}

static void mp_ins_error (MP mp, const char *msg, const char *hlp)
{
    /* back up one inserted token and call |error| */
    mp_back_input(mp);
    token_type = mp_inserted_text;
    mp_error(mp, msg, hlp);
}

@ The |begin_file_reading| procedure starts a new level of input for lines of
characters to be read from a file, or as an insertion from the terminal. It does
not take care of opening the file, nor does it set |loc| or |limit| or |line|.
@^system dependencies@>

@c
void mp_begin_file_reading (MP mp)
{
    if (mp->in_open == (mp->max_in_open-1)) {
        mp_reallocate_input_stack (mp, (mp->max_in_open + mp->max_in_open / 4));
    }
    if (mp->first == mp->buf_size) {
        mp_reallocate_buffer(mp, (mp->buf_size + mp->buf_size / 4));
    }
    mp->in_open++;
    mp_push_input(mp);
    iindex = (int) mp->in_open;
    if (mp->in_open_max < mp->in_open) {
        mp->in_open_max = mp->in_open;
    }
    start = (int) mp->first;
    name = is_term; /* |terminal_input| is now |true| */
}

@ Conversely, the variables must be downdated when such a level of input is
finished. While finishing preloading, it is possible that the file does not
actually end with 'dump', so we capture that case here as well.

@c
static void mp_end_file_reading (MP mp)
{
    if (mp->in_open > iindex) {
        if ((name <= max_spec_src)) {
            mp_confusion(mp, "endinput");
            @:this can't happen endinput}{\quad endinput@>
        } else {
            (mp->close_file) (mp, mp->input_file[mp->in_open]);
            --mp->in_open;
        }
    }
    mp->first = (size_t) start;
    if (iindex != mp->in_open) {
        mp_confusion(mp, "endinput");
    } else {
        if (name > max_spec_src) {
            (mp->close_file) (mp, cur_file);
        }
        mp_pop_input(mp);
        --mp->in_open;
    }
}

@* Getting the next token.

The heart of \MP's input mechanism is the |get_next| procedure, which we shall
develop in the next few sections of the program. Perhaps we shouldn't actually
call it the \quote {heart,} however; it really acts as \MP's eyes and mouth, reading
the source files and gobbling them up. And it also helps \MP\ to regurgitate
stored token lists that are to be processed again.

The main duty of |get_next| is to input one token and to set |cur_cmd| and
|cur_mod| to that token's command code and modifier. Furthermore, if the input
token is a symbolic token, that token's |hash| address is stored in |cur_sym|;
otherwise |cur_sym| is set to zero.

Underlying this simple description is a certain amount of complexity because of
all the cases that need to be handled. However, the inner loop of |get_next| is
reasonably short and fast.

@ Before getting into |get_next|, we need to consider a mechanism by which \MP\
helps keep errors from propagating too far. Whenever the program goes into a mode
where it keeps calling |get_next| repeatedly until a certain condition is met, it
sets |scanner_status| to some value other than |normal|. Then if an input file
ends, or if an |outer| symbol appears, an appropriate error recovery will be
possible.

The global variable |warning_info| helps in this error recovery by providing
additional information. For example, |warning_info| might indicate the name of a
macro whose replacement text is being scanned.

@ @<Enumeration types@>=
typedef enum mp_scanner_states {
    mp_normal_state,        /* |scanner_status| at \quote {quiet times} */
    mp_skipping_state,      /* |scanner_status| when false conditional text is being skipped */
    mp_flushing_state,      /* |scanner_status| when junk after a statement is being ignored */
    mp_absorbing_state,     /* |scanner_status| when a |text| parameter is being scanned */
    mp_var_defining_state,  /* |scanner_status| when a |vardef| is being scanned */
    mp_op_defining_state,   /* |scanner_status| when a macro |def| is being scanned */
    mp_loop_defining_state, /* |scanner_status| when a |for| loop is being scanned */
    mp_tex_flushing_state,
} mp_scanner_states;

@ @<Glob...@>=
int     scanner_status;  /* are we scanning at high speed? */
mp_sym  warning_info;    /* if so, what else do we need to know, in case an error occurs? */
int     warning_line;
mp_node warning_info_node;

@ The following subroutine is called when an |outer| symbolic token has been
scanned or when the end of a file has been reached. These two cases are
distinguished by |cur_sym|, which is zero at the end of a file.

@c
static int mp_check_outer_validity (MP mp)
{
    if (mp->scanner_status == mp_normal_state) {
        return 1;
    } else if (mp->scanner_status == mp_tex_flushing_state) {
        @<Check if the file has ended while flushing \TeX\ material and set the result value for |check_outer_validity|@>
    } else {
        @<Back up an outer symbolic token so that it can be reread@>
        if (mp->scanner_status > mp_skipping_state) {
            @<Tell the user what has run away and try to recover@>
        } else {
            char msg[256];
            const char *hlp = NULL;
            mp_snprintf(msg, 256, "Incomplete if; all text was ignored after line %d", (int) mp->warning_line);
            @.Incomplete if...@>
            if (cur_sym == NULL) {
                hlp =
                    "The file ended while I was skipping conditional text. This kind of error happens\n"
                    "when you say 'if ...' and forget the matching 'fi'. I've inserted a 'fi'; this\n"
                    "might work.";
            } else {
                hlp =
                    "A forbidden 'outer' token occurred in skipped text. This kind of error happens\n"
                    "when you say 'if ...' and forget the matching 'fi'. I've inserted a 'fi'; this\n"
                    "might work.";
            }
            set_cur_sym(mp->frozen_fi);
            mp_ins_error(mp, msg, hlp);
        }
        return 0;
    }
}

@ @<Check if the file has ended while flushing \TeX\ material and set...@>=
if (cur_sym != NULL) {
    return 1;
} else {
    char msg[256];
    mp_snprintf(msg, 256, "TeX mode didn't end; all text was ignored after line %d", (int) mp->warning_line);
    set_cur_sym(mp->frozen_etex);
    mp_ins_error(
        mp,
        msg,
        "The file ended while I was looking for the 'etex' to finish this TeX material.\n"
        "I've inserted 'etex' now."
    );
    return 0;
}

@ @<Back up an outer symbolic token so that it can be reread@>=
// if (cur_sym != NULL) {
//     mp_node p = mp_new_symbolic_node(mp);
//     mp_set_sym_sym(p, cur_sym);
//     mp_name_type(p) = cur_sym_mod;
//     /* prepare to read the symbolic token again */
//     mp_begin_token_list(mp, p, mp_backed_up_text);
// }

@ @<Tell the user what has run away...@>=
{
    char msg[256];
    const char *mst = NULL;
    const char *hlp =
        "I suspect you have forgotten an 'enddef', causing me to read past where you\n"
        "wanted me to stop. I'll try to recover.";
    mp_runaway(mp);
    /* print the definition-so-far */
    if (cur_sym == NULL) {
        mst = "File ended while scanning";
        @.File ended while scanning...@>
    } else {
        mst = "Forbidden token found while scanning";
        @.Forbidden token found...@>
    }
    switch (mp->scanner_status) {
        case mp_flushing_state:
            {
                mp_snprintf(msg, 256, "%s to the end of the statement", mst);
                hlp =
                    "A previous error seems to have propagated, causing me to read past where\n"
                    "you wanted me to stop. I'll try to recover.";
                set_cur_sym(mp->frozen_semicolon);
            }
            break;
        case mp_absorbing_state:
            {
                mp_snprintf(msg, 256, "%s a text argument",  mst);
                hlp =
                    "It seems that a right delimiter was left out, causing me to read past where\n"
                    "you wanted me to stop. I'll try to recover.";
                if (mp->warning_info == NULL) {
                    set_cur_sym(mp->frozen_end_group);
                } else {
                    set_cur_sym(mp->frozen_right_delimiter);
                    /*
                        The next line makes sure that the inserted delimiter will match the
                        delimiter that already was read.
                    */
                    set_equiv_sym(cur_sym, mp->warning_info);
                }
            }
            break;
        case mp_var_defining_state:
            {
                mp_string s;
                int selector = mp->selector;
                mp->selector = mp_new_string_selector;
                mp_print_variable_name(mp, mp->warning_info_node);
                s = mp_make_string(mp);
                mp->selector = selector;
                mp_snprintf(msg, 256, "%s the definition of %s", mst, s->str);
                delete_str_ref(s);
                set_cur_sym(mp->frozen_end_def);
            }
            break;
        case mp_op_defining_state:
            {
                char *s = mp_str(mp, text(mp->warning_info));
                mp_snprintf(msg, 256, "%s the definition of %s", mst, s);
                set_cur_sym(mp->frozen_end_def);
            }
            break;
        case mp_loop_defining_state:
            {
                char *s = mp_str(mp, text(mp->warning_info));
                mp_snprintf(msg, 256, "%s the text of a %s loop", mst, s);
                hlp =
                    "I suspect you have forgotten an 'endfor', causing me to read past where\n"
                    "you wanted me to stop. I'll try to recover.";
                    set_cur_sym(mp->frozen_end_for);
            }
        break;
    }
    mp_ins_error(mp, msg, hlp);
}

@ The |runaway| procedure displays the first part of the text that occurred when
\MP\ began its special |scanner_status|, if that text has been saved.

@<Declarations@>=
static void mp_runaway (MP mp);

@ @c
void mp_runaway (MP mp)
{
    if (mp->scanner_status > mp_flushing_state) {
        mp_print_nl(mp, "Runaway ");
        switch (mp->scanner_status) {
            case mp_absorbing_state:
                mp_print_str(mp, "text?");
                break;
            case mp_var_defining_state:
            case mp_op_defining_state:
                mp_print_str(mp, "definition?");
                break;
            case mp_loop_defining_state:
                mp_print_str(mp, "loop?");
                break;
        }
        mp_print_ln(mp);
        mp_show_token_list(mp, mp_link(mp->hold_head), NULL);
    }
}

@ We need to mention a procedure that may be called by |get_next|.

@<Declarations@>=
static void mp_firm_up_the_line (MP mp);

@ And now we're ready to take the plunge into |get_next| itself. Note that the
behavior depends on the |scanner_status| because percent signs and double quotes
need to be passed over when skipping TeX material.

@c
void mp_get_next (MP mp)
{
    /* sets |cur_cmd|, |cur_mod|, |cur_sym| to next token */
    mp_sym cur_sym_; /* speed up access */
  RESTART:
    set_cur_sym(NULL);
    set_cur_sym_mod(0);
    if (file_state) {
        int k;           /* an index into |buffer| */
        unsigned char c; /* the current character in the buffer */
        int cclass;      /* its class number */
        /*
            Input from external file; |goto restart| if no input found, or
            |return| if a non-symbolic token is found. A percent sign appears in
            |buffer[limit]|; this makes it unnecessary to have a special test for
            end-of-line.
        */
      SWITCH:
        c = mp->buffer[loc];
        ++loc;
        cclass = mp->char_class[c];
        switch (cclass) {
            case mp_digit_class:
                scan_numeric_token((c - '0'));
                return;
            case mp_period_class:
                cclass = mp->char_class[mp->buffer[loc]];
                if (cclass > mp_period_class) {
                    goto SWITCH;
                } else if (cclass < mp_period_class) {
                    /* |class=digit_class| */
                    scan_fractional_token(0);
                    return;
                } else {
                    break;
                }
            case mp_space_class:
                goto SWITCH;
            case mp_percent_class:
                if (mp->scanner_status == mp_tex_flushing_state && loc < limit) {
                    /* btex .. etex */
                    goto SWITCH;
                }
                /*
                    Move to next line of file, or |goto restart| if there is no
                    next line.
                */
                if (mp_move_to_next_line(mp)) {
                    goto RESTART;
                } else {
                    goto SWITCH;
                }
            case mp_string_class:
                if (mp->scanner_status == mp_tex_flushing_state) {
                    goto SWITCH;
                } else {
                    unsigned char cend = c == '"' ? '"' : 3 ; /* ASCII BTX ... ETX */
                    if (mp->buffer[loc] == cend) {
                        set_cur_mod_str(mp_rts(mp,""));
                    } else {
                        k = loc;
                        mp->buffer[limit + 1] = cend;
                        do {
                            ++loc;
                        } while (mp->buffer[loc] != cend);
                        if (loc > limit) {
                            /*
                                Decry the missing string delimiter and |goto restart|. We go to
                                |restart| after this error message, not to |SWITCH|, because the
                                |clear_for_error_prompt| routine might have reinstated
                                |token_state| after |error| has finished.
                            */
                            loc = limit;
                            /* the next character to be read on this line will be |"%"| */
                            mp_error(
                                mp,
                                "Incomplete string token has been flushed",
                                "Strings should finish on the same line as they began. I've deleted the partial\n"
                                "string."
                            );
                            goto RESTART;
                        }
                        mp_str_room(mp, (size_t) (loc - k));
                        do {
                            mp_append_char(mp, mp->buffer[k]);
                            ++k;
                        } while (k != loc);
                        set_cur_mod_str(mp_make_string(mp));
                    }
                    ++loc;
                    set_cur_cmd(mp_string_command);
                    return;
                }
            case mp_comma_class:
            case mp_semicolon_class:
            case mp_left_parenthesis_class:
            case mp_right_parenthesis_class:
                k = loc - 1;
                goto FOUND;
            case mp_invalid_class:
                if (mp->scanner_status == mp_tex_flushing_state) {
                    goto SWITCH;
                } else {
                    /*
                        Decry the invalid character and |goto restart|. We go to
                        |restart| instead of to |SWITCH|, because we might enter
                        |token_state| after the error has been dealt with (cf.\
                        |clear_for_error_prompt|).
                    */
                    mp_error(
                        mp,
                        "Text line contains an invalid character",
                        "A funny symbol that I can\'t read has just been input. Continue, and I'll forget\n"
                        "that it ever happened."
                    );
                    goto RESTART;
                }
            default:
                /* letters, etc. */
                break;
        }
        k = loc - 1;
        while (mp->char_class[mp->buffer[loc]] == cclass) {
            ++loc;
        }
      FOUND:
        set_cur_sym(mp_id_lookup(mp, (char *) (mp->buffer + k), (size_t) (loc - k), 1));
    } else {
        /*
            Input from token list; |goto restart| if end of list or if a parameter
            needs to be expanded, or |return| if a non-symbolic token is found.
        */
        if (nloc != NULL && mp_type(nloc) == mp_symbol_node_type) {
             /* symbolic token */
            int cur_sym_mod_ = mp_name_type(nloc);
            int cur_info = mp_get_sym_info(nloc);
            set_cur_sym(mp_get_sym_sym(nloc));
            set_cur_sym_mod(cur_sym_mod_);
            /* move to next */
            nloc = mp_link(nloc);
            if (cur_sym_mod_ == mp_expr_operation) {
                set_cur_cmd(mp_capsule_command);
                set_cur_mod_node(mp->param_stack[param_start + cur_info]);
                set_cur_sym_mod(0);
                set_cur_sym(NULL);
                return;
            } else if (cur_sym_mod_ == mp_suffix_operation || cur_sym_mod_ == mp_text_operation) {
                mp_begin_token_list(mp, mp->param_stack[param_start + cur_info], (int) mp_parameter_text);
                goto RESTART;
            }
        } else if (nloc != NULL) {
            /* Get a stored numeric or string or capsule token and |return| */
            if (mp_name_type(nloc) == mp_token_operation) {
                if (mp_type(nloc) == mp_known_type) {
                    set_cur_mod_number(mp_get_value_number(nloc));
                    set_cur_cmd(mp_numeric_command);
                } else {
                    set_cur_mod_str(mp_get_value_str(nloc));
                    set_cur_cmd(mp_string_command);
                    add_str_ref(cur_mod_str);
                }
            } else {
                set_cur_mod_node(nloc);
                set_cur_cmd(mp_capsule_command);
            }
            nloc = mp_link(nloc);
            return;
        } else {
            /* we are done with this token list */
            mp_end_token_list(mp);
            /* resume previous level */
            goto RESTART;
        }
    }
    /*
        When a symbolic token is declared to be |outer|, its command code is
        increased by |outer_tag|.
    */
    cur_sym_ = cur_sym;
    set_cur_cmd(eq_type(cur_sym_));
    set_cur_mod(equiv(cur_sym_));
    set_cur_mod_node(equiv_node(cur_sym_));
 // if (cur_cmd >= mp_outer_tag_command) {
 //     if (mp_check_outer_validity(mp)) {
 //         set_cur_cmd(cur_cmd - mp_outer_tag_command);
 //     } else {
 //         goto RESTART;
 //     }
 // }
}

@ The global variable |force_eof| is normally |false|; it is set |true| by an
|endinput| command.

@<Glob...@>=
int force_eof; /* should the next |input| be aborted early? */

@ @<Declarations@>=
static int mp_move_to_next_line (MP mp);

@ @c
static int mp_move_to_next_line (MP mp)
{
    if (name > max_spec_src) {
        /*
            Read next line of file into |buffer|, or return 1 (|goto restart|) if
            the file has ended. We must decrement |loc| in order to leave the
            buffer in a valid state when an error condition causes us to |goto
            restart| without calling |end_file_reading|.
        */
        ++line;
        mp->first = (size_t) start;
        if (! mp->force_eof) {
            if (mp_input_ln(mp, cur_file)) { /* not end of file */
                mp_firm_up_the_line(mp);  /* this sets |limit| */
            } else {
                mp->force_eof = 1;
            }
        };
        if (mp->force_eof) {
            mp->force_eof = 0;
            --loc;
            if (mp->interaction < mp_silent_mode) {
                mp_print_chr(mp, ')');
                --mp->open_parens;
                /* show user that file has been read */
                update_terminal();
            }
            /* resume previous level */
            mp_end_file_reading(mp);
            mp_check_outer_validity(mp);
            return 1;
        } else {
            mp->buffer[limit] = '%';
            mp->first = (size_t) (limit + 1);
            loc = start; /* ready to read */
        }
    } else if (mp->input_ptr > 0) {
        /* text was inserted during error recovery or by |scantokens| */
        mp_end_file_reading(mp);
        /* goto RESTART */
        return 1; /* resume previous level */
    } else if (mp->interaction > mp_nonstop_mode) {
        if (limit == start && mp->interaction < mp_silent_mode) {
            /* previous line was empty */
            mp_print_nl(mp, "(Please type a command or say `end')");
        }
        mp_print_ln(mp);
        mp->first = (size_t) start;
        /* get a line from the terminal, prompt delegated */
        if (! mp_input_ln(mp, mp->term_in)) {
            longjmp(*(mp->jump_buf), 1);
        }
        mp->buffer[mp->last] = '%';
        /* done */
        limit = (int) mp->last;
        mp->buffer[limit] = '%';
        mp->first = (size_t) (limit + 1);
        loc = start;
    } else {
        mp_fatal_error(mp, "job aborted, no legal end found");
    }
    return 0;
}

@ If the user has set the |mp_pausing| parameter to some positive value, and if
nonstop mode has not been selected, each line of input is displayed on the
terminal and the transcript file, followed by |=>|. \MP\ waits for a
response. If the response is NULL (i.e., if nothing is typed except perhaps a few
blank spaces), the original line is accepted as it stands; otherwise the line
typed is used instead of the line in the file.

@c
void mp_firm_up_the_line (MP mp)
{
    limit = (int) mp->last;
}

@* Dealing with \TeX\ material.

The |btex|$\,\ldots\,$|etex| and |verbatimtex|$\,\ldots\,$|etex| features
need to be implemented at a low level in the scanning process so that \MP\ can
stay in synch with the a preprocessor that treats blocks of \TeX\ material as
they occur in the input file without trying to expand \MP\ macros. Thus we need a
special version of |get_next| that does not expand macros and such but does
handle |btex|, |verbatimtex|, etc.

@ @<Enumeration types@>=
typedef enum mp_verbatim_codes {
    mp_btex_code,
    mp_verbatim_code,
} mp_verbatim_codes;

@ @<Put each...@>=
mp_primitive(mp, "btex", mp_btex_command, mp_btex_code);
@:btex_}{|btex| primitive@>
mp_primitive(mp, "verbatimtex", mp_btex_command, mp_verbatim_code);
@:verbatimtex_}{|verbatimtex| primitive@>
mp_primitive(mp, "etex", mp_etex_command, 0);
mp->frozen_etex = mp_frozen_primitive (mp, "etex", mp_etex_command, 0);
@:etex_}{|etex| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_btex_command: return m == mp_btex_code ? "btex" : "verbatimtex";
case mp_etex_command: return "etex";

@ Actually, |get_t_next| is a macro that avoids procedure overhead except in the
unusual case where |btex|, |verbatimtex| or |etex| is encountered. Nowadays
the compiler deals with this so it might become a function.

@d get_t_next(mp) do {
    mp_get_next(mp);
    if (cur_cmd <= mp_max_pre_command) {
        mp_t_next(mp); /* will probably get inlined anyway */
    }
} while (0)

@c
@ @<Declarations@>=
static void mp_t_next (MP mp);

@ @c
static void mp_t_next (MP mp)
{
    if ((mp->extensions == 1) && (cur_cmd == mp_btex_command)) {
        @<Pass btex ... etex to script@>
    } else {
        @<Complain about a misplaced |btex|@>
    }
}

@ @<Complain about a misplaced |btex|@>=
{
    mp_error(
        mp,
        "A 'btex/verbatimtex ... etex' definition needs an extension",
        "This file contains picture expressions for 'btex ... etex' blocks. Such files\n"
        "need an extension (plugin) that seems to be absent."
    );
}

@* Scanning macro definitions.

\MP\ has a variety of ways to tuck tokens away into token lists for later use:
Macros can be defined with |def|, |vardef|, |primarydef|, etc.; repeatable
code can be defined with |for|, |forever|, |forsuffixes|. All such
operations are handled by the routines in this part of the program.

The modifier part of each command code is zero for the \quote {ending delimiters} like
|enddef| and |endfor|.

@ @<Enumeration types@>=
typedef enum mp_def_codes {
    mp_end_def_code,       /* command modifier for |enddef| */
    mp_def_code,           /* command modifier for |def| */
    mp_var_def_code,       /* command modifier for |vardef| */
    mp_primary_def_code,   /* command modifier for |primarydef| */
    mp_secondary_def_code, /* command modifier for |secondarydef| */
    mp_tertiary_def_code,  /* command modifier for |tertiarydef| */
} mp_def_codes;

@ @<Enumeration types@>=
typedef enum mp_only_set_codes {
    mp_random_seed_code,
    mp_max_knot_pool_code,
} mp_only_set_codes;

@ @<Enumeration types@>=
typedef enum mp_for_codes {
    mp_end_for_code,           /* command modifier for |endfor| */
    mp_start_forever_code,     /* command modifier for |forever| */
    mp_start_for_code,         /* command modifier for |for| */
    mp_start_forsuffixes_code, /* command modifier for |forsuffixes| */
} mp_for_codes;

@ @<Put each...@>=
mp_primitive(mp, "def", mp_macro_def_command, mp_def_code);
@:def_}{|def| primitive@>
mp_primitive(mp, "vardef", mp_macro_def_command, mp_var_def_code);
@:var_def_}{|vardef| primitive@>
mp_primitive(mp, "primarydef", mp_macro_def_command, mp_primary_def_code);
@:primary_def_}{|primarydef| primitive@>
mp_primitive(mp, "secondarydef", mp_macro_def_command, mp_secondary_def_code);
@:secondary_def_}{|secondarydef| primitive@>
mp_primitive(mp, "tertiarydef", mp_macro_def_command, mp_tertiary_def_code);
@:tertiary_def_}{|tertiarydef| primitive@>
mp_primitive(mp, "enddef", mp_macro_def_command, mp_end_def_code);
mp->frozen_end_def = mp_frozen_primitive(mp, "enddef", mp_macro_def_command, mp_end_def_code);
@:end_def_}{|enddef| primitive@>
mp_primitive(mp, "for", mp_iteration_command, mp_start_for_code);
@:for_}{|for| primitive@>
mp_primitive(mp, "forsuffixes", mp_iteration_command, mp_start_forsuffixes_code);
@:for_suffixes_}{|forsuffixes| primitive@>
mp_primitive(mp, "forever", mp_iteration_command, mp_start_forever_code);
@:forever_}{|forever| primitive@>
mp_primitive(mp, "endfor", mp_iteration_command, mp_end_for_code);
mp->frozen_end_for = mp_frozen_primitive (mp, "endfor", mp_iteration_command, mp_end_for_code);
@:end_for_}{|endfor| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_macro_def_command:
    switch (m) {
        /* low numbers, command specifiers */
        case mp_end_def_code      : return "enddef";
        case mp_def_code          : return "def";
        case mp_var_def_code      : return "vardef";
        case mp_primary_def_code  : return "primarydef";
        case mp_secondary_def_code: return "secondarydef";
        case mp_tertiary_def_code : return "tertiarydef";
        default:                    return "?def";
    }
    break;

case mp_iteration_command:
    switch (m) {
        case mp_end_for_code          : return "endfor";
        case mp_start_forever_code    : return "forever";
        case mp_start_for_code        : return "for";
        case mp_start_forsuffixes_code: return "forsuffixes";
    }
    break;

case mp_only_set_command:
    switch (m) {
        case mp_random_seed_code  : return"randomseed";
        case mp_max_knot_pool_code: return"maxknotpool";
    }
    break;

@ Different macro-absorbing operations have different syntaxes, but they also
have a lot in common. There is a list of special symbols that are to be replaced
by parameter tokens; there is a special command code that ends the definition;
the quotation conventions are identical. Therefore it makes sense to have most of
the work done by a single subroutine. That subroutine is called |scan_toks|.

The first parameter to |scan_toks| is the command code that will terminate
scanning (either |macro_def| or |iteration|).

The second parameter, |subst_list|, points to a (possibly empty) list of
non-symbolic nodes whose |info| and |value| fields specify symbol tokens before
and after replacement. The list will be returned to free storage by |scan_toks|.

The third parameter is simply appended to the token list that is built. And the
final parameter tells how many of the special operations |\#\AT!|, |\AT!|,
and |\AT!\#| are to be replaced by suffix parameters. When such parameters are
present, they are called |(SUFFIX0)|, |(SUFFIX1)|, and |(SUFFIX2)|.

@<Types...@>=
typedef struct mp_subst_list_item {
    mp_name_type_type          info_mod;
    int                        value_mod;
    int                        value_data;
    int                        padding;
    mp_sym                     info;
    struct mp_subst_list_item *link;
} mp_subst_list_item;

@ @c
static mp_node mp_scan_toks (MP mp, mp_command_code terminator, mp_subst_list_item * subst_list, mp_node tail_end, int suffix_count)
{
    int cur_data;
    int cur_data_mod = 0;
    mp_node p = mp->hold_head;    /* tail of the token list being built */
    int balance = 1;              /* left delimiters minus right delimiters */
    mp_link(mp->hold_head) = NULL;
    while (1) {
        get_t_next(mp);
        cur_data = -1;
        if (cur_sym != NULL) {
            @<Substitute for |cur_sym|, if it's on the |subst_list|@>
            if (cur_cmd == terminator) {
                @<Adjust the balance; |break| if it's zero@>
            } else if (cur_cmd == mp_macro_special_command) {
                /* Handle quoted symbols, |\#\AT!|, |\AT!|, or |\AT!\#| */
                if (cur_mod == mp_macro_quote_code) {
                    get_t_next(mp);
                } else if (cur_mod <= suffix_count) {
                    cur_data = cur_mod - 1;
                    cur_data_mod = mp_suffix_operation;
                }
            }
        }
        if (cur_data != -1) {
            mp_node pp = mp_new_symbolic_node(mp);
            mp_set_sym_info(pp, cur_data);
            mp_name_type(pp) = cur_data_mod;
            mp_link(p) = pp;
        } else {
            mp_link(p) = mp_cur_tok(mp);
        }
        p = mp_link(p);
    }
    mp_link(p) = tail_end;
    while (subst_list) {
        mp_subst_list_item *q = subst_list->link;
        mp_memory_free(subst_list);
        subst_list = q;
    }
    return mp_link(mp->hold_head);
}

@ @<Substitute for |cur_sym|...@>=
{
    mp_subst_list_item *q = subst_list;
    while (q != NULL) {
        if (q->info == cur_sym && q->info_mod == cur_sym_mod) {
            cur_data = q->value_data;
            cur_data_mod = q->value_mod;
            set_cur_cmd(mp_relax_command);
            break;
        }
        q = q->link;
    }
}

@ @<Adjust the balance; |break| if it's zero@>=
if (cur_mod > 0) {
    ++balance;
} else {
    --balance;
    if (balance == 0)
        break;
}

@ Four commands are intended to be used only within macro texts: |quote|,
|\#\AT!|, |\AT!|, and |\AT!\#|. They are variants of a single command code
called |macro_special|.

@ @<Enumeration types@>=
typedef enum mp_macro_fix_codes {
    mp_macro_quote_code,  /* |macro_special| modifier for |quote| */
    mp_macro_prefix_code, /* |macro_special| modifier for |\#\AT!| */
    mp_macro_at_code,     /* |macro_special| modifier for |\AT!| */
    mp_macro_suffix_code, /* |macro_special| modifier for |\AT!\#| */
} mp_macro_fix_codes;

@ @<Put each...@>=
mp_primitive(mp, "quote", mp_macro_special_command, mp_macro_quote_code);
@:quote_}{|quote| primitive@>
mp_primitive(mp, "#@@", mp_macro_special_command, mp_macro_prefix_code);
@:]]]\#\AT!_}{|\#\AT!| primitive@>
mp_primitive(mp, "@@", mp_macro_special_command, mp_macro_at_code);
@:]]]\AT!_}{|\AT!| primitive@>
mp_primitive(mp, "@@#", mp_macro_special_command, mp_macro_suffix_code);
@:]]]\AT!\#_}{|\AT!\#| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_macro_special_command:
    switch (m) {
        case mp_macro_prefix_code: return "#@@";
        case mp_macro_at_code    : return "@@";
        case mp_macro_suffix_code: return "@@#";
        case mp_macro_quote_code : return "quote";
    }
    break;

@ Here is a routine that's used whenever a token will be redefined. If the user's
token is unredefinable, the |mp->frozen_inaccessible| token is substituted; the
latter is redefinable but essentially impossible to use, hence \MP's tables won't
get fouled up.

@c
static void mp_get_symbol (MP mp)
{
    /* sets |cur_sym| to a safe symbol */
  RESTART:
    get_t_next(mp);
    if ((cur_sym == NULL) || mp_is_frozen(mp, cur_sym)) {
        const char *hlp = NULL;
        if (cur_sym != NULL) {
            hlp =
                "Sorry: You can't redefine my error-recovery tokens. I've inserted an\n"
                "inaccessible symbol so that your definition will be completed without\n"
                "mixing me up too badly.";
        } else {
            hlp =
                "Sorry: You can't redefine a number, string, or expr. I've inserted an\n"
                "inaccessible symbol so that your definition will be completed without\n"
                "mixing me up too badly.";
            if (cur_cmd == mp_string_command) {
                delete_str_ref(cur_mod_str);
            }
        }
        set_cur_sym(mp->frozen_inaccessible);
        mp_ins_error(mp, "Missing symbolic token inserted", hlp);
        @.Missing symbolic token...@>
        goto RESTART;
    }
}


@ Before we actually redefine a symbolic token, we need to clear away its former
value, if it was a variable. The following stronger version of |get_symbol| does
that.

@c
static void mp_get_clear_symbol (MP mp)
{
    mp_get_symbol(mp);
    mp_clear_symbol(mp, cur_sym, 0);
}

@ Here's another little subroutine; it checks that an equals sign or assignment
sign comes along at the proper place in a macro definition.

@c
static void mp_check_equals (MP mp)
{
    if (cur_cmd != mp_equals_command && cur_cmd != mp_assignment_command) {
        mp_back_error(
            mp,
            "Missing '=' has been inserted",
            "The next thing in this 'def' should have been '=', because I've already looked at\n"
            "the definition heading. But don't worry; I'll pretend that an equals sign was\n"
            "present. Everything from here to 'enddef' will be the replacement text of this\n"
            "macro."
        );
        @.Missing `='@>
    }
}

@ A |primarydef|, |secondarydef|, or |tertiarydef| is rather easily handled
now that we have |scan_toks|. In this case there are two parameters, which will
be |EXPR0| and |EXPR1|.

@c
static void mp_make_op_def (MP mp, int code)
{
    mp_node q, r;
    mp_command_code m = (code == mp_primary_def_code) ? mp_primary_def_command : (code == mp_secondary_def_code ? mp_secondary_def_command : mp_tertiary_def_command);
    mp_subst_list_item *qm = NULL;
    mp_subst_list_item *qn = NULL;
    mp_get_symbol(mp);
    qm = mp_memory_allocate(sizeof(mp_subst_list_item));
    qm->link = NULL;
    qm->info = cur_sym;
    qm->info_mod = cur_sym_mod;
    qm->value_data = 0;
    qm->value_mod = mp_expr_operation;
    mp_get_clear_symbol(mp);
    mp->warning_info = cur_sym;
    mp_get_symbol(mp);
    qn = mp_memory_allocate(sizeof(mp_subst_list_item));
    qn->link = qm;
    qn->info = cur_sym;
    qn->info_mod = cur_sym_mod;
    qn->value_data = 1;
    qn->value_mod = mp_expr_operation;
    get_t_next(mp);
    mp_check_equals(mp);
    mp->scanner_status = mp_op_defining_state;
    q = mp_new_symbolic_node(mp);
    mp_set_ref_count(q, 0);
    r = mp_new_symbolic_node(mp);
    mp_link(q) = r;
    mp_set_sym_info(r, mp_general_macro);
    mp_name_type(r) = mp_macro_operation;
    mp_link(r) = mp_scan_toks(mp, mp_macro_def_command, qn, NULL, 0);
    mp->scanner_status = mp_normal_state;
    set_eq_type(mp->warning_info, m);
    set_equiv_node(mp->warning_info, q);
    mp_get_x_next(mp);
}

@ Parameters to macros are introduced by the keywords |expr|, |suffix|,
|text|, |primary|, |secondary|, and |tertiary|.

@<Put each...@>=
mp_primitive(mp, "expr", mp_parameter_commmand, mp_expr_parameter);
@:expr_}{|expr| primitive@>
mp_primitive(mp, "suffix", mp_parameter_commmand, mp_suffix_parameter);
@:suffix_}{|suffix| primitive@>
mp_primitive(mp, "text", mp_parameter_commmand, mp_text_parameter);
@:text_}{|text| primitive@>
mp_primitive(mp, "primary", mp_parameter_commmand, mp_primary_macro);
@:primary_}{|primary| primitive@>
mp_primitive(mp, "secondary", mp_parameter_commmand, mp_secondary_macro);
@:secondary_}{|secondary| primitive@>
mp_primitive(mp, "tertiary", mp_parameter_commmand, mp_tertiary_macro);
@:tertiary_}{|tertiary| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_parameter_commmand:
    switch (m) {
        case mp_expr_parameter  : return "expr";
        case mp_suffix_parameter: return "suffix";
        case mp_text_parameter  : return "text";
        case mp_primary_macro   : return "primary";
        case mp_secondary_macro : return "secondary";
        default                 : return "tertiary";
    }
    break;

@ Let's turn next to the more complex processing associated with |def| and
|vardef|. When the following procedure is called, |cur_mod| should be either
|start_def| or |var_def|.

Note that although the macro scanner allows |def = := enddef| and |def := =
enddef|; |def = = enddef| and |def := := enddef| will generate an error because
by the time the second of the two identical tokens is seen, its meaning has
already become undefined.

@c
static void mp_scan_def (MP mp, int code)
{
    int n;                         /* the number of special suffix parameters */
    int k;                         /* the total number of parameters */
    mp_subst_list_item *r = NULL;  /* parameter-substitution list */
    mp_subst_list_item *rp = NULL; /* parameter-substitution list */
    mp_node q;                     /* tail of the macro token list */
    mp_node p;                     /* temporary storage */
    int sym_type;                  /* |expr_sym|, |suffix_sym|, or |text_sym| */
    mp_sym l_delim, r_delim;       /* matching delimiters */
    int c = mp_general_macro;      /* the kind of macro we're defining */
    mp_link(mp->hold_head) = NULL;
    q = mp_new_symbolic_node(mp);
    mp_set_ref_count(q, 0);
    r = NULL;
    /*
        Scan the token or variable to be defined; set |n|, |scanner_status|, and
        |warning_info|
    */
    if (code == mp_def_code) {
        mp_get_clear_symbol(mp);
        mp->warning_info = cur_sym;
        get_t_next(mp);
        mp->scanner_status = mp_op_defining_state;
        n = 0;
        set_eq_type(mp->warning_info, mp_defined_macro_command);
        set_equiv_node(mp->warning_info, q);
    } else {
        /* |var_def| */
        p = mp_scan_declared_variable(mp);
        mp_flush_variable(mp, equiv_node(mp_get_sym_sym(p)), mp_link(p), 1);
        mp->warning_info_node = mp_find_variable(mp, p);
        mp_flush_node_list(mp, p);
        if (mp->warning_info_node == NULL) {
            mp_error(
                mp,
                "This variable already starts with a macro",
                "After 'vardef a' you can't say 'vardef a.b'. So I'll have to discard this\n"
                "definition."
            );
            mp->warning_info_node = mp->bad_vardef;
        }
        mp->scanner_status = mp_var_defining_state;
        n = 2;
        if (cur_cmd == mp_macro_special_command && cur_mod == mp_macro_suffix_code) {
            /* |\AT!\#| */
            n = 3;
            get_t_next(mp);
        }
        mp_type(mp->warning_info_node) = mp_unsuffixed_macro_type - 2 + n;
        /* |mp_suffixed_macro=mp_unsuffixed_macro+1| */
        mp_set_value_node(mp->warning_info_node, q);
    }
    k = n;
    if (cur_cmd == mp_left_delimiter_command) {
        /* Absorb delimited parameters, putting them into lists |q| and |r| */
        do {
            l_delim = cur_sym;
            r_delim = equiv_sym(cur_sym);
            get_t_next(mp);
            if (cur_cmd == mp_parameter_commmand) {
                switch (cur_mod) {
                    case mp_expr_parameter:
                        sym_type = mp_expr_operation;
                        goto OKAY;
                        break;
                    case mp_suffix_parameter:
                        sym_type = mp_suffix_operation;
                        goto OKAY;
                        break;
                    case mp_text_parameter:
                        sym_type = mp_text_operation;
                        goto OKAY;
                        break;
                    default:
                        break;
                }
            }
            mp_back_error(
                mp,
                "Missing parameter type; 'expr' will be assumed",
                "You should've had 'expr' or 'suffix' or 'text' here."
            );
            sym_type = mp_expr_operation;
         OKAY:
            /* Absorb parameter tokens for type |sym_type| */
            do {
                mp_link(q) = mp_new_symbolic_node(mp);
                q = mp_link(q);
                mp_name_type(q) = sym_type;
                mp_set_sym_info(q, k);
                mp_get_symbol(mp);
                rp = mp_memory_allocate(sizeof(mp_subst_list_item));
                rp->link = NULL;
                rp->value_data = k;
                rp->value_mod = sym_type;
                rp->info = cur_sym;
                rp->info_mod = cur_sym_mod;
                mp_check_param_size(mp, k);
                ++k;
                rp->link = r;
                r = rp;
                get_t_next(mp);
            } while (cur_cmd == mp_comma_command);

            mp_check_delimiter(mp, l_delim, r_delim);
            get_t_next(mp);
        } while (cur_cmd == mp_left_delimiter_command);

    }
    if (cur_cmd == mp_parameter_commmand) {
        /* Absorb undelimited parameters, putting them into list |r| */
        rp = mp_memory_allocate(sizeof(mp_subst_list_item));
        rp->link = NULL;
        rp->value_data = k;
        switch (cur_mod) {
            case mp_expr_parameter:
                rp->value_mod = mp_expr_operation;
                c = mp_expr_macro;
                break;
            case mp_suffix_parameter:
                rp->value_mod = mp_suffix_operation;
                c = mp_suffix_macro;
                break;
            case mp_text_parameter:
                rp->value_mod = mp_text_operation;
                c = mp_text_macro;
                break;
            default:
                c = cur_mod;
                rp->value_mod = mp_expr_operation;
                break;
        }
        mp_check_param_size(mp, k);
        ++k;
        mp_get_symbol(mp);
        rp->info = cur_sym;
        rp->info_mod = cur_sym_mod;
        rp->link = r;
        r = rp;
        get_t_next(mp);
        if (c == mp_expr_macro && cur_cmd == mp_of_command) {
            c = mp_of_macro;
            rp = mp_memory_allocate(sizeof(mp_subst_list_item));
            rp->link = NULL;
            mp_check_param_size(mp, k);
            rp->value_data = k;
            rp->value_mod = mp_expr_operation;
            mp_get_symbol(mp);
            rp->info = cur_sym;
            rp->info_mod = cur_sym_mod;
            rp->link = r;
            r = rp;
            get_t_next(mp);
        }
    }
    mp_check_equals(mp);
    p = mp_new_symbolic_node(mp);
    mp_set_sym_info(p, c);
    mp_name_type(p) = mp_macro_operation;
    mp_link(q) = p;
    /*
        Attach the replacement text to the tail of node |p|. We don't put
        |mp->frozen_end_group| into the replacement text of a |vardef|,
        because the user may want to redefine |endgroup|.
    */
    if (code == mp_def_code) {
        mp_link(p) = mp_scan_toks(mp, mp_macro_def_command, r, NULL, (int) n);
    } else {
        mp_node qq = mp_new_symbolic_node(mp);
        mp_set_sym_sym(qq, mp->bg_loc);
        mp_link(p) = qq;
        p = mp_new_symbolic_node(mp);
        mp_set_sym_sym(p, mp->eg_loc);
        mp_link(qq) = mp_scan_toks(mp, mp_macro_def_command, r, p, (int) n);
    }
    if (mp->warning_info_node == mp->bad_vardef) {
        mp_flush_token_list(mp, mp_get_value_node(mp->bad_vardef));
    }
    mp->scanner_status = mp_normal_state;
    mp_get_x_next(mp);
}

@ @<Glob...@>=
mp_sym bg_loc;
mp_sym eg_loc;  /* hash addresses of |begingroup| and |endgroup| */

@ @<Initialize table entries@>=
mp->bad_vardef = mp_new_value_node(mp);
mp_name_type(mp->bad_vardef) = mp_root_operation;
mp_set_value_sym(mp->bad_vardef, mp->frozen_bad_vardef);

@ @<Free table entries@>=
mp_free_value_node(mp, mp->bad_vardef);

@* Expanding the next token.

Only a few command codes |<min_command| can possibly be returned by |get_t_next|;
in increasing order, they are |if_test|, |fi_or_else|, |input|, |iteration|,
|repeat_loop|, |exit_test|, |relax|, |scan_tokens|, |run_script|, |expand_after|,
and |defined_macro|.

\MP\ usually gets the next token of input by saying |get_x_next|. This is like
|get_t_next| except that it keeps getting more tokens until finding
|cur_cmd>=min_command|. In other words, |get_x_next| expands macros and removes
conditionals or iterations or input instructions that might be present.

It follows that |get_x_next| might invoke itself recursively. In fact, there is
massive recursion, since macro expansion can involve the scanning of arbitrarily
complex expressions, which in turn involve macro expansion and conditionals, etc.
@^recursion@>

Therefore it's necessary to declare a whole bunch of |forward| procedures at this
point, and to insert some other procedures that will be invoked by |get_x_next|.

@<Declarations@>=
static void mp_scan_primary     (MP mp);
static void mp_scan_secondary   (MP mp);
static void mp_scan_tertiary    (MP mp);
static void mp_scan_expression  (MP mp);
static void mp_scan_suffix      (MP mp);
static void mp_pass_text        (MP mp);
static void mp_conditional      (MP mp);
static void mp_start_input      (MP mp);
static void mp_begin_iteration  (MP mp);
static void mp_resume_iteration (MP mp);
static void mp_stop_iteration   (MP mp);

@ A recursion depth counter is used to discover infinite recursions. (Near)
infinite recursion is a problem because it translates into C function calls that
eat up the available call stack. A better solution would be to depend on signal
trapping, but that is problematic when Metapost is used as a library.

@<Global...@>=
int expand_depth_count; /* current expansion depth */
int expand_depth;       /* current expansion depth */

@ The limit is set at |10000|, which should be enough to allow normal usages of
metapost while preventing the most obvious crashes on most all operating systems,
but the value can be raised if the runtime system allows a larger C stack.
@^system dependencies@>

@<Set initial...@>=
mp->expand_depth = 10000;

@ Even better would be if the system allows discovery of the amount of space
available on the call stack. @^system dependencies@>

In any case, when the limit is crossed, that is a fatal error.

@c
static void mp_check_expansion_depth (MP mp)
{
    if (++mp->expand_depth_count >= mp->expand_depth) {
        if (mp->interaction >= mp_error_stop_mode) {
            mp->interaction=mp_scroll_mode; /* no more interaction */
        }
        mp_error(
            mp,
            "Maximum expansion depth reached",
            "Recursive macro expansion cannot be unlimited because of runtime stack\n"
            "constraints. The limit is 10000 recursion levels in total."
        );
        mp->history=mp_fatal_error_stop;
        mp_jump_out(mp);
    }
}

@ An auxiliary subroutine called |expand| is used by |get_x_next|
when it has to do exotic expansion commands.

@c
static void mp_expand (MP mp)
{
    mp_check_expansion_depth(mp);
    if (number_greater(internal_value(mp_tracing_commands_internal), unity_t) && cur_cmd != mp_defined_macro_command) {
        mp_show_cmd_mod(mp, cur_cmd, cur_mod);
    }
    switch (cur_cmd) {
        case mp_if_test_command:
            mp_conditional(mp); /* this procedure is discussed in Part 36 below */
            break;
        case mp_fi_or_else_command:
            @<Terminate the current conditional and skip to |fi|@>
            break;
        case mp_input_command:
            @<Initiate or terminate input from a file@>
            break;
        case mp_iteration_command:
            if (cur_mod == mp_end_for_code) {
                @<Scold the user for having an extra |endfor|@>
            } else {
                mp_begin_iteration(mp); /* this procedure is discussed in Part 37 below */
            }
            break;
        case mp_repeat_loop_command:
            @<Repeat a loop@>
            break;
        case mp_exit_test_command:
            @<Exit a loop if the proper time has come@>
            break;
        case mp_relax_command:
            break;
        case mp_expand_after_command:
            @<Expand the token after the next token@>
            break;
        case mp_scan_tokens_command:
            @<Put a string into the input buffer@>
            break;
        case mp_runscript_command:
            @<Put a script result string into the input buffer@>
            break;
        case mp_maketext_command:
            @<Put a maketext result string into the input buffer@>
            break;
        case mp_defined_macro_command:
            mp_macro_call(mp, cur_mod_node, NULL, cur_sym);
            break;
        default:
            break;
    };
    mp->expand_depth_count--;
}

@ @<Scold the user...@>=
{
    mp_error(
        mp,
        "Extra 'endfor'",
        "I'm not currently working on a for loop, so I had better not try to end anything."
    );
    @.Extra `endfor'@>
}

@ The processing of |input| involves the |start_input| subroutine, which will
be declared later; the processing of |endinput| is trivial.

@<Put each...@>=
mp_primitive(mp, "input", mp_input_command, 0);
@:input_}{|input| primitive@>
mp_primitive(mp, "endinput", mp_input_command, 1);
@:end_input_}{|endinput| primitive@>

@ @<Cases of |print_cmd_mod|...@>=
case mp_input_command:
    return m == 0 ? "input" : "endinput";

@ @<Initiate or terminate input...@>=
if (cur_mod > 0) {
    mp->force_eof = 1;
} else {
    mp_start_input(mp);
}

@ We'll discuss the complicated parts of loop operations later. For now it
suffices to know that there's a global variable called |loop_ptr| that will be
|NULL| if no loop is in progress.

@<Repeat a loop@>=
{
    while (token_state && (nloc == NULL)) {
        mp_end_token_list(mp); /* conserve stack space */
    }
    if (mp->loop_ptr == NULL) {
        mp_error(
            mp,
            "Lost loop",
            "I'm confused; after exiting from a loop, I still seem to want to repeat it. I'll\n"
            "try to forget the problem."
        );
        @.Lost loop@>
    } else {
        mp_resume_iteration(mp); /* this procedure is in Part 37 below */
    }
}

@ @<Exit a loop if the proper time has come@>=
{
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_boolean_type) {
        do_boolean_error(mp);
    }
    if (number_greater(internal_value(mp_tracing_commands_internal), unity_t)) {
        mp_show_cmd_mod(mp, mp_nullary_command, cur_exp_value_boolean);
    }
    if (cur_exp_value_boolean == mp_true_operation) {
        if (mp->loop_ptr != NULL) {
            @<Exit prematurely from an iteration@>
        } else if (cur_cmd == mp_semicolon_command) {
            mp_error(
                mp,
                "No loop is in progress",
                "Why say 'exitif' when there's nothing to exit from?"
            );
        } else {
            mp_back_error(
                mp,
                "No loop is in progress",
                "Why say 'exitif' when there's nothing to exit from?"
            );
            @.No loop is in progress@>
        }
    } else if (cur_cmd != mp_semicolon_command) {
        mp_back_error(
            mp,
            "Missing ';' has been inserted",
            "After 'exitif <boolean exp>' I expect to see a semicolon. I shall pretend that\n"
            "one was there."
        );
        @.Missing `;'@>
    }
}

@ Here we use the fact that |forever_text| is the only |token_type| that is less
than |loop_text|.

@<Exit prematurely...@>=
mp_node p = NULL;
do {
    if (file_state) {
        mp_end_file_reading(mp);
    } else {
        if (token_type <= mp_loop_text) {
            p = nstart;
        }
        mp_end_token_list(mp);
    }
} while (p == NULL);
if (p != mp->loop_ptr->info) {
    mp_fatal_error(mp, "*** (loop confusion)");
    @.loop confusion@>
}
mp_stop_iteration(mp); /* this procedure is in Part 34 below */

@ @<Expand the token after the next token@>=
{
    mp_node p;
    get_t_next(mp);
    p = mp_cur_tok(mp);
    get_t_next(mp);
    if (cur_cmd < mp_min_command) {
        mp_expand(mp);
    } else {
        mp_back_input(mp);
    }
    mp_begin_token_list(mp, p, mp_backed_up_text);
}

@ @<Put a string into the input buffer@>=
{
    mp_get_x_next(mp);
    mp_scan_primary(mp);
    if (mp->cur_exp.type != mp_string_type) {
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Not a string",
            "I'm going to flush this expression, since scantokens should be followed by a\n"
            "known string."
        );
        @.Not a string@>
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    } else {
        mp_back_input(mp);
        if (cur_exp_str->len > 0) {
            @<Pretend we're reading a new one-line file@>
        }
    }
}

@ @<Declarations@>=
static void check_script_result (MP mp, char *s);

@c
void check_script_result (MP mp, char *s)
{
    if (s) {
        size_t size = strlen(s);
        if (size > 0) {
            size_t k ;
            mp_value new_expr;
            memset(&new_expr, 0, sizeof(mp_value));
            new_number(new_expr.data.n);
            mp_begin_file_reading(mp);
            name = is_scantok;
            mp->last = mp->first;
            k = mp->first + size;
            if (k >= mp->max_buf_stack) {
                while (k >= mp->buf_size) {
                    mp_reallocate_buffer(mp, (mp->buf_size + (mp->buf_size / 4)));
                }
                mp->max_buf_stack = k + 1;
            }
            limit = (int) k;
            memcpy((mp->buffer + mp->first), s, size);
            mp->buffer[limit] = '%';
            mp->first = (size_t) (limit + 1);
            loc = start;
            mp_flush_cur_exp(mp, new_expr);
        }
        lmt_memory_free(s);
    }
}

@ @<Put a script result string into the input buffer@>=
{
   if (mp->extensions) {
       mp_get_x_next(mp);
       mp_scan_primary(mp);
       switch (mp->cur_exp.type) {
            case mp_string_type:
                {
                    mp_back_input(mp);
                    if (cur_exp_str->len > 0) {
                       check_script_result(mp, mp->run_script(mp, (const char*) cur_exp_str->str, cur_exp_str->len, 0));
                    }
                }
                break;
            case mp_numeric_type:
            case mp_known_type:
                {
                    int n = 0 ;
                    mp_back_input(mp);
                    n = (int) number_to_scaled (cur_exp_value_number) / 65536;
                    if (n > 0) {
                        check_script_result(mp, mp->run_script(mp, NULL, 0, n));
                    }
                }
                break;
            default:
                {
                    mp_value new_expr;
                    memset(&new_expr, 0, sizeof(mp_value));
                    new_number(new_expr.data.n);
                    mp_disp_err(mp, NULL);
                    mp_back_error(
                        mp,
                        "Not a string",
                        "I'm going to flush this expression, since runscript should be followed by a known\n"
                        "string or number."
                    );
                    @.Not a string@>
                    mp_get_x_next(mp);
                    mp_flush_cur_exp(mp, new_expr);
                }
                break;
        }
    }
}

@ The |texscriptmode| parameter controls how spaces and newlines get honoured in
|btex| or |verbatimtex| ... |etex|. The default value is~1. Possible values are:
0: no newlines, 1: newlines in |verbatimtex|, 2: newlines in |verbatimtex| and
|etex|, 3: no leading and trailing strip in |verbatimtex|, 4: no leading and
trailing strip in |verbatimtex| and |btex|. That way the Lua handler can do what
it likes. An |etex| has to be followed by a space or |;| or be at the end of a
line and preceded by a space or at the beginning of a line.

@<Pass btex ... etex to script@>=
char *txt = NULL;
char *ptr = NULL;
int slin = line;
int size = 0;
int done = 0;
int mode = round_unscaled(internal_value(mp_texscriptmode_internal)) ; /* default: 1 */
int verb = cur_mod == mp_verbatim_code;
int first;
/* we had a (mandate) trailing space */
if (loc <= limit && mp->char_class[mp->buffer[loc]] == mp_space_class) {
    ++loc;
} else {
    /* maybe issue an error message and quit */
}
/* we loop over lines */
first = loc;
while (1) {
    /* we don't need to check when we have less than 4 characters left */
    if (loc < limit - 4) {
        if (mp->buffer[loc] == 'e') {
            ++loc;
            if (mp->buffer[loc] == 't') {
                ++loc;
                if (mp->buffer[loc] == 'e') {
                    ++loc;
                    if (mp->buffer[loc] == 'x') {
                        /* let's see if we have the right boundary */
                        if (first == (loc - 3)) {
                            /* when we're at the start of a line no leading space is required */
                            done = 1;
                        } else if (mp->char_class[mp->buffer[loc - 4]] == mp_space_class) {
                            /* when we're beyond the start of a line a leading space is required */
                            done = 2;
                        }
                        if (done) {
                            if ((loc + 1) <= limit) {
                                int c = mp->char_class[mp->buffer[loc + 1]] ;
                                if (c != mp_letter_class) {
                                    ++loc;
                                    /* we're past the 'x' */
                                    break;
                                } else {
                                    /* this is no valid etex */
                                    done = 0;
                                }
                            } else {
                                /* when we're at the end of a line we're ok */
                                ++loc;
                                /* we're past the 'x' */
                                break;
                            }
                        }
                    }
                }
            }
        }
    }
    /* no etex seen (yet) */
    if (loc >= limit) {
        if (size) {
            txt = mp_memory_reallocate(txt, (size_t) (size + limit - first + 1));
        } else {
            txt = mp_memory_allocate((size_t) (limit - first + 1));
        }
        memcpy(txt + size, mp->buffer + first, limit - first);
        size += limit - first + 1;
        if (mode <= 0) {
            txt[size - 1] = ' ';
        } else if (verb) {
            /* modes $\geq 1$ permit a newline in verbatimtex */
            txt[size - 1] = '\n';
        } else if (mode >= 2) {
            /* modes $\geq 2$ permit a newline in btex */
            txt[size - 1] = '\n';
        } else {
            txt[size - 1] = ' ';
        }
        if (mp_move_to_next_line(mp)) {
            /* we abort the scanning */
            goto FATAL_ERROR;
        }
        first = loc;
    } else {
        ++loc;
    }
}
if (done) {
    /* we're past the 'x' */
    int l = loc - 5 ; // 4
    int n = l - first + 1 ;
    /* we're before the 'etex' */
    if (done == 2) {
        /* we had ' etex' */
        l -= 1;
        n -= 1;
        /* we're before the ' etex' */
    }
    if (size) {
        txt = mp_memory_reallocate(txt, (size_t) (size + n + 1));
    } else {
        txt = mp_memory_allocate((size_t) (n + 1));
    }
    memcpy(txt + size, mp->buffer + first, n); /* 0 */
    size += n;
    if (verb && mode >= 3) {
        /* don't strip verbatimtex */
        txt[size] = '\0';
        ptr = txt;
    } else if (mode >= 4) {
        /* don't strip btex */
        txt[size] = '\0';
        ptr = txt;
    } else {
        /* strip trailing whitespace, we have a |'\0'| so we are off by one */
        while ((size > 1) && (mp->char_class[(unsigned char) txt[size-1]] == mp_space_class || txt[size-1] == '\n')) {
            --size;
        }
        /* prune the string */
        txt[size] = '\0';
        /* strip leading whitespace */
        ptr = txt;
        while ((size > 1) && (mp->char_class[(unsigned char) ptr[0]] == mp_space_class || ptr[0] == '\n')) {
            ++ptr;
            --size;
        }
    }
    /* action */
    check_script_result(mp, mp->make_text(mp, ptr, size, verb));
    mp_memory_free(txt);
    /* really needed */
    mp_get_next(mp);
    return;
}
/*
    We don't recover because in practice the graphic will be broken anyway and
    we're not really interacting in mplib .. just fix the input.
*/
FATAL_ERROR:
{
    /* line numbers are not always meaningfull so we can get a 0 reported */
    char msg[256];
    if (slin > 0) {
        mp_snprintf(msg, 256, "No matching 'etex' for '%stex'.", verb ? "verbatim" : "b");
    } else {
        mp_snprintf(msg, 256, "No matching 'etex' for '%stex' in line %d.", verb ? "verbatim" : "b",slin);
    }
    mp_error(mp, msg, "An 'etex' is missing at this input level, nothing gets done.");
    mp_memory_free(txt);
}

@ @<Put a maketext result string into the input buffer@>=
{
    if (mp->extensions) {
        mp_get_x_next(mp);
        mp_scan_primary(mp);
        if (mp->cur_exp.type == mp_string_type) {
            mp_back_input(mp);
            if (cur_exp_str->len > 0) {
                check_script_result(mp, mp->make_text(mp, (const char*) cur_exp_str->str, cur_exp_str->len, 0));
            }
        } else {
            mp_value new_expr;
            memset(&new_expr, 0, sizeof(mp_value));
            new_number(new_expr.data.n);
            mp_disp_err(mp, NULL);
            mp_back_error(
                mp,
                "Not a string",
                "I'm going to flush this expression, since 'maketext' should be followed by a\n"
                "known string."
            );
            @.Not a string@>
            mp_get_x_next(mp);
            mp_flush_cur_exp(mp, new_expr);
        }
    }
}

@ @<Pretend we're reading a new one-line file@>=
size_t k; /* something that we hope is |<=buf_size| */
size_t j; /* index into |str_pool| */
mp_value new_expr;
memset(&new_expr, 0, sizeof(mp_value));
new_number(new_expr.data.n);
mp_begin_file_reading(mp);
name = is_scantok;
k = mp->first + (size_t) cur_exp_str->len;
if (k >= mp->max_buf_stack) {
    while (k >= mp->buf_size) {
        mp_reallocate_buffer(mp, (mp->buf_size + (mp->buf_size / 4)));
    }
    mp->max_buf_stack = k + 1;
}
j = 0;
limit = (int) k;
while (mp->first < (size_t) limit) {
    mp->buffer[mp->first] = *(cur_exp_str->str + j);
    j++;
    ++mp->first;
}
mp->buffer[limit] = '%';
mp->first = (size_t) (limit + 1);
loc = start;
mp_flush_cur_exp(mp, new_expr);

@ Here finally is |get_x_next|.

The expression scanning routines to be considered later communicate via the
global quantities |cur_type| and |cur_exp|; we must be very careful to save and
restore these quantities while macros are being expanded. @^inner loop@>

@<Declarations@>=
static void mp_get_x_next (MP mp);

@ @c
static void mp_get_x_next (MP mp)
{
    get_t_next(mp);
    if (cur_cmd < mp_min_command) {
        /* the capsule to save |cur_type| and |cur_exp| */
        mp_node save_exp = mp_stash_cur_exp(mp);
        do {
            if (cur_cmd == mp_defined_macro_command) {
                mp_macro_call(mp, cur_mod_node, NULL, cur_sym);
            } else {
                mp_expand(mp);
            }
            get_t_next(mp);
        } while (cur_cmd < mp_min_command);
        /* that restores |cur_type| and |cur_exp| */
        mp_unstash_cur_exp(mp, save_exp);
    }
}

@ Now let's consider the |macro_call| procedure, which is used to start up all
user-defined macros. Since the arguments to a macro might be expressions,
|macro_call| is recursive. @^recursion@>

The first parameter to |macro_call| points to the reference count of the token
list that defines the macro. The second parameter contains any arguments that
have already been parsed (see below). The third parameter points to the symbolic
token that names the macro. If the third parameter is |NULL|, the macro was
defined by |vardef|, so its name can be reconstructed from the prefix and
\quote {at} arguments found within the second parameter.

What is this second parameter? It's simply a linked list of symbolic items, whose
|info| fields point to the arguments. In other words, if |arg_list=NULL|, no
arguments have been scanned yet; otherwise |mp_info(arg_list)| points to the
first scanned argument, and |mp_link(arg_list)| points to the list of further
arguments (if any).

Arguments of type |expr| are so-called capsules, which we will discuss later
when we concentrate on expressions; they can be recognized easily because their
|link| field is |void|. Arguments of type |suffix| and |text| are token lists
without reference counts.

@ After argument scanning is complete, the arguments are moved to the
|param_stack|. (They can't be put on that stack any sooner, because the stack is
growing and shrinking in unpredictable ways as more arguments are being
acquired.) Then the macro body is fed to the scanner; i.e., the replacement text
of the macro is placed at the top of the \MP's input stack, so that |get_t_next|
will proceed to read it next.

@<Declarations@>=
static void mp_macro_call (MP mp, mp_node def_ref, mp_node arg_list, mp_sym macro_name);

@ This invokes a user-defined control sequence.

@c
static void mp_macro_call (MP mp, mp_node def_ref, mp_node arg_list, mp_sym macro_name)
{
    int n;                        /* the number of arguments */
    mp_node tail = 0;             /* tail of the argument list */
    mp_sym l_delim = NULL;        /* a delimiter pair */
    mp_sym r_delim = NULL;        /* a delimiter pair */
    mp_node r = mp_link(def_ref); /* current node in the macro's token list */
    mp_add_mac_ref(def_ref);
    if (arg_list == NULL) {
        n = 0;
    } else {
        @<Determine the number |n| of arguments already supplied, and set |tail| to the tail of |arg_list|@>
    }
    if (number_positive(internal_value(mp_tracing_macros_internal))) {
        @<Show the text of the macro being expanded, and the existing arguments@>
    }
    @<Scan the remaining arguments, if any; set |r| to the first token of the replacement text@>
    @<Feed the arguments and replacement text to the scanner@>
}

@ @<Show the text of the macro...@>=
mp_begin_diagnostic(mp);
mp_print_ln(mp);
mp_print_macro_name(mp, arg_list, macro_name);
if (n == 3) {
    mp_print_str(mp, "@@#"); /* indicate a suffixed macro */
}
mp_show_macro (mp, def_ref, NULL);
if (arg_list != NULL) {
    mp_node p = arg_list;
    n = 0;
    do {
        mp_node q = (mp_node) mp_get_sym_sym(p);
        mp_print_arg(mp, q, n, 0, 0);
        ++n;
        p = mp_link(p);
    } while (p != NULL);
}
mp_end_diagnostic(mp, 0);

@ @<Declarations@>=
static void mp_print_macro_name (MP mp, mp_node a, mp_sym n);

@ @c
static void mp_print_macro_name (MP mp, mp_node a, mp_sym n)
{
    if (n) {
        mp_print_mp_str(mp,text(n));
    } else {
        mp_node p = (mp_node) mp_get_sym_sym(a);
        if (p) {
            mp_node q = p; /* they traverse the first part of |a| */
            while (mp_link(q) != NULL) {
                q = mp_link(q);
            }
            mp_link(q) = (mp_node) mp_get_sym_sym(mp_link(a));
            mp_show_token_list(mp, p, NULL);
            mp_link(q) = NULL;
        } else {
            mp_print_mp_str(mp,text(mp_get_sym_sym((mp_node) mp_get_sym_sym(mp_link(a)))));
        }
    }
}

@ @<Declarations@>=
static void mp_print_arg (MP mp, mp_node q, int n, int b, int bb);

@ @c
static void mp_print_arg (MP mp, mp_node q, int n, int b, int bb)
{
    if (q && mp_link(q) == MP_VOID) {
        mp_print_nl(mp, "(EXPR");
    } else if ((bb < mp_text_operation) && (b != mp_text_macro)) {
        mp_print_nl(mp, "(SUFFIX");
    } else {
        mp_print_nl(mp, "(TEXT");
    }
    mp_print_int(mp, n);
    mp_print_str(mp, ")<-");
    if (q && mp_link(q) == MP_VOID) {
        mp_print_exp(mp, q, 1);
    } else {
        mp_show_token_list(mp, q, NULL);
    }
}

@ @<Determine the number |n| of arguments already supplied...@>=
n = 1;
tail = arg_list;
while (mp_link(tail) != NULL) {
    ++n;
    tail = mp_link(tail);
}

@ @<Scan the remaining arguments, if any; set |r|...@>=
set_cur_cmd(mp_comma_command + 1); /* anything |<>comma| will do */
while (mp_name_type(r) == mp_expr_operation || mp_name_type(r) == mp_suffix_operation || mp_name_type(r) == mp_text_operation) {
    @<Scan the delimited argument represented by |mp_get_sym_info(r)|@>
    r = mp_link(r);
}
if (cur_cmd == mp_comma_command) {
    char msg[256];
    mp_string rname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_print_macro_name(mp, arg_list, macro_name);
    rname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "Too many arguments to %s; Missing '%s' has been inserted",
    mp_str(mp, rname), mp_str(mp, text(r_delim)));
    delete_str_ref(rname);
    @.Too many arguments...@>
    @.Missing `)'...@>
    mp_error(
        mp,
        msg,
        "I'm going to assume that the comma I just read was a right delimiter, and then:\n"
        "I'll begin expanding the macro."
    );
}
if (mp_get_sym_info(r) != mp_general_macro) {
    @<Scan undelimited argument(s)@>
}
r = mp_link(r);

@ At this point, the reader will find it advisable to review the explanation of
token list format that was presented earlier, paying special attention to the
conventions that apply only at the beginning of a macro's token list.

On the other hand, the reader will have to take the expression-parsing aspects of
the following program on faith; we will explain |cur_type| and |cur_exp| later.
(Several things in this program depend on each other, and it's necessary to jump
into the circle somewhere.)

@<Scan the delimited argument represented by |mp_get_sym_info(r)|@>=
if (cur_cmd != mp_comma_command) {
    mp_get_x_next(mp);
    if (cur_cmd != mp_left_delimiter_command) {
        char msg[256];
        mp_string sname;
        int selector = mp->selector;
        mp->selector = mp_new_string_selector;
        mp_print_macro_name(mp, arg_list, macro_name);
        sname = mp_make_string(mp);
        mp->selector = selector;
        mp_snprintf(msg, 256, "Missing argument to %s", mp_str(mp, sname));
        @.Missing argument...@>
        delete_str_ref(sname);
        if (mp_name_type(r) == mp_suffix_operation || mp_name_type(r) == mp_text_operation) {
            mp_set_cur_exp_value_number(mp, &zero_t);    /* todo: this was |null| */
            mp->cur_exp.type = mp_token_list_type;
        } else {
            mp_set_cur_exp_value_number(mp, &zero_t);
            mp->cur_exp.type = mp_known_type;
        }
        mp_back_error(
            mp,
            msg,
            "That macro has more parameters than you thought. I'll continue by pretending that\n"
            "each missing argument is either zero or null."
        );
        set_cur_cmd(mp_right_delimiter_command);
        goto FOUND;
    }
    l_delim = cur_sym;
    r_delim = equiv_sym(cur_sym);
}
@<Scan the argument represented by |mp_get_sym_info(r)|@>
if ((cur_cmd != mp_comma_command) && ((cur_cmd != mp_right_delimiter_command) || (equiv_sym(cur_sym) != l_delim))) {
    switch (mp_name_type(mp_link(r))) {
        case mp_expr_operation:
        case mp_suffix_operation:
        case mp_text_operation:
            {
                mp_back_error(
                    mp,
                    "Missing ',' has been inserted",
                    "I've finished reading a macro argument and am about to read another; the\n"
                    "arguments weren't delimited correctly."
                );
                @.Missing `,'@>
                set_cur_cmd(mp_comma_command);
            }
            break;
        default:
            {
                char msg[256];
                mp_snprintf(msg, 256, "Missing '%s' has been inserted", mp_str(mp, text(r_delim)));
                @.Missing `)'@>
                mp_back_error(mp, msg, "I've gotten to the end of the macro parameter list.");
            }
            break;
    }
}
FOUND:
@<Append the current expression to |arg_list|@>

@ A |suffix| or |text| parameter will have been scanned as a token list
pointed to by |cur_exp|, in which case we will have |cur_type=token_list|.

@<Append the current expression to |arg_list|@>=
{
    mp_node p = mp_new_symbolic_node(mp);
    if (mp->cur_exp.type == mp_token_list_type) {
        mp_set_sym_sym(p, mp->cur_exp.data.node);
    } else {
        mp_set_sym_sym(p, mp_stash_cur_exp(mp));
    }
    if (number_positive(internal_value(mp_tracing_macros_internal))) {
        mp_begin_diagnostic(mp);
        mp_print_arg(mp, (mp_node) mp_get_sym_sym(p), n, mp_get_sym_info(r), mp_name_type(r));
        mp_end_diagnostic(mp, 0);
    }
    if (arg_list == NULL) {
        arg_list = p;
    } else {
        mp_link(tail) = p;
    }
    tail = p;
    ++n;
}

@ @<Scan the argument represented by |mp_get_sym_info(r)|@>=
if (mp_name_type(r) == mp_text_operation) {
    mp_scan_text_arg(mp, l_delim, r_delim);
} else {
    mp_get_x_next(mp);
    if (mp_name_type(r) == mp_suffix_operation) {
        mp_scan_suffix(mp);
    } else {
        mp_scan_expression(mp);
    }
}

@ The parameters to |scan_text_arg| are either a pair of delimiters or zero; the
latter case is for undelimited text arguments, which end with the first semicolon
or |endgroup| or |end| that is not contained in a group.

@<Declarations@>=
static void mp_scan_text_arg (MP mp, mp_sym l_delim, mp_sym r_delim);

@ @c
void mp_scan_text_arg (MP mp, mp_sym l_delim, mp_sym r_delim)
{
    int balance = 1; /* excess of |l_delim| over |r_delim| */
    mp->warning_info = l_delim;
    mp->scanner_status = mp_absorbing_state;
    mp_node p = mp->hold_head; /* list tail */
    mp_link(mp->hold_head) = NULL;
    while (1) {
        get_t_next(mp);
        if (l_delim == NULL) {
            @<Adjust the balance for an undelimited argument; |break| if done@>
        } else {
            @<Adjust the balance for a delimited argument; |break| if done@>
        }
        mp_link(p) = mp_cur_tok(mp);
        p = mp_link(p);
    }
    mp_set_cur_exp_node(mp, mp_link(mp->hold_head));
    mp->cur_exp.type = mp_token_list_type;
    mp->scanner_status = mp_normal_state;
}

@ @<Adjust the balance for a delimited argument...@>=
if (cur_cmd == mp_right_delimiter_command) {
    if (equiv_sym(cur_sym) == l_delim) {
        --balance;
        if (balance == 0) {
            break;
        }
    }
} else if (cur_cmd == mp_left_delimiter_command) {
    if (equiv_sym(cur_sym) == r_delim) {
        ++balance;
    }
}

@ @<Adjust the balance for an undelimited...@>=
if (mp_end_of_statement) {
    /* |cur_cmd=semicolon|, |end_group|, or |stop| */
    if (balance == 1) {
        break;
    } else if (cur_cmd == mp_end_group_command) {
        --balance;
    }
} else if (cur_cmd == mp_begin_group_command) {
    ++balance;
}

@ @<Scan undelimited argument(s)@>=
if (mp_get_sym_info(r) < mp_text_macro) {
    mp_get_x_next(mp);
    if (mp_get_sym_info(r) != mp_suffix_macro) {
        if ((cur_cmd == mp_equals_command) || (cur_cmd == mp_assignment_command)) {
            mp_get_x_next(mp);
        }
    }
}
switch (mp_get_sym_info(r)) {
    case mp_primary_macro:
        mp_scan_primary(mp);
        break;
    case mp_secondary_macro:
        mp_scan_secondary(mp);
        break;
    case mp_tertiary_macro:
        mp_scan_tertiary(mp);
        break;
    case mp_expr_macro:
        mp_scan_expression(mp);
        break;
    case mp_of_macro:
        {
            @<Scan an expression followed by |of| $\langle$primary$\rangle$@>
        }
        break;
    case mp_suffix_macro:
        {
            @<Scan a suffix with optional delimiters@>
        }
        break;
    case mp_text_macro:
        mp_scan_text_arg(mp, NULL, NULL);
        break;
}
mp_back_input(mp);
@<Append the current expression to |arg_list|@>

@ @<Scan an expression followed by |of| $\langle$primary$\rangle$@>=
mp_node p;
mp_scan_expression(mp);
p = mp_new_symbolic_node(mp);
mp_set_sym_sym(p, mp_stash_cur_exp(mp));
if (number_positive(internal_value(mp_tracing_macros_internal))) {
    mp_begin_diagnostic(mp);
    mp_print_arg(mp, (mp_node) mp_get_sym_sym(p), n, 0, 0);
    mp_end_diagnostic(mp, 0);
}
if (arg_list == NULL) {
    arg_list = p;
} else {
    mp_link(tail) = p;
}
tail = p;
++n;
if (cur_cmd != mp_of_command) {
    char msg[256];
    mp_string sname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_print_macro_name(mp, arg_list, macro_name);
    sname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "Missing 'of' has been inserted for %s", mp_str(mp, sname));
    delete_str_ref(sname);
    @.Missing `of'@>
    mp_back_error(mp, msg, "I've got the first argument; will look now for the other.");
}
mp_get_x_next(mp);
mp_scan_primary(mp);

@ @<Scan a suffix with optional delimiters@>=
if (cur_cmd != mp_left_delimiter_command) {
    l_delim = NULL;
} else {
    l_delim = cur_sym;
    r_delim = equiv_sym(cur_sym);
    mp_get_x_next(mp);
}
mp_scan_suffix(mp);
if (l_delim != NULL) {
    if ((cur_cmd != mp_right_delimiter_command) || (equiv_sym(cur_sym) != l_delim)) {
        char msg[256];
        mp_snprintf(msg, 256, "Missing '%s' has been inserted", mp_str(mp, text(r_delim)));
        @.Missing `)'@>
        mp_back_error(mp, msg, "I've gotten to the end of the macro parameter list.");
    }
    mp_get_x_next(mp);
}

@ Before we put a new token list on the input stack, it is wise to clean off
all token lists that have recently been depleted. Then a user macro that ends
with a call to itself will not require unbounded stack space.

@<Feed the arguments and replacement text to the scanner@>=
while (token_state && (nloc == NULL)) {
    /* conserve stack space */
    mp_end_token_list(mp);
}
if (mp->param_ptr + n > mp->max_param_stack) {
    mp->max_param_stack = mp->param_ptr + n;
    mp_check_param_size(mp, mp->max_param_stack);
    @:MetaPost capacity exceeded parameter stack size}{\quad parameter stack size@>
}
mp_begin_token_list(mp, def_ref, mp_macro_text);
name = macro_name ? text(macro_name) : NULL;
nloc = r;
if (n > 0) {
    mp_node p = arg_list;
    do {
        mp->param_stack[mp->param_ptr] = (mp_node) mp_get_sym_sym(p);
        ++mp->param_ptr;
        p = mp_link(p);
    } while (p != NULL);
    mp_flush_node_list(mp, arg_list);
}

@ It's sometimes necessary to put a single argument onto |param_stack|. The
|stack_argument| subroutine does this.

@c
static void mp_stack_argument (MP mp, mp_node p)
{
    if (mp->param_ptr == mp->max_param_stack) {
        ++mp->max_param_stack;
        mp_check_param_size(mp, mp->max_param_stack);
    }
    mp->param_stack[mp->param_ptr] = p;
    ++mp->param_ptr;
}

@* Conditional processing.

Let's consider now the way |if| commands are handled.

Conditions can be inside conditions, and this nesting has a stack that is
independent of other stacks. Four global variables represent the top of the
condition stack: |cond_ptr| points to pushed-down entries, if~any; |cur_if| tells
whether we are processing |if| or |elseif|; |if_limit| specifies the largest
code of a |fi_or_else| command that is syntactically legal; and |if_line| is the
line number at which the current conditional began.

If no conditions are currently in progress, the condition stack has the special
state |cond_ptr=NULL|, |if_limit=normal|, |cur_if=0|, |if_line=0|. Otherwise
|cond_ptr| points to a non-symbolic node; the |type|, |name_type|, and |link|
fields of the first word contain |if_limit|, |cur_if|, and |cond_ptr| at the next
level, and the second word contains the corresponding |if_line|.

@ @d mp_if_line_field(A) ((mp_if_node) (A))->if_line_field

@ @<Enumeration types@>=
typedef enum mp_if_codes {
    mp_no_if_code,
    mp_if_code,      /* code for |if| being evaluated */
    mp_fi_code,      /* code for |fi| */
    mp_else_code,    /* code for |else| */
    mp_else_if_code, /* code for |elseif| */
} mp_if_codes;

@ @<MPlib internal header stuff@>=
typedef struct mp_if_node_data {
    mp_variable_type     type;
    mp_name_type_type    name_type;
    int                  hasnumber;
    int                  if_line_field;
    struct mp_node_data *link;
} mp_if_node_data;

typedef struct mp_if_node_data *mp_if_node;

@c
static mp_node mp_get_if_node (MP mp) {
    mp_if_node p = (mp_if_node) mp_allocate_node(mp, sizeof(mp_if_node_data));
    mp_type(p) = mp_if_node_type;
    return (mp_node) p;
}

@ @<Glob...@>=
mp_node cond_ptr; /* top of the condition stack */
int     if_limit; /* upper bound on |fi_or_else| codes */
int     cur_if;   /* type of conditional being worked on */
int     if_line;  /* line where that conditional began */

@ @<Set init...@>=
mp->cond_ptr = NULL;
mp->if_limit = mp_no_if_code;
mp->cur_if   = 0;
mp->if_line  = 0;

@ @<Put each...@>=
mp_primitive(mp, "if", mp_if_test_command, mp_if_code);
@:if_}{|if| primitive@>
mp_primitive(mp, "fi", mp_fi_or_else_command, mp_fi_code);
mp->frozen_fi = mp_frozen_primitive (mp, "fi", mp_fi_or_else_command, mp_fi_code);
@:fi_}{|fi| primitive@>
mp_primitive(mp, "else", mp_fi_or_else_command, mp_else_code);
@:else_}{|else| primitive@>
mp_primitive(mp, "elseif", mp_fi_or_else_command, mp_else_if_code);
@:else_if_}{|elseif| primitive@>

@ @<Cases of |print_cmd_mod|...@>=
case mp_if_test_command:
case mp_fi_or_else_command:
    switch (m) {
        case mp_if_code     : return "if";
        case mp_fi_code     : return "fi";
        case mp_else_code   : return "else";
        case mp_else_if_code: return "elseif";
    }
    break;

@ Here is a procedure that ignores text until coming to an |elseif|, |else|,
or |fi| at level zero of $|if|\ldots|fi|$ nesting. After it has acted,
|cur_mod| will indicate the token that was found.

\MP's smallest two command codes are |if_test| and |fi_or_else|; this makes the
skipping process a bit simpler.

@c
void mp_pass_text (MP mp)
{
    int level = 0;
    mp->scanner_status = mp_skipping_state;
    mp->warning_line = mp_true_line(mp);
    while (1) {
        get_t_next(mp);
        if (cur_cmd <= mp_fi_or_else_command) {
            if (cur_cmd < mp_fi_or_else_command) {
                ++level;
            } else if (level == 0) {
                break;
            } else if (cur_mod == mp_fi_code) {
                --level;
            }
        } else {
            @<Decrease the string reference count, if the current token is a string@>
        }
    }
    mp->scanner_status = mp_normal_state;
}

@ @<Decrease the string reference count...@>=
if (cur_cmd == mp_string_command) {
    delete_str_ref(cur_mod_str);
}

@ When we begin to process a new |if|, we set |if_limit:=mp_if_code|; then if
|elseif| or |else| or |fi| occurs before the current |if| condition has
been evaluated, a colon will be inserted. A construction like |if fi| would
otherwise get \MP\ confused.

@<Declarations@>=
static void mp_push_condition_stack (MP mp);
static void mp_pop_condition_stack  (MP mp);

@ Push and pop the condition stack:

@c
static void mp_push_condition_stack (MP mp)
{
    mp_node p = mp_get_if_node(mp);
    mp_link(p) = mp->cond_ptr;
    mp_type(p) = (int) mp->if_limit;
    mp_name_type(p) = mp->cur_if;
    mp_if_line_field(p) = mp->if_line;
    mp->cond_ptr = p;
    mp->if_limit = mp_if_code;
    mp->if_line = mp_true_line(mp);
    mp->cur_if = mp_if_code;
}

static void mp_pop_condition_stack (MP mp)
{
    mp_node p = mp->cond_ptr;
    mp->if_line = mp_if_line_field(p);
    mp->cur_if = mp_name_type(p);
    mp->if_limit = mp_type(p);
    mp->cond_ptr = mp_link(p);
    mp_free_node(mp, p, sizeof(mp_if_node_data));
}
@ Here's a procedure that changes the |if_limit| code corresponding to
a given value of |cond_ptr|.

@c
static void mp_change_if_limit (MP mp, int l, mp_node p)
{
    if (p == mp->cond_ptr) {
        /* that's the easy case */
        mp->if_limit = l;
    } else {
        mp_node q = mp->cond_ptr;
        while (1) {
            if (q == NULL) {
                mp_confusion(mp, "if");
                @:this can't happen if}{\quad if@>
                return;
            } else if (mp_link(q) == p) {
                mp_type(q) = l;
                return;
            } else {
                q = mp_link(q);
            }
        }
    }
}

@ The user is supposed to put colons into the proper parts of conditional
statements. Therefore, \MP\ has to check for their presence.

@c
static void mp_check_colon (MP mp)
{
    if (cur_cmd != mp_colon_command) {
        mp_back_error(
            mp,
            "Missing ':' has been inserted",
            "There should've been a colon after the condition. I shall pretend that one was\n"
            "there."
        );
        @.Missing `:'@>
    }
}

@ A condition is started when the |get_x_next| procedure encounters an |if_test|
command; in that case |get_x_next| calls |conditional|, which is a recursive
procedure. @^recursion@>

@c
void mp_conditional (MP mp)
{
    mp_node save_cond_ptr; /* |cond_ptr| corresponding to this conditional */
    int new_if_limit;      /* future value of |if_limit| */
    mp_push_condition_stack(mp);
    save_cond_ptr = mp->cond_ptr;
  RESWITCH:
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_boolean_type) {
        do_boolean_error(mp);
    }
    new_if_limit = mp_else_if_code;
    if (number_greater(internal_value(mp_tracing_commands_internal), unity_t)) {
        @<Display the boolean value of |cur_exp|@>
    }
  FOUND:
    mp_check_colon(mp);
    if (cur_exp_value_boolean == mp_true_operation) {
        mp_change_if_limit (mp, (int) new_if_limit, save_cond_ptr);
        /* wait for |elseif|, |else|, or |fi| */
        return;
    }
    @<Skip to |elseif| or |else| or |fi|, then |goto done|@>
  DONE:
    mp->cur_if = (int) cur_mod;
    mp->if_line = mp_true_line(mp);
    if (cur_mod == mp_fi_code) {
        mp_pop_condition_stack(mp);
    } else if (cur_mod == mp_else_if_code) {
        goto RESWITCH;
    } else {
        mp_set_cur_exp_value_boolean(mp, mp_true_operation);
        new_if_limit = mp_fi_code;
        mp_get_x_next(mp);
        goto FOUND;
    }
}

@ In a construction like `|if| |if| |true|: $0=1$: |foo| |else|:
|bar| |fi|', the first |else| that we come to after learning that the
|if| is false is not the |else| we're looking for. Hence the following
curious logic is needed.

@<Skip to |elseif|...@>=
while (1) {
    mp_pass_text(mp);
    if (mp->cond_ptr == save_cond_ptr) {
        goto DONE;
    } else if (cur_mod == mp_fi_code) {
        mp_pop_condition_stack(mp);
    }
}

@ @<Display the boolean value...@>=
mp_begin_diagnostic(mp);
mp_print_str(mp, cur_exp_value_boolean == mp_true_operation ? "{true}" : "{false}");
mp_end_diagnostic(mp, 0);

@ The processing of conditionals is complete except for the following code, which
is actually part of |get_x_next|. It comes into play when |elseif|, |else|,
or |fi| is scanned.

@<Terminate the current conditional and skip to |fi|@>=
if (cur_mod > mp->if_limit) {
    if (mp->if_limit == mp_if_code) {
        /* condition not yet evaluated */
        mp_back_input(mp);
        set_cur_sym(mp->frozen_colon);
        mp_ins_error(mp, "Missing ':' has been inserted", "Something was missing here");
        @.Missing `:'@>
    } else {
        const char *hlp = "I'm ignoring this; it doesn't match any if.";
        switch (cur_mod) {
            case mp_fi_code:
                mp_error(mp, "Extra 'fi'", hlp);
                @.Extra fi@>
                break;
            case mp_else_code:
                mp_error(mp, "Extra 'else'", hlp);
                @.Extra else@>
                break;
            default:
                mp_error(mp, "Extra 'elseif'", hlp);
                @.Extra elseif@>
                break;
        }
    }
} else {
    while (cur_mod != mp_fi_code) {
        /* skip to |fi| */
        mp_pass_text(mp);
    }
    mp_pop_condition_stack(mp);
}

@* Iterations.

To bring our treatment of |get_x_next| to a close, we need to consider what \MP\
does when it sees |for|, |forsuffixes|, and |forever|.

There's a global variable |loop_ptr| that keeps track of the |for| loops that
are currently active. If |loop_ptr=NULL|, no loops are in progress; otherwise
|loop_ptr.info| points to the iterative text of the current (innermost) loop, and
|loop_ptr.link| points to the data for any other loops that enclose the current
one.

A loop-control node also has two other fields, called |type| and |list|, whose
contents depend on the type of loop:

\yskip\indent|loop_ptr.type=NULL| means that the link of |loop_ptr.list| points
to a list of symbolic nodes whose |info| fields point to the remaining argument
values of a suffix list and expression list. In this case, an extra field
|loop_ptr.start_list| is needed to make sure that |resume_operation| skips ahead.

\yskip\indent|loop_ptr.type=MP_VOID| means that the current loop is
|forever|.

\yskip\indent|loop_ptr.type=MP_PROGRESSION_FLAG| means that |loop_ptr.value|,
|loop_ptr.step_size|, and |loop_ptr.final_value| contain the data for an
arithmetic progression.

\yskip\indent|loop_ptr.type=p>MP_PROGRESSION_FLAG| means that |p| points to an edge
header and |loop_ptr.list| points into the graphical object list for that edge
header.

@d MP_VOID             (mp_node) (1) /* |NULL+1|, a |NULL| pointer different from |NULL| */
@d MP_PROGRESSION_FLAG (mp_node) (2) /* |NULL+2| */

/* |loop_type| value when |loop_list| points to a progression node */

@<Types...@>=
typedef struct mp_loop_data {
    mp_sym               var ;        /* the var of the loop */
    mp_node              info;        /* iterative text of this loop */
    mp_node              type;        /* the special type of this loop, or a pointer into mem */
    mp_node              list;        /* the remaining list elements */
    mp_node              list_start;  /* head fo the list of elements */
    mp_number            old_value;   /* previous value of current arithmetic value */
    mp_number            value;       /* current arithmetic value */
    mp_number            step_size;   /* arithmetic step size */
    mp_number            final_value; /* end arithmetic value */
    struct mp_loop_data *link;        /* the enclosing loop, if any */
    mp_knot              point;
} mp_loop_data;

@ @<Glob...@>=
mp_loop_data *loop_ptr; /* top of the loop-control-node stack */

@ @<Set init...@>=
mp->loop_ptr = NULL;

@ If the expressions that define an arithmetic progression in a |for| loop
don't have known numeric values, the |bad_for| subroutine screams at the user.

@c
static void mp_bad_for (MP mp, const char *s)
{
    char msg[256];
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_disp_err(mp, NULL);
    /* show the bad expression above the message */
    mp_snprintf(msg, 256, "Improper %s has been replaced by 0", s);
    @.Improper...replaced by 0@>
    mp_back_error(
        mp,
        msg,
        "When you say 'for x=a step b until c', the initial value 'a' and the step size\n"
        "'b' and the final value 'c' must have known numeric values. I'm zeroing this one.\n"
        "Proceed, with fingers crossed."
    );
    mp_get_x_next(mp);
    mp_flush_cur_exp(mp, new_expr);
}

@ Here's what \MP\ does when |for|, |forsuffixes|, or |forever| has just
been scanned. (This code requires slight familiarity with expression-parsing
routines that we have not yet discussed; but it seems to belong in the present
part of the program, even though the original author didn't write it until later.
The reader may wish to come back to it.)

@c
void mp_begin_iteration (MP mp)
{
    mp_node q;                    /* link manipulation register */
    mp_sym n = cur_sym;           /* hash address of the current symbol */
    mp_subst_list_item *p = NULL; /* substitution list for |scan_toks| */
    int m = cur_mod;              /* |start_for| (|for|) or |start_forsuffixes| (|forsuffixes|) */
    mp_loop_data *s = mp_memory_allocate(sizeof(mp_loop_data)); /* the new loop-control node */
    s->type = NULL;
    s->list = NULL;
    s->info = NULL;
    s->list_start = NULL;
    s->link = NULL;
    s->var = NULL;
    s->point = NULL;
    new_number(s->value);
    new_number(s->old_value);
    new_number(s->step_size);
    new_number(s->final_value);
    if (m == mp_start_forever_code) {
        s->type = MP_VOID;
        mp_get_x_next(mp);
    } else {
        mp_get_symbol(mp);
        p = mp_memory_allocate(sizeof(mp_subst_list_item));
        p->link = NULL;
        p->info = cur_sym;
        s->var  = cur_sym;
        p->info_mod = cur_sym_mod;
        p->value_data = 0;
        if (m == mp_start_for_code) {
            p->value_mod = mp_expr_operation;
        } else {
            /* |start_forsuffixes| */
            p->value_mod = mp_suffix_operation;
        }
        mp_get_x_next(mp);
        if (p->value_mod == mp_expr_operation && cur_cmd == mp_within_command) {
            @<Set up a picture iteration@>
        } else {
            @<Check for the assignment in a loop header@>
            @<Scan the values to be used in the loop@>
        }
    }
    @<Check for the presence of a colon@>
    @<Scan the loop text and put it on the loop control stack@>
    mp_resume_iteration(mp);
}


@ @<Check for the assignment in a loop header@>=
if ((cur_cmd != mp_equals_command) && (cur_cmd != mp_assignment_command)) {
    mp_back_error(
        mp,
        "Missing '=' has been inserted",
        "The next thing in this loop should have been '=' or ':='. But don't worry; I'll\n"
        "pretend that an equals sign was present, and I'll look for the values next."
    );
    @.Missing `='@>
}

@ @<Check for the presence of a colon@>=
if (cur_cmd != mp_colon_command) {
    mp_back_error(
        mp,
        "Missing ':' has been inserted",
        "The next thing in this loop should have been a ':'. So I'll pretend that a colon\n"
        "was present; everything from here to 'endfor' will be iterated."
    );
    @.Missing `:'@>
}

@ We append a special |mp->frozen_repeat_loop| token in place of the |endfor|
at the end of the loop. This will come through \MP's scanner at the proper time
to cause the loop to be repeated.

(If the user tries some shenanigan like `|for| $\ldots$ |let| |endfor|', he
will be foiled by the |get_symbol| routine, which keeps frozen tokens unchanged.
Furthermore the |mp->frozen_repeat_loop| is an |outer| token, so it won't be
lost accidentally.)

@ @<Scan the loop text...@>=
q = mp_new_symbolic_node(mp);
mp_set_sym_sym(q, mp->frozen_repeat_loop);
mp->scanner_status = mp_loop_defining_state;
mp->warning_info = n;
s->info = mp_scan_toks(mp, mp_iteration_command, p, q, 0);
mp->scanner_status = mp_normal_state;
s->link = mp->loop_ptr;
mp->loop_ptr = s;

@ @<Initialize table...@>=
mp->frozen_repeat_loop =
//mp_frozen_primitive (mp, " ENDFOR", mp_repeat_loop_command + mp_outer_tag_command, 0);
mp_frozen_primitive (mp, " ENDFOR", mp_repeat_loop_command, 0);

@ The loop text is inserted into \MP's scanning apparatus by the
|resume_iteration| routine.

@c
void mp_resume_iteration (MP mp)
{
    mp_node p, q; /* link registers */
    p = mp->loop_ptr->type;
    if (p == MP_PROGRESSION_FLAG) {
        mp_set_cur_exp_value_number(mp, &(mp->loop_ptr->value));
        if ((number_positive(mp->loop_ptr->step_size) && number_greater(cur_exp_value_number, mp->loop_ptr->final_value))
         || (number_negative(mp->loop_ptr->step_size) && number_less   (cur_exp_value_number, mp->loop_ptr->final_value))) {
            mp_stop_iteration(mp);
            return;
        }
        mp->cur_exp.type = mp_known_type;
        /* make |q| an |expr| argument */
        q = mp_stash_cur_exp(mp);
        number_clone(mp->loop_ptr->old_value, cur_exp_value_number);
        set_number_from_addition(mp->loop_ptr->value, cur_exp_value_number, mp->loop_ptr->step_size);
        /* Set |value(p)| for the next iteration and detect numeric overflow */
        if (number_positive(mp->loop_ptr->step_size) && number_less(mp->loop_ptr->value, cur_exp_value_number)) {
            if (number_positive(mp->loop_ptr->final_value)) {
                number_clone(mp->loop_ptr->value, mp->loop_ptr->final_value);
                number_add_scaled(mp->loop_ptr->final_value, -1);
            } else {
                number_clone(mp->loop_ptr->value, mp->loop_ptr->final_value);
                number_add_scaled(mp->loop_ptr->value, 1);
            }
        } else if (number_negative(mp->loop_ptr->step_size) && number_greater(mp->loop_ptr->value, cur_exp_value_number)) {
            if (number_negative(mp->loop_ptr->final_value)) {
                number_clone(mp->loop_ptr->value, mp->loop_ptr->final_value);
                number_add_scaled(mp->loop_ptr->final_value, 1);
            } else {
                number_clone(mp->loop_ptr->value, mp->loop_ptr->final_value);
                number_add_scaled(mp->loop_ptr->value, -1);
            }
        }
        if (mp->loop_ptr->point != NULL) {
            mp->loop_ptr->point = mp_next_knot(mp->loop_ptr->point);
        }
    } else if (p == NULL) {
        p = mp->loop_ptr->list;
        if (p != NULL && p == mp->loop_ptr->list_start) {
            q = p;
            p = mp_link(p);
            mp_free_symbolic_node(mp, q);
            mp->loop_ptr->list = p;
        }
        if (p == NULL) {
            mp_stop_iteration(mp);
            return;
        }
        mp->loop_ptr->list = mp_link(p);
        q = (mp_node) mp_get_sym_sym(p);
        if (q) {
            number_clone(mp->loop_ptr->old_value, q->data.n);
        }
        mp_free_symbolic_node(mp, p);
    } else if (p == MP_VOID) {
        mp_begin_token_list(mp, mp->loop_ptr->info, mp_forever_text);
        return;
    } else {
        @<Make |q| a capsule containing the next picture component from |loop_list(loop_ptr)| or |goto not_found|@>
    }
    mp_begin_token_list(mp, mp->loop_ptr->info, mp_loop_text);
    mp_stack_argument(mp, q);
    if (number_greater(internal_value(mp_tracing_commands_internal), unity_t)) {
        @<Trace the start of a loop@>
    }
    return;
  NOT_FOUND:
    mp_stop_iteration(mp);
}

@ @<Trace the start of a loop@>=
mp_begin_diagnostic(mp);
mp_print_nl(mp, "{loop value=");
@.loop value=n@>
if ((q != NULL) && (mp_link(q) == MP_VOID)) {
    mp_print_exp(mp, q, 1);
} else {
    mp_show_token_list(mp, q, NULL);
}
mp_print_chr(mp, '}');
mp_end_diagnostic(mp, 0);

@ @<Make |q| a capsule containing the next picture component from...@>=
q = mp->loop_ptr->list;
if (q == NULL) {
    goto NOT_FOUND;
} else if (! mp_is_start_or_stop(q)) {
    q = mp_link(q);
} else if (! mp_is_stop(q)) {
    q = mp_skip_1component(mp, q);
} else {
    goto NOT_FOUND;
}
mp_set_cur_exp_node(mp, (mp_node) mp_copy_objects (mp, mp->loop_ptr->list, q));
mp_init_bbox(mp, (mp_edge_header_node) cur_exp_node);
mp->cur_exp.type = mp_picture_type;
mp->loop_ptr->list = q;
q = mp_stash_cur_exp(mp);

@ A level of loop control disappears when |resume_iteration| has decided not to
resume, or when an |exitif| construction has removed the loop text from the
input stack.

@c
void mp_stop_iteration (MP mp)
{
    mp_node p = mp->loop_ptr->type;
    if (p == MP_PROGRESSION_FLAG) {
        mp_free_symbolic_node(mp, mp->loop_ptr->list);
        if (mp->loop_ptr->point) {
            mp_toss_knot_list(mp, mp->loop_ptr->point);
        }
    } else if (p == NULL) {
        mp_node q = mp->loop_ptr->list;
        while (q != NULL) {
            p = (mp_node) mp_get_sym_sym(q);
            if (p != NULL) {
                if (mp_link(p) == MP_VOID) {
                    /* it's an |expr| parameter */
                    mp_recycle_value(mp, p);
                    mp_free_value_node(mp, p);
                } else {
                    /* it's a |suffix| or |text| parameter */
                    mp_flush_token_list(mp, p);
                }
            }
            p = q;
            q = mp_link(q);
            mp_free_symbolic_node(mp, p);
        }
    } else if (p > MP_PROGRESSION_FLAG) {
        mp_delete_edge_ref(mp, p);
    }
    {
        mp_loop_data *tmp = mp->loop_ptr;
        mp->loop_ptr = tmp->link;
        mp_flush_token_list(mp, tmp->info);
        free_number(tmp->value);
        free_number(tmp->step_size);
        free_number(tmp->final_value);
        mp_memory_free(tmp);
    }
}

@ Now that we know all about loop control, we can finish up the missing portion
of |begin_iteration| and we'll be done.

The following code is performed after the |=| has been scanned in a |for|
construction (if |m=start_for|) or a |forsuffixes| construction (if
|m=start_forsuffixes|).

@<Scan the values to be used in the loop@>=
s->type = NULL;
s->list = mp_new_symbolic_node(mp);
s->list_start = s->list;
q = s->list;
do {
    mp_get_x_next(mp);
    if (m != mp_start_for_code) {
        mp_scan_suffix(mp);
    } else {
        if (cur_cmd >= mp_colon_command && cur_cmd <= mp_comma_command) {
            goto CONTINUE;
        }
        mp_scan_expression(mp);
        if (cur_cmd == mp_step_command && q == s->list) {
            @<Prepare for step-until construction and |break|@>
        }
        mp_set_cur_exp_node(mp, mp_stash_cur_exp(mp));
    }
    mp_link(q) = mp_new_symbolic_node(mp);
    q = mp_link(q);
    mp_set_sym_sym(q, mp->cur_exp.data.node);
    if (m == mp_start_for_code) {
        mp_name_type(q) = mp_expr_operation;
    } else if (m == mp_start_forsuffixes_code) {
        mp_name_type(q) = mp_suffix_operation;
    }
    mp->cur_exp.type = mp_vacuous_type;
  CONTINUE:
  ; /* needed */
} while (cur_cmd == mp_comma_command);

@ @<Prepare for step-until construction and |break|@>=
{
    if (mp->cur_exp.type != mp_known_type) {
        mp_bad_for (mp, "initial value");
    }
    number_clone(s->value, cur_exp_value_number);
    number_clone(s->old_value, cur_exp_value_number);
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_known_type) {
        mp_bad_for (mp, "step size");
    }
    number_clone(s->step_size, cur_exp_value_number);
    if (cur_cmd != mp_until_command) {
        mp_back_error(
            mp,
            "Missing 'until' has been inserted",
            "I assume you meant to say 'until' after 'step'. So I'll look for the final value\n"
            "and colon next."
        );
        @.Missing `until'@>
    }
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_known_type) {
        mp_bad_for (mp, "final value");
    }
    number_clone(s->final_value, cur_exp_value_number);
    s->type = MP_PROGRESSION_FLAG;
    break;
}

@ The last case is when we have just seen |within|, and we need to parse a
picture expression and prepare to iterate over it.

@<Set up a picture iteration@>=
mp_get_x_next(mp);
mp_scan_expression(mp);
if (mp->cur_exp.type == mp_path_type) {
    number_clone(s->value, zero_t);
    number_clone(s->old_value, zero_t);
    number_clone(s->step_size, unity_t);
    /* */
    {
        mp_knot p = cur_exp_knot;
     // int l = mp_left_type(p) == mp_endpoint_knot ? -1 : 0;
        int l = 0;
        while (1) {
            mp_knot n = mp_next_knot(p);
            if (n == cur_exp_knot) {
                /* So we actually start at the end because we next first. */
                s->point = p;
                set_number_from_int(s->final_value, l);
                break;
            } else {
                p = n;
                ++l;
            }
        }
    }
    /* */
    s->type = MP_PROGRESSION_FLAG;
    s->list = mp_new_symbolic_node(mp);
    s->list_start = s->list;
    q = s->list;
} else {
    @<Make sure the current expression is a known picture@>
    s->type = mp->cur_exp.data.node;
    mp->cur_exp.type = mp_vacuous_type;
    q = mp_link(mp_edge_list(mp->cur_exp.data.node));
    if (q != NULL && mp_is_start_or_stop (q) && mp_skip_1component(mp, q) == NULL) {
        q = mp_link(q);
    }
    s->list = q;
}

@ @<Make sure the current expression is a known picture@>=
if (mp->cur_exp.type != mp_picture_type) {
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    new_expr.data.node = (mp_node) mp_get_edge_header_node(mp);
    mp_disp_err(mp, NULL);
    mp_back_error(
        mp,
        "Improper iteration spec has been replaced by nullpicture",
        "When you say 'for x in p', p must be a known picture."
    );
    mp_get_x_next(mp);
    mp_flush_cur_exp(mp, new_expr);
    mp_init_edges(mp, (mp_edge_header_node) mp->cur_exp.data.node);
    mp->cur_exp.type = mp_picture_type;
}

@* File names.

It's time now to fret about file names. Besides the fact that different operating
systems treat files in different ways, we must cope with the fact that completely
different naming conventions are used by different groups of people. The
following programs show what is required for one particular operating system;
similar routines for other systems are not difficult to devise. @^system
dependencies@>

\MP\ assumes that a file name has three parts: the name proper; its
\quote {extension}; and a \quote {file area} where it is found in an external file system.
The extension of an input file is assumed to be |.mp| unless otherwise
specified; it is |.log| on the transcript file that records each run of \MP;
it is |.tfm| on the font metric files that describe characters in any fonts
created by \MP; it is |.ps| or `.{\it nnn}' for some number {\it nnn} on the
\ps\ output files. The file area can be arbitrary on input files, but files are
usually output to the user's current area. If an input file cannot be found on
the specified area, \MP\ will look for it on a special system area; this special
area is intended for commonly used input files.

Simple uses of \MP\ refer only to file names that have no explicit extension or
area. For example, a person usually says `|input| |cmr10|' instead of
`|input| |cmr10.new|'. Simple file names are best, because they make the \MP\
source files portable; whenever a file name consists entirely of letters and
digits, it should be treated in the same way by all implementations of \MP.
However, users need the ability to refer to other files in their environment,
especially when responding to error messages concerning unopenable files;
therefore we want to let them use the syntax that appears in their favorite
operating system.

@ \MP\ uses the same conventions that have proved to be satisfactory for \TeX\
and \MF. In order to isolate the system-dependent aspects of file names, @^system
dependencies@> the system-independent parts of \MP\ are expressed in terms of
three system-dependent procedures called |begin_name|, |more_name|, and
|end_name|. In essence, if the user-specified characters of the file name are
$c_1\ldots c_n$, the system-independent driver program does the operations
$$|begin_name|;\,|more_name|(c_1);\,\ldots\,;\,|more_name|(c_n); \,|end_name|.$$
These three procedures communicate with each other via global variables.
Afterwards the file name will appear in the string pool as |cur_name|.

Actually the situation is slightly more complicated, because \MP\ needs to know
when the file name ends. The |more_name| routine is a function (with side
effects) that returns |true| on the calls |more_name|$(c_1)$, \dots,
|more_name|$(c_{n-1})$. The final call |more_name|$(c_n)$ returns |false|; or, it
returns |true| and $c_n$ is the last character on the current input line. In
other words, |more_name| is supposed to return |true| unless it is sure that the
file name has been completely scanned; and |end_name| is supposed to be able to
finish the assembly of |cur_name| regardless of whether $|more_name|(c_n)$ returned
|true| or |false|.

@<Glob...@>=
char *cur_name; /* name of file just scanned */

@ It is easier to maintain reference counts if we assign initial values.

@<Set init...@>=
mp->cur_name = mp_strdup("");

@ @<Dealloc variables@>=
mp_memory_free(mp->cur_name);

@ The file names we shall deal with for illustrative purposes have the following
structure: If the name contains |>| or |:|, the file area consists of all
characters up to and including the final such character; otherwise the file area
is null. If the remaining file name contains |.|, the file extension consists
of all such characters from the first remaining |.| to the end, otherwise the
file extension is null. @^system dependencies@>

We can scan such file names easily by using two global variables that keep track
of the occurrences of area and extension delimiters.

@<Glob...@>=
int quoted_filename; /* whether the filename is wrapped in " markers */

@ Here are the routines for file name scanning.

@<Declarations@>=
static void mp_begin_name (MP mp);
static int  mp_more_name  (MP mp, unsigned char c);
static void mp_end_name   (MP mp);

@ @c
void mp_begin_name (MP mp)
{
    mp_memory_free(mp->cur_name);
    mp->cur_name = NULL;
    mp->quoted_filename = 0;
}

int mp_more_name (MP mp, unsigned char c)
{
    if (c == '"') {
        mp->quoted_filename = ! mp->quoted_filename;
    } else if ((c == ' ' || c == '\t') && (mp->quoted_filename == 0)) {
        return 0;
    } else {
        mp_str_room(mp, 1);
        mp_append_char(mp, c);
    }
    return 1;
}

void mp_end_name (MP mp)
{
    mp->cur_name = mp_memory_allocate((size_t) (mp->cur_length + 1) * sizeof(char));
    (void) memcpy(mp->cur_name, (char *) (mp->cur_string), mp->cur_length);
    mp->cur_name[mp->cur_length] = 0;
    mp_reset_cur_string(mp);
}

void mp_pack_file_name (MP mp, const char *n)
{
    mp_memory_free(mp->name_of_file);
    mp->name_of_file = mp_strdup(n);
}

@ @<Internal library declarations@>=
void mp_pack_file_name (MP mp, const char *n);

@ Operating systems often make it possible to determine the exact name (and
possible version number) of a file that has been opened. The following routine,
which simply makes a \MP\ string from the value of |name_of_file|, should ideally
be changed to deduce the full name of file~|f|, which is the file most recently
opened, if it is possible to do this. @^system dependencies@>

@ @c
static mp_string mp_make_name_string (MP mp)
{
    int name_length = (int) strlen(mp->name_of_file);
    mp_str_room(mp, name_length);
    for (int k = 0; k < name_length; k++) {
        mp_append_char(mp, (unsigned char) mp->name_of_file[k]);
    }
    return mp_make_string(mp);
}

@ Now let's consider the \quote {driver} routines by which \MP\ deals with file names
in a system-independent manner. First comes a procedure that looks for a file
name in the input by taking the information from the input buffer. (We can't use
|get_next|, because the conversion to tokens would destroy necessary
information.)

This procedure doesn't allow semicolons or percent signs to be part of file
names, because of other conventions of \MP. {\sl The {\logos METAFONT}book}
doesn't use semicolons or percents immediately after file names, but some users
no doubt will find it natural to do so; therefore system-dependent changes to
allow such characters in file names should probably be made with reluctance, and
only when an entire file name that includes special characters is \quote {quoted}
somehow. @^system dependencies@>

@c
static void mp_scan_file_name (MP mp)
{
    mp_begin_name(mp);
    while (mp->buffer[loc] == ' ') {
        ++loc;
    }
    while (1) {
        if ((mp->buffer[loc] == ';') || (mp->buffer[loc] == '%')) {
            break;
        } else if (! mp_more_name(mp, mp->buffer[loc])) {
            break;
        } else {
            ++loc;
        }
    }
    mp_end_name(mp);
}

static void mp_ptr_scan_file (MP mp, char *s)
{
    char *p = s;
    char *q = p + strlen(s);
    mp_begin_name(mp);
    while (p < q) {
        if (! mp_more_name(mp, (unsigned char) (*p))) {
            break;
        } else {
            p++;
        }
    }
    mp_end_name(mp);
}

@ The option variable |job_name| has no real meaning and is dealt with by the caller, but
it is available in a variable in \MP.

@ @<Option variables@>=
char *job_name;

@ Initially |job_name = NULL| and when it is not set the initializer will quit. Setting
it happens elsewhere.

@ @<Dealloc variables@>=
mp_memory_free(mp->job_name);

@ Cannot do this earlier because at the |<Allocate or ...>|, the string pool is
not yet initialized.

@<Fix up |job_name|@>=
if (mp->job_name != NULL) {
    if (internal_string(mp_job_name_internal) != 0) {
        delete_str_ref(internal_string(mp_job_name_internal));
    }
    set_internal_string(mp_job_name_internal, mp_rts(mp, mp->job_name));
}

@ Let's turn now to the procedure that is used to initiate file reading when an
|input| command is being processed.

@c
void mp_start_input (MP mp)
{
    @<Put the desired file name in |cur_name|@>
    mp_begin_file_reading(mp); /* set up |cur_file| and new level of input */
    mp_pack_file_name(mp, mp->cur_name);
    if (mp_open_in(mp, &cur_file, mp_filetype_program)) {
        char *fname = NULL;
        name = mp_make_name_string(mp);
        fname = mp_strdup(mp->name_of_file);
        if (mp->interaction < mp_silent_mode) {
            /* This needs a cleanup! */
            if ((mp->term_offset > 0) || (mp->file_offset > 0)) {
                mp_print_chr(mp, ' ');
            }
            mp_print_chr(mp, '(');
            ++mp->open_parens;
            mp_print_str(mp, fname);
        }
        mp_memory_free(fname);
        update_terminal();
        @<Flush |name| and replace it with |cur_name| if it won't be needed@>
        @<Read the first line of the new file@>
    } else {
        mp_fatal_error(mp, "invalid input file");
        mp_end_file_reading(mp);
    }
}

@<Flush |name| and replace it with |cur_name| if it won't be needed@>=
mp_flush_string(mp, name);
name = mp_rts(mp, mp->cur_name);
mp_memory_free(mp->cur_name);
mp->cur_name = NULL;

@ If the file is empty, it is considered to contain a single blank line, so there
is no need to test the return value.

@<Read the first line...@>=
line = 1;
mp_input_ln(mp, cur_file);
mp_firm_up_the_line(mp);
mp->buffer[limit] = '%';
mp->first = (size_t) (limit + 1);
loc = start;

@ @<Put the desired file name in |cur_name|@>=
while (token_state && (nloc == NULL)) {
    mp_end_token_list(mp);
}
if (token_state) {
    mp_error(
        mp,
        "File names can't appear within macros",
        "Sorry ... I've converted what follows to tokens, possibly garbaging the name you\n"
        "gave. Please delete the tokens and insert the name again."
    );
    @.File names can't...@>
}
if (file_state) {
    mp_scan_file_name(mp);
} else {
    mp_memory_free(mp->cur_name);
    mp->cur_name = mp_strdup("");
}

@ The last file-opening commands are for files accessed via the |readfrom|
@:read_from_}{|readfrom| primitive@> operator and the |write| command. Such
files are stored in separate arrays. @:write_}{|write| primitive@>


@ @<Glob...@>=
int    max_read_files;  /* maximum number of simultaneously open |readfrom| files */
void **rd_file;         /* |readfrom| files */
char **rd_fname;        /* corresponding file name or 0 if file not open */
int    read_files;      /* number of valid entries in the above arrays */
int    max_write_files; /* maximum number of simultaneously open |write| */
void **wr_file;         /* |write| files */
char **wr_fname;        /* corresponding file name or 0 if file not open */
int    write_files;     /* number of valid entries in the above arrays */

@ @<Allocate or initialize ...@>=
mp->max_read_files  = 8;
mp->rd_file         = mp_memory_allocate((size_t) (mp->max_read_files + 1) * sizeof(void *));
mp->rd_fname        = mp_memory_allocate((size_t) (mp->max_read_files + 1) * sizeof(char *));
mp->max_write_files = 8;
mp->wr_file         = mp_memory_allocate((size_t) (mp->max_write_files + 1) * sizeof(void *));
mp->wr_fname        = mp_memory_allocate((size_t) (mp->max_write_files + 1) * sizeof(char *));

memset(mp->rd_fname, 0, sizeof(char *) * (mp->max_read_files  + 1));
memset(mp->wr_fname, 0, sizeof(char *) * (mp->max_write_files + 1));

@ This routine starts reading the file named by string~|s| without setting
|loc|, |limit|, or |name|.  It returns |false| if the file is empty or cannot
be opened.  Otherwise it updates |rd_file[n]| and |rd_fname[n]|.

@c
static int mp_start_read_input (MP mp, char *s, int n)
{
    mp_ptr_scan_file(mp, s);
    mp_pack_file_name(mp, mp->cur_name);
    mp_begin_file_reading(mp);
    if (! mp_open_in(mp, &mp->rd_file[n], mp_filetype_text + n)) {
        mp_end_file_reading(mp);
        return 0;
    } else if (! mp_input_ln(mp, mp->rd_file[n])) {
        (mp->close_file)(mp, mp->rd_file[n]);
        mp_end_file_reading(mp);
        return 0;
    } else {
        mp->rd_fname[n] = mp_strdup(s);
        return 1;
    }
}

@ Open |wr_file[n]| using file name~|s| and update |wr_fname[n]|.

@<Declarations@>=
static void mp_open_write_file (MP mp, char *s, int n);

@ @c
void mp_open_write_file (MP mp, char *s, int n)
{
    mp_ptr_scan_file(mp, s);
    mp_pack_file_name(mp, mp->cur_name);
    if (mp_open_out(mp, &mp->wr_file[n], mp_filetype_text + n)) {
        mp->wr_fname[n] = mp_strdup(s);
    } else {
        mp_fatal_error(mp, "invalid write file");
    }
}

@* Introduction to the parsing routines.

We come now to the central nervous system that sparks many of \MP's activities.
By evaluating expressions, from their primary constituents to ever larger
subexpressions, \MP\ builds the structures that ultimately define complete
pictures or fonts of type.

Four mutually recursive subroutines are involved in this process: We call them

$$\hbox{|scan_primary|, |scan_secondary|, |scan_tertiary|, and
|scan_expression|.}$$

@^recursion@> Each of them is parameterless and begins with the first token to be
scanned already represented in |cur_cmd|, |cur_mod|, and |cur_sym|. After
execution, the value of the primary or secondary or tertiary or expression that
was found will appear in the global variables |cur_type| and |cur_exp|. The token
following the expression will be represented in |cur_cmd|, |cur_mod|, and
|cur_sym|.

Technically speaking, the parsing algorithms are \quote {LL(1),} more or less; backup
mechanisms have been added in order to provide reasonable error recovery.

@d cur_exp_value_boolean number_to_int(mp->cur_exp.data.n)
@d cur_exp_value_number  mp->cur_exp.data.n
@d cur_exp_node          mp->cur_exp.data.node
@d cur_exp_str           mp->cur_exp.data.str
@d cur_exp_knot          mp->cur_exp.data.p

@<Declarations@>=
static void mp_set_cur_exp_knot          (MP mp, mp_knot n);
static void mp_set_cur_exp_node          (MP mp, mp_node n);
static void mp_set_cur_exp_value_boolean (MP mp, int b);
static void mp_set_cur_exp_value_scaled  (MP mp, int s);
static void mp_set_cur_exp_value_number  (MP mp, mp_number *n);
static void mp_set_cur_exp_str           (MP mp, mp_string s);

@ @c
void mp_set_cur_exp_node (MP mp, mp_node n)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    cur_exp_node = n;
    cur_exp_str = NULL;
    cur_exp_knot = NULL;
    set_number_to_zero(mp->cur_exp.data.n);
}

void mp_set_cur_exp_knot (MP mp, mp_knot n)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    cur_exp_knot = n;
    cur_exp_node = NULL;
    cur_exp_str = NULL;
    set_number_to_zero(mp->cur_exp.data.n);
}

void mp_set_cur_exp_value_boolean (MP mp, int b)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    set_number_from_boolean(mp->cur_exp.data.n, b);
    cur_exp_node = NULL;
    cur_exp_str = NULL;
    cur_exp_knot = NULL;
}

void mp_set_cur_exp_value_scaled (MP mp, int s)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    set_number_from_scaled(mp->cur_exp.data.n, s);
    cur_exp_node = NULL;
    cur_exp_str = NULL;
    cur_exp_knot = NULL;
}

void mp_set_cur_exp_value_number (MP mp, mp_number *n)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    number_clone(mp->cur_exp.data.n, *n);
    cur_exp_node = NULL;
    cur_exp_str = NULL;
    cur_exp_knot = NULL;
}

void mp_set_cur_exp_str (MP mp, mp_string s)
{
    if (cur_exp_str) {
        delete_str_ref(cur_exp_str);
    }
    cur_exp_str = s;
    add_str_ref(cur_exp_str);
    cur_exp_node = NULL;
    cur_exp_knot = NULL;
    set_number_to_zero(mp->cur_exp.data.n);
}

@ @<Glob...@>=
mp_value cur_exp; /* the value of the expression just found */

@ @<Set init...@>=
memset(&mp->cur_exp.data, 0, sizeof(mp_value));
new_number(mp->cur_exp.data.n);

@ @<Free table ...@>=
free_number(mp->cur_exp.data.n);

@ Many different kinds of expressions are possible, so it is wise to have precise
descriptions of what |cur_type| and |cur_exp| mean in all cases:

\smallskip\hang |cur_type=mp_vacuous| means that this expression didn't turn out
to have a value at all, because it arose from a
|begingroup|$\,\ldots\,$|endgroup| construction in which there was no
expression before the |endgroup|. In this case |cur_exp| has some irrelevant
value.

\smallskip\hang |cur_type = mp_boolean_type| means that |cur_exp| is either
|true_code| or |false_code|.

\smallskip\hang |cur_type = mp_unknown_boolean| means that |cur_exp| points to a
capsule node that is in a ring of equivalent booleans whose value has not yet
been defined.

\smallskip\hang |cur_type = mp_string_type| means that |cur_exp| is a string number
(i.e., an integer in the range |0<=cur_exp<str_ptr|). That string's reference
count includes this particular reference.

\smallskip\hang |cur_type = mp_unknown_string| means that |cur_exp| points to a
capsule node that is in a ring of equivalent strings whose value has not yet been
defined.

\smallskip\hang |cur_type = mp_pen_type| means that |cur_exp| points to a node in a
pen. Nobody else points to any of the nodes in this pen. The pen may be polygonal
or elliptical.

\smallskip\hang |cur_type=mp_unknown_pen| means that |cur_exp| points to a
capsule node that is in a ring of equivalent pens whose value has not yet been
defined.

\smallskip\hang |cur_type = mp_path_type| means that |cur_exp| points to a the
first node of a path; nobody else points to this particular path. The control
points of the path will have been chosen.

\smallskip\hang
|cur_type = mp_unknown_path| means that |cur_exp| points to a capsule
node that is in
a ring of equivalent paths whose value has not yet been defined.

\smallskip\hang
|cur_type = mp_picture_type| means that |cur_exp| points to an edge header node.
There may be other pointers to this particular set of edges.  The header node
contains a reference count that includes this particular reference.

\smallskip\hang |cur_type = mp_unknown_picture| means that |cur_exp| points to a
capsule node that is in a ring of equivalent pictures whose value has not yet
been defined.

\smallskip\hang |cur_type = mp_transform_type| means that |cur_exp| points to a
|mp_transform_type| capsule node. The |value| part of this capsule points to a
transform node that contains six numeric values, each of which is |independent|,
|dependent|, |mp_proto_dependent|, or |known|.

\smallskip\hang |cur_type = mp_color_type| means that |cur_exp| points to a
|color_type| capsule node. The |value| part of this capsule points to a color
node that contains three numeric values, each of which is |independent|,
|dependent|, |mp_proto_dependent|, or |known|.

\smallskip\hang |cur_type = mp_cmykcolor_type| means that |cur_exp| points to a
|mp_cmykcolor_type| capsule node. The |value| part of this capsule points to a
color node that contains four numeric values, each of which is |independent|,
|dependent|, |mp_proto_dependent|, or |known|.

\smallskip\hang |cur_type = mp_pair_type| means that |cur_exp| points to a capsule
node whose type is |mp_pair_type|. The |value| part of this capsule points to a
pair node that contains two numeric values, each of which is |independent|,
|dependent|, |mp_proto_dependent|, or |known|.

\smallskip\hang |cur_type = mp_known| means that |cur_exp| is a |scaled| value.

\smallskip\hang |cur_type = mp_dependent| means that |cur_exp| points to a capsule
node whose type is |dependent|. The |dep_list| field in this capsule points to
the associated dependency list.

\smallskip\hang |cur_type = mp_proto_dependent| means that |cur_exp| points to a
|mp_proto_dependent| capsule node. The |dep_list| field in this capsule points to
the associated dependency list.

\smallskip\hang |cur_type = independent| means that |cur_exp| points to a capsule
node whose type is |independent|. This somewhat unusual case can arise, for
example, in the expression `$x+|begingroup|\penalty0\,|string|\,x;
0\,|endgroup|$'.

\smallskip\hang |cur_type = mp_token_list| means that |cur_exp| points to a linked
list of tokens.

\smallskip\noindent The possible settings of |cur_type| have been listed here in
increasing numerical order. Notice that |cur_type| will never be
|mp_numeric_type| or |suffixed_macro| or |mp_unsuffixed_macro|, although
variables of those types are allowed. Conversely, \MP\ has no variables of type
|mp_vacuous| or |token_list|.

@ Capsules are non-symbolic nodes that have a similar meaning to |cur_type| and
|cur_exp|. Such nodes have |name_type=capsule|, and their |type| field is one of
the possibilities for |cur_type| listed above. Also |link<=void| in capsules that
aren't part of a token list.

The |value| field of a capsule is, in most cases, the value that corresponds to
its |type|, as |cur_exp| corresponds to |cur_type|. However, when |cur_exp| would
point to a capsule, no extra layer of indirection is present; the |value| field
is what would have been called |value(cur_exp)| if it had not been encapsulated.
Furthermore, if the type is |dependent| or |mp_proto_dependent|, the |value|
field of a capsule is replaced by |dep_list| and |prev_dep| fields, since
dependency lists in capsules are always part of the general |dep_list| structure.

The |get_x_next| routine is careful not to change the values of |cur_type| and
|cur_exp| when it gets an expanded token. However, |get_x_next| might call a
macro, which might parse an expression, which might execute lots of commands in a
group; hence it's possible that |cur_type| might change from, say,
|mp_unknown_boolean| to |mp_boolean_type|, or from |dependent| to |known| or
|independent|, during the time |get_x_next| is called. The programs below are
careful to stash sensitive intermediate results in capsules, so that \MP's
generality doesn't cause trouble.

Here's a procedure that illustrates these conventions. It takes the contents of
$(|cur_type|\kern-.3pt,|cur_exp|\kern-.3pt)$ and stashes them away in a capsule.
It is not used when |cur_type=mp_token_list|. After the operation,
|cur_type=mp_vacuous|; hence there is no need to copy path lists or to update
reference counts, etc.

The special link |MP_VOID| is put on the capsule returned by |stash_cur_exp|,
because this procedure is used to store macro parameters that must be easily
distinguishable from token lists.

@<Declarations@>=
static mp_node mp_stash_cur_exp (MP mp);

@ @c
static mp_node mp_stash_cur_exp (MP mp)
{
    mp_node p; /* the capsule that will be returned */
    mp_variable_type exp_type = mp->cur_exp.type;
    switch (exp_type) {
        case mp_unknown_boolean_type:
        case mp_unknown_string_type:
        case mp_unknown_pen_type:
        case mp_unknown_nep_type:
        case mp_unknown_path_type:
        case mp_unknown_picture_type:
        case mp_transform_type:
        case mp_color_type:
        case mp_pair_type:
        case mp_dependent_type:
        case mp_proto_dependent_type:
        case mp_independent_type:
        case mp_cmykcolor_type:
            p = cur_exp_node;
            break;
        default: /* |case mp_path_type: case mp_pen_type: case mp_string_type:| */
            p = mp_new_value_node(mp);
            mp_name_type(p) = mp_capsule_operation;
            mp_type(p) = mp->cur_exp.type;
            mp_set_value_number(p, cur_exp_value_number); /* this also resets the rest to 0/NULL */
            if (cur_exp_str)    {
                mp_set_value_str(p, cur_exp_str);
            } else if (cur_exp_knot) {
                mp_set_value_knot(p, cur_exp_knot);
            } else if (cur_exp_node) {
                mp_set_value_node(p, cur_exp_node);
            }
            break;
    }
    mp->cur_exp.type = mp_vacuous_type;
    mp_link(p) = MP_VOID;
    return p;
}

@ The inverse of |stash_cur_exp| is the following procedure, which deletes an
unnecessary capsule and puts its contents into |cur_type| and |cur_exp|.

The program steps of \MP\ can be divided into two categories: those in which
|cur_type| and |cur_exp| are \quote {alive} and those in which they are \quote {dead,} in
the sense that |cur_type| and |cur_exp| contain relevant information or not. It's
important not to ignore them when they're alive, and it's important not to pay
attention to them when they're dead.

There's also an intermediate category: If |cur_type=mp_vacuous|, then |cur_exp|
is irrelevant, hence we can proceed without caring if |cur_type| and |cur_exp|
are alive or dead. In such cases we say that |cur_type| and |cur_exp| are {\sl
dormant}. It is permissible to call |get_x_next| only when they are alive or
dormant.

The |stash| procedure above assumes that |cur_type| and |cur_exp| are alive or
dormant. The |unstash| procedure assumes that they are dead or dormant; it
resuscitates them.

@ @c
void mp_unstash_cur_exp (MP mp, mp_node p)
{
    mp->cur_exp.type = mp_type(p);
    switch (mp->cur_exp.type) {
        case mp_unknown_boolean_type:
        case mp_unknown_string_type:
        case mp_unknown_pen_type:
        case mp_unknown_nep_type:
        case mp_unknown_path_type:
        case mp_unknown_picture_type:
        case mp_transform_type:
        case mp_color_type:
        case mp_pair_type:
        case mp_dependent_type:
        case mp_proto_dependent_type:
        case mp_independent_type:
        case mp_cmykcolor_type:
            mp_set_cur_exp_node(mp, p);
            break;
        case mp_token_list_type: /* this is how symbols are stashed */
            mp_set_cur_exp_node(mp, mp_get_value_node(p));
            mp_free_value_node(mp, p);
            break;
        case mp_path_type:
        case mp_pen_type:
        case mp_nep_type:
            mp_set_cur_exp_knot(mp, mp_get_value_knot(p));
            mp_free_value_node(mp, p);
            break;
        case mp_string_type:
            mp_set_cur_exp_str(mp, mp_get_value_str(p));
            mp_free_value_node(mp, p);
            break;
        case mp_picture_type:
            mp_set_cur_exp_node(mp, mp_get_value_node(p));
            mp_free_value_node(mp, p);
            break;
        case mp_boolean_type:
        case mp_known_type:
            mp_set_cur_exp_value_number(mp, &(mp_get_value_number(p)));
            mp_free_value_node(mp, p);
            break;
        default:
            mp_set_cur_exp_value_number(mp, &(mp_get_value_number(p)));
            if (mp_get_value_knot(p)) {
                mp_set_cur_exp_knot(mp, mp_get_value_knot(p));
            } else if (mp_get_value_node(p)) {
                mp_set_cur_exp_node(mp, mp_get_value_node(p));
            } else if (mp_get_value_str(p)) {
                mp_set_cur_exp_str(mp, mp_get_value_str(p));
            }
            mp_free_value_node(mp, p);
            break;
    }
}

@ The following procedure prints the values of expressions in an abbreviated
format. If its first parameter |p| is NULL, the value of |(cur_type,cur_exp)| is
displayed; otherwise |p| should be a capsule containing the desired value. The
second parameter controls the amount of output. If it is~0, dependency lists will
be abbreviated to |linearform| unless they consist of a single term. If it is
greater than~1, complicated structures (pens, pictures, and paths) will be
displayed in full. @.linearform@>

@<Declarations@>=
static void mp_print_dp        (MP mp, int t, mp_value_node p, int verbosity);
static void mp_unstash_cur_exp (MP mp, mp_node p);
static void mp_print_exp       (MP mp, mp_node p, int verbosity);
static void mp_print_big_node  (MP mp, mp_node p, int verbosity);

@ @c
void mp_print_exp (MP mp, mp_node p, int verbosity)
{
    int restore_cur_exp;     /* should |cur_exp| be restored? */
    mp_variable_type t;      /* the type of the expression */
    mp_number vv;            /* the value of the expression */
    mp_node v = NULL;
    new_number(vv);
    if (p != NULL) {
        restore_cur_exp = 0;
    } else {
        p = mp_stash_cur_exp(mp);
        restore_cur_exp = 1;
    }
    t = mp_type(p);
    if (t < mp_dependent_type) {
        /* no dep list, could be a capsule */
        if (t != mp_vacuous_type && t != mp_known_type && mp_get_value_node(p) != NULL) {
            v = mp_get_value_node(p);
        } else {
            number_clone(vv, mp_get_value_number(p));
        }
    } else if (t < mp_independent_type) {
        v = (mp_node) mp_get_dep_list((mp_value_node) p);
    }
    @<Print an abbreviated value of |v| or |vv| with format depending on |t|@>
    if (restore_cur_exp) {
        mp_unstash_cur_exp(mp, p);
    }
    free_number(vv);
}

void mp_print_big_node (MP mp, mp_node v, int verbosity)
{
    switch (mp_type(v)) {
        case mp_known_type:
            print_number(mp_get_value_number(v));
            break;
        case mp_independent_type:
            mp_print_variable_name(mp, v);
            break;
        default:
            mp_print_dp(mp, mp_type(v), (mp_value_node) mp_get_dep_list((mp_value_node) v), verbosity);
            break;
    }
}

@ @<Print an abbreviated value of |v| or |vv| with format depending on |t|@>=
switch (t) {
    case mp_vacuous_type:
        mp_print_str(mp, "vacuous");
        break;
    case mp_boolean_type:
        mp_print_str(mp, number_to_boolean(vv) == mp_true_operation ? "true": "false");
        break;
    case mp_unknown_boolean_type:
    case mp_unknown_string_type:
    case mp_unknown_pen_type:
    case mp_unknown_nep_type:
    case mp_unknown_path_type:
    case mp_unknown_picture_type:
    case mp_numeric_type:
        {
            @<Display a variable that's been declared but not defined@>
        }
        break;
    case mp_string_type:
        mp_print_chr(mp, '"');
        mp_print_mp_str(mp, mp_get_value_str(p));
        mp_print_chr(mp, '"');
        break;
    case mp_pen_type:
    case mp_nep_type:
    case mp_path_type:
    case mp_picture_type:
        {
            @<Display a complex type@>
        }
        break;
    case mp_transform_type:
        if (number_zero(vv) && v == NULL) {
            mp_print_type(mp, t);
        } else {
            @<Display a transform node@>
        }
        break;
    case mp_color_type:
        if (number_zero(vv) && v == NULL) {
            mp_print_type(mp, t);
        } else {
            @<Display a color node@>
        }
        break;
    case mp_pair_type:
        if (number_zero(vv) && v == NULL) {
            mp_print_type(mp, t);
        } else {
            @<Display a pair node@>
        }
        break;
    case mp_cmykcolor_type:
        if (number_zero(vv) && v == NULL) {
            mp_print_type(mp, t);
        } else {
            @<Display a cmykcolor node@>
        }
        break;
    case mp_known_type:
        print_number(vv);
        break;
    case mp_dependent_type:
    case mp_proto_dependent_type:
        mp_print_dp(mp, t, (mp_value_node) v, verbosity);
        break;
    case mp_independent_type:
        mp_print_variable_name(mp, p);
        break;
    default:
        mp_confusion(mp, "expression");
        break;
        @:this can't happen exp}{\quad exp@>
}

@ In these cases, |v| starts as the big node.

@<Display a pair node@>=
mp_print_chr(mp, '(');
mp_print_big_node(mp, mp_x_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_y_part(v), verbosity);
mp_print_chr(mp, ')');

@ @<Display a transform node@>=
mp_print_chr(mp, '(');
mp_print_big_node(mp, mp_tx_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_ty_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_xx_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_xy_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_yx_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_yy_part(v), verbosity);
mp_print_chr(mp, ')');

@ @<Display a color node@>=
mp_print_chr(mp, '(');
mp_print_big_node(mp, mp_red_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_green_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_blue_part(v), verbosity);
mp_print_chr(mp, ')');

@ @<Display a cmykcolor node@>=
mp_print_chr(mp, '(');
mp_print_big_node(mp, mp_cyan_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_magenta_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_yellow_part(v), verbosity);
mp_print_chr(mp, ',');
mp_print_big_node(mp, mp_black_part(v), verbosity);
mp_print_chr(mp, ')');

@ Values of type |picture|, |path|, and |pen| are displayed verbosely in
the log file only, unless the user has given a positive value to
|tracingonline|.

@<Display a complex type@>=
if (verbosity <= 1) {
    mp_print_type(mp, t);
} else {
    if (mp->selector == mp_term_and_log_selector)
        if (number_nonpositive(internal_value(mp_tracing_online_internal))) {
            mp->selector = mp_term_only_selector;
            mp_print_type(mp, t);
            mp_print_str(mp, " (see the transcript file)");
            mp->selector = mp_term_and_log_selector;
        };
    switch (t) {
        case mp_pen_type:
        case mp_nep_type:
            mp_print_pen(mp, mp_get_value_knot(p), "", 0);
            break;
        case mp_path_type:
            mp_print_path(mp, mp_get_value_knot(p), "", 0);
            break;
        case mp_picture_type:
            mp_print_edges(mp, v, "", 0);
            break;
        default:
            break;
    }
}

@ @c
static void mp_print_dp (MP mp, int t, mp_value_node p, int verbosity)
{
    mp_value_node q = (mp_value_node) mp_link(p); /* the node following |p| */
    if ((mp_get_dep_info(q) == NULL) || (verbosity > 0)) {
        mp_print_dependency(mp, p, t);
    } else {
        mp_print_str(mp, "linearform");
    }
}

@ The displayed name of a variable in a ring will not be a capsule unless
the ring consists entirely of capsules.

@<Display a variable that's been declared but not defined@>=
{
    mp_print_type(mp, t);
    if (v != NULL) {
        mp_print_chr(mp, ' ');
        while ((mp_name_type(v) == mp_capsule_operation) && (v != p)) {
            v = mp_get_value_node(v);
        }
        mp_print_variable_name(mp, v);
    };
}

@ When errors are detected during parsing, it is often helpful to display an
expression just above the error message, using |disp_err| just before |mp_error|.

@<Declarations@>=
static void mp_disp_err (MP mp, mp_node p);

@ @c
void mp_disp_err (MP mp, mp_node p)
{
    if (mp->interaction >= mp_error_stop_mode) {
        wake_up_terminal();
    }
 /* mp_print_nl(mp, ">> "); */
    mp_print_nl(mp, "<error> ");
    @.>>@>
    mp_print_exp(mp, p, 1);
}

@ If |cur_type| and |cur_exp| contain relevant information that should be
recycled, we will use the following procedure, which changes |cur_type| to
|known| and stores a given value in |cur_exp|. We can think of |cur_type| and
|cur_exp| as either alive or dormant after this has been done, because |cur_exp|
will not contain a pointer value.

@ @c
void mp_flush_cur_exp (MP mp, mp_value v)
{
    if (is_number(mp->cur_exp.data.n)) {
        free_number(mp->cur_exp.data.n);
    }
    switch (mp->cur_exp.type) {
        case mp_unknown_boolean_type:
        case mp_unknown_string_type:
        case mp_unknown_pen_type:
        case mp_unknown_nep_type:
        case mp_unknown_path_type:
        case mp_unknown_picture_type:
        case mp_transform_type:
        case mp_color_type:
        case mp_pair_type:
        case mp_dependent_type:
        case mp_proto_dependent_type:
        case mp_independent_type:
        case mp_cmykcolor_type:
            mp_recycle_value(mp, cur_exp_node);
            mp_free_value_node(mp, cur_exp_node);
            break;
        case mp_string_type:
            delete_str_ref(cur_exp_str);
            break;
        case mp_pen_type:
        case mp_nep_type:
        case mp_path_type:
            mp_toss_knot_list(mp, cur_exp_knot);
            break;
        case mp_picture_type:
            mp_delete_edge_ref(mp, cur_exp_node);
            break;
        default:
            break;
    }
    mp->cur_exp = v;
  mp->cur_exp.type = mp_known_type;
}

@ There's a much more general procedure that is capable of releasing the storage
associated with any non-symbolic value packet.

@<Declarations@>=
static void mp_recycle_value (MP mp, mp_node p);

@ @c
static void mp_recycle_value (MP mp, mp_node p)
{
    if (p != NULL && p != MP_VOID) {
        mp_variable_type t = mp_type(p);
        switch (t) {
            case mp_vacuous_type:
            case mp_boolean_type:
            case mp_known_type:
            case mp_numeric_type:
                break;
            case mp_unknown_boolean_type:
            case mp_unknown_string_type:
            case mp_unknown_pen_type:
            case mp_unknown_nep_type:
            case mp_unknown_path_type:
            case mp_unknown_picture_type:
                mp_ring_delete (mp, p);
                break;
            case mp_string_type:
                delete_str_ref(mp_get_value_str(p));
                break;
            case mp_path_type:
            case mp_pen_type:
            case mp_nep_type:
                mp_toss_knot_list(mp, mp_get_value_knot(p));
                break;
            case mp_picture_type:
                mp_delete_edge_ref(mp, mp_get_value_node(p));
                break;
            case mp_cmykcolor_type:
                if (mp_get_value_node(p) != NULL) {
                    mp_recycle_value(mp, mp_cyan_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_magenta_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_yellow_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_black_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_cyan_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_magenta_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_black_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_yellow_part(mp_get_value_node(p)));
                    mp_free_node(mp, mp_get_value_node(p), sizeof(mp_color_node_data));
                }
                break;
            case mp_pair_type:
                if (mp_get_value_node(p) != NULL) {
                    mp_recycle_value(mp, mp_x_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_y_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_x_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_y_part(mp_get_value_node(p)));
                    mp_free_pair_node(mp, mp_get_value_node(p));
                }
                break;
            case mp_color_type:
                if (mp_get_value_node(p) != NULL) {
                    mp_recycle_value(mp, mp_red_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_green_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_blue_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_red_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_green_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_blue_part(mp_get_value_node(p)));
                    mp_free_node(mp, mp_get_value_node(p), sizeof(mp_color_node_data));
                }
                break;
            case mp_transform_type:
                if (mp_get_value_node(p) != NULL) {
                    mp_recycle_value(mp, mp_tx_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_ty_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_xx_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_xy_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_yx_part(mp_get_value_node(p)));
                    mp_recycle_value(mp, mp_yy_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_tx_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_ty_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_xx_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_xy_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_yx_part(mp_get_value_node(p)));
                    mp_free_value_node(mp, mp_yy_part(mp_get_value_node(p)));
                    mp_free_node(mp, mp_get_value_node(p), sizeof(mp_transform_node_data));
                }
                break;
            case mp_dependent_type:
            case mp_proto_dependent_type:
                /* Recycle a dependency list */
                {
                    mp_value_node qq = (mp_value_node) mp_get_dep_list((mp_value_node) p);
                    while (mp_get_dep_info(qq) != NULL) {
                        qq = (mp_value_node) mp_link(qq);
                    }
                    mp_set_link(mp_get_prev_dep((mp_value_node) p), mp_link(qq));
                    mp_set_prev_dep(mp_link(qq), mp_get_prev_dep((mp_value_node) p));
                    mp_set_link(qq, NULL);
                    mp_flush_node_list(mp, (mp_node) mp_get_dep_list((mp_value_node) p));
                }
                break;
            case mp_independent_type:
                mp_recycle_independent_value(mp, p);
                break;
            case mp_token_list_type:
            case mp_structured_type:
                mp_confusion(mp, "recycle");
                break;
            case mp_unsuffixed_macro_type:
            case mp_suffixed_macro_type:
                mp_delete_mac_ref(mp, mp_get_value_node(p));
                break;
            default:
                break;
        }
        mp_type(p) = mp_undefined_type;
    }
}

@ When an independent variable disappears, it simply fades away, unless something
depends on it. In the latter case, a dependent variable whose coefficient of
dependence is maximal will take its place. The relevant algorithm is due to
Ignacio~A. Zabala, who implemented it as part of his Ph.n->data. thesis (Stanford
University, December 1982). @^Zabala Salelles, Ignacio Andr\'es@>

For example, suppose that variable $x$ is being recycled, and that the only
variables depending on~$x$ are $y=2x+a$ and $z=x+b$. In this case we want to make
$y$ independent and $z=.5y-.5a+b$; no other variables will depend on~$y$. If
$|tracingequations|>0$ in this situation, we will print |\#\#\# -2x=-y+a|.

There's a slight complication, however: An independent variable $x$ can occur
both in dependency lists and in proto-dependency lists. This makes it necessary
to be careful when deciding which coefficient is maximal.

Furthermore, this complication is not so slight when a proto-dependent variable
is chosen to become independent. For example, suppose that $y=2x+100a$ is
proto-dependent while $z=x+b$ is dependent; then we must change $z=.5y-50a+b$ to
a proto-dependency, because of the large coefficient `50'.

In order to deal with these complications without wasting too much time, we shall
link together the occurrences of~$x$ among all the linear dependencies,
maintaining separate lists for the dependent and proto-dependent cases.

@<Declarations@>=
static void mp_recycle_independent_value (MP mp, mp_node p);

@ @c
static void mp_recycle_independent_value (MP mp, mp_node p)
{
    mp_value_node q, r, s;
    mp_node pp;        /* link manipulation register */
    mp_number v ;      /* a value */
    mp_number test;    /* a temporary value */
    mp_variable_type t = mp_type(p);
    new_number(test);
    new_number(v);
    if (t < mp_dependent_type) {
        number_clone(v, mp_get_value_number(p));
    }
    set_number_to_zero(mp->max_c[mp_dependent_type]);
    set_number_to_zero(mp->max_c[mp_proto_dependent_type]);
    mp->max_link[mp_dependent_type] = NULL;
    mp->max_link[mp_proto_dependent_type] = NULL;
    q = (mp_value_node) mp_link(mp->dep_head);
    while (q != mp->dep_head) {
        s = (mp_value_node) mp->temp_head;
        mp_set_link(s, mp_get_dep_list(q));
        while (1) {
            r = (mp_value_node) mp_link(s);
            if (mp_get_dep_info(r) == NULL) {
                break;
            } else if (mp_get_dep_info(r) != p) {
                s = r;
            } else {
                t = mp_type(q);
                if (mp_link(s) == mp_get_dep_list(q)) {
                    /* reset the |dep_list| */
                    mp_set_dep_list(q, mp_link(r));
                }
                mp_set_link(s, mp_link(r));
                mp_set_dep_info(r, (mp_node) q);
                number_abs_clone(test, mp_get_dep_value(r));
                if (number_greater(test, mp->max_c[t])) {
                    /* Record a new maximum coefficient of type |t| */
                    if (number_positive(mp->max_c[t])) {
                        mp_set_link(mp->max_ptr[t], (mp_node) mp->max_link[t]);
                        mp->max_link[t] = mp->max_ptr[t];
                    }
                    number_clone(mp->max_c[t], test);
                    mp->max_ptr[t] = r;
                } else {
                    mp_set_link(r, mp->max_link[t]);
                    mp->max_link[t] = r;
                }
            }
        }
        q = (mp_value_node) mp_link(r);
    }
    if (number_positive(mp->max_c[mp_dependent_type]) || number_positive(mp->max_c[mp_proto_dependent_type])) {
        /*
            Choose a dependent variable to take the place of the disappearing
            independent variable, and change all remaining dependencies
            accordingly
        */
        mp_number test, ret; /* temporary use */
        new_number(ret);
        new_number_clone(test, mp->max_c[mp_dependent_type]);
        number_divide_int(test, 4096);
        if (number_greaterequal(test, mp->max_c[mp_proto_dependent_type])) {
            t = mp_dependent_type;
        } else {
            t = mp_proto_dependent_type;
        }
        /*
             Let |s=max_ptr[t]|. At this point we have
             $|value|(s)=\pm|max_c|[t]$, and |mp_get_dep_info(s)| points to the
             dependent variable~|pp| of type~|t| from whose dependency list we
             have removed node~|s|. We must reinsert node~|s| into the dependency
             list, with coefficient $-1.0$, and with |pp| as the new independent
             variable. Since |pp| will have a larger serial number than any other
             variable, we can put node |s| at the head of the list.

             Determine the dependency list |s| to substitute for the independent
             variable~|p|
        */
        s = mp->max_ptr[t];
        pp = (mp_node) mp_get_dep_info(s);
        number_clone(v, mp_get_dep_value(s));
        if (t == mp_dependent_type) {
            mp_set_dep_value(s, fraction_one_t);
        } else {
            mp_set_dep_value(s, unity_t);
        }
        number_negate(mp_get_dep_value(s));
        r = (mp_value_node) mp_get_dep_list((mp_value_node) pp);
        mp_set_link(s, r);
        while (mp_get_dep_info(r) != NULL) {
            r = (mp_value_node) mp_link(r);
        }
        q = (mp_value_node) mp_link(r);
        mp_set_link(r, NULL);
        mp_set_prev_dep(q, mp_get_prev_dep((mp_value_node) pp));
        mp_set_link(mp_get_prev_dep((mp_value_node) pp), (mp_node) q);
        mp_new_indep(mp, pp);
        if (cur_exp_node == pp && mp->cur_exp.type == t) {
            mp->cur_exp.type = mp_independent_type;
        }
        if (number_positive(internal_value(mp_tracing_equations_internal)) && mp_interesting(mp, p)) {
            mp_begin_diagnostic(mp);
            mp_show_transformed_dependency(mp, &v, t, p);
            mp_print_dependency(mp, s, t);
            mp_end_diagnostic(mp, 0);
        }
        /* complement |t| */
        t = mp_dependent_type + mp_proto_dependent_type - t;
        if (number_positive(mp->max_c[t])) {
            /* we need to pick up an unchosen dependency */
            mp_set_link(mp->max_ptr[t], (mp_node) mp->max_link[t]);
            mp->max_link[t] = mp->max_ptr[t];
        }
        /*
            Finally, there are dependent and proto-dependent variables whose
            dependency lists must be brought up to date.
        */
        if (t != mp_dependent_type) {
            /* Substitute new dependencies in place of |p| */
            for (t = mp_dependent_type; t <= mp_proto_dependent_type; t=t+1) {
                r = mp->max_link[t];
                while (r != NULL) {
                    q = (mp_value_node) mp_get_dep_info(r);
                    number_negated_clone(test, v);
                    make_fraction(ret, mp_get_dep_value(r), test);
                    mp_set_dep_list(q, mp_p_plus_fq(mp, (mp_value_node) mp_get_dep_list(q), &ret, s, t, mp_dependent_type));
                    if (mp_get_dep_list(q) == (mp_node) mp->dep_final) {
                        mp_make_known(mp, q, mp->dep_final);
                    }
                    q = r;
                    r = (mp_value_node) mp_link(r);
                    mp_free_dep_node(mp, q);
                }
            }
        } else {
            /* Substitute new proto-dependencies in place of |p| */
            for (t = mp_dependent_type; t <= mp_proto_dependent_type; t++) {
                r = mp->max_link[t];
                while (r != NULL) {
                    q = (mp_value_node) mp_get_dep_info(r);
                    if (t == mp_dependent_type) {
                        /* for safety's sake, we change |q| to |mp_proto_dependent| */
                        if (cur_exp_node == (mp_node) q && mp->cur_exp.type == mp_dependent_type) {
                            mp->cur_exp.type = mp_proto_dependent_type;
                        }
                        mp_set_dep_list(q, mp_p_over_v(mp, (mp_value_node) mp_get_dep_list(q), &unity_t, mp_dependent_type, mp_proto_dependent_type));
                        mp_type(q) = mp_proto_dependent_type;
                        fraction_to_round_scaled(mp_get_dep_value(r));
                    }
                    number_negated_clone(test, v);
                    make_scaled(ret, mp_get_dep_value(r), test);
                    mp_set_dep_list(q, mp_p_plus_fq(mp, (mp_value_node) mp_get_dep_list(q), &ret, s, mp_proto_dependent_type, mp_proto_dependent_type));
                    if (mp_get_dep_list(q) == (mp_node) mp->dep_final) {
                        mp_make_known(mp, q, mp->dep_final);
                    }
                    q = r;
                    r = (mp_value_node) mp_link(r);
                    mp_free_dep_node(mp, q);
                }
            }
        }
        mp_flush_node_list(mp, (mp_node) s);
        if (mp->fix_needed) {
            mp_fix_dependencies(mp);
        }
        check_arith();
        free_number(ret);
    }
    free_number(v);
    free_number(test);
}

@ @<Declarations@>=
static void mp_show_transformed_dependency (MP mp, mp_number *v, mp_variable_type t, mp_node p);

@ @c
static void mp_show_transformed_dependency (MP mp, mp_number *v, mp_variable_type t, mp_node p)
{
    mp_number vv; /* for temp use */
    mp_print_nl(mp, "### ");
    if (number_positive(*v)) {
        mp_print_chr(mp, '-');
    }
    if (t == mp_dependent_type) {
        new_number_clone(vv, mp->max_c[mp_dependent_type]);
        fraction_to_round_scaled(vv);
    } else {
        new_number_clone(vv, mp->max_c[mp_proto_dependent_type]);
    }
    if (! number_equal(vv, unity_t)) {
        print_number(vv);
    }
    mp_print_variable_name(mp, p);
    while (mp_get_indep_scale(p) > 0) {
        mp_print_str(mp, "*4");
        mp_set_indep_scale(p, mp_get_indep_scale(p)-2);
    }
    if (t == mp_dependent_type) {
        mp_print_chr(mp, '=');
    } else {
        mp_print_str(mp, " = ");
    }
    free_number(vv);
}

@ The code for independency removal makes use of three non-symbolic arrays.

@<Glob...@>=
mp_number max_c[mp_proto_dependent_type + 1];        /* max coefficient magnitude */
mp_value_node max_ptr[mp_proto_dependent_type + 1];  /* where |p| occurs with |max_c| */
mp_value_node max_link[mp_proto_dependent_type + 1]; /* other occurrences of |p| */


@ @<Initialize table ... @>=
for (int i = 0; i < mp_proto_dependent_type + 1; i++) {
    new_number(mp->max_c[i]);
}

@ @<Dealloc...@>=
for (int i = 0; i < mp_proto_dependent_type + 1; i++) {
    free_number(mp->max_c[i]);
}

@ A global variable |var_flag| is set to a special command code just before \MP\
calls |scan_expression|, if the expression should be treated as a variable when
this command code immediately follows. For example, |var_flag| is set to
|assignment| at the beginning of a statement, because we want to know the {\sl
location} of a variable at the left of |:=|, not the {\sl value} of that
variable.

The |scan_expression| subroutine calls |scan_tertiary|, which calls
|scan_secondary|, which calls |scan_primary|, which sets |var_flag:=0|. In this
way each of the scanning routines \quote {knows} when it has been called with a
special |var_flag|, but |var_flag| is usually zero.

A variable preceding a command that equals |var_flag| is converted to a token
list rather than a value. Furthermore, an |=| sign following an expression
with |var_flag=assignment| is not considered to be a relation that produces
boolean expressions.

@<Glob...@>=
int var_flag; /* command that wants a variable */

@ @<Set init...@>=
mp->var_flag = 0;

@* Parsing primary expressions.

The first parsing routine, |scan_primary|, is also the most complicated one,
since it involves so many different cases. But each case---with one
exception---is fairly simple by itself.

When |scan_primary| begins, the first token of the primary to be scanned should
already appear in |cur_cmd|, |cur_mod|, and |cur_sym|. The values of |cur_type|
and |cur_exp| should be either dead or dormant, as explained earlier. If
|cur_cmd| is not between |min_primary_command| and |max_primary_command|,
inclusive, a syntax error will be signaled.

Later we'll come to procedures that perform actual operations like addition,
square root, and so on; our purpose now is to do the parsing. But we might as
well mention those future procedures now, so that the suspense won't be too bad:

\smallskip |do_nullary(c)| does primitive operations that have no operands (e.g.,
|true| or |pencircle|);

\smallskip |do_unary(c)| applies a primitive operation to the current expression;

\smallskip |do_binary(p,c)| applies a primitive operation to the capsule~|p| and
the current expression.

@<Declare the basic parsing subroutines@>=
static void check_for_mediation (MP mp);

static void mp_primary_error(MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    mp_disp_err(mp, NULL);
    new_number(new_expr.data.n);
    mp_back_error(
        mp,
        "Nonnumeric part has been replaced by 0",
        "I've started to scan a pair (x,y), color (r,g,b), cmykcolor (c,m,y,k) or\n"
        "transform (tx,ty,xx,xy,yx,yy) but ran into a non-numeric type. I'll recover\n"
        "as good as possible."
    );
    mp_get_x_next(mp);
    mp_flush_cur_exp(mp, new_expr);
}

void mp_scan_primary (MP mp)
{
    mp_command_code my_var_flag = mp->var_flag;
    mp->var_flag = 0;
  RESTART:
    check_arith();
    /* Supply diagnostic information, if requested */
    switch (cur_cmd) {
        case mp_left_delimiter_command:
            {
                /* Scan a delimited primary */
                mp_sym l_delim = cur_sym;
                mp_sym r_delim = equiv_sym(cur_sym);
                mp_get_x_next(mp);
                mp_scan_expression(mp);
                if ((cur_cmd == mp_comma_command) && (mp->cur_exp.type >= mp_known_type)) {
                    /* Scan the rest of a delimited set of numerics. */
                    mp_node q = mp_new_value_node(mp);
                    mp_node p1 = mp_stash_cur_exp(mp);
                    mp_node r; /* temporary node */
                    mp_name_type(q) = mp_capsule_operation;
                    mp_get_x_next(mp);
                    mp_scan_expression(mp);
                    /* Make sure the second part of a pair or color has a numeric type */
                    if (mp->cur_exp.type < mp_known_type) {
                        mp_primary_error(mp);
                    }
                    if (cur_cmd != mp_comma_command) {
                        /* Package the pair. */
                        mp_init_pair_node(mp, q);
                        r = mp_get_value_node(q);
                        mp_stash_in(mp, mp_y_part(r));
                        mp_unstash_cur_exp(mp, p1);
                        mp_stash_in(mp, mp_x_part(r));
                    } else {
                        mp_node p2 = mp_stash_cur_exp(mp);
                        /* Scan the last of a triplet of numerics */
                        mp_get_x_next(mp);
                        mp_scan_expression(mp);
                        if (mp->cur_exp.type < mp_known_type) {
                            mp_primary_error(mp);
                        }
                        if (cur_cmd != mp_comma_command) {
                            /* Package the rgb color. */
                            mp_init_color_node(mp, q, mp_color_type);
                            r = mp_get_value_node(q);
                            mp_stash_in(mp, mp_blue_part(r));
                            mp_unstash_cur_exp(mp, p1);
                            mp_stash_in(mp, mp_red_part(r));
                            mp_unstash_cur_exp(mp, p2);
                            mp_stash_in(mp, mp_green_part(r));
                        } else {
                            mp_node p3 = mp_stash_cur_exp(mp);
                            mp_get_x_next(mp);
                            mp_scan_expression(mp);
                            if (mp->cur_exp.type < mp_known_type) {
                                mp_primary_error(mp);
                            }
                            if (cur_cmd != mp_comma_command) {
                                /* Package the cmyk color. */
                                mp_init_color_node(mp, q, mp_cmykcolor_type);
                                r = mp_get_value_node(q);
                                mp_stash_in(mp, mp_black_part(r));
                                mp_unstash_cur_exp(mp, p1);
                                mp_stash_in(mp, mp_cyan_part(r));
                                mp_unstash_cur_exp(mp, p2);
                                mp_stash_in(mp, mp_magenta_part(r));
                                mp_unstash_cur_exp(mp, p3);
                                mp_stash_in(mp, mp_yellow_part(r));
                            } else {
                                mp_node p4 = mp_stash_cur_exp(mp);
                                mp_node p5;
                                mp_get_x_next(mp);
                                mp_scan_expression(mp);
                                if (mp->cur_exp.type < mp_known_type) {
                                    mp_primary_error(mp);
                                    p5 = mp_stash_cur_exp(mp);
                                    goto HERE;
                                }
                                if (cur_cmd != mp_comma_command) {
                                    mp_primary_error(mp);
                                    p5 = mp_stash_cur_exp(mp);
                                    goto HERE;
                                }
                                p5 = mp_stash_cur_exp(mp);
                                mp_get_x_next(mp);
                                mp_scan_expression(mp);
                                if (mp->cur_exp.type < mp_known_type) {
                                    mp_primary_error(mp);
                                }
                              HERE:
                                mp_init_transform_node(mp, q);
                                /* Package the transform: xx xy yx yy tx ty */
                                r = mp_get_value_node(q);
                                mp_stash_in(mp, mp_ty_part(r));
                                mp_unstash_cur_exp(mp, p5);
                                mp_stash_in(mp, mp_tx_part(r));
                                mp_unstash_cur_exp(mp, p4);
                                mp_stash_in(mp, mp_yy_part(r));
                                mp_unstash_cur_exp(mp, p3);
                                mp_stash_in(mp, mp_yx_part(r));
                                mp_unstash_cur_exp(mp, p2);
                                mp_stash_in(mp, mp_xy_part(r));
                                mp_unstash_cur_exp(mp, p1);
                                mp_stash_in(mp, mp_xx_part(r));
                            }
                        }
                    }
                    mp_check_delimiter(mp, l_delim, r_delim);
                    mp->cur_exp.type = mp_type(q);
                    mp_set_cur_exp_node(mp, q);
                } else {
                    mp_check_delimiter(mp, l_delim, r_delim);
                }
            }
            break;
        case mp_begin_group_command:
            /* Scan a grouped primary. The local variable |group_line| keeps
               track of the line where a |begingroup| command occurred; this
               will be useful in an error message if the group doesn't actually
               end.
            */
            {
                int group_line = mp_true_line(mp); /* where a group began */
                if (number_positive(internal_value(mp_tracing_commands_internal))) {
                    mp_show_cmd_mod(mp, cur_cmd, cur_mod);
                }
                mp_save_boundary(mp);
                do {
                    mp_do_statement(mp); /* ends with |cur_cmd>=semicolon| */
                } while (cur_cmd == mp_semicolon_command);
                if (cur_cmd != mp_end_group_command) {
                    char msg[256];
                    mp_snprintf(msg, 256, "A group begun on line %d never ended", (int) group_line);
                    mp_back_error(
                        mp,
                        msg,
                        "I saw a 'begingroup' back there that hasn't been matched by 'endgroup'. So I've\n"
                        "inserted 'endgroup' now."
                    );
                    set_cur_cmd(mp_end_group_command);
                }
                mp_unsave(mp);
                /* this might change |cur_type|, if independent variables are recycled */
                if (number_positive(internal_value(mp_tracing_commands_internal))) {
                    mp_show_cmd_mod(mp, cur_cmd, cur_mod);
                }
            }
            break;
        case mp_string_command:
            /* Scan a string constant */
            mp->cur_exp.type = mp_string_type;
            mp_set_cur_exp_str(mp, cur_mod_str);
            break;
        case mp_numeric_command:
            {
                /*
                    Scan a primary that starts with a numeric token. A numeric token
                    might be a primary by itself, or it might be the numerator of a
                    fraction composed solely of numeric tokens, or it might multiply
                    the primary that follows (provided that the primary doesn't begin
                    with a plus sign or a minus sign). The code here uses the facts
                    that |max_primary_command=plus_or_minus| and
                    |max_primary_command-1=numeric_token|. If a fraction is found
                    that is less than unity, we try to retain higher precision when
                    we use it in scalar multiplication.
                */
                mp_number num, denom; /* for primaries that are fractions, like `1/2' */
                mp_set_cur_exp_value_number(mp, &cur_mod_number);
                mp->cur_exp.type = mp_known_type;
                mp_get_x_next(mp);
//new_number(num);
//new_number(denom);
                if (cur_cmd != mp_slash_command) {
                    new_number(num);
                    new_number(denom);
                } else {
                    mp_get_x_next(mp);
                    if (cur_cmd != mp_numeric_command) {
                        mp_back_input(mp);
                        set_cur_cmd(mp_slash_command);
                        set_cur_mod(mp_over_operation);
                        set_cur_sym(mp->frozen_slash);
//                      goto DONOTHING;
                        goto DONE;
                    } else {
                        new_number_clone(num, cur_exp_value_number);
                        new_number_clone(denom, cur_mod_number);
//number_clone(num, cur_exp_value_number);
//number_clone(denom, cur_mod_number);
                        if (number_zero(denom)) {
                            mp_error(mp, "Division by zero", "I'll pretend that you meant to divide by 1.");
                        } else {
                            mp_number ret;
                            new_number(ret);
                            make_scaled(ret, num, denom);
                            mp_set_cur_exp_value_number(mp, &ret);
                            free_number(ret);
                        }
                        check_arith();
                        mp_get_x_next(mp);
                    }
                }
                if (cur_cmd >= mp_min_primary_command && cur_cmd < mp_numeric_command) {
                    /* in particular, |cur_cmd<>plus_or_minus| */
                    mp_number absnum, absdenom;
                    mp_node p = mp_stash_cur_exp(mp);
                    mp_scan_primary(mp);
                    new_number_abs(absnum, num);
                    new_number_abs(absdenom, denom);
                    if (number_greaterequal(absnum, absdenom) || (mp->cur_exp.type < mp_color_type)) {
                        mp_do_binary(mp, p, mp_times_operation);
                    } else {
                        mp_frac_mult(mp, &num, &denom);
                        mp_free_value_node(mp, p);
                    }
                    free_number(absnum);
                    free_number(absdenom);
                }
//              DONOTHING:
                free_number(num);
                free_number(denom);
                goto DONE;
            }
        case mp_nullary_command:
            /* Scan a nullary operation */
            mp_do_nullary(mp, (int) cur_mod);
            break;
        case mp_unary_command:
        case mp_type_name_command:
        case mp_cycle_command:
        case mp_plus_or_minus_command:
            {
                /* Scan a unary operation */
                int c = (int) cur_mod; /* a primitive operation code */
                mp_get_x_next(mp);
                mp_scan_primary(mp);
                mp_do_unary(mp, c);
                goto DONE;
            }
        case mp_of_binary_command:
            {
                /* Scan a binary operation with |of| between its operands */
                mp_node p; /* for list manipulation */
                int c = (int) cur_mod; /* a primitive operation code */
                mp_get_x_next(mp);
                mp_scan_expression(mp);
                if (cur_cmd != mp_of_command) {
                    char msg[256];
                    mp_string sname;
                    int selector = mp->selector;
                    mp->selector = mp_new_string_selector;
                    mp_print_cmd_mod(mp, mp_of_binary_command, c);
                    mp->selector = selector;
                    sname = mp_make_string(mp);
                    mp_snprintf(msg, 256, "Missing 'of' has been inserted for %s", mp_str(mp, sname));
                    delete_str_ref(sname);
                    mp_back_error(mp, msg, "I've got the first argument; will look now for the other.");
                }
                p = mp_stash_cur_exp(mp);
                mp_get_x_next(mp);
                mp_scan_primary(mp);
                mp_do_binary(mp, p, c);
                goto DONE;
            }
        case mp_str_command:
            {
                /* Convert a suffix to a string */
                int selector = mp->selector;
                mp_get_x_next(mp);
                mp_scan_suffix(mp);
                mp->selector = mp_new_string_selector;
                /* Here the periods creep in, we could have a simple one. */
                mp_show_token_list(mp, cur_exp_node, NULL);
                /* */
                mp_flush_token_list(mp, cur_exp_node);
                mp_set_cur_exp_str(mp, mp_make_string(mp));
                mp->selector = selector;
                mp->cur_exp.type = mp_string_type;
                goto DONE;
            }
        case mp_void_command:
            {
                /* Convert a suffix to a boolean */
                mp_value new_expr;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_get_x_next(mp);
                mp_scan_suffix(mp);
                if (cur_exp_node == NULL) {
                    set_number_from_boolean(new_expr.data.n, mp_true_operation);
                } else {
                    set_number_from_boolean(new_expr.data.n, mp_false_operation);
                }
                mp_flush_cur_exp(mp, new_expr);
                cur_exp_node = NULL; /* !! do not replace with |mp_set_cur_exp_node(mp, )| !! */
                mp->cur_exp.type = mp_boolean_type;
                goto DONE;
            }
        case mp_internal_command:
            /*
                Scan an internal numeric quantity. If an internal quantity appears
                all by itself on the left of an assignment, we return a token
                list of length one, containing the address of the internal
                quantity, with |name_type| equal to |mp_internal_operation|. (This
                accords with the conventions of the save stack, as described
                earlier.)
            */
            {
                int qq = cur_mod;
                if (my_var_flag == mp_assignment_command) {
                    mp_get_x_next(mp);
                    if (cur_cmd == mp_assignment_command) {
                        mp_set_cur_exp_node(mp, mp_new_symbolic_node(mp));
                        mp_set_sym_info(cur_exp_node, qq);
                        mp_name_type(cur_exp_node) = mp_internal_operation;
                        mp->cur_exp.type = mp_token_list_type;
                        goto DONE;
                    }
                    mp_back_input(mp);
                }
                if (internal_type(qq) == mp_string_type) {
                    mp_set_cur_exp_str(mp, internal_string(qq));
                } else {
                    mp_set_cur_exp_value_number(mp, &(internal_value(qq)));
                 // if (qq == mp_tracing_online_internal) {
                 //     mp->run_internal(mp, 3, qq, number_to_int(internal_value(qq)), internal_name(qq));
                 // }
                }
                mp->cur_exp.type = internal_type(qq);
            }
            break;
        case mp_capsule_command:
            mp_make_exp_copy(mp, cur_mod_node);
            break;
        case mp_tag_command:
            @<Scan a variable primary; |goto restart| if it turns out to be a macro@>
            break;
        default:
            mp_bad_exp(mp, "A primary");
            goto RESTART;
            break;
    }
    mp_get_x_next(mp); /* the routines |goto done| if they don't want this */
  DONE:
    check_for_mediation(mp);
}

@ Expressions of the form |a[b,c]| are converted into |b+a*(c-b)|,
without checking the types of \.b~or~\.c, provided that \.a is numeric.

@<Declare the basic parsing subroutines@>=
static void check_for_mediation (MP mp)
{
    if (cur_cmd == mp_left_bracket_command && mp->cur_exp.type >= mp_known_type) {
        /* Scan a mediation construction */
        mp_node p = mp_stash_cur_exp(mp);
        mp_get_x_next(mp);
        mp_scan_expression(mp);
        if (cur_cmd != mp_comma_command) {
            /*
                Put the left bracket and the expression back to be rescanned.
                The left bracket that we thought was introducing a subscript
                might have actually been the left bracket in a mediation
                construction like |x[a,b]|. So we don't issue an error
                message at this point; but we do want to back up so as to
                avoid any embarrassment about our incorrect assumption.
            */
            mp_back_input(mp);
            /* that was the token following the current expression */
            mp_back_expr(mp);
            set_cur_cmd(mp_left_bracket_command);
            set_cur_mod_number(zero_t);
            set_cur_sym(mp->frozen_left_bracket);
            mp_unstash_cur_exp(mp, p);
        } else {
            mp_node q = mp_stash_cur_exp(mp);
            mp_node r;
            mp_get_x_next(mp);
            mp_scan_expression(mp);
            if (cur_cmd != mp_right_bracket_command) {
                mp_back_error(
                    mp,
                    "Missing ']' has been inserted",
                    "I've scanned an expression of the form 'a[b,c', so a right bracket should have\n"
                    "come next. I shall pretend that one was there."
                );
            }
            r = mp_stash_cur_exp(mp);
            mp_make_exp_copy(mp, q);
            mp_do_binary(mp, r, mp_minus_operation);
            mp_do_binary(mp, p, mp_times_operation);
            mp_do_binary(mp, q, mp_plus_operation);
            mp_get_x_next(mp);
        }
    }
}

@ Errors at the beginning of expressions are flagged by |bad_exp|.

@c
static void mp_bad_exp (MP mp, const char *s)
{
    char msg[256];
    int save_flag;
    @:METAFONTbook}{\sl The {\logos METAFONT}book@>
    {
         mp_string cm;
         int selector = mp->selector;
         mp->selector = mp_new_string_selector;
         mp_print_cmd_mod(mp, cur_cmd, cur_mod);
         mp->selector = selector;
         cm = mp_make_string(mp);
         mp_snprintf(msg, 256, "%s expression can't begin with '%s'", s, mp_str(mp, cm));
         delete_str_ref(cm);
    }
    mp_back_input(mp);
    set_cur_sym(NULL);
    set_cur_cmd(mp_numeric_command);
    set_cur_mod_number(zero_t);
    mp_ins_error(
        mp,
        msg,
        "I'm afraid I need some sort of value in order to continue, so I've tentatively\n"
        "inserted '0'."
    );
    save_flag = mp->var_flag;
    mp->var_flag = 0;
    mp_get_x_next(mp);
    mp->var_flag = save_flag;
}


@ The |stash_in| subroutine puts the current (numeric) expression into a field
within a \quote {big node.}

@c
static void mp_stash_in (MP mp, mp_node p)
{
    mp_type(p) = mp->cur_exp.type;
    if (mp->cur_exp.type == mp_known_type) {
        mp_set_value_number(p, cur_exp_value_number);
    } else if (mp->cur_exp.type == mp_independent_type) {
        /*
            Stash an independent |cur_exp| into a big node. In rare cases the current
            expression can become |independent|. There may be many dependency lists
            pointing to such an independent capsule, so we can't simply move it into
            place within a big node. Instead, we copy it, then recycle it.
        */
        mp_value_node q = mp_single_dependency(mp, cur_exp_node);
        if (q == mp->dep_final) {
            mp_type(p) = mp_known_type;
            mp_set_value_number(p, zero_t);
            mp_free_dep_node(mp, q);
        } else {
            mp_new_dep(mp, p, mp_dependent_type, q);
        }
        mp_recycle_value(mp, cur_exp_node);
        mp_free_value_node(mp, cur_exp_node);
    } else {
        mp_set_dep_list((mp_value_node) p, mp_get_dep_list((mp_value_node) cur_exp_node));
        mp_set_prev_dep((mp_value_node) p, mp_get_prev_dep((mp_value_node) cur_exp_node));
        mp_set_link(mp_get_prev_dep((mp_value_node) p), p);
        mp_free_dep_node(mp, (mp_value_node) cur_exp_node);
    }
    mp->cur_exp.type = mp_vacuous_type;
}

@ The most difficult part of |scan_primary| has been saved for last, since it was
necessary to build up some confidence first. We can now face the task of scanning
a variable.

As we scan a variable, we build a token list containing the relevant names and
subscript values, simultaneously following along in the \quote {collective} structure
to see if we are actually dealing with a macro instead of a value.

The local variables |pre_head| and |post_head| will point to the beginning of the
prefix and suffix lists; |tail| will point to the end of the list that is
currently growing.

Another local variable, |tt|, contains partial information about the declared
type of the variable-so-far. If |tt>=mp_unsuffixed_macro|, the relation
|tt=mp_type(q)| will always hold. If |tt=undefined|, the routine doesn't bother
to update its information about type. And if |undefined<tt<mp_unsuffixed_macro|,
the precise value of |tt| isn't critical.

@ @<Scan a variable primary...@>=
{
    mp_node p = 0;         /* for list manipulation */
    mp_node q = 0;         /* for list manipulation */
    mp_node t = 0;
    mp_node macro_ref = 0;    /* reference count for a suffixed macro */
    int tt = mp_vacuous_type; /* approximation to the type of the variable-so-far */
    mp_node pre_head = mp_new_symbolic_node(mp);
    mp_node tail = pre_head;
    mp_node post_head = NULL;
    while (1) {
        t = mp_cur_tok(mp);
        mp_link(tail) = t;
        if (tt != mp_undefined_type) {
            /*
                Find the approximate type |tt| and corresponding~|q|. Every time we call
                |get_x_next|, there's a chance that the variable we've been looking at
                will disappear. Thus, we cannot safely keep |q| pointing into the
                variable structure; we need to start searching from the root each time.
            */
            mp_sym qq;
            p = mp_link(pre_head);
            qq = mp_get_sym_sym(p);
            tt = mp_undefined_type;
         // if (eq_type(qq) % mp_outer_tag_command == mp_tag_command) {
            if (eq_type(qq) == mp_tag_command) {
                q = equiv_node(qq);
                if (q == NULL) {
                    goto DONE2;
                }
                while (1) {
                    p = mp_link(p);
                    if (p == NULL) {
                        tt = mp_type(q);
                        goto DONE2;
                    }
                    if (mp_type(q) != mp_structured_type) {
                        goto DONE2;
                    }
                    q = mp_link(mp_get_attribute_head(q)); /* the |mp_collective_subscript| attribute */
                    if (mp_type(p) == mp_symbol_node_type) {
                        /* it's not a subscript */
                        do {
                            q = mp_link(q);
                        } while (! (mp_get_hashloc(q) >= mp_get_sym_sym(p)));
                        if (mp_get_hashloc(q) > mp_get_sym_sym(p)) {
                            goto DONE2;
                        }
                    }
                }
            }
          DONE2:
            if (tt >= mp_unsuffixed_macro_type) {
                /* Either begin an unsuffixed macro call or prepare for a suffixed one */
                mp_link(tail) = NULL;
                if (tt > mp_unsuffixed_macro_type) {
                    /* |tt=mp_suffixed_macro| */
                    post_head = mp_new_symbolic_node(mp);
                    tail = post_head;
                    mp_link(tail) = t;
                    tt = mp_undefined_type;
                    macro_ref = mp_get_value_node(q);
                    mp_add_mac_ref(macro_ref);
                } else {
                    /*
                        Set up unsuffixed macro call and |goto restart|. The only
                        complication associated with macro calling is that the
                        prefix and \quote {at} parameters must be packaged in an
                        appropriate list of lists.
                    */
                    p = mp_new_symbolic_node(mp);
                    mp_set_sym_sym(pre_head, mp_link(pre_head));
                    mp_link(pre_head) = p;
                    mp_set_sym_sym(p, t);
                    mp_macro_call(mp, mp_get_value_node(q), pre_head, NULL);
                    mp_get_x_next(mp);
                    goto RESTART;
                }
            }
        }
        mp_get_x_next(mp);
        tail = t;
        if (cur_cmd == mp_left_bracket_command) {
            /* Scan for a subscript; replace |cur_cmd| by |numeric_token| if found */
            mp_get_x_next(mp);
            mp_scan_expression(mp);
            if (cur_cmd != mp_right_bracket_command) {
                /*
                    Put the left bracket and the expression back to be rescanned.
                    The left bracket that we thought was introducing a subscript
                    might have actually been the left bracket in a mediation
                    construction like |x[a,b]|. So we don't issue an error
                    message at this point; but we do want to back up so as to
                    avoid any embarrassment about our incorrect assumption.
                */
                mp_back_input(mp); /* that was the token following the current expression */
                mp_back_expr(mp);
                set_cur_cmd(mp_left_bracket_command);
                set_cur_mod_number(zero_t);
                set_cur_sym(mp->frozen_left_bracket);
            } else {
                if (mp->cur_exp.type != mp_known_type) {
                    mp_bad_subscript(mp);
                }
                set_cur_cmd(mp_numeric_command);
                set_cur_mod_number(cur_exp_value_number);
                set_cur_sym(NULL);
            }
        }
        if (cur_cmd > mp_max_suffix_token) {
            break;
        } else if (cur_cmd < mp_min_suffix_token) {
            break;
        }
    }
    /*
        Now |cur_cmd| is |internal_quantity|, |tag_token|, or |numeric_token|.
        Handle unusual cases that masquerade as variables, and |goto restart| or
        |goto done| if appropriate; otherwise make a copy of the variable and
        |goto done| If the variable does exist, we also need to check for a few
        other special cases before deciding that a plain old ordinary variable
        has, indeed, been scanned.
    */
    if (post_head != NULL) {
        /*
            Set up suffixed macro call and |goto restart|. If the \quote {variable}
            that turned out to be a suffixed macro no longer exists, we don't
            care, because we have reserved a pointer (|macro_ref|) to its token
            list.
        */
        mp_back_input(mp);
        p = mp_new_symbolic_node(mp);
        q = mp_link(post_head);
        mp_set_sym_sym(pre_head, mp_link(pre_head));
        mp_link(pre_head) = post_head;
        mp_set_sym_sym(post_head, q);
        mp_link(post_head) = p;
        mp_set_sym_sym(p, mp_link(q));
        mp_link(q) = NULL;
        mp_macro_call(mp, macro_ref, pre_head, NULL);
        mp_decr_mac_ref(macro_ref);
        mp_get_x_next(mp);
        goto RESTART;
    }
    q = mp_link(pre_head);
    mp_free_symbolic_node(mp, pre_head);
    if (cur_cmd == my_var_flag) {
        mp->cur_exp.type = mp_token_list_type;
        mp_set_cur_exp_node(mp, q);
        goto DONE;
    }
    p = mp_find_variable(mp, q);
    if (p != NULL) {
        mp_make_exp_copy(mp, p);
    } else {
        mp_value new_expr;
        char *msg = mp_obliterated (mp, q);
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_back_error(
            mp,
            msg,
            "While I was evaluating the suffix of this variable, something was redefined, and\n"
            "it's no longer a variable! In order to get back on my feet, I've inserted '0'\n"
            "instead."
        );
        mp_memory_free(msg);
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    }
    mp_flush_node_list(mp, q);
    goto DONE;
}

@ Here's a routine that puts the current expression back to be read again.

@c
static void mp_back_expr (MP mp)
{
    mp_node p = mp_stash_cur_exp(mp); /* capsule token */
    mp_link(p) = NULL;
    mp_begin_token_list(mp, p, mp_backed_up_text);
}

@ Unknown subscripts lead to the following error message.

@c
static void mp_bad_subscript (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_disp_err(mp, NULL);
    mp_error(
        mp,
        "Improper subscript has been replaced by zero",
        "A bracketed subscript must have a known numeric value; unfortunately, what I\n"
        "found was the value that appears just above this error message. So I'll try a\n"
        "zero subscript."
    );
    @.Improper subscript...@>
    mp_flush_cur_exp(mp, new_expr);
}

@ How do things stand now? Well, we have scanned an entire variable name,
including possible subscripts and/or attributes; |cur_cmd|, |cur_mod|, and
|cur_sym| represent the token that follows. If |post_head=NULL|, a token list for
this variable name starts at |mp_link(pre_head)|, with all subscripts evaluated.
But if |post_head<>NULL|, the variable turned out to be a suffixed macro;
|pre_head| is the head of the prefix list, while |post_head| is the head of a
token list containing both |\AT!| and the suffix.

Our immediate problem is to see if this variable still exists. (Variable
structures can change drastically whenever we call |get_x_next|; users aren't
supposed to do this, but the fact that it is possible means that we must be
cautious.)

The following procedure creates an error message for when a variable unexpectedly
disappears.

@c
static char *mp_obliterated (MP mp, mp_node q)
{
    char msg[256];
    mp_string sname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_show_token_list(mp, q, NULL);
    sname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "Variable %s has been obliterated", mp_str(mp, sname));
    @.Variable...obliterated@>
    delete_str_ref(sname);
    return mp_strdup(msg);
}

@ Our remaining job is simply to make a copy of the value that has been found.
Some cases are harder than others, but complexity arises solely because of the
multiplicity of possible cases.

@<Declare the procedure called |make_exp_copy|@>=
@<Declare subroutines needed by |make_exp_copy|@>
static void mp_make_exp_copy (MP mp, mp_node p)
{
  RESTART:
    mp->cur_exp.type = mp_type(p);
    switch (mp->cur_exp.type) {
        case mp_vacuous_type:
        case mp_boolean_type:
        case mp_known_type:
            mp_set_cur_exp_value_number(mp, &(mp_get_value_number(p)));
            break;
        case mp_unknown_boolean_type:
        case mp_unknown_string_type:
        case mp_unknown_pen_type:
        case mp_unknown_nep_type:
        case mp_unknown_path_type:
        case mp_unknown_picture_type:
            {
                mp_node t = mp_new_ring_entry(mp, p);
                mp_set_cur_exp_node(mp, t);
            }
            break;
        case mp_string_type:
            mp_set_cur_exp_str(mp, mp_get_value_str(p));
            break;
        case mp_picture_type:
            mp_set_cur_exp_node(mp, mp_get_value_node(p));
            mp_add_edge_ref(mp, cur_exp_node);
            break;
        case mp_pen_type:
        case mp_nep_type:
            mp_set_cur_exp_knot(mp, mp_copy_pen(mp, mp_get_value_knot(p)));
            break;
        case mp_path_type:
            mp_set_cur_exp_knot(mp, mp_copy_path(mp, mp_get_value_knot(p)));
            break;
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
            {
                /*
                    Copy the big node |p|. The most tedious case arises when the user
                    refers to a |pair|, |color|, or |transform| variable; we must
                    copy several fields, each of which can be |independent|, |dependent|,
                    |mp_proto_dependent|, or |known|.
                */
                mp_node t;
                mp_value_node q;
                if (mp_get_value_node(p) == NULL) {
                    switch (mp_type(p)) {
                        case mp_pair_type:
                            mp_init_pair_node(mp, p);
                            break;
                        case mp_color_type:
                            mp_init_color_node(mp, p, mp_color_type);
                            break;
                        case mp_cmykcolor_type:
                            mp_init_color_node(mp, p, mp_cmykcolor_type);
                            break;
                        case mp_transform_type:
                            mp_init_transform_node(mp, p);
                            break;
                        default:
                            break;
                    }
                }
                t = mp_new_value_node(mp);
                mp_name_type(t) = mp_capsule_operation;
                q = (mp_value_node) mp_get_value_node(p);
                switch (mp->cur_exp.type) {
                    case mp_pair_type:
                        mp_init_pair_node(mp, t);
                        mp_install(mp, mp_y_part(mp_get_value_node(t)), mp_y_part(q));
                        mp_install(mp, mp_x_part(mp_get_value_node(t)), mp_x_part(q));
                        break;
                    case mp_color_type:
                        mp_init_color_node(mp, t, mp_color_type);
                        mp_install(mp, mp_blue_part(mp_get_value_node(t)),  mp_blue_part(q));
                        mp_install(mp, mp_green_part(mp_get_value_node(t)), mp_green_part(q));
                        mp_install(mp, mp_red_part(mp_get_value_node(t)),   mp_red_part(q));
                        break;
                    case mp_cmykcolor_type:
                        mp_init_color_node(mp, t, mp_cmykcolor_type);
                        mp_install(mp, mp_black_part(mp_get_value_node(t)),   mp_black_part(q));
                        mp_install(mp, mp_yellow_part(mp_get_value_node(t)),  mp_yellow_part(q));
                        mp_install(mp, mp_magenta_part(mp_get_value_node(t)), mp_magenta_part(q));
                        mp_install(mp, mp_cyan_part(mp_get_value_node(t)),    mp_cyan_part(q));
                        break;
                    case mp_transform_type:
                        mp_init_transform_node(mp, t);
                        mp_install(mp, mp_yy_part(mp_get_value_node(t)), mp_yy_part(q));
                        mp_install(mp, mp_yx_part(mp_get_value_node(t)), mp_yx_part(q));
                        mp_install(mp, mp_xy_part(mp_get_value_node(t)), mp_xy_part(q));
                        mp_install(mp, mp_xx_part(mp_get_value_node(t)), mp_xx_part(q));
                        mp_install(mp, mp_ty_part(mp_get_value_node(t)), mp_ty_part(q));
                        mp_install(mp, mp_tx_part(mp_get_value_node(t)), mp_tx_part(q));
                        break;
                    default:
                        break;
                }
                mp_set_cur_exp_node(mp, t);
            }
            break;
        case mp_dependent_type:
        case mp_proto_dependent_type:
            mp_encapsulate (mp, mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) p)));
            break;
        case mp_numeric_type:
            mp_new_indep(mp, p);
            goto RESTART;
        case mp_independent_type:
            {
                mp_value_node q = mp_single_dependency(mp, p);
                if (q == mp->dep_final) {
                    mp->cur_exp.type = mp_known_type;
                    mp_set_cur_exp_value_number(mp, &zero_t);
                    mp_free_dep_node(mp, q);
                } else {
                    mp->cur_exp.type = mp_dependent_type;
                    mp_encapsulate (mp, q);
                }
            }
            break;
        case mp_undefined_type:
            mp_confusion(mp, "undefined copy");
            break;
        default:
            mp_confusion(mp, "copy");
            @:this can't happen copy}{\quad copy@>
            break;
    }
}

@ The |encapsulate| subroutine assumes that |dep_final| is the tail of dependency
list~|p|.

@<Declare subroutines needed by |make_exp_copy|@>=
static void mp_encapsulate (MP mp, mp_value_node p)
{
    mp_node q = mp_new_value_node(mp);
    mp_name_type(q) = mp_capsule_operation;
    mp_new_dep(mp, q, mp->cur_exp.type, p);
    mp_set_cur_exp_node(mp, q);
}

@ The |install| procedure copies a numeric field~|q| into field~|r| of
a big node that will be part of a capsule.

@<Declare subroutines needed by |make_exp_copy|@>=
static void mp_install (MP mp, mp_node r, mp_node q)
{
    if (mp_type(q) == mp_known_type) {
        mp_type(r) = mp_known_type;
        mp_set_value_number(r, mp_get_value_number(q));
    } else if (mp_type(q) == mp_independent_type) {
        mp_value_node p = mp_single_dependency(mp, q);
        if (p == mp->dep_final) {
            mp_type(r) = mp_known_type;
            mp_set_value_number(r, zero_t);
            mp_free_dep_node(mp, p);
        } else {
            mp_new_dep(mp, r, mp_dependent_type, p);
        }
    } else {
        mp_new_dep(mp, r, mp_type(q), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) q)));
    }
}

@ Here is a comparatively simple routine that is used to scan the |suffix|
parameters of a macro.

@<Declare the basic parsing subroutines@>=
static void mp_scan_suffix (MP mp)
{
    mp_node h = mp_new_symbolic_node(mp); /* head of the list being built */
    mp_node t = h;                        /* tail of the list being built */
    while (1) {
        mp_node p;
        if (cur_cmd == mp_left_bracket_command) {
            /* Scan a bracketed subscript and set |cur_cmd:=numeric_token| */
            mp_get_x_next(mp);
            mp_scan_expression(mp);
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_subscript(mp);
            }
            if (cur_cmd != mp_right_bracket_command) {
                mp_back_error(
                    mp,
                    "Missing ']' has been inserted",
                    "I've seen a '[' and a subscript value, in a suffix, so a right bracket should\n"
                    "have come next. I shall pretend that one was there."
                );
            }
            set_cur_cmd(mp_numeric_command);
            set_cur_mod_number(cur_exp_value_number);
        }
        if (cur_cmd == mp_numeric_command) {
            mp_number arg1;
            new_number_clone(arg1, cur_mod_number);
            p = mp_new_num_tok(mp, &arg1);
            free_number(arg1);
        } else if ((cur_cmd == mp_tag_command) || (cur_cmd == mp_internal_command)) {
            p = mp_new_symbolic_node(mp);
            mp_set_sym_sym(p, cur_sym);
            mp_name_type(p) = cur_sym_mod;
        } else {
            break;
        }
        mp_link(t) = p;
        t = p;
        mp_get_x_next(mp);
    }
    mp_set_cur_exp_node(mp, mp_link(h));
    mp_free_symbolic_node(mp, h);
    mp->cur_exp.type = mp_token_list_type;
}

@* Parsing secondary and higher expressions.

After the intricacies of |scan_primary|\kern-1pt, the |scan_secondary| routine is
refreshingly simple. It's not trivial, but the operations are relatively
straightforward; the main difficulty is, again, that expressions and data
structures might change drastically every time we call |get_x_next|, so a
cautious approach is mandatory. For example, a macro defined by |primarydef|
might have disappeared by the time its second argument has been scanned; we solve
this by increasing the reference count of its token list, so that the macro can
be called even after it has been clobbered.

@<Declare the basic parsing subroutines@>=
static void mp_scan_secondary (MP mp)
{
    mp_node cc = NULL;
    mp_sym mac_name = NULL; /* token defined with |primarydef| */
  RESTART:
    if ((cur_cmd < mp_min_primary_command) || (cur_cmd > mp_max_primary_command)) {
        mp_bad_exp(mp, "A secondary");
    }
    @.A secondary expression...@>
    mp_scan_primary(mp);
  CONTINUE:
    if (cur_cmd <= mp_max_secondary_command && cur_cmd >= mp_min_secondary_command) {
        mp_node p = mp_stash_cur_exp(mp);
        int d = cur_cmd;
        int c = cur_mod;
        if (d == mp_primary_def_command) {
            cc = cur_mod_node;
            mac_name = cur_sym;
            mp_add_mac_ref(cc);
        }
        mp_get_x_next(mp);
        mp_scan_primary(mp);
        if (d != mp_primary_def_command) {
            mp_do_binary(mp, p, c);
        } else {
            mp_back_input(mp);
            mp_binary_mac(mp, p, cc, mac_name);
            mp_decr_mac_ref(cc);
            mp_get_x_next(mp);
            goto RESTART;
        }
        goto CONTINUE;
    }
}

@ The following procedure calls a macro that has two parameters, |p| and
|cur_exp|.

@c
static void mp_binary_mac (MP mp, mp_node p, mp_node c, mp_sym n)
{
    mp_node q = mp_new_symbolic_node(mp);
    mp_node r = mp_new_symbolic_node(mp);
    mp_link(q) = r;
    mp_set_sym_sym(q, p);
    mp_set_sym_sym(r, mp_stash_cur_exp(mp));
    mp_macro_call(mp, c, q, n);
}

@ The next procedure, |scan_tertiary|, is pretty much the same deal.

@<Declare the basic parsing subroutines@>=
static void mp_scan_tertiary (MP mp)
{
    mp_node cc = NULL;
    mp_sym mac_name = NULL; /* token defined with |secondarydef| */
  RESTART:
    if ((cur_cmd < mp_min_primary_command) || (cur_cmd > mp_max_primary_command)) {
        mp_bad_exp(mp, "A tertiary");
    }
    @.A tertiary expression...@>
    mp_scan_secondary(mp);
  CONTINUE:
    if (cur_cmd <= mp_max_tertiary_command && cur_cmd >= mp_min_tertiary_command) {
        mp_node p = mp_stash_cur_exp(mp);
        int c = cur_mod;
        int d = cur_cmd;
        if (d == mp_secondary_def_command) {
            cc = cur_mod_node;
            mac_name = cur_sym;
            mp_add_mac_ref(cc);
        }
        mp_get_x_next(mp);
        mp_scan_secondary(mp);
        if (d != mp_secondary_def_command) {
            mp_do_binary(mp, p, c);
        } else {
            mp_back_input(mp);
            mp_binary_mac(mp, p, cc, mac_name);
            mp_decr_mac_ref(cc);
            mp_get_x_next(mp);
            goto RESTART;
        }
        goto CONTINUE;
    }
}

@ Finally we reach the deepest level in our quartet of parsing routines.
This one is much like the others; but it has an extra complication from
paths, which materialize here.

@<Declare the basic parsing subroutines@>=

static int mp_scan_path (MP mp);

static void mp_scan_expression (MP mp)
{
    int my_var_flag = mp->var_flag;
    mp_check_expansion_depth(mp);
  RESTART:
    if ((cur_cmd < mp_min_primary_command) || (cur_cmd > mp_max_primary_command)) {
        mp_bad_exp(mp, "An");
    }
    @.An expression...@>
    mp_scan_tertiary(mp);
  CONTINUE:
    if (cur_cmd <= mp_max_expression_command) {
        if (cur_cmd >= mp_min_expression_command) {
            if ((cur_cmd != mp_equals_command) || (my_var_flag != mp_assignment_command)) {
                mp_node cc = NULL;
                mp_sym mac_name;   /* token defined with |tertiarydef| */
                mac_name = NULL;
                mp_node p = mp_stash_cur_exp(mp);
                int d = cur_cmd;
                int c = cur_mod;
                if (d == mp_tertiary_def_command) {
                    cc = cur_mod_node;
                    mac_name = cur_sym;
                    mp_add_mac_ref(cc);
                }
                if ((d < mp_ampersand_command) || ((d == mp_ampersand_command) && ((mp_type(p) == mp_pair_type) || (mp_type(p) == mp_path_type)))) {
                    /* Scan a path construction operation;    but |return| if |p| has the wrong type */
                    mp_unstash_cur_exp(mp, p);
                    if (! mp_scan_path(mp)) {
                        mp->expand_depth_count--;
                        return;
                    }
                } else {
                    mp_get_x_next(mp);
                    mp_scan_tertiary(mp);
                    if (d != mp_tertiary_def_command) {
                        mp_do_binary(mp, p, c);
                    } else {
                        mp_back_input(mp);
                        mp_binary_mac(mp, p, cc, mac_name);
                        mp_decr_mac_ref(cc);
                        mp_get_x_next(mp);
                        goto RESTART;
                    }
                }
                goto CONTINUE;
            }
        }
    }
    mp->expand_depth_count--;
}

@ The reader should review the data structure conventions for paths before hoping
to understand the next part of this code.

@d min_tension three_quarter_unit_t

@<Declare the basic parsing subroutines@>=
static void force_valid_tension_setting (MP mp)
{
    if ((mp->cur_exp.type != mp_known_type) || number_less(cur_exp_value_number, min_tension)) {
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_disp_err(mp, NULL);
        number_clone(new_expr.data.n, unity_t);
        mp_back_error(
            mp,
            "Improper tension has been set to 1",
            "The expression above should have been a number >= 3/4."
        );
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    }
}

static int mp_scan_path (MP mp)
{
    mp_knot path_p, path_q, r;
    mp_knot pp = NULL;
    mp_knot qq = NULL;
    int d, dd;           /* operation code or modifier */
    int cycle_hit = 0;   /* did a path expression just end with |cycle|? */
    mp_number x, y;      /* explicit coordinates or tension at a path join */
    int t = mp_endpoint_knot; /* knot type following a path join */
    /*
        Convert the left operand, |p|, into a partial path ending at~|q|; but
        |return| if |p| doesn't have a suitable type
    */
    if (mp->cur_exp.type == mp_pair_type) {
        path_p = mp_pair_to_knot(mp);
    } else if (mp->cur_exp.type == mp_path_type) {
        path_p = cur_exp_knot;
    } else {
        return 0;
    }
    path_q = path_p;
    while (mp_next_knot(path_q) != path_p) {
        path_q = mp_next_knot(path_q);
    }
    if (mp_left_type(path_p) != mp_endpoint_knot) {
        /* open up a cycle */
        r = mp_copy_knot(mp, path_p);
        mp_prev_knot(r) = path_q;
        mp_next_knot(path_q) = r;
        path_q = r;
    }
    mp_left_type(path_p) = mp_open_knot;
    mp_right_type(path_q) = mp_open_knot;
    new_number(y);
    new_number(x);
  CONTINUE_PATH:
    /*
        Determine the path join parameters; but |goto finish_path| if there's only a
        direction specifier At this point |cur_cmd| is either |ampersand|,
        |left_brace|, or |path_join|.
    */
    if (cur_cmd == mp_left_brace_command) {
        /*
            Put the pre-join direction information into node |q|. At this point
            |mp_right_type(q)| is usually |open|, but it may have been set to some
            other value by a previous operation. We must maintain the value of
            |mp_right_type(q)| in cases such as `|..\{curl2\|z\{0,0\}..}'.
        */
        t = mp_scan_direction(mp);
        if (t != mp_open_knot) {
            mp_right_type(path_q) = (unsigned char) t;
            number_clone(path_q->right_given, cur_exp_value_number);
            if (mp_left_type(path_q) == mp_open_knot) {
                mp_left_type(path_q) = (unsigned char) t;
                number_clone(path_q->left_given, cur_exp_value_number);
            }     /* note that |left_given(q)=left_curl(q)| */
        }
    }
    d = cur_cmd;
    dd = cur_mod;
    if (d == mp_path_join_command) {
        /* Determine the tension and/or control points */
        mp_get_x_next(mp);
        switch (cur_cmd) {
            case mp_tension_command:
                /* Set explicit tensions */
                mp_get_x_next(mp);
                set_number_from_scaled(y, cur_cmd);
                if (cur_cmd == mp_at_least_command) {
                    mp_get_x_next(mp);
                }
                mp_scan_primary(mp);
                force_valid_tension_setting(mp);
                if (number_to_scaled(y) == mp_at_least_command && is_number(cur_exp_value_number)) {
                    number_negate(cur_exp_value_number);
                }
                number_clone(path_q->right_tension, cur_exp_value_number);
                if (cur_cmd == mp_and_command) {
                    mp_get_x_next(mp);
                    set_number_from_scaled(y, cur_cmd);
                    if (cur_cmd == mp_at_least_command) {
                        mp_get_x_next(mp);
                    }
                    mp_scan_primary(mp);
                    force_valid_tension_setting(mp);
                    if (number_to_scaled(y) == mp_at_least_command && is_number(cur_exp_value_number)) {
                        number_negate(cur_exp_value_number);
                    }
                }
                number_clone(y, cur_exp_value_number);
                break;
            case mp_controls_command:
                /* Set explicit control points */
                mp_right_type(path_q) = mp_explicit_knot;
                t = mp_explicit_knot;
                mp_get_x_next(mp);
                mp_scan_primary(mp);
                mp_known_pair(mp);
                number_clone(path_q->right_x, mp->cur_x);
                number_clone(path_q->right_y, mp->cur_y);
                if (cur_cmd != mp_and_command) {
                    number_clone(x, path_q->right_x);
                    number_clone(y, path_q->right_y);
                } else {
                    mp_get_x_next(mp);
                    mp_scan_primary(mp);
                    mp_known_pair(mp);
                    number_clone(x, mp->cur_x);
                    number_clone(y, mp->cur_y);
                }
                break;
            default:
                set_number_to_unity(path_q->right_tension);
                set_number_to_unity(y);
                /* default tension */
                mp_back_input(mp);
                goto DONE;
                break;
        }
        if (cur_cmd != mp_path_join_command) {
            mp_back_error(
                mp,
                "Missing '..' has been inserted",
                "A path join command should end with two dots."
            );
        }
  DONE:
    ; /* needed */
    } else if (d != mp_ampersand_command) {
        goto FINISH_PATH;
    }
    mp_get_x_next(mp);
    if (cur_cmd == mp_left_brace_command) {
        /*
            Put the post-join direction information into |x| and |t|. Since
            |left_tension| and |mp_left_y| share the same position in knot nodes,
            and since |left_given| is similarly equivalent to |left_x|, we use
            |x| and |y| to hold the given direction and tension information when
            there are no explicit control points.
        */
        t = mp_scan_direction(mp);
        if (mp_right_type(path_q) != mp_explicit_knot) {
            number_clone(x, cur_exp_value_number);
        } else {
            /* the direction information is superfluous */
            t = mp_explicit_knot;
        }
    } else if (mp_right_type(path_q) != mp_explicit_knot) {
        t = mp_open_knot;
        set_number_to_zero(x);
    }
    if (cur_cmd == mp_cycle_command) {
        /*
            Get ready to close a cycle. If a person tries to define an entire
            path by saying |(x,y)\&cycle|, we silently change the
            specification to |(x,y)..cycle|, since a cycle shouldn't have
            length zero.
        */
        if (cur_mod == mp_cycle_operation) {
            cycle_hit = 1;
            mp_get_x_next(mp);
            pp = path_p;
            qq = path_p;
            if (d == mp_ampersand_command && path_p == path_q) {
                d = mp_path_join_command;
                set_number_to_unity(path_q->right_tension);
                set_number_to_unity(y);
            }
        } else {
            mp_get_x_next(mp);
            qq = pp;
            goto FINISH_PATH;
        }
    } else {
        mp_scan_tertiary(mp);
        /*
            Convert the right operand, |cur_exp|, into a partial path from |pp|
            to~|qq|
        */
        if (mp->cur_exp.type != mp_path_type) {
            pp = mp_pair_to_knot(mp);
        } else {
            pp = cur_exp_knot;
        }
        qq = pp;
        while (mp_next_knot(qq) != pp) {
            qq = mp_next_knot(qq);
        }
        if (mp_left_type(pp) != mp_endpoint_knot) {             /* open up a cycle */
            r = mp_copy_knot(mp, pp);
            mp_prev_knot(r) = qq;
            mp_next_knot(qq) = r;
            qq = r;
        }
        mp_left_type(pp) = mp_open_knot;
        mp_right_type(qq) = mp_open_knot;
    }
    /*
        Join the partial paths and reset |p| and |q| to the head and tail of the
        result
    */
    if (d == mp_ampersand_command && dd != mp_just_append_operation) {
        if (! (number_equal(path_q->x_coord, pp->x_coord)) || ! (number_equal(path_q->y_coord, pp->y_coord))) {
            mp_back_error(
                mp,
                "Paths don't touch; '&' will be changed to '..'",
                "When you join paths 'p & q', the ending point of p must be exactly equal to the\n"
                "starting point of q. So I'm going to pretend that you said 'p .. q' instead."
            );
            @.Paths don't touch@>
            mp_get_x_next(mp);
            d = mp_path_join_command;
            set_number_to_unity(path_q->right_tension);
            set_number_to_unity(y);
        }
    }
    /* Plug an opening in |mp_right_type(pp)|, if possible */
    if (mp_right_type(pp) == mp_open_knot && ((t == mp_curl_knot) || (t == mp_given_knot))) {
        mp_right_type(pp) = (unsigned char) t;
        number_clone(pp->right_given, x);
    }
    if (d == mp_ampersand_command) {
        /* Splice independent paths together */
        if (dd == mp_just_append_operation) {
            mp_left_type(pp) = mp_explicit_knot;
            mp_right_type(path_q) = mp_explicit_knot;
            mp_prev_knot(pp) = path_q;
            mp_next_knot(path_q) = pp;
            number_clone(pp->left_x, path_q->x_coord);
            number_clone(pp->left_y, path_q->y_coord);
            number_clone(path_q->right_x, pp->x_coord);
            number_clone(path_q->right_y, pp->y_coord);
            mp_knotstate(pp) = mp_begin_knot;
            mp_knotstate(path_q) = mp_end_knot;
            path_q = pp;
        } else {
            if (mp_left_type(path_q) == mp_open_knot && mp_right_type(path_q) == mp_open_knot) {
                mp_left_type(path_q) = mp_curl_knot;
                set_number_to_unity(path_q->left_curl);
            }
            if (mp_right_type(pp) == mp_open_knot && t == mp_open_knot) {
                mp_right_type(pp) = mp_curl_knot;
                set_number_to_unity(pp->right_curl);
            }
            mp_right_type(path_q) = mp_right_type(pp);
            mp_prev_knot(pp) = mp_next_knot(path_q);
            mp_next_knot(path_q) = mp_next_knot(pp);
            number_clone(path_q->right_x, pp->right_x);
            number_clone(path_q->right_y, pp->right_y);
            mp_memory_free(pp);
        }
        if (qq == pp) {
            qq = path_q;
        }
    } else {
        /* Plug an opening in |mp_right_type(q)|, if possible */
        if (mp_right_type(path_q) == mp_open_knot && ((mp_left_type(path_q) == mp_curl_knot) || (mp_left_type(path_q) == mp_given_knot))) {
            mp_right_type(path_q) = mp_left_type(path_q);
            number_clone(path_q->right_given, path_q->left_given);
        }
        mp_prev_knot(pp) = path_q;
        mp_next_knot(path_q) = pp;
        number_clone(pp->left_y, y);
        if (t != mp_open_knot) {
            number_clone(pp->left_x, x);
            mp_left_type(pp) = (unsigned char) t;
        };
    }
    path_q = qq;
    if (cur_cmd >= mp_min_expression_command && cur_cmd <= mp_ampersand_command && ! cycle_hit) {
        goto CONTINUE_PATH;
    }
  FINISH_PATH:
    /*
        Choose control points for the path and put the result into |cur_exp|
    */
    if (cycle_hit) {
        if (d == mp_ampersand_command) {
            path_p = path_q;
        }
    } else {
        mp_left_type(path_p) = mp_endpoint_knot;
        if (mp_right_type(path_p) == mp_open_knot) {
            mp_right_type(path_p) = mp_curl_knot;
            set_number_to_unity(path_p->right_curl);
        }
        mp_right_type(path_q) = mp_endpoint_knot;
        if (mp_left_type(path_q) == mp_open_knot) {
            mp_left_type(path_q) = mp_curl_knot;
            set_number_to_unity(path_q->left_curl);
        }
        mp_prev_knot(path_p) = path_q;
        mp_next_knot(path_q) = path_p;
    }
    mp_make_choices(mp, path_p);
    mp->cur_exp.type = mp_path_type;
    mp_set_cur_exp_knot(mp, path_p);
    free_number(x);
    free_number(y);
    return 1;
}

@ A pair of numeric values is changed into a knot node for a one-point path when
\MP\ discovers that the pair is part of a path.

@c
static mp_knot mp_pair_to_knot (MP mp)
{
    /* convert a pair to a knot with two endpoints */
    mp_knot q = mp_new_knot(mp);
    mp_left_type(q) = mp_endpoint_knot;
    mp_right_type(q) = mp_endpoint_knot;
    mp_originator(q) = mp_metapost_user;
    mp_knotstate(q) = mp_regular_knot;
    mp_prev_knot(q) = q;
    mp_next_knot(q) = q;
    mp_known_pair(mp);
    number_clone(q->x_coord, mp->cur_x);
    number_clone(q->y_coord, mp->cur_y);
    return q;
}

@ The |known_pair| subroutine sets |cur_x| and |cur_y| to the components of the
current expression, assuming that the current expression is a pair of known
numerics. Unknown components are zeroed, and the current expression is flushed.

@<Declarations@>=
static void mp_known_pair (MP mp);

@ @c
void mp_known_pair (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    if (mp->cur_exp.type != mp_pair_type) {
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Undefined coordinates have been replaced by (0,0)",
            "I need x and y numbers for this part of the path. The value I found (see above)\n"
            "was no good; so I'll try to keep going by using zero instead."
        );
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
        set_number_to_zero(mp->cur_x);
        set_number_to_zero(mp->cur_y);
    } else {
        mp_node p = mp_get_value_node(cur_exp_node);
        /*
            Make sure that both |x| and |y| parts of |p| are known; copy them into
            |cur_x| and |cur_y|
        */
        if (mp_type(mp_x_part(p)) == mp_known_type) {
            number_clone(mp->cur_x, mp_get_value_number(mp_x_part(p)));
        } else {
            mp_disp_err(mp, mp_x_part(p));
            mp_back_error(
                mp,
                "Undefined x coordinate has been replaced by 0",
                "I need a 'known' x value for this part of the path. The value I found (see above)\n"
                "was no good; so I'll try to keep going by using zero instead."
            );
            mp_get_x_next(mp);
            mp_recycle_value(mp, mp_x_part(p));
            set_number_to_zero(mp->cur_x);
        }
        if (mp_type(mp_y_part(p)) == mp_known_type) {
            number_clone(mp->cur_y, mp_get_value_number(mp_y_part(p)));
        } else {
            mp_disp_err(mp, mp_y_part(p));
            mp_back_error(
                mp,
                "Undefined y coordinate has been replaced by 0",
                "I need a 'known' y value for this part of the path. The value I found (see above)\n"
                "was no good; so I'll try to keep going by using zero instead."
            );
            mp_get_x_next(mp);
            mp_recycle_value(mp, mp_y_part(p));
            set_number_to_zero(mp->cur_y);
        }
        mp_flush_cur_exp(mp, new_expr);
    }
}

@ The |scan_direction| subroutine looks at the directional information that is
enclosed in braces, and also scans ahead to the following character. A type code
is returned, either |open| (if the direction was $(0,0)$), or |curl| (if the
direction was a curl of known value |cur_exp|), or |given| (if the direction is
given by the |angle| value that now appears in |cur_exp|).

There's nothing difficult about this subroutine, but the program is rather
lengthy because a variety of potential errors need to be nipped in the bud.

@c
static int mp_scan_direction (MP mp)
{
    int t; /* the type of information found */
    mp_get_x_next(mp);
    if (cur_cmd == mp_curl_command) {
        /* Scan a curl specification */
        mp_get_x_next(mp);
        mp_scan_expression(mp);
        if ((mp->cur_exp.type != mp_known_type) || (number_negative(cur_exp_value_number))) {
            mp_value new_expr;
            memset(&new_expr, 0, sizeof(mp_value));
            new_number(new_expr.data.n);
            set_number_to_unity(new_expr.data.n);
            mp_disp_err(mp, NULL);
            mp_back_error(
                mp,
                "Improper curl has been replaced by 1",
                "A curl must be a known, nonnegative number."
            );
            mp_get_x_next(mp);
            mp_flush_cur_exp(mp, new_expr);
        }
        t = mp_curl_knot;
    } else {
        /* Scan a given direction */
        mp_scan_expression(mp);
        if (mp->cur_exp.type > mp_pair_type) {
            /* Get given directions separated by commas */
            mp_number xx;
            new_number(xx);
            if (mp->cur_exp.type != mp_known_type) {
                mp_value new_expr;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_disp_err(mp, NULL);
                mp_back_error(
                    mp,
                    "Undefined x coordinate has been replaced by 0",
                    "I need a 'known' x value for this part of the path. The value I found (see above)\n"
                    "was no good; so I'll try to keep going by using zero instead."
                );
                mp_get_x_next(mp);
                mp_flush_cur_exp(mp, new_expr);
            }
            number_clone(xx, cur_exp_value_number);
            if (cur_cmd != mp_comma_command) {
                mp_back_error(
                    mp,
                    "Missing ',' has been inserted",
                    "I've got the x coordinate of a path direction; will look for the y coordinate\n"
                    "next."
                );
            }
            mp_get_x_next(mp);
            mp_scan_expression(mp);
            if (mp->cur_exp.type != mp_known_type) {
                mp_value new_expr;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_disp_err(mp, NULL);
                mp_back_error(
                    mp,
                    "Undefined y coordinate has been replaced by 0",
                    "I need a 'known' y value for this part of the path. The value I found (see above)\n"
                    "was no good; so I'll try to keep going by using zero instead."
                );
                mp_get_x_next(mp);
                mp_flush_cur_exp(mp, new_expr);
            }
            number_clone(mp->cur_y, cur_exp_value_number);
            number_clone(mp->cur_x, xx);
            free_number(xx);
        } else {
            mp_known_pair(mp);
        }
        if (number_zero(mp->cur_x) && number_zero(mp->cur_y)) {
            t = mp_open_knot;
        } else {
            mp_number narg;
            new_angle(narg);
            n_arg(narg, mp->cur_x, mp->cur_y);
            t = mp_given_knot;
            mp_set_cur_exp_value_number(mp, &narg);
            free_number(narg);
        }
    }
    if (cur_cmd != mp_right_brace_command) {
        mp_back_error(
            mp,
            "Missing '}' has been inserted",
            "I've scanned a direction spec for part of a path, so a right brace should have\n"
            "come next. I shall pretend that one was there."
        );
    }
    mp_get_x_next(mp);
    return t;
}

@<Declare the basic parsing subroutines@>=
static void do_boolean_error (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_disp_err(mp, NULL);
    set_number_from_boolean(new_expr.data.n, mp_false_operation);
    mp_back_error(
        mp,
        "Undefined condition will be treated as 'false'",
        "The expression shown above should have had a definite true-or-false value. I'm\n"
        "changing it to 'false'."
    );
    mp_get_x_next(mp);
    mp_flush_cur_exp(mp, new_expr);
    mp->cur_exp.type = mp_boolean_type;
}

@ @<Declarations@>=
static void do_boolean_error (MP mp);

@* Doing the operations.

The purpose of parsing is primarily to permit people to avoid piles of
parentheses. But the real work is done after the structure of an expression has
been recognized; that's when new expressions are generated. We turn now to the
guts of \MP, which handles individual operators that have come through the
parsing mechanism.

We'll start with the easy ones that take no operands, then work our way up to
operators with one and ultimately two arguments. In other words, we will write
the three procedures |do_nullary|, |do_unary|, and |do_binary| that are invoked
periodically by the expression scanners.

First let's make sure that all of the primitive operators are in the hash table.
Although |scan_primary| and its relatives made use of the |cmd| code for these
operators, the |do| routines base everything on the |mod| code. For example,
|do_binary| doesn't care whether the operation it performs is a |primary_binary|
or |secondary_binary|, etc.

@<Put each...@>=
mp_primitive(mp, "true", mp_nullary_command, mp_true_operation);
@:true_}{|true| primitive@>
mp_primitive(mp, "false", mp_nullary_command, mp_false_operation);
@:false_}{|false| primitive@>
mp_primitive(mp, "nullpicture", mp_nullary_command, mp_null_picture_operation);
@:null_picture_}{|nullpicture| primitive@>
mp_primitive(mp, "nullpen", mp_nullary_command, mp_null_pen_operation);
@:null_pen_}{|nullpen| primitive@>
mp_primitive(mp, "readstring", mp_nullary_command, mp_read_string_operation);
@:read_string_}{|readstring| primitive@>
mp_primitive(mp, "pencircle", mp_nullary_command, mp_pen_circle_operation);
@:pen_circle_}{|pencircle| primitive@>
mp_primitive(mp, "normaldeviate", mp_nullary_command, mp_normal_deviate_operation);
@:normal_deviate_}{|normaldeviate| primitive@>
mp_primitive(mp, "readfrom", mp_unary_command, mp_read_from_operation);
@:read_from_}{|readfrom| primitive@>
mp_primitive(mp, "closefrom", mp_unary_command, mp_close_from_operation);
@:close_from_}{|closefrom| primitive@>
mp_primitive(mp, "odd", mp_unary_command, mp_odd_operation);
@:odd_}{|odd| primitive@>
mp_primitive(mp, "known", mp_unary_command, mp_known_operation);
@:known_}{|known| primitive@>
mp_primitive(mp, "unknown", mp_unary_command, mp_unknown_operation);
@:unknown_}{|unknown| primitive@>
mp_primitive(mp, "not", mp_unary_command, mp_not_operation);
@:not_}{|not| primitive@>
mp_primitive(mp, "decimal", mp_unary_command, mp_decimal_operation);
@:decimal_}{|decimal| primitive@>
mp_primitive(mp, "reverse", mp_unary_command, mp_reverse_operation);
@:reverse_}{|reverse| primitive@>
mp_primitive(mp, "uncycle", mp_unary_command, mp_uncycle_operation);
@:uncycle_}{|uncycle| primitive@>
mp_primitive(mp, "makepath", mp_unary_command, mp_make_path_operation);
@:make_path_}{|makepath| primitive@>
mp_primitive(mp, "makepen", mp_unary_command, mp_make_pen_operation);
@:make_pen_}{|makepen| primitive@>
mp_primitive(mp, "makenep", mp_unary_command, mp_make_nep_operation);
@:make_nep_}{|makenep| primitive@>
mp_primitive(mp, "convexed", mp_unary_command, mp_convexed_operation);
@:convexed_}{|convexed| primitive@>
mp_primitive(mp, "uncontrolled", mp_unary_command, mp_uncontrolled_operation);
@:convexed_}{|uncontrolled| primitive@>
mp_primitive(mp, "oct", mp_unary_command, mp_oct_operation);
@:oct_}{|oct| primitive@>
mp_primitive(mp, "hex", mp_unary_command, mp_hex_operation);
@:hex_}{|hex| primitive@>
mp_primitive(mp, "ASCII", mp_unary_command, mp_ASCII_operation);
@:ASCII_}{|ASCII| primitive@>
mp_primitive(mp, "char", mp_unary_command, mp_char_operation);
@:char_}{|char| primitive@>
mp_primitive(mp, "length", mp_unary_command, mp_length_operation);
@:length_}{|length| primitive@>
mp_primitive(mp, "turningnumber", mp_unary_command, mp_turning_operation);
@:turning_number_}{|turningnumber| primitive@>
mp_primitive(mp, "xpart", mp_unary_command, mp_x_part_operation);
@:x_part_}{|xpart| primitive@>
mp_primitive(mp, "ypart", mp_unary_command, mp_y_part_operation);
@:y_part_}{|ypart| primitive@>
mp_primitive(mp, "xxpart", mp_unary_command, mp_xx_part_operation);
@:xx_part_}{|xxpart| primitive@>
mp_primitive(mp, "xypart", mp_unary_command, mp_xy_part_operation);
@:xy_part_}{|xypart| primitive@>
mp_primitive(mp, "yxpart", mp_unary_command, mp_yx_part_operation);
@:yx_part_}{|yxpart| primitive@>
mp_primitive(mp, "yypart", mp_unary_command, mp_yy_part_operation);
@:yy_part_}{|yypart| primitive@>
mp_primitive(mp, "redpart", mp_unary_command, mp_red_part_operation);
@:red_part_}{|redpart| primitive@>
mp_primitive(mp, "greenpart", mp_unary_command, mp_green_part_operation);
@:green_part_}{|greenpart| primitive@>
mp_primitive(mp, "bluepart", mp_unary_command, mp_blue_part_operation);
@:blue_part_}{|bluepart| primitive@>
mp_primitive(mp, "cyanpart", mp_unary_command, mp_cyan_part_operation);
@:cyan_part_}{|cyanpart| primitive@>
mp_primitive(mp, "magentapart", mp_unary_command, mp_magenta_part_operation);
@:magenta_part_}{|magentapart| primitive@>
mp_primitive(mp, "yellowpart", mp_unary_command, mp_yellow_part_operation);
@:yellow_part_}{|yellowpart| primitive@>
mp_primitive(mp, "blackpart", mp_unary_command, mp_black_part_operation);
@:black_part_}{|blackpart| primitive@>
mp_primitive(mp, "greypart", mp_unary_command, mp_grey_part_operation);
@:grey_part_}{|greypart| primitive@>
mp_primitive(mp, "colormodel", mp_unary_command, mp_color_model_operation);
@:color_model_part_}{|colormodel| primitive@>
mp_primitive(mp, "prescriptpart", mp_unary_command, mp_prescript_part_operation);
@:prescript_part_}{|prescriptpart| primitive@>
mp_primitive(mp, "postscriptpart", mp_unary_command, mp_postscript_part_operation);
@:postscript_part_}{|postscriptpart| primitive@>
mp_primitive(mp, "stackingpart", mp_unary_command, mp_stacking_part_operation);
@:stacking_part_}{|stackingpart| primitive@>
mp_primitive(mp, "pathpart", mp_unary_command, mp_path_part_operation);
@:path_part_}{|pathpart| primitive@>
mp_primitive(mp, "penpart", mp_unary_command, mp_pen_part_operation);
@:pen_part_}{|penpart| primitive@>
mp_primitive(mp, "dashpart", mp_unary_command, mp_dash_part_operation);
@:dash_part_}{|dashpart| primitive@>
mp_primitive(mp, "sqrt", mp_unary_command, mp_sqrt_operation);
@:sqrt_}{|sqrt| primitive@>
mp_primitive(mp, "mexp", mp_unary_command, mp_m_exp_operation);
@:m_exp_}{|mexp| primitive@>
mp_primitive(mp, "mlog", mp_unary_command, mp_m_log_operation);
@:m_log_}{|mlog| primitive@>
mp_primitive(mp, "sind", mp_unary_command, mp_sin_d_operation);
@:sin_d_}{|sind| primitive@>
mp_primitive(mp, "cosd", mp_unary_command, mp_cos_d_operation);
@:cos_d_}{|cosd| primitive@>
mp_primitive(mp, "floor", mp_unary_command, mp_floor_operation);
@:floor_}{|floor| primitive@>
mp_primitive(mp, "uniformdeviate", mp_unary_command, mp_uniform_deviate_operation);
@:uniform_deviate_}{|uniformdeviate| primitive@>
mp_primitive(mp, "llcorner", mp_unary_command, mp_ll_corner_operation);
@:ll_corner_}{|llcorner| primitive@>
mp_primitive(mp, "lrcorner", mp_unary_command, mp_lr_corner_operation);
@:lr_corner_}{|lrcorner| primitive@>
mp_primitive(mp, "ulcorner", mp_unary_command, mp_ul_corner_operation);
@:ul_corner_}{|ulcorner| primitive@>
mp_primitive(mp, "urcorner", mp_unary_command, mp_ur_corner_operation);
@:ur_corner_}{|urcorner| primitive@>
mp_primitive(mp, "centerof", mp_unary_command, mp_center_of_operation);
@:center_}{|center| primitive@>
mp_primitive(mp, "centerofmass", mp_unary_command, mp_center_of_mass_operation);
@:center_}{|centerofmass| primitive@>
mp_primitive(mp, "corners", mp_unary_command, mp_corners_operation);
@:corners_}{|corners| primitive@>
mp_primitive(mp, "xrange", mp_unary_command, mp_x_range_operation);
@:xrange_}{|xrange| primitive@>
mp_primitive(mp, "yrange", mp_unary_command, mp_y_range_operation);
@:yrange_}{|xrange| primitive@>
mp_primitive(mp, "deltapoint", mp_unary_command, mp_delta_point_operation);
@:deltapoint_}{|deltapoint| primitive@>
mp_primitive(mp, "deltaprecontrol", mp_unary_command, mp_delta_precontrol_operation);
@:deltaprecontrol_}{|deltaprecontrol| primitive@>
mp_primitive(mp, "deltapostcontrol", mp_unary_command, mp_delta_postcontrol_operation);
@:deltapostcontrol_}{|deltapostcontrol| primitive@>
mp_primitive(mp, "deltadirection", mp_unary_command, mp_delta_direction_operation);
@:deltadirection_}{|deltadirection| primitive@>
mp_primitive(mp, "arclength", mp_unary_command, mp_arc_length_operation);
@:arc_length_}{|arclength| primitive@>
mp_primitive(mp, "angle", mp_unary_command, mp_angle_operation);
@:angle_}{|angle| primitive@>
mp_primitive(mp, "cycle", mp_cycle_command, mp_cycle_operation);
@:cycle_}{|cycle| primitive@>
mp_primitive(mp, "nocycle", mp_cycle_command, mp_no_cycle_operation);
@:nocycle_}{|nocycle| primitive@>
mp_primitive(mp, "stroked", mp_unary_command, mp_stroked_operation);
@:stroked_}{|stroked| primitive@>
mp_primitive(mp, "filled", mp_unary_command, mp_filled_operation);
@:filled_}{|filled| primitive@>
mp_primitive(mp, "clipped", mp_unary_command, mp_clipped_operation);
@:clipped_}{|clipped| primitive@>
mp_primitive(mp, "grouped", mp_unary_command, mp_grouped_operation);
@:clipped_}{|grouped| primitive@>
mp_primitive(mp, "bounded", mp_unary_command, mp_bounded_operation);
@:bounded_}{|bounded| primitive@>
mp_primitive(mp, "+", mp_plus_or_minus_command, mp_plus_operation);
@:+ }{|+| primitive@>
mp_primitive(mp, "-", mp_plus_or_minus_command, mp_minus_operation);
@:- }{|-| primitive@>
mp_primitive(mp, "*", mp_secondary_binary_command, mp_times_operation);
@:* }{|*| primitive@>
mp_primitive(mp, "/", mp_slash_command, mp_over_operation);
mp->frozen_slash = mp_frozen_primitive (mp, "/", mp_slash_command, mp_over_operation);
@:/ }{|/| primitive@>
mp_primitive(mp, "^", mp_secondary_binary_command, mp_power_operation);
@:^ }{|^| primitive@>
mp_primitive(mp, "++", mp_tertiary_binary_command, mp_pythag_add_operation);
@:++_}{|++| primitive@>
mp_primitive(mp, "+-+", mp_tertiary_binary_command, mp_pythag_sub_operation);
@:+-+_}{|+-+| primitive@>
mp_primitive(mp, "or", mp_tertiary_binary_command, mp_or_operation);
@:or_}{|or| primitive@>
mp_primitive(mp, "and", mp_and_command, mp_and_operation);
@:and_}{|and| primitive@>
mp_primitive(mp, "<", mp_primary_binary_command, mp_less_than_operation);
@:< }{|<| primitive@>
mp_primitive(mp, "<=", mp_primary_binary_command, mp_less_or_equal_operation);
@:<=_}{|<=| primitive@>
mp_primitive(mp, ">", mp_primary_binary_command, mp_greater_than_operation);
@:> }{|>| primitive@>
mp_primitive(mp, ">=", mp_primary_binary_command, mp_greater_or_equal_operation);
@:>=_}{|>=| primitive@>
mp_primitive(mp, "=", mp_equals_command, mp_equal_operation);
@:= }{|=| primitive@>
mp_primitive(mp, "<>", mp_primary_binary_command, mp_unequal_operation);
@:<>_}{|<>| primitive@>
mp_primitive(mp, "substring", mp_of_binary_command, mp_substring_operation);
@:substring_}{|substring| primitive@>
mp_primitive(mp, "subpath", mp_of_binary_command, mp_subpath_operation);
@:subpath_}{|subpath| primitive@>
mp_primitive(mp, "directiontime", mp_of_binary_command, mp_direction_time_operation);
@:direction_time_}{|directiontime| primitive@>
mp_primitive(mp, "point", mp_of_binary_command, mp_point_operation);
@:point_}{|point| primitive@>
mp_primitive(mp, "precontrol", mp_of_binary_command, mp_precontrol_operation);
@:precontrol_}{|precontrol| primitive@>
mp_primitive(mp, "postcontrol", mp_of_binary_command, mp_postcontrol_operation);
@:direction_}{|direction| primitive@>
mp_primitive(mp, "direction", mp_of_binary_command, mp_direction_operation);
@:postcontrol_}{|postcontrol| primitive@>
mp_primitive(mp, "pathpoint", mp_nullary_command, mp_path_point_operation);
@:pathpoint_}{|pathpoint| primitive@>
mp_primitive(mp, "pathprecontrol", mp_nullary_command, mp_path_precontrol_operation);
@:pathprecontrol_}{|pathprecontrol| primitive@>
mp_primitive(mp, "pathpostcontrol", mp_nullary_command, mp_path_postcontrol_operation);
@:pathpostcontrol_}{|pathpostcontrol| primitive@>
mp_primitive(mp, "pathdirection", mp_nullary_command, mp_path_direction_operation);
@:pathdirection_}{|pathdirection| primitive@>
mp_primitive(mp, "penoffset", mp_of_binary_command, mp_pen_offset_operation);
@:pen_offset_}{|penoffset| primitive@>
mp_primitive(mp, "arctime", mp_of_binary_command, mp_arc_time_operation);
@:arc_time_of_}{|arctime| primitive@>
mp_primitive(mp, "arcpoint", mp_of_binary_command, mp_arc_point_operation);
@:arc_point_of_}{|arcpoint| primitive@>
mp_primitive(mp, "arcpointlist", mp_of_binary_command, mp_arc_point_list_operation);
@:arc_point_list_of_}{|arcpointlist| primitive@>
mp_primitive(mp, "subarclength", mp_of_binary_command, mp_subarc_length_operation);
@:subarc_length_of_}{|subarclength| primitive@>
mp_primitive(mp, "mpversion", mp_nullary_command, mp_version_operation);
@:mp_version_}{|mpversion| primitive@>
mp_primitive(mp, "&", mp_ampersand_command, mp_concatenate_operation);
@:!!!}{|\&| primitive@>
mp_primitive(mp, "&&", mp_ampersand_command, mp_just_append_operation);
@:!!!!!!}{|\&\&| primitive@>
mp_primitive(mp, "rotated", mp_secondary_binary_command, mp_rotated_operation);
@:rotated_}{|rotated| primitive@>
mp_primitive(mp, "slanted", mp_secondary_binary_command, mp_slanted_operation);
@:slanted_}{|slanted| primitive@>
mp_primitive(mp, "scaled", mp_secondary_binary_command, mp_scaled_operation);
@:scaled_}{|scaled| primitive@>
mp_primitive(mp, "shifted", mp_secondary_binary_command, mp_shifted_operation);
@:shifted_}{|shifted| primitive@>
mp_primitive(mp, "transformed", mp_secondary_binary_command, mp_transformed_operation);
@:transformed_}{|transformed| primitive@>
mp_primitive(mp, "xscaled", mp_secondary_binary_command, mp_x_scaled_operation);
@:x_scaled_}{|xscaled| primitive@>
mp_primitive(mp, "yscaled", mp_secondary_binary_command, mp_y_scaled_operation);
@:y_scaled_}{|yscaled| primitive@>
mp_primitive(mp, "zscaled", mp_secondary_binary_command, mp_z_scaled_operation);
@:z_scaled_}{|zscaled| primitive@>
mp_primitive(mp, "intersectiontimes", mp_tertiary_binary_command, mp_intertimes_operation);
@:intersection_times_}{|intersectiontimes| primitive@>
mp_primitive(mp, "intersectiontimeslist", mp_tertiary_binary_command, mp_intertimes_list_operation);
@:intersection_times_list_}{|intersectiontimeslist| primitive@>
mp_primitive(mp, "envelope", mp_of_binary_command, mp_envelope_operation);
@:envelope_}{|envelope| primitive@>
mp_primitive(mp, "boundingpath", mp_of_binary_command, mp_boundingpath_operation);
@:boundingpath_}{|boundingpath| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_nullary_command:
case mp_unary_command:
case mp_of_binary_command:
case mp_secondary_binary_command:
case mp_tertiary_binary_command:
case mp_primary_binary_command:
case mp_cycle_command:
case mp_plus_or_minus_command:
case mp_slash_command:
case mp_ampersand_command:
case mp_equals_command:
case mp_and_command:
    return mp_op_string((int) m);

@ @<Declarations@>=
static void push_of_path_result (MP mp, int what, mp_knot p);

@ @c
static void push_of_path_result (MP mp, int what, mp_knot p)
{
    switch (what) {
        case 0:
            mp_pair_value(mp, &(p->x_coord), &(p->y_coord));
            break;
        case 1:
            if (mp_left_type(p) == mp_endpoint_knot) {
                mp_pair_value(mp, &(p->x_coord), &(p->y_coord));
            } else {
                mp_pair_value(mp, &(p->left_x), &(p->left_y));
            }
            break;
        case 2:
            if (mp_right_type(p) == mp_endpoint_knot) {
                mp_pair_value(mp, &(p->x_coord), &(p->y_coord));
            } else {
                mp_pair_value(mp, &(p->right_x), &(p->right_y));
            }
            break;
        case 3:
            {
                mp_number x, y;
                if (mp_right_type(p) == mp_endpoint_knot) {
                    new_number_clone(x, p->x_coord);
                    new_number_clone(y, p->y_coord);
                } else {
                    new_number_clone(x, p->right_x);
                    new_number_clone(y, p->right_y);
                }
                if (mp_left_type(p) == mp_endpoint_knot) {
                    number_subtract(x, p->x_coord);
                    number_subtract(y, p->y_coord);
                } else {
                    number_subtract(x, p->left_x);
                    number_subtract(y, p->left_y);
                }
                mp_pair_value(mp, &x, &y);
                free_number(x);
                free_number(y);
            }
            break;
    }
}

@ OK, let's look at the simplest |do| procedure first.

@c
@<Declare nullary action procedure@>
static void mp_do_nullary (MP mp, int c)
{
    check_arith();
    if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
        mp_show_cmd_mod(mp, mp_nullary_command, c);
    }
    switch (c) {
        case mp_true_operation:
        case mp_false_operation:
            mp->cur_exp.type = mp_boolean_type;
            mp_set_cur_exp_value_boolean(mp, c);
            break;
        case mp_null_picture_operation:
            mp->cur_exp.type = mp_picture_type;
            mp_set_cur_exp_node(mp, (mp_node) mp_get_edge_header_node(mp));
            mp_init_edges(mp, (mp_edge_header_node) cur_exp_node);
            break;
        case mp_null_pen_operation:
            mp->cur_exp.type = mp_pen_type;
            mp_set_cur_exp_knot(mp, mp_get_pen_circle(mp, &zero_t));
            break;
        case mp_normal_deviate_operation:
            {
                mp_number r;
                new_number(r);
                /*|mp_norm_rand (mp, &r)|;*/
                m_norm_rand(r);
                mp->cur_exp.type = mp_known_type;
                mp_set_cur_exp_value_number(mp, &r);
                free_number(r);
            }
            break;
        case mp_pen_circle_operation:
            mp->cur_exp.type = mp_pen_type;
            mp_set_cur_exp_knot(mp, mp_get_pen_circle(mp, &unity_t));
            break;
        case mp_version_operation:
            mp->cur_exp.type = mp_string_type;
            mp_set_cur_exp_str(mp, mp_intern(mp, metapost_version));
            break;
        /* these are new */
        case mp_path_point_operation:
        case mp_path_precontrol_operation:
        case mp_path_postcontrol_operation:
        case mp_path_direction_operation:
            if (mp->loop_ptr && mp->loop_ptr->point != NULL) {
                push_of_path_result(mp, c - mp_path_point_operation, mp->loop_ptr->point);
            } else {
                mp_pair_value(mp, &zero_t, &zero_t);
            }
            break;
    }
    check_arith();
}

@ @<Declare nullary action procedure@>=
static void mp_finish_read (MP mp)
{
    /* copy |buffer| line to |cur_exp| */
    mp_str_room(mp, (int) mp->last - (int) start);
    for (size_t k = (size_t) start; k < mp->last; k++) {
        mp_append_char(mp, mp->buffer[k]);
    }
    mp_end_file_reading(mp);
    mp->cur_exp.type = mp_string_type;
    mp_set_cur_exp_str(mp, mp_make_string(mp));
    }

@ Things get a bit more interesting when there's an operand. The operand to
|do_unary| appears in |cur_type| and |cur_exp|.

This complicated if test makes sure that any |bounds| or |clip| picture objects
that get passed into |within| do not raise an error when queried using the
color part primitives (this is needed for backward compatibility) .

@c
static int mp_pict_color_type (MP mp, int c)
{
    /* cur_pic_item = mp_link(mp_edge_list(cur_exp_node)) */
    return (
        (mp_link(mp_edge_list(cur_exp_node)) != NULL)
        &&
        (
            (! mp_has_color(mp_link(mp_edge_list(cur_exp_node))))
            ||
            ((
                (mp_color_model(mp_link(mp_edge_list(cur_exp_node))) == c)
                ||
                (
                    (mp_color_model(mp_link(mp_edge_list(cur_exp_node))) == mp_uninitialized_model)
                    &&
                    (number_to_scaled(internal_value(mp_default_color_model_internal))/number_to_scaled(unity_t)) == c
                )
            ))
        )
    );
}

@<Declarations@>=
static mp_knot mp_simple_knot(MP mp, mp_number *x, mp_number *y);
static mp_knot mp_complex_knot(MP mp, mp_knot o);

@ @c
static mp_knot mp_simple_knot(MP mp, mp_number *x, mp_number *y)
{
    mp_knot k = mp_new_knot(mp);
    mp_left_type(k) = mp_explicit_knot;
    mp_right_type(k) = mp_explicit_knot;
    mp_originator(k) = mp_program_code;
    mp_knotstate(k) = mp_regular_knot;
    number_clone(k->x_coord, *x);
    number_clone(k->y_coord, *y);
    number_clone(k->left_x, *x);
    number_clone(k->left_y, *y);
    number_clone(k->right_x, *x);
    number_clone(k->right_y, *y);
    return k;
}

static mp_knot mp_complex_knot(MP mp, mp_knot o)
{
    mp_knot k = mp_new_knot(mp);
    mp_left_type(k) = mp_explicit_knot;
    mp_right_type(k) = mp_explicit_knot;
    mp_originator(k) = mp_program_code;
    mp_knotstate(k) = mp_regular_knot;
    number_clone(k->x_coord, o->x_coord);
    number_clone(k->y_coord, o->y_coord);
    number_clone(k->left_x, o->left_x);
    number_clone(k->left_y, o->left_y);
    number_clone(k->right_x, o->right_x);
    number_clone(k->right_y, o->right_y);
    return k;
}

@<Declarations@>=
static int mp_pict_color_type (MP mp, int c);

@c
@<Declare unary action procedures@>

static void mp_do_unary (MP mp, int c)
{
    check_arith();
    if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
        /* Trace the current unary operation */
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "{");
        mp_print_op(mp, c);
        mp_print_chr(mp, '(');
        mp_print_exp(mp, NULL, 0); /* show the operand, but not verbosely */
        mp_print_str(mp, ")}");
        mp_end_diagnostic(mp, 0);
    }
    /*
        This is a mix of combined and not combined. We could combine more or less
        and let the compiler deal with it.
    */
    switch (c) {
        case mp_plus_operation:
            if (mp->cur_exp.type < mp_color_type) {
                mp_bad_unary(mp, mp_plus_operation);
            }
            break;
        case mp_minus_operation:
            negate_cur_expr(mp);
            break;
        case mp_not_operation:
            if (mp->cur_exp.type != mp_boolean_type) {
                mp_bad_unary(mp, mp_not_operation);
            } else {
                mp_set_cur_exp_value_boolean(mp, (cur_exp_value_boolean == mp_true_operation) ? mp_false_operation : mp_true_operation);
            }
            break;
            /* We could use something function[mp_sqrt_operation] here: */
        case mp_sqrt_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n;
                new_number(n);
                square_rt(n, cur_exp_value_number);
                mp_set_cur_exp_value_number(mp, &n);
                free_number(n);
            }
            break;
        case mp_m_exp_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n;
                new_number(n);
                m_exp(n, cur_exp_value_number);
                mp_set_cur_exp_value_number(mp, &n);
                free_number(n);
            }
            break;
        case mp_m_log_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n;
                new_number(n);
                m_log(n, cur_exp_value_number);
                mp_set_cur_exp_value_number(mp, &n);
                free_number(n);
            }
            break;
        case mp_sin_d_operation:
        case mp_cos_d_operation:
            /*
               This is rather inefficient, esp decimal, to calculate both each time. We could
               pass NULL as signal to do only one.
            */
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n_sin, n_cos, arg1, arg2;
                new_number(arg1);
                new_number(arg2);
                new_fraction(n_sin);
                new_fraction(n_cos);
                number_clone(arg1, cur_exp_value_number);
                number_clone(arg2, unity_t);
                number_multiply_int(arg2, 360);
                number_modulo(arg1, arg2);
                convert_scaled_to_angle(arg1);
                n_sin_cos(arg1, n_cos, n_sin);
                if (c == mp_sin_d_operation) {
                    fraction_to_round_scaled(n_sin);
                    mp_set_cur_exp_value_number(mp, &n_sin);
                } else {
                    fraction_to_round_scaled(n_cos);
                    mp_set_cur_exp_value_number(mp, &n_cos);
                }
                free_number(arg1);
                free_number(arg2);
                free_number(n_sin);
                free_number(n_cos);
            }
            break;
        case mp_floor_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n;
                new_number(n);
                number_clone(n, cur_exp_value_number);
                floor_scaled(n);
                mp_set_cur_exp_value_number(mp, &n);
                free_number(n);
            }
            break;
        case mp_uniform_deviate_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_number n;
                new_number(n);
                m_unif_rand(n, cur_exp_value_number);
                mp_set_cur_exp_value_number(mp, &n);
                free_number(n);
            }
            break;
        case mp_odd_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_set_cur_exp_value_boolean(mp, number_odd(cur_exp_value_number) ? mp_true_operation : mp_false_operation);
                mp->cur_exp.type = mp_boolean_type;
            }
            break;
        case mp_angle_operation:
            if (mp_nice_pair (mp, cur_exp_node, mp->cur_exp.type)) {
                mp_value expr;
                mp_node p; /* for list manipulation */
                mp_number narg;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                new_angle(narg);
                p = mp_get_value_node(cur_exp_node);
                n_arg(narg, mp_get_value_number(mp_x_part(p)), mp_get_value_number(mp_y_part(p)));
                number_clone(expr.data.n, narg);
                convert_angle_to_scaled(expr.data.n);
                free_number(narg);
                mp_flush_cur_exp(mp, expr);
            } else {
                mp_bad_unary(mp, mp_angle_operation);
            }
            break;
        case mp_x_part_operation:
        case mp_y_part_operation:
            switch (mp->cur_exp.type) {
                case mp_pair_type:
                case mp_transform_type:
                    mp_take_part(mp, c);
                    break;
                case mp_picture_type:
                    mp_take_pict_part(mp, c);
                    break;
                default:
                    mp_bad_unary(mp, c);
                    break;
            }
            break;
        case mp_xx_part_operation:
        case mp_xy_part_operation:
        case mp_yx_part_operation:
        case mp_yy_part_operation:
            switch (mp->cur_exp.type) {
                case mp_transform_type:
                    mp_take_part(mp, c);
                    break;
                case mp_picture_type:
                    mp_take_pict_part(mp, c);
                    break;
                default:
                    mp_bad_unary(mp, c);
                    break;
            }
            break;
        case mp_red_part_operation:
        case mp_green_part_operation:
        case mp_blue_part_operation:
            switch (mp->cur_exp.type) {
                case mp_color_type:
                    mp_take_part(mp, c);
                    break;
                case mp_picture_type:
                    if (mp_pict_color_type(mp, mp_rgb_model)) {
                        mp_take_pict_part(mp, c);
                    } else {
                        mp_bad_color_part(mp, c);
                    }
                    break;
                default:
                    mp_bad_unary(mp, c);
                    break;
            }
            break;
        case mp_cyan_part_operation:
        case mp_magenta_part_operation:
        case mp_yellow_part_operation:
        case mp_black_part_operation:
            switch (mp->cur_exp.type) {
                case mp_cmykcolor_type:
                    mp_take_part(mp, c);
                    break;
                case mp_picture_type:
                    if (mp_pict_color_type(mp, mp_cmyk_model)) {
                        mp_take_pict_part(mp, c);
                    } else {
                        mp_bad_color_part(mp, c);
                    }
                    break;
                default:
                    mp_bad_unary(mp, c);
                    break;
            }
            break;
        case mp_grey_part_operation:
            switch (mp->cur_exp.type) {
                case mp_known_type:
                    break;
                case mp_picture_type:
                    if (mp_pict_color_type(mp, mp_grey_model)) {
                        mp_take_pict_part(mp, c);
                    } else {
                        mp_bad_color_part(mp, c);
                    }
                    break;
                default:
                    mp_bad_unary(mp, c);
                    break;
            }
            break;
        case mp_color_model_operation:
        case mp_path_part_operation:
        case mp_pen_part_operation:
        case mp_dash_part_operation:
        case mp_prescript_part_operation:
        case mp_postscript_part_operation:
        case mp_stacking_part_operation:
            if (mp->cur_exp.type == mp_picture_type) {
                mp_take_pict_part(mp, c);
            } else {
                mp_bad_unary(mp, c);
            }
            break;
        case mp_char_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, mp_char_operation);
            } else {
                int n = round_unscaled(cur_exp_value_number) % 256;
                unsigned char s[2];
                mp_set_cur_exp_value_scaled(mp, n);
                mp->cur_exp.type = mp_string_type;
                if (number_negative(cur_exp_value_number)) {
                    n = number_to_scaled(cur_exp_value_number) + 256;
                    mp_set_cur_exp_value_scaled(mp, n);
                }
                s[0] = (unsigned char) number_to_scaled(cur_exp_value_number);
                s[1] = '\0';
                mp_set_cur_exp_str(mp, mp_rtsl (mp, (char *) s, 1));
            }
            break;
        case mp_decimal_operation:
            if (mp->cur_exp.type != mp_known_type) {
                mp_bad_unary(mp, mp_decimal_operation);
            } else {
                int selector = mp->selector;
                mp->selector = mp_new_string_selector;
                print_number(cur_exp_value_number);
                mp_set_cur_exp_str(mp, mp_make_string(mp));
                mp->selector = selector;
                mp->cur_exp.type = mp_string_type;
            }
            break;
        case mp_oct_operation:
        case mp_hex_operation:
        case mp_ASCII_operation:
            if (mp->cur_exp.type != mp_string_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_str_to_num(mp);
            }
            break;
        case mp_length_operation:
            /*
                The length operation is somewhat unusual in that it applies to a variety of
                different types of operands. *
            */
            switch (mp->cur_exp.type) {
                case mp_string_type:
                    {
                        mp_value expr;
                        memset(&expr, 0, sizeof(mp_value));
                        new_number(expr.data.n);
                        number_clone(expr.data.n, unity_t);
                        number_multiply_int(expr.data.n, (int) cur_exp_str->len);
                        mp_flush_cur_exp(mp, expr);
                        break;
                    }
                case mp_path_type:
                    {
                        mp_value expr;
                        memset(&expr, 0, sizeof(mp_value));
                        new_number(expr.data.n);
                        mp_path_length(mp, &expr.data.n);
                        mp_flush_cur_exp(mp, expr);
                        break;
                    }
                case mp_known_type:
                    {
                        mp_set_cur_exp_value_number(mp, &cur_exp_value_number);
                        number_abs(cur_exp_value_number);
                        break;
                    }
                case mp_picture_type:
                    {
                        mp_value expr;
                        memset(&expr, 0, sizeof(mp_value));
                        new_number(expr.data.n);
                        mp_picture_length(mp, &expr.data.n);
                        mp_flush_cur_exp(mp, expr);
                        break;
                    }
                default:
                    if (mp_nice_pair (mp, cur_exp_node, mp->cur_exp.type)) {
                        mp_value expr;
                        memset(&expr, 0, sizeof(mp_value));
                        new_number(expr.data.n);
                        pyth_add(expr.data.n,
                            mp_get_value_number(mp_x_part(mp_get_value_node(cur_exp_node))),
                            mp_get_value_number(mp_y_part(mp_get_value_node(cur_exp_node)))
                        );
                        mp_flush_cur_exp(mp, expr);
                    } else {
                        mp_bad_unary(mp, c);
                    }
                    break;
            }
            break;
        case mp_turning_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                mp_flush_cur_exp(mp, expr);
            } else if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, mp_turning_operation);
            } else if (mp_left_type(cur_exp_knot) == mp_endpoint_knot) {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                expr.data.p = NULL;
                mp_flush_cur_exp(mp, expr); /* not a cyclic path */
            } else {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                mp_turn_cycles_wrapper(mp, &expr.data.n, cur_exp_knot);
                mp_flush_cur_exp(mp, expr);
            }
            break;
        /* Here we could do some delta(operation,type) trickery as with filled. */

        case mp_boolean_type_operation:
        case mp_string_type_operation:
        case mp_pen_type_operation:
        case mp_nep_type_operation:
        case mp_path_type_operation:
        case mp_picture_type_operation:
            {
                mp_value expr;
                /*they are parallel but with 2 increments (known and unknown): */
                int type = (c - mp_boolean_type_operation) * 2 + mp_boolean_type ;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                set_number_from_boolean(expr.data.n, (mp->cur_exp.type == type || mp->cur_exp.type == (type + 1)) ? mp_true_operation : mp_false_operation);
                mp_flush_cur_exp(mp, expr);
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_transform_type_operation:
        case mp_color_type_operation:
        case mp_cmykcolor_type_operation:
        case mp_pair_type_operation:
            {
                mp_value expr;
                /* they are parallel: */
                int type = (c - mp_transform_type_operation) + mp_transform_type;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                set_number_from_boolean(expr.data.n, mp->cur_exp.type == type ? mp_true_operation : mp_false_operation);
                mp_flush_cur_exp(mp, expr);
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_numeric_type_operation:
            {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                set_number_from_boolean(expr.data.n, (mp->cur_exp.type >= mp_known_type && mp->cur_exp.type <= mp_independent_type) ? mp_true_operation : mp_false_operation);
                mp_flush_cur_exp(mp, expr);
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_known_operation:
        case mp_unknown_operation:
            {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                set_number_from_boolean(expr.data.n, mp_test_known(mp, c));
                mp_flush_cur_exp(mp, expr);
                /* !! do not replace with |mp_set_cur_exp_node(mp, )| !! */
                cur_exp_node = NULL;
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_cycle_operation:
        case mp_no_cycle_operation:
            {
                mp_value expr;
                int b = 0;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                if (mp->cur_exp.type != mp_path_type) {
                    b = (c == mp_cycle_operation) ? mp_false_operation : mp_true_operation;
                } else if (mp_left_type(cur_exp_knot) != mp_endpoint_knot) {
                    b = (c == mp_cycle_operation) ? mp_true_operation : mp_false_operation;
                } else {
                    b = (c == mp_cycle_operation) ? mp_false_operation : mp_true_operation;
                }
                set_number_from_boolean(expr.data.n, b);
                mp_flush_cur_exp(mp, expr);
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_arc_length_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, mp_arc_length_operation);
            } else {
                mp_value expr;
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                mp_get_arc_length(mp, &expr.data.n, cur_exp_knot);
                mp_flush_cur_exp(mp, expr);
            }
            break;
        case mp_filled_operation:
        case mp_stroked_operation:
        case mp_clipped_operation:
        case mp_grouped_operation:
        case mp_bounded_operation:
            {
                mp_value expr;
                @^data structure assumptions@>
                memset(&expr, 0, sizeof(mp_value));
                new_number(expr.data.n);
                if (mp->cur_exp.type != mp_picture_type) {
                    set_number_from_boolean(expr.data.n, mp_false_operation);
                } else if (mp_link(mp_edge_list(cur_exp_node)) == NULL) {
                    set_number_from_boolean(expr.data.n, mp_false_operation);
                } else {
                    /* they are parallel: */
                    int type = c - mp_filled_operation + mp_fill_node_type;
                    set_number_from_boolean(expr.data.n, mp_type(mp_link(mp_edge_list(cur_exp_node))) == type ? mp_true_operation: mp_false_operation);
                }
                mp_flush_cur_exp(mp, expr);
                mp->cur_exp.type = mp_boolean_type;
                break;
            }
        case mp_make_pen_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, mp_make_pen_operation);
            } else {
                mp->cur_exp.type = mp_pen_type;
                mp_set_cur_exp_knot(mp, mp_make_pen(mp, cur_exp_knot, 1));
            }
            break;
        case mp_make_nep_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, c);
            } else {
                mp->cur_exp.type = mp_nep_type;
                mp_set_cur_exp_knot(mp, cur_exp_knot);
            }
            break;
        case mp_convexed_operation:
            if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, mp_convexed_operation);
            } else {
                mp->cur_exp.type = mp_path_type;
                mp_set_cur_exp_knot(mp, mp_convex_hull(mp, cur_exp_knot));
                mp_simplify_path(mp, cur_exp_knot);
            }
            break;
        case mp_uncontrolled_operation:
            if (mp->cur_exp.type != mp_path_type) {
                mp_bad_unary(mp, mp_uncontrolled_operation);
            } else {
                mp->cur_exp.type = mp_path_type;
                mp_simplify_path(mp, cur_exp_knot);
            }
            break;
        case mp_make_path_operation:
            if (mp->cur_exp.type != mp_pen_type && mp->cur_exp.type != mp_nep_type) {
                mp_bad_unary(mp, mp_make_path_operation);
            } else {
                mp->cur_exp.type = mp_path_type;
                mp_make_path(mp, cur_exp_knot);
            }
            break;
        case mp_reverse_operation:
            switch (mp->cur_exp.type) {
                case mp_path_type:
                    {
                        mp_knot pk = mp_htap_ypoc(mp, cur_exp_knot);
                        if (mp_right_type(pk) == mp_endpoint_knot) {
                            pk = mp_next_knot(pk);
                        }
                        mp_toss_knot_list(mp, cur_exp_knot);
                        mp_set_cur_exp_knot(mp, pk);
                    }
                    break;
                case mp_pair_type:
                    mp_pair_to_path(mp);
                    break;
                default:
                    mp_bad_unary(mp, mp_reverse_operation);
                    break;
            }
            break;
        case mp_uncycle_operation:
            switch (mp->cur_exp.type) {
                case mp_path_type:
                    mp_right_type(mp_prev_knot(cur_exp_knot)) = mp_endpoint_knot;
                    mp_left_type(cur_exp_knot) = mp_endpoint_knot;
                    break;
                case mp_pair_type:
                    mp_pair_to_path(mp);
                    break;
                default:
                    mp_bad_unary(mp, mp_uncycle_operation);
                    break;
            }
            break;
        case mp_ll_corner_operation:
            if (mp_get_cur_bbox(mp)) {
                mp_pair_value(mp, &mp_minx, &mp_miny);
            } else {
                mp_bad_unary(mp, mp_ll_corner_operation);
            }
            break;
        case mp_lr_corner_operation:
            if (mp_get_cur_bbox(mp)) {
                mp_pair_value(mp, &mp_maxx, &mp_miny);
            } else {
                mp_bad_unary(mp, mp_lr_corner_operation);
            }
            break;
        case mp_ul_corner_operation:
            if (mp_get_cur_bbox(mp)) {
                mp_pair_value(mp, &mp_minx, &mp_maxy);
            } else {
                mp_bad_unary(mp, mp_ul_corner_operation);
            }
            break;
        case mp_ur_corner_operation:
            if (! mp_get_cur_bbox(mp)) {
                mp_bad_unary(mp, mp_ur_corner_operation);
            } else {
                mp_pair_value(mp, &mp_maxx, &mp_maxy);
            }
            break;
        case mp_center_of_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                /* keep the pair */
            } else if (mp_get_cur_bbox(mp)) {
                /* todo: make this a function call */
                mp_number x, y;
                new_number(x);
                new_number(y);
                set_number_half_from_subtraction(x, mp_maxx, mp_minx);
                set_number_half_from_subtraction(y, mp_maxy, mp_miny);
                number_add(x, mp_minx);
                number_add(y, mp_miny);
                mp_pair_value(mp, &x, &y);
            } else {
                mp_bad_unary(mp, mp_center_of_operation);
            }
            break;
        case mp_center_of_mass_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                /* keep the pair */
            } else if (mp->cur_exp.type == mp_path_type) {
                /* no overflow detection here .. todo: make this a function call */
                mp_knot p = cur_exp_knot;
                int l = 0;
                mp_number x, y;
                new_number(x);
                new_number(y);
                do {
                    ++l;
                    p = mp_next_knot(p);
                    number_add(x, p->x_coord);
                    number_add(y, p->y_coord);
                } while (p != cur_exp_knot);
                number_divide_int(x, l);
                number_divide_int(y, l);
                mp_pair_value(mp, &x, &y);
                free_number(x);
                free_number(y);
            } else {
                mp_bad_unary(mp, mp_center_of_mass_operation);
            }
            break;
        case mp_corners_operation:
            if (! mp_get_cur_bbox(mp)) {
                mp_bad_unary(mp, mp_corners_operation);
            } else {
                mp_knot ll = mp_simple_knot(mp, &mp_minx, &mp_miny);
                mp_knot lr = mp_simple_knot(mp, &mp_maxx, &mp_miny);
                mp_knot ur = mp_simple_knot(mp, &mp_maxx, &mp_maxy);
                mp_knot ul = mp_simple_knot(mp, &mp_minx, &mp_maxy);
                mp_prev_knot(lr) = ll;
                mp_next_knot(ll) = lr;
                mp_prev_knot(ur) = lr;
                mp_next_knot(lr) = ur;
                mp_prev_knot(ul) = ur;
                mp_next_knot(ur) = ul;
                mp_prev_knot(ll) = ul;
                mp_next_knot(ul) = ll;
                mp->cur_exp.type = mp_path_type;
                mp_set_cur_exp_knot(mp, ll);
            }
            break;
        case mp_x_range_operation:
            if (mp_get_cur_xbox(mp)) {
                mp_pair_value(mp, &mp_minx, &mp_maxx);
            } else {
                mp_bad_unary(mp, mp_x_range_operation);
            }
            break;
        case mp_y_range_operation:
            if (mp_get_cur_ybox(mp)) {
                mp_pair_value(mp, &mp_miny, &mp_maxy);
            } else {
                mp_bad_unary(mp, mp_y_range_operation);
            }
            break;
        case mp_delta_point_operation:
        case mp_delta_precontrol_operation:
        case mp_delta_postcontrol_operation:
        case mp_delta_direction_operation:
            if (mp->cur_exp.type == mp_known_type) {
                mp_set_cur_exp_value_number(mp, &cur_exp_value_number);
                if (mp->loop_ptr && mp->loop_ptr->point != NULL) {
                    mp_knot p = mp->loop_ptr->point;
                    int n = round_unscaled(cur_exp_value_number);
                    if (n > 0) {
                        while (n--) {
                            p = mp_next_knot(p);
                        }
                    } else if (n < 0) {
                        while (n++) {
                            p = mp_prev_knot(p);
                        }
                    }
                    push_of_path_result(mp, c - mp_delta_point_operation, p);
                }
            } else {
                mp_bad_unary(mp, c);
            }
            break;
        case mp_read_from_operation:
        case mp_close_from_operation:
            if (mp->cur_exp.type != mp_string_type) {
                mp_bad_unary(mp, c);
            } else {
                mp_do_read_or_close(mp, c);
            }
            break;
    }
    check_arith();
}

@ The |nice_pair| function returns |true| if both components of a pair are known.

@<Declare unary action procedures@>=
static int mp_nice_pair (MP mp, mp_node p, int t)
{
    (void) mp;
    if (t == mp_pair_type) {
        p = mp_get_value_node(p);
        if (mp_type(mp_x_part(p)) == mp_known_type && mp_type(mp_y_part(p)) == mp_known_type)
            return 1;
    }
    return 0;
}

@ The |nice_color_or_pair| function is analogous except that it also accepts
fully known colors.

@<Declare unary action procedures@>=
static int mp_nice_color_or_pair (MP mp, mp_node p, int t)
{
    mp_node q;
    (void) mp;
    switch (t) {
        case mp_pair_type:
            q = mp_get_value_node(p);
            if (mp_type(mp_x_part(q)) == mp_known_type
             && mp_type(mp_y_part(q)) == mp_known_type)
                return 1;
            break;
        case mp_color_type:
            q = mp_get_value_node(p);
            if (mp_type(mp_red_part  (q)) == mp_known_type
             && mp_type(mp_green_part(q)) == mp_known_type
             && mp_type(mp_blue_part (q)) == mp_known_type)
                return 1;
            break;
        case mp_cmykcolor_type:
            q = mp_get_value_node(p);
            if (mp_type(mp_cyan_part   (q)) == mp_known_type
             && mp_type(mp_magenta_part(q)) == mp_known_type
             && mp_type(mp_yellow_part (q)) == mp_known_type
             && mp_type(mp_black_part  (q)) == mp_known_type)
                return 1;
            break;
    }
    return 0;
}

@ @<Declare unary action...@>=
static void mp_print_known_or_unknown_type (MP mp, int t, mp_node v)
{
    mp_print_chr(mp, '(');
    if (t > mp_known_type) {
        mp_print_str(mp, "unknown numeric");
    } else {
        switch (t) {
            case mp_pair_type:
            case mp_color_type:
            case mp_cmykcolor_type:
                if (! mp_nice_color_or_pair (mp, v, t)) {
                    mp_print_str(mp, "unknown ");
                }
                break;
        }
        mp_print_type(mp, t);
    }
    mp_print_chr(mp, ')');
}

@ @<Declare unary action...@>=
static void mp_bad_unary (MP mp, int c)
{
    char msg[256];
    mp_string sname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_print_op(mp, c);
    mp_print_known_or_unknown_type(mp, mp->cur_exp.type, cur_exp_node);
    sname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "Not implemented: %s", mp_str(mp, sname));
    delete_str_ref(sname);
    mp_disp_err(mp, NULL);
    mp_back_error(
        mp,
        msg,
        "I'm afraid I don't know how to apply that operation to that particular type.\n"
        "Continue, and I'll simply return the argument (shown above) as the result of the\n"
        "operation."
    );
    @.Not implemented...@>
    mp_get_x_next(mp);
}

@ Negation is easy except when the current expression is of type |independent|,
or when it is a pair with one or more |independent| components.

@<Declare unary action...@>=
static void mp_negate_dep_list (MP mp, mp_value_node p)
{
    (void) mp;
    while (1) {
        number_negate(mp_get_dep_value(p));
        if (mp_get_dep_info(p) == NULL)
            return;
        p = (mp_value_node) mp_link(p);
    }
}

@ It is tempting to argue that the negative of an independent variable is an
independent variable, hence we don't have to do anything when negating it. The
fallacy is that other dependent variables pointing to the current expression must
change the sign of their coefficients if we make no change to the current
expression.

Instead, we work around the problem by copying the current expression and
recycling it afterwards (cf.~the |stash_in| routine).

@<Declare unary action...@>=

static void mp_negate_value(MP mp, mp_node r)
{
    if (mp_type(r) == mp_known_type) {
        mp_set_value_number(r, mp_get_value_number(r)); /* to clear the rest */
        number_negate(mp_get_value_number(r));
    } else {
        mp_negate_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) r));
    }
}

static void negate_cur_expr (MP mp)
{
    switch (mp->cur_exp.type) {
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
        case mp_independent_type:
            {
                mp_node q = cur_exp_node;
                mp_make_exp_copy(mp, q);
                if (mp->cur_exp.type == mp_dependent_type) {
                    mp_negate_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) cur_exp_node));
                } else if (mp->cur_exp.type <= mp_pair_type) {
                    /* |mp_color_type| |mp_cmykcolor_type|, or |mp_pair_type| */
                    mp_node p = mp_get_value_node(cur_exp_node);
                 // mp_node r; /* for list manipulation */
                    switch (mp->cur_exp.type) {
                        case mp_pair_type:
                            mp_negate_value(mp, mp_x_part(p));
                            mp_negate_value(mp, mp_y_part(p));
                            break;
                        case mp_color_type:
                            mp_negate_value(mp, mp_red_part(p));
                            mp_negate_value(mp, mp_green_part(p));
                            mp_negate_value(mp, mp_blue_part(p));
                            break;
                        case mp_cmykcolor_type:
                            mp_negate_value(mp, mp_cyan_part(p));
                            mp_negate_value(mp, mp_magenta_part(p));
                            mp_negate_value(mp, mp_yellow_part(p));
                            mp_negate_value(mp, mp_black_part(p));
                            break;
                        default:
                            break;
                    }
                }
                /* if |cur_type=mp_known| then |cur_exp=0| */
                mp_recycle_value(mp, q);
                mp_free_value_node(mp, q);
            }
            break;
        case mp_dependent_type:
        case mp_proto_dependent_type:
            mp_negate_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) cur_exp_node));
            break;
        case mp_known_type:
            if (is_number(cur_exp_value_number)) {
                number_negate(cur_exp_value_number);
            }
            break;
        default:
            mp_bad_unary(mp, mp_minus_operation);
            break;
    }
}

@ If the current expression is a pair, but the context wants it to be a path, we
call |pair_to_path|.

@<Declare unary action...@>=
static void mp_pair_to_path (MP mp) {
    mp_set_cur_exp_knot(mp, mp_pair_to_knot(mp));
    mp->cur_exp.type = mp_path_type;
}

@ @<Declarations@>=
static void mp_bad_color_part (MP mp, int c);

@ @c
static void mp_bad_color_part (MP mp, int c)
{
    mp_node p; /* the big node */
    mp_value new_expr;
    char msg[256];
    int selector;
    mp_string sname;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    p = mp_link(mp_edge_list(cur_exp_node));
    mp_disp_err(mp, NULL);
    selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_print_op(mp, c);
    sname = mp_make_string(mp);
    mp->selector = selector;
    @.Wrong picture color model...@>
    switch (mp_color_model(p)) {
        case mp_grey_model: mp_snprintf(msg, 256, "Wrong picture color model: %s of grey object",      mp_str(mp, sname)); break;
        case mp_cmyk_model: mp_snprintf(msg, 256, "Wrong picture color model: %s of cmyk object",      mp_str(mp, sname)); break;
        case mp_rgb_model:  mp_snprintf(msg, 256, "Wrong picture color model: %s of rgb object",       mp_str(mp, sname)); break;
        case mp_no_model:   mp_snprintf(msg, 256, "Wrong picture color model: %s of marking object",   mp_str(mp, sname)); break;
        default:            mp_snprintf(msg, 256, "Wrong picture color model: %s of defaulted object", mp_str(mp, sname)); break;
    }
    delete_str_ref(sname);
    mp_error(
        mp,
        msg,
        "You can only ask for the redpart, greenpart, bluepart of a rgb object, the\n"
        "cyanpart, magentapart, yellowpart or blackpart of a cmyk object, or the greypart\n"
        "of a grey object. No mixing and matching, please."
    );
    if (c == mp_black_part_operation) {
        number_clone(new_expr.data.n, unity_t);
    } else {
        set_number_to_zero(new_expr.data.n);
    }
    mp_flush_cur_exp(mp, new_expr);
}

@ In the following procedure, |cur_exp| points to a capsule, which points to a
big node. We want to delete all but one part of the big node.

@<Declare unary action...@>=
static void mp_take_part (MP mp, int c)
{
    mp_node p = mp_get_value_node(cur_exp_node); /* the big node */
    mp_set_value_node(mp->temp_val, p);
    mp_type(mp->temp_val) = mp->cur_exp.type;
    mp_link(p) = mp->temp_val;
    mp_free_value_node(mp, cur_exp_node);
    switch (c) {
        case mp_x_part_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_make_exp_copy(mp, mp_x_part(p));
            } else {
                mp_make_exp_copy(mp, mp_tx_part(p));
            }
            break;
        case mp_y_part_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_make_exp_copy(mp, mp_y_part(p));
            } else {
                mp_make_exp_copy(mp, mp_ty_part(p));
            }
            break;
        case mp_xx_part_operation:
            mp_make_exp_copy(mp, mp_xx_part(p));
            break;
        case mp_xy_part_operation:
            mp_make_exp_copy(mp, mp_xy_part(p));
            break;
        case mp_yx_part_operation:
            mp_make_exp_copy(mp, mp_yx_part(p));
            break;
        case mp_yy_part_operation:
            mp_make_exp_copy(mp, mp_yy_part(p));
            break;
        case mp_red_part_operation:
            mp_make_exp_copy(mp, mp_red_part(p));
            break;
        case mp_green_part_operation:
            mp_make_exp_copy(mp, mp_green_part(p));
            break;
        case mp_blue_part_operation:
            mp_make_exp_copy(mp, mp_blue_part(p));
            break;
        case mp_cyan_part_operation:
            mp_make_exp_copy(mp, mp_cyan_part(p));
            break;
        case mp_magenta_part_operation:
            mp_make_exp_copy(mp, mp_magenta_part(p));
            break;
        case mp_yellow_part_operation:
            mp_make_exp_copy(mp, mp_yellow_part(p));
            break;
        case mp_black_part_operation:
            mp_make_exp_copy(mp, mp_black_part(p));
            break;
        case mp_grey_part_operation:
            mp_make_exp_copy(mp, mp_grey_part(p));
            break;
    }
    mp_recycle_value(mp, mp->temp_val);
}

@ @<Initialize table entries@>=
mp->temp_val = mp_new_value_node(mp);
mp_name_type(mp->temp_val) = mp_capsule_operation;

@ @<Free table entries@>=
mp_free_value_node(mp, mp->temp_val);

@ @<Declarations@>=
static mp_edge_header_node mp_scale_edges (MP mp, mp_number *se_sf, mp_edge_header_node se_pic);

@ @<Declare unary action...@>=
static void mp_take_pict_part (MP mp, int c)
{
    mp_node p; /* first graphical object in |cur_exp| */
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    p = mp_link(mp_edge_list(cur_exp_node));
    if (p != NULL) {
        switch (c) {
            case mp_x_part_operation:
            case mp_y_part_operation:
            case mp_xx_part_operation:
            case mp_xy_part_operation:
            case mp_yx_part_operation:
            case mp_yy_part_operation:
                goto NOT_FOUND;
            case mp_red_part_operation:
            case mp_green_part_operation:
            case mp_blue_part_operation:
                if (mp_has_color(p)) {
                    switch (c) {
                        case mp_red_part_operation:
                            number_clone(new_expr.data.n, ((mp_shape_node) p)->red);
                            break;
                        case mp_green_part_operation:
                            number_clone(new_expr.data.n, ((mp_shape_node) p)->green);
                            break;
                        case mp_blue_part_operation:
                            number_clone(new_expr.data.n, ((mp_shape_node) p)->blue);
                            break;
                    }
                    mp_flush_cur_exp(mp, new_expr);
                } else
                    goto NOT_FOUND;
                break;
            case mp_cyan_part_operation:
            case mp_magenta_part_operation:
            case mp_yellow_part_operation:
            case mp_black_part_operation:
                if (mp_has_color(p)) {
                    if (mp_color_model(p) == mp_uninitialized_model && c == mp_black_part_operation) {
                        set_number_to_unity(new_expr.data.n);
                    } else {
                        switch (c) {
                            case mp_cyan_part_operation:
                                number_clone(new_expr.data.n, ((mp_shape_node) p)->cyan);
                                break;
                            case mp_magenta_part_operation:
                                number_clone(new_expr.data.n, ((mp_shape_node) p)->magenta);
                                break;
                            case mp_yellow_part_operation:
                                number_clone(new_expr.data.n, ((mp_shape_node) p)->yellow);
                                break;
                            case mp_black_part_operation:
                                number_clone(new_expr.data.n, ((mp_shape_node) p)->black);
                                break;
                        }
                    }
                    mp_flush_cur_exp(mp, new_expr);
                } else
                    goto NOT_FOUND;
                break;
            case mp_grey_part_operation:
                if (mp_has_color(p)) {
                    number_clone(new_expr.data.n, ((mp_shape_node) p)->grey);
                    mp_flush_cur_exp(mp, new_expr);
                } else
                    goto NOT_FOUND;
                break;
            case mp_color_model_operation:
                if (mp_has_color(p)) {
                    if (mp_color_model(p) == mp_uninitialized_model) {
                        /* could use the else branch with int variant */
                        number_clone(new_expr.data.n, internal_value(mp_default_color_model_internal));
                    } else {
                        number_clone(new_expr.data.n, unity_t);
                        number_multiply_int(new_expr.data.n, mp_color_model(p));
                    }
                    mp_flush_cur_exp(mp, new_expr);
                } else
                    goto NOT_FOUND;
                break;
            case mp_prescript_part_operation:
                if (! mp_has_script(p)) {
                    goto NOT_FOUND;
                } else {
                    if (mp_pre_script(p)) {
                        new_expr.data.str = mp_pre_script(p);
                        add_str_ref(new_expr.data.str);
                    } else {
                        new_expr.data.str = mp_rts(mp,"");
                    }
                    mp_flush_cur_exp(mp, new_expr);
                    mp->cur_exp.type = mp_string_type;
                };
                break;
            case mp_postscript_part_operation:
                if (! mp_has_script(p)) {
                    goto NOT_FOUND;
                } else {
                    if (mp_post_script(p)) {
                        new_expr.data.str = mp_post_script(p);
                        add_str_ref(new_expr.data.str);
                    } else {
                        new_expr.data.str = mp_rts(mp,"");
                    }
                    mp_flush_cur_exp(mp, new_expr);
                    mp->cur_exp.type = mp_string_type;
                };
                break;
            case mp_stacking_part_operation:
                number_clone(new_expr.data.n, unity_t);
                number_multiply_int(new_expr.data.n, mp_stacking(p));
                mp_flush_cur_exp(mp, new_expr);
                break;
            case mp_path_part_operation:
                if (mp_is_stop(p)) {
                    mp_confusion(mp, "picture");
                } else {
                    new_expr.data.node = NULL;
                    switch (mp_type(p)) {
                        case mp_fill_node_type:
                        case mp_stroked_node_type:
                            new_expr.data.p = mp_copy_path(mp, mp_path_ptr((mp_shape_node) p));
                            break;
                        case mp_start_clip_node_type:
                        case mp_start_group_node_type:
                        case mp_start_bounds_node_type:
                            new_expr.data.p = mp_copy_path(mp, mp_path_ptr((mp_start_node) p));
                            break;
                        default:
                            break;
                    }
                    mp_flush_cur_exp(mp, new_expr);
                    mp->cur_exp.type = mp_path_type;
                }
                break;
            case mp_pen_part_operation:
                if (! mp_has_pen(p)) {
                    goto NOT_FOUND;
                } else {
                    switch (mp_type(p)) {
                        case mp_fill_node_type:
                        case mp_stroked_node_type:
                            if (mp_pen_ptr((mp_shape_node) p) == NULL) {
                                goto NOT_FOUND;
                            } else {
                                new_expr.data.p = mp_copy_pen(mp, mp_pen_ptr((mp_shape_node) p));
                                mp_flush_cur_exp(mp, new_expr);
                                mp->cur_exp.type = mp_pen_type((mp_shape_node) p) ? mp_nep_type : mp_pen_type ;
                            }
                            break;
                        default:
                            break;
                    }
                }
                break;
            case mp_dash_part_operation:
                if (mp_type(p) != mp_stroked_node_type) {
                    goto NOT_FOUND;
                } else if (mp_dash_ptr(p) == NULL) {
                    goto NOT_FOUND;
                } else {
                    mp_add_edge_ref(mp, mp_dash_ptr(p));
                    new_expr.data.node = (mp_node) mp_scale_edges(mp,
                        &(((mp_shape_node) p)->dashscale), (mp_edge_header_node) mp_dash_ptr(p));
                    mp_flush_cur_exp(mp, new_expr);
                    mp->cur_exp.type = mp_picture_type;
                }
                break;
        }
        return;
    };
  NOT_FOUND:
    /* Convert the current expression to a NULL value appropriate for |c| */
    switch (c) {
        case mp_prescript_part_operation:
        case mp_postscript_part_operation:
            new_expr.data.str = mp_rts(mp,"");
            mp_flush_cur_exp(mp, new_expr);
            mp->cur_exp.type = mp_string_type;
            break;
        case mp_path_part_operation:
            new_expr.data.p = mp_new_knot(mp);
            mp_flush_cur_exp(mp, new_expr);
            mp_left_type(cur_exp_knot) = mp_endpoint_knot;
            mp_right_type(cur_exp_knot) = mp_endpoint_knot;
            mp_prev_knot(cur_exp_knot) = cur_exp_knot;
            mp_next_knot(cur_exp_knot) = cur_exp_knot;
            set_number_to_zero(cur_exp_knot->x_coord);
            set_number_to_zero(cur_exp_knot->y_coord);
            mp_originator(cur_exp_knot) = mp_metapost_user;
            mp_knotstate(cur_exp_knot) = mp_regular_knot;
            mp->cur_exp.type = mp_path_type;
            break;
        case mp_pen_part_operation:
            new_expr.data.p = mp_get_pen_circle(mp, &zero_t);
            mp_flush_cur_exp(mp, new_expr);
            mp->cur_exp.type = mp_pen_type; /* todo: mp_nep_type */
            break;
        case mp_dash_part_operation:
            new_expr.data.node = (mp_node) mp_get_edge_header_node(mp);
            mp_flush_cur_exp(mp, new_expr);
            mp_init_edges(mp, (mp_edge_header_node) cur_exp_node);
            mp->cur_exp.type = mp_picture_type;
            break;
        default:
            set_number_to_zero(new_expr.data.n);
            mp_flush_cur_exp(mp, new_expr);
            break;
    }
}

@ This one is stripped because it only handles |ASCII|. Watch out, the |ASCII|
operator only looks at the first character and then just interprets the character
as byte. One can implement a \UTF\ interpreter in \LUA.

@<Declare unary action...@>=
static void mp_str_to_num (MP mp)
{
    /* converts a string to a number */
    int n; /* accumulator */
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    if (cur_exp_str->len == 0) {
       n = -1;
    } else {
       n = cur_exp_str->str[0];
    }
    number_clone(new_expr.data.n, unity_t);
    number_multiply_int(new_expr.data.n, n);
    mp_flush_cur_exp(mp, new_expr);
}

@ This computes the length of the current path or picture. The only benefit from
not using the numbers but a temporary |int| instead is .5K smaller which is due
to less interfacing. But it also demonstrates that on the one hand the number
system indirectness adds quite some bytes but on the other hand todays compilers
do a pretty good job at optimizing (for performance). Which of course doesn't
mean that scaled outperforms double manyfold while decimal is always way slower.

@<Declarations@>=
static void mp_path_length (MP mp, mp_number *n);

@ @<Declare unary action...@>=
static void mp_path_length (MP mp, mp_number *n)
{
    mp_knot p = cur_exp_knot;
    int l = mp_left_type(p) == mp_endpoint_knot ? -1 : 0;
    do {
        p = mp_next_knot(p);
        ++l;
    } while (p != cur_exp_knot);
    set_number_from_int(*n, l);
}

static void mp_picture_length (MP mp, mp_number *n)
{
    /* counts interior components in picture |cur_exp| */
    mp_node p = mp_link(mp_edge_list(cur_exp_node));
    int l = 0;
    if (p != NULL) {
        if (mp_is_start_or_stop(p) && mp_skip_1component(mp, p) == NULL) {
            p = mp_link(p);
        }
        while (p != NULL) {
            if (! mp_is_start_or_stop(p)) {
                p = mp_link(p);
            } else if (! mp_is_stop(p)) {
                p = mp_skip_1component(mp, p);
            } else {
                break;
            }
            ++l;
        }
    }
    set_number_from_int(*n, l);
}

@ The function |an_angle| returns the value of the |angle| primitive, or $0$ if
the argument is |origin|.

@<Declare unary action...@>=
static void mp_an_angle (MP mp, mp_number *ret, mp_number *xpar, mp_number *ypar)
{
    set_number_to_zero(*ret);
    if (! (number_zero(*xpar) && number_zero(*ypar))) {
        n_arg(*ret, *xpar, *ypar);
    }
}

@ The actual turning number is (for the moment) computed in a C function that
receives eight integers corresponding to the four controlling points, and returns
a single angle. Besides those, we have to account for discrete moves at the
actual points.

@d mp_floor(a)  ((a) >= 0 ? (int) (a) : -(int) (-(a)))
@d bezier_error (720*(256*256*16))+1
@d mp_sign(v)   ((v) > 0 ? 1 : ((v)<0 ? -1 : 0 ))
@d mp_out(A)    (double)((A)/16)

@<Declare unary action...@>=
static void mp_bezier_slope (MP mp,
    mp_number *ret, mp_number *AX, mp_number *AY, mp_number *BX,
    mp_number *BY, mp_number *CX, mp_number *CY, mp_number *DX,
    mp_number *DY
);

@ @c
static void mp_bezier_slope (MP mp,
    mp_number *ret, mp_number *AX, mp_number *AY, mp_number *BX,
    mp_number *BY, mp_number *CX, mp_number *CY, mp_number *DX,
    mp_number *DY
)
{
    double a, b, c;
    mp_number deltax, deltay;
    mp_number xi, xo, xm;
    double res = 0.0;
    double ax = number_to_double(*AX);
    double ay = number_to_double(*AY);
    double bx = number_to_double(*BX);
    double by = number_to_double(*BY);
    double cx = number_to_double(*CX);
    double cy = number_to_double(*CY);
    double dx = number_to_double(*DX);
    double dy = number_to_double(*DY);
    new_number(deltax);
    new_number(deltay);
    set_number_from_subtraction(deltax, *BX, *AX);
    set_number_from_subtraction(deltay, *BY, *AY);
    if (number_zero(deltax) && number_zero(deltay)) {
        set_number_from_subtraction(deltax, *CX, *AX);
        set_number_from_subtraction(deltay, *CY, *AY);
    }
    if (number_zero(deltax) && number_zero(deltay)) {
        set_number_from_subtraction(deltax, *DX, *AX);
        set_number_from_subtraction(deltay, *DY, *AY);
    }
    new_number(xi);
    new_number(xm);
    new_number(xo);
    mp_an_angle(mp, &xi, &deltax, &deltay);
    set_number_from_subtraction(deltax, *CX, *BX);
    set_number_from_subtraction(deltay, *CY, *BY);
    mp_an_angle(mp, &xm, &deltax, &deltay); /* !!! never used? */
    set_number_from_subtraction(deltax, *DX, *CX);
    set_number_from_subtraction(deltay, *DY, *CY);
    if (number_zero(deltax) && number_zero(deltay)) {
        set_number_from_subtraction(deltax, *DX, *BX);
        set_number_from_subtraction(deltay, *DY, *BY);
    }
    if (number_zero(deltax) && number_zero(deltay)) {
        set_number_from_subtraction(deltax, *DX, *AX);
        set_number_from_subtraction(deltay, *DY, *AY);
    }
    mp_an_angle(mp, &xo, &deltax, &deltay);
    a = (bx - ax) * (cy - by) - (cx - bx) * (by - ay); /* a = (bp-ap)x(cp-bp); */
    b = (bx - ax) * (dy - cy) - (by - ay) * (dx - cx); /* b = (bp-ap)x(dp-cp); */
    c = (cx - bx) * (dy - cy) - (dx - cx) * (cy - by); /* c = (cp-bp)x(dp-cp); */
    if ((a == 0.0) && (c == 0.0)) {
        res = (b == 0.0 ? 0.0 : (mp_out(number_to_double(xo)) - mp_out(number_to_double(xi))));
    } else if ((a == 0.0) || (c == 0.0)) {
        if ((mp_sign (b) == mp_sign (a)) || (mp_sign (b) == mp_sign (c))) {
            res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi)); /* ? */
            if (res < -180.0) {
                res += 360.0;
            } else if (res > 180.0) {
                res -= 360.0;
            }
        } else {
            res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi)); /* ? */
        }
    } else if ((mp_sign (a) * mp_sign (c)) < 0.0) {
        res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi));
        if (res < -180.0) {
            res += 360.0;
        } else if (res > 180.0) {
            res -= 360.0;
        }
    } else if (mp_sign (a) == mp_sign (b)) {
        res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi));
        if (res < -180.0) {
            res += 360.0;
        } else if (res > 180.0) {
            res -= 360.0;
        }
    } else if ((b * b) == (4.0 * a * c)) {
        res = (double) bezier_error;
    } else if ((b * b) < (4.0 * a * c)) {
        res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi));
        if (res <= 0.0 && res > -180.0) {
            res += 360.0;
        } else if (res >= 0.0 && res < 180.0) {
            res -= 360.0;
        }
    } else {
        res = mp_out(number_to_double(xo)) - mp_out(number_to_double(xi));
        if (res < -180.0) {
            res += 360.0;
        } else if (res > 180.0) {
            res -= 360.0;
        }
    }
    free_number(deltax);
    free_number(deltay);
    free_number(xi);
    free_number(xo);
    free_number(xm);
    set_number_from_double(*ret, res);
    convert_scaled_to_angle(*ret);
}

@d p_nextnext mp_next_knot(mp_next_knot(p))
@d p_next mp_next_knot(p)

@<Declare unary action...@>=
static void mp_turn_cycles (MP mp, mp_number *turns, mp_knot c)
{
    int selector;                 /* saved |selector| setting */
    mp_angle res, ang;            /* the angles of intermediate results */
    mp_knot p;                    /* for running around the path */
    mp_number xp, yp;             /* coordinates of next point */
    mp_number x, y;               /* helper coordinates */
    mp_number arg1, arg2;
    mp_angle in_angle, out_angle; /* helper angles */
    mp_angle seven_twenty_deg_t;
    set_number_to_zero(*turns);
    new_number(arg1);
    new_number(arg2);
    new_number(xp);
    new_number(yp);
    new_number(x);
    new_number(y);
    new_angle(in_angle);
    new_angle(out_angle);
    new_angle(ang);
    new_angle(res);
    new_angle(seven_twenty_deg_t);
    number_clone(seven_twenty_deg_t, three_sixty_deg_t);
    number_double(seven_twenty_deg_t);
    p = c;
    selector = mp->selector;
    mp->selector = mp_term_only_selector;
    if (number_greater(internal_value(mp_tracing_commands_internal), unity_t)) {
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "");
        mp_end_diagnostic(mp, 0);
    }
    do {
        number_clone(xp, p_next->x_coord);
        number_clone(yp, p_next->y_coord);
        mp_bezier_slope(mp, &ang, &(p->x_coord),  &(p->y_coord), &(p->right_x), &(p->right_y), &(p_next->left_x), &(p_next->left_y), &xp, &yp);
        if (number_greater(ang, seven_twenty_deg_t)) {
            mp_error(mp, "Strange path", NULL);
            mp->selector = selector;
            set_number_to_zero(*turns);
            goto DONE;
        }
        number_add(res, ang);
        if (number_greater(res, one_eighty_deg_t)) {
            number_subtract(res, three_sixty_deg_t);
            number_add(*turns, unity_t);
        }
        if (number_lessequal(res, negative_one_eighty_deg_t)) {
            number_add(res, three_sixty_deg_t);
            number_subtract(*turns, unity_t);
        }
        /* incoming angle at next point */
        number_clone(x, p_next->left_x);
        number_clone(y, p_next->left_y);
        if (number_equal(xp, x) && number_equal(yp, y)) {
            number_clone(x, p->right_x);
            number_clone(y, p->right_y);
        }
        if (number_equal(xp, x) && number_equal(yp, y)) {
            number_clone(x, p->x_coord);
            number_clone(y, p->y_coord);
        }
        set_number_from_subtraction(arg1, xp, x);
        set_number_from_subtraction(arg2, yp, y);
        mp_an_angle(mp, &in_angle, &arg1, &arg2);
        /* outgoing angle at next point */
        number_clone(x, p_next->right_x);
        number_clone(y, p_next->right_y);
        if (number_equal(xp, x) && number_equal(yp, y)) {
            number_clone(x, p_nextnext->left_x);
            number_clone(y, p_nextnext->left_y);
        }
        if (number_equal(xp, x) && number_equal(yp, y)) {
            number_clone(x, p_nextnext->x_coord);
            number_clone(y, p_nextnext->y_coord);
        }
        set_number_from_subtraction(arg1, x, xp);
        set_number_from_subtraction(arg2, y, yp);
        mp_an_angle(mp, &out_angle, &arg1, &arg2);
        set_number_from_subtraction(ang, out_angle, in_angle);
        mp_reduce_angle(mp, &ang);
        if (number_nonzero(ang)) {
            number_add(res, ang);
            if (number_greaterequal(res, one_eighty_deg_t)) {
                number_subtract(res, three_sixty_deg_t);
                number_add(*turns, unity_t);
            }
            if (number_lessequal(res, negative_one_eighty_deg_t)) {
                number_add(res, three_sixty_deg_t);
                number_subtract(*turns, unity_t);
            }
        }
        p = mp_next_knot(p);
    } while (p != c);
    mp->selector = selector;
  DONE:
    free_number(xp);
    free_number(yp);
    free_number(x);
    free_number(y);
    free_number(seven_twenty_deg_t);
    free_number(in_angle);
    free_number(out_angle);
    free_number(ang);
    free_number(res);
    free_number(arg1);
    free_number(arg2);
}

@ @<Declare unary action...@>=
static void mp_turn_cycles_wrapper (MP mp, mp_number *ret, mp_knot c)
{
    if (mp_next_knot(c) == c) {
        /* one-knot paths always have a turning number of 1 */
        set_number_to_unity(*ret);
    } else {
        mp_turn_cycles (mp, ret, c);
    }
}

@ @<Declare unary action procedures@>=
static int mp_test_known (MP mp, int c)
{
    int b = mp_false_operation; /* is the current expression known? */
    switch (mp->cur_exp.type) {
        case mp_vacuous_type:
        case mp_boolean_type:
        case mp_string_type:
        case mp_pen_type:
        case mp_nep_type:
        case mp_path_type:
        case mp_picture_type:
        case mp_known_type:
            b = mp_true_operation;
            break;
        case mp_transform_type:
            {
                mp_node p = mp_get_value_node(cur_exp_node);
                if ( (mp_type(mp_tx_part(p)) == mp_known_type) &&
                     (mp_type(mp_ty_part(p)) == mp_known_type) &&
                     (mp_type(mp_xx_part(p)) == mp_known_type) &&
                     (mp_type(mp_xy_part(p)) == mp_known_type) &&
                     (mp_type(mp_yx_part(p)) == mp_known_type) &&
                     (mp_type(mp_yy_part(p)) == mp_known_type) ) {
                    b = mp_true_operation;
                }
            }
            break;
        case mp_color_type:
            {
                mp_node p = mp_get_value_node(cur_exp_node);
                if ( (mp_type(mp_red_part(p))   == mp_known_type) &&
                     (mp_type(mp_green_part(p)) == mp_known_type) &&
                     (mp_type(mp_blue_part(p))  == mp_known_type) ) {
                    b = mp_true_operation;
                }
            }
            break;
        case mp_cmykcolor_type:
            {
                mp_node p = mp_get_value_node(cur_exp_node);
                if ( (mp_type(mp_cyan_part(p))    == mp_known_type) &&
                     (mp_type(mp_magenta_part(p)) == mp_known_type) &&
                     (mp_type(mp_yellow_part(p))  == mp_known_type) &&
                     (mp_type(mp_black_part(p))   == mp_known_type) ) {
                    b = mp_true_operation;
                }
            }
            break;
        case mp_pair_type:
            {
                mp_node p = mp_get_value_node(cur_exp_node);
                if ( (mp_type(mp_x_part(p)) == mp_known_type) &&
                     (mp_type(mp_y_part(p)) == mp_known_type) ) {
                    b = mp_true_operation;
                }
            }
            break;
        default:
            break;
    }
    if (c == mp_known_operation) {
        return b;
    } else {
        return b == mp_true_operation ? mp_false_operation : mp_true_operation;
    }
}

@ The |pair_value| routine changes the current expression to a given ordered pair
of values.

@<Declarations@>=
static void mp_pair_value (MP mp, mp_number *x, mp_number *y);

@ @<Declare unary action procedures@>=
static void mp_pair_value (MP mp, mp_number *x, mp_number *y)
{
    mp_node p; /* a pair node */
    mp_value new_expr;
    mp_number x1, y1;
    new_number_clone(x1, *x);
    new_number_clone(y1, *y);
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    p = mp_new_value_node(mp);
    new_expr.type = mp_type(p);
    new_expr.data.node = p;
    mp_flush_cur_exp(mp, new_expr);
    mp->cur_exp.type = mp_pair_type;
    mp_name_type(p) = mp_capsule_operation;
    mp_init_pair_node(mp, p);
    p = mp_get_value_node(p);
    mp_type(mp_x_part(p)) = mp_known_type;
    mp_set_value_number(mp_x_part(p), x1);
    mp_type(mp_y_part(p)) = mp_known_type;
    mp_set_value_number(mp_y_part(p), y1);
    free_number(x1);
    free_number(y1);
}

@ Here is a function that sets |minx|, |maxx|, |miny|, |maxy| to the bounding
box of the current expression.  The boolean result is |false| if the expression
has the wrong type.

@<Declare unary action procedures@>=
static int mp_get_cur_bbox (MP mp)
{
    switch (mp->cur_exp.type) {
        case mp_picture_type:
            {
                mp_edge_header_node p = (mp_edge_header_node) cur_exp_node;
                mp_set_bbox(mp, p, 1);
                if (number_greater(p->minx, p->maxx)) {
                    set_number_to_zero(mp_minx);
                    set_number_to_zero(mp_maxx);
                    set_number_to_zero(mp_miny);
                    set_number_to_zero(mp_maxy);
                } else {
                    number_clone(mp_minx, p->minx);
                    number_clone(mp_maxx, p->maxx);
                    number_clone(mp_miny, p->miny);
                    number_clone(mp_maxy, p->maxy);
                }
            }
            break;
        case mp_path_type:
            mp_path_bbox(mp, cur_exp_knot);
            break;
        case mp_pen_type:
        case mp_nep_type:
            mp_pen_bbox(mp, cur_exp_knot);
            break;
        default:
            return 0;
    }
    return 1;
}

static int mp_get_cur_xbox (MP mp)
{
    if (mp->cur_exp.type == mp_path_type) {
        mp_path_xbox(mp, cur_exp_knot);
        return 1;
    } else {
        return mp_get_cur_bbox(mp);
    }
}

static int mp_get_cur_ybox (MP mp)
{
    if (mp->cur_exp.type == mp_path_type) {
        mp_path_ybox(mp, cur_exp_knot);
        return 1;
    } else {
        return mp_get_cur_bbox(mp);
    }
}

@ Here is a routine that interprets |cur_exp| as a file name and tries to read a
line from the file or to close the file.

@<Declare unary action procedures@>=
static void mp_do_read_or_close (MP mp, int c)
{
    int n = mp->read_files;
    int n0 = mp->read_files;
    char *fn = mp_strdup(mp_str(mp, cur_exp_str));
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    /*
        Find the |n| where |rd_fname[n]=cur_exp|; if |cur_exp| must be inserted,
        call |start_read_input| and |goto found| or |not_found|. Free slots in
        the |rd_file| and |rd_fname| arrays are marked with NULL's in |rd_fname|.
    */
    while (mp_strcmp(fn, mp->rd_fname[n]) != 0) {
        if (n > 0) {
            --n;
        } else if (c == mp_close_from_operation) {
            goto CLOSE_FILE;
        } else {
            if (n0 == mp->read_files) {
                if (mp->read_files < mp->max_read_files) {
                    ++mp->read_files;
                } else {
                    void **rd_file;
                    char **rd_fname;
                    int l;
                    l = mp->max_read_files + (mp->max_read_files / 4);
                    rd_file = mp_memory_allocate((size_t) (l + 1) * sizeof(void *));
                    rd_fname = mp_memory_allocate((size_t) (l + 1) * sizeof(char *));
                    for (int k = 0; k <= l; k++) {
                        if (k <= mp->max_read_files) {
                            rd_file[k] = mp->rd_file[k];
                            rd_fname[k] = mp->rd_fname[k];
                        } else {
                            rd_file[k] = 0;
                            rd_fname[k] = NULL;
                        }
                    }
                    mp_memory_free(mp->rd_file);
                    mp_memory_free(mp->rd_fname);
                    mp->max_read_files = l;
                    mp->rd_file = rd_file;
                    mp->rd_fname = rd_fname;
                }
            }
            n = n0;
            if (mp_start_read_input(mp, fn, n)) {
                goto FOUND;
            } else {
                goto NOT_FOUND;
            }
        }
        if (mp->rd_fname[n] == NULL) {
            n0 = n;
        }
    }
    if (c == mp_close_from_operation) {
        (mp->close_file) (mp, mp->rd_file[n]);
        goto NOT_FOUND;
    }
    mp_begin_file_reading(mp);
    name = is_read;
    if (mp_input_ln(mp, mp->rd_file[n])) {
        goto FOUND;
    }
    mp_end_file_reading(mp);
  NOT_FOUND:
    /* Record the end of file and set |cur_exp| to a dummy value    */
    mp_memory_free(mp->rd_fname[n]);
    mp->rd_fname[n] = NULL;
    if (n == mp->read_files - 1) {
        mp->read_files = n;
    }
    if (c == mp_close_from_operation) {
        goto CLOSE_FILE;
    }
 // new_expr.data.str = mp->eof_line;
    new_expr.data.str = mp->eof_file;
    add_str_ref(new_expr.data.str);
    mp_flush_cur_exp(mp, new_expr);
    mp->cur_exp.type = mp_string_type;
    return;
  CLOSE_FILE:
    mp_flush_cur_exp(mp, new_expr);
    mp->cur_exp.type = mp_vacuous_type;
    return;
  FOUND:
    mp_flush_cur_exp(mp, new_expr);
    mp_finish_read(mp);
}

@ The string denoting end-of-file is a one-byte string at position zero, by
definition. I have to cheat a little here because

@<Glob...@>=
mp_string eof_line;
mp_string eof_file;

@ @<Set init...@>=
mp->eof_line = mp_rtsl (mp, "\0", 1);
mp->eof_line->refs = MAX_STR_REF;
mp->eof_file = mp_rtsl (mp, "%", 1);
mp->eof_file->refs = MAX_STR_REF;

@ Finally, we have the operations that combine a capsule~|p| with the current
expression.

Several of the binary operations are potentially complicated by the fact that
|independent| values can sneak into capsules. For example, we've seen an instance
of this difficulty in the unary operation of negation. In order to reduce the
number of cases that need to be handled, we first change the two operands (if
necessary) to rid them of |independent| components. The original operands are put
into capsules called |old_p| and |old_exp|, which will be recycled after the
binary operation has been safely carried out.

@c
@<Declare binary action procedures@>
static void mp_finish_binary (MP mp, mp_node old_p, mp_node old_exp)
{
    check_arith();
    /* Recycle any sidestepped |independent| capsules */
    if (old_p != NULL) {
        mp_recycle_value(mp, old_p);
        mp_free_value_node(mp, old_p);
    }
    if (old_exp != NULL) {
        mp_recycle_value(mp, old_exp);
        mp_free_value_node(mp, old_exp);
    }
}

static void mp_do_binary (MP mp, mp_node p, int c)
{
    mp_node old_p, old_exp; /* capsules to recycle */
    mp_value new_expr;
    check_arith();
    if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
        /* Trace the current binary operation */
        mp_begin_diagnostic(mp);
        mp_print_nl(mp, "{(");
        /* show the operand, but not verbosely */
        mp_print_exp(mp, p, 0);
        mp_print_chr(mp, ')');
        mp_print_op(mp, (int) c);
        mp_print_chr(mp, '(');
        mp_print_exp(mp, NULL, 0);
        mp_print_str(mp, ")}");
        mp_end_diagnostic(mp, 0);
    }
    /*
        Sidestep |independent| cases in capsule |p|. A big node is considered to be
        \quote {tarnished} if it contains at least one independent component. We will
        define a simple function called |tarnished| that returns |NULL| if and only
        if its argument is not tarnished.
    */
    switch (mp_type(p)) {
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
            old_p = mp_tarnished(mp, p);
            break;
        case mp_independent_type:
            old_p = MP_VOID;
            break;
        default:
            old_p = NULL;
            break;
    }
    if (old_p != NULL) {
        mp_node q = mp_stash_cur_exp(mp);
        old_p = p;
        mp_make_exp_copy(mp, old_p);
        p = mp_stash_cur_exp(mp);
        mp_unstash_cur_exp(mp, q);
    }
    /* Sidestep |independent| cases in the current expression */
    switch (mp->cur_exp.type) {
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
            old_exp = mp_tarnished(mp, cur_exp_node);
            break;
        case mp_independent_type:
            old_exp = MP_VOID;
            break;
        default:
            old_exp = NULL;
            break;
    }
    if (old_exp != NULL) {
        old_exp = cur_exp_node;
        mp_make_exp_copy(mp, old_exp);
    }
    switch (c) {
        case mp_plus_operation:
        case mp_minus_operation:
            /* Add or subtract the current expression from |p| */
            if ((mp->cur_exp.type < mp_color_type) || (mp_type(p) < mp_color_type)) {
                mp_bad_binary(mp, p, c);
            } else {
                if ((mp->cur_exp.type > mp_pair_type) && (mp_type(p) > mp_pair_type)) {
                    mp_add_or_subtract(mp, p, NULL, c);
                } else if (mp->cur_exp.type != mp_type(p)) {
                    /*
                        We catch a mismatch, so we can handle intermediates (assuming a flexible withcolor);
                        if we would go double only live would be easier ... I might eventually make a more
                        generic color type.
                    */
                    /*
                    if (mp->cur_exp.type == mp_color_type && mp_type(p) == mp_cmykcolor_type) {
                        mp_node q = mp_get_value_node(p);
                        mp_node r = mp_get_value_node(cur_exp_node);
                        number_negate((mp_cyan_part(q))->data.n);
                        number_negate((mp_magenta_part(q))->data.n);
                        number_negate((mp_yellow_part(q))->data.n);
                        number_add((mp_cyan_part(q))->data.n, unity_t);
                        number_add((mp_magenta_part(q))->data.n, unity_t);
                        number_add((mp_yellow_part(q))->data.n, unity_t);
                        mp_add_or_subtract(mp, mp_cyan_part(q), mp_red_part(r), c);
                        mp_add_or_subtract(mp, mp_magenta_part(q), mp_green_part(r), c);
                        mp_add_or_subtract(mp, mp_yellow_part(q), mp_blue_part(r), c);
                    } else if (mp->cur_exp.type == mp_cmykcolor_type && mp_type(p) == mp_color_type) {
                        mp_node q = mp_get_value_node(p);
                        mp_node r = mp_get_value_node(cur_exp_node);
                        number_negate((mp_red_part(q))->data.n);
                        number_negate((mp_green_part(q))->data.n);
                        number_negate((mp_blue_part(q))->data.n);
                        number_add((mp_red_part(q))->data.n, unity_t);
                        number_add((mp_green_part(q))->data.n, unity_t);
                        number_add((mp_blue_part(q))->data.n, unity_t);
                        mp_add_or_subtract(mp, mp_red_part(q), mp_cyan_part(r), c);
                        mp_add_or_subtract(mp, mp_green_part(q), mp_magenta_part(r), c);
                        mp_add_or_subtract(mp, mp_blue_part(q), mp_yellow_part(r), c);
                     } else {
                  */
                        mp_bad_binary(mp, p, c);
                  /* } */
               } else {
                    mp_node q = mp_get_value_node(p);
                    mp_node r = mp_get_value_node(cur_exp_node);
                    switch (mp->cur_exp.type) {
                        case mp_pair_type:
                            mp_add_or_subtract(mp, mp_x_part(q), mp_x_part(r), c);
                            mp_add_or_subtract(mp, mp_y_part(q), mp_y_part(r), c);
                            break;
                        case mp_color_type:
                            mp_add_or_subtract(mp, mp_red_part(q), mp_red_part(r), c);
                            mp_add_or_subtract(mp, mp_green_part(q), mp_green_part(r), c);
                            mp_add_or_subtract(mp, mp_blue_part(q), mp_blue_part(r), c);
                            break;
                        case mp_cmykcolor_type:
                            mp_add_or_subtract(mp, mp_cyan_part(q), mp_cyan_part(r), c);
                            mp_add_or_subtract(mp, mp_magenta_part(q), mp_magenta_part(r), c);
                            mp_add_or_subtract(mp, mp_yellow_part(q), mp_yellow_part(r), c);
                            mp_add_or_subtract(mp, mp_black_part(q), mp_black_part(r), c);
                            break;
                        case mp_transform_type:
                            mp_add_or_subtract(mp, mp_tx_part(q), mp_tx_part(r), c);
                            mp_add_or_subtract(mp, mp_ty_part(q), mp_ty_part(r), c);
                            mp_add_or_subtract(mp, mp_xx_part(q), mp_xx_part(r), c);
                            mp_add_or_subtract(mp, mp_xy_part(q), mp_xy_part(r), c);
                            mp_add_or_subtract(mp, mp_yx_part(q), mp_yx_part(r), c);
                            mp_add_or_subtract(mp, mp_yy_part(q), mp_yy_part(r), c);
                            break;
                        default:
                            break;
                    }
                }
            }
            break;
        case mp_less_than_operation:
        case mp_less_or_equal_operation:
        case mp_greater_than_operation:
        case mp_greater_or_equal_operation:
        case mp_equal_operation:
        case mp_unequal_operation:
            check_arith();
            /* at this point |arith_error| should be |false|? */
            if ((mp->cur_exp.type > mp_pair_type) && (mp_type(p) > mp_pair_type)) {
                /* |cur_exp:=(p)-cur_exp| */
                mp_add_or_subtract(mp, p, NULL, mp_minus_operation);
            } else if (mp->cur_exp.type != mp_type(p)) {
                mp_bad_binary(mp, p, (int) c);
                goto DONE;
            } else {
                /*
                    Reduce comparison of big nodes to comparison of scalars. In the
                    following, the |while| loops exist just so that |break| can be
                    used, each loop runs exactly once.
                */
                switch (mp->cur_exp.type) {
                    case mp_string_type:
                        {
                            memset(&new_expr, 0, sizeof(mp_value));
                            new_number(new_expr.data.n);
                            set_number_from_scaled(new_expr.data.n, mp_str_vs_str(mp, mp_get_value_str(p), cur_exp_str));
                            mp_flush_cur_exp(mp, new_expr);
                        }
                        break;
                    case mp_unknown_string_type:
                    case mp_unknown_boolean_type:
                        {
                            /*
                                Check if unknowns have been equated. When two unknown strings are
                                in the same ring, we know that they are equal. Otherwise, we
                                don't know whether they are equal or not, so we make no change.
                            */
                            mp_node q = mp_get_value_node(cur_exp_node);
                            while ((q != cur_exp_node) && (q != p)) {
                                q = mp_get_value_node(q);
                            }
                            if (q == p) {
                                memset(&new_expr, 0, sizeof(mp_value));
                                new_number(new_expr.data.n);
                                mp_set_cur_exp_node(mp, NULL);
                                mp_flush_cur_exp(mp, new_expr);
                            }
                        }
                        break;
                    case mp_pair_type:
                        {
                            int part_type = 0;
                            mp_node q = mp_get_value_node(p);
                            mp_node r = mp_get_value_node(cur_exp_node);
                            while (part_type == 0) {
                                mp_node rr = mp_x_part(r);
                                part_type = mp_x_part_operation;
                                mp_add_or_subtract(mp, mp_x_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_y_part(r);
                                part_type = mp_y_part_operation;
                                mp_add_or_subtract(mp, mp_y_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                            }
                            mp_take_part(mp, part_type);
                        }
                        break;
                    case mp_color_type:
                        {
                            int part_type = 0;
                            mp_node q = mp_get_value_node(p);
                            mp_node r = mp_get_value_node(cur_exp_node);
                            while (part_type == 0) {
                                mp_node rr = mp_red_part(r);
                                part_type = mp_red_part_operation;
                                mp_add_or_subtract(mp, mp_red_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_green_part(r);
                                part_type = mp_green_part_operation;
                                mp_add_or_subtract(mp, mp_green_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_blue_part(r);
                                part_type = mp_blue_part_operation;
                                mp_add_or_subtract(mp, mp_blue_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                            }
                            mp_take_part(mp, part_type);
                        }
                        break;
                    case mp_cmykcolor_type:
                        {
                            int part_type = 0;
                            mp_node q = mp_get_value_node(p);
                            mp_node r = mp_get_value_node(cur_exp_node);
                            while (part_type == 0) {
                                mp_node rr = mp_cyan_part(r);
                                part_type = mp_cyan_part_operation;
                                mp_add_or_subtract(mp, mp_cyan_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_magenta_part(r);
                                part_type = mp_magenta_part_operation;
                                mp_add_or_subtract(mp, mp_magenta_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_yellow_part(r);
                                part_type = mp_yellow_part_operation;
                                mp_add_or_subtract(mp, mp_yellow_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_black_part(r);
                                part_type = mp_black_part_operation;
                                mp_add_or_subtract(mp, mp_black_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                            }
                            mp_take_part(mp, part_type);
                        }
                        break;
                    case mp_transform_type:
                        {
                            int part_type = 0;
                            mp_node q = mp_get_value_node(p);
                            mp_node r = mp_get_value_node(cur_exp_node);
                            while (part_type == 0) {
                                mp_node rr = mp_tx_part(r);
                                part_type = mp_x_part_operation;
                                mp_add_or_subtract(mp, mp_tx_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_ty_part(r);
                                part_type = mp_y_part_operation;
                                mp_add_or_subtract(mp, mp_ty_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_xx_part(r);
                                part_type = mp_xx_part_operation;
                                mp_add_or_subtract(mp, mp_xx_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_xy_part(r);
                                part_type = mp_xy_part_operation;
                                mp_add_or_subtract(mp, mp_xy_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_yx_part(r);
                                part_type = mp_yx_part_operation;
                                mp_add_or_subtract(mp, mp_yx_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                                rr = mp_yy_part(r);
                                part_type = mp_yy_part_operation;
                                mp_add_or_subtract(mp, mp_yy_part(q), rr, mp_minus_operation);
                                if (mp_type(rr) != mp_known_type || ! number_zero(mp_get_value_number(rr))) {
                                    break;
                                }
                            }
                            mp_take_part(mp, part_type);
                        }
                        break;
                    case mp_boolean_type:
                        {
                            memset(&new_expr, 0, sizeof(mp_value));
                            new_number(new_expr.data.n);
                            set_number_from_boolean(new_expr.data.n, number_to_scaled(cur_exp_value_number) - number_to_scaled(mp_get_value_number(p)));
                            mp_flush_cur_exp(mp, new_expr);
                        }
                        break;
                    default:
                        mp_bad_binary(mp, p, (int) c);
                        goto DONE;
                        break;
                }
            }
            /* Compare the current expression with zero */
            if (mp->cur_exp.type != mp_known_type) {
                const char *hlp = NULL;
                if (mp->cur_exp.type < mp_known_type) {
                    mp_disp_err(mp, p);
                    hlp = "The quantities shown above have not been equated.";
                } else {
                    hlp =
                        "Oh dear. I can't decide if the expression above is positive, negative, or zero.\n"
                        "So this comparison test won't be 'true'.";
                }
                mp_disp_err(mp, NULL);
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                set_number_from_boolean(new_expr.data.n, mp_false_operation);
                mp_back_error(mp, "Unknown relation will be considered false", hlp);
                @.Unknown relation...@>
                mp_get_x_next(mp);
                mp_flush_cur_exp(mp, new_expr);
            } else {
                int b = 0;
                switch (c) {
                    case mp_less_than_operation:
                        b = number_negative(cur_exp_value_number);
                        break;
                    case mp_less_or_equal_operation:
                        b = number_nonpositive(cur_exp_value_number);
                        break;
                    case mp_greater_than_operation:
                        b = number_positive(cur_exp_value_number);
                        break;
                    case mp_greater_or_equal_operation:
                        b = number_nonnegative(cur_exp_value_number);
                        break;
                    case mp_equal_operation:
                        b = number_zero(cur_exp_value_number);
                        break;
                    case mp_unequal_operation:
                        b = number_nonzero(cur_exp_value_number);
                        break;
                };
                mp_set_cur_exp_value_boolean(mp, b ? mp_true_operation : mp_false_operation);
            }
            mp->cur_exp.type = mp_boolean_type;
          DONE:
            /* ignore overflow in comparisons */
            mp->arith_error = 0;
            break;
        case mp_and_operation:
        case mp_or_operation:
            /* Here we use the sneaky fact that |and_op-false_code=or_op-true_code| */
            if ((mp_type(p) != mp_boolean_type) || (mp->cur_exp.type != mp_boolean_type)) {
                mp_bad_binary(mp, p, (int) c);
            } else if (number_to_boolean(p->data.n) == c + mp_false_operation - mp_and_operation) {
                mp_set_cur_exp_value_boolean(mp, number_to_boolean(p->data.n));
            }
            break;
        case mp_times_operation:
            if ((mp->cur_exp.type < mp_color_type) || (mp_type(p) < mp_color_type)) {
                mp_bad_binary(mp, p, mp_times_operation);
            } else if ((mp->cur_exp.type == mp_known_type) || (mp_type(p) == mp_known_type)) {
                /* Multiply when at least one operand is known */
                mp_number vv;
                new_fraction(vv);
                if (mp_type(p) == mp_known_type) {
                    number_clone(vv, mp_get_value_number(p));
                    mp_free_value_node(mp, p);
                } else {
                    number_clone(vv, cur_exp_value_number);
                    mp_unstash_cur_exp(mp, p);
                }
                switch (mp->cur_exp.type) {
                    case mp_known_type:
                        {
                            mp_number ret;
                            new_number(ret);
                            take_scaled(ret, cur_exp_value_number, vv);
                            mp_set_cur_exp_value_number(mp, &ret);
                            free_number(ret);
                        }
                        break;
                    case mp_pair_type:
                        {
                            mp_dep_mult(mp, (mp_value_node) mp_x_part(mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_y_part(mp_get_value_node(cur_exp_node)), &vv, 1);
                        }
                        break;
                    case mp_color_type:
                        {
                            mp_dep_mult(mp, (mp_value_node) mp_red_part  (mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_green_part(mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_blue_part (mp_get_value_node(cur_exp_node)), &vv, 1);
                        }
                        break;
                    case mp_cmykcolor_type:
                        {
                            mp_dep_mult(mp, (mp_value_node) mp_cyan_part   (mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_magenta_part(mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_yellow_part (mp_get_value_node(cur_exp_node)), &vv, 1);
                            mp_dep_mult(mp, (mp_value_node) mp_black_part  (mp_get_value_node(cur_exp_node)), &vv, 1);
                        }
                        break;
                    default:
                        {
                            mp_dep_mult(mp, NULL, &vv, 1);
                        }
                        break;
                }
                free_number(vv);
                mp_finish_binary(mp, old_p, old_exp);
                return;
            } else if ((mp_nice_color_or_pair(mp, p, mp_type(p))                  && (mp->cur_exp.type > mp_pair_type))
                    || (mp_nice_color_or_pair(mp, cur_exp_node, mp->cur_exp.type) && (mp_type(p)       > mp_pair_type))) {
                mp_hard_times(mp, p);
                mp_finish_binary(mp, old_p, old_exp);
                return;
            } else {
                mp_bad_binary(mp, p, mp_times_operation);
            }
            break;
        case mp_over_operation:
            if ((mp->cur_exp.type != mp_known_type) || (mp_type(p) < mp_color_type)) {
                mp_bad_binary(mp, p, mp_over_operation);
            } else {
                mp_number v_n;
                new_number_clone(v_n, cur_exp_value_number);
                mp_unstash_cur_exp(mp, p);
                if (number_zero(v_n)) {
                    /* Squeal about division by zero */
                    mp_disp_err(mp, NULL);
                    mp_back_error(
                        mp,
                        "Division by zero",
                        "You're trying to divide the quantity shown above the error message by zero. I'm\n"
                        "going to divide it by one instead."
                    );
                    mp_get_x_next(mp);
                } else {
                    switch (mp->cur_exp.type) {
                        case mp_known_type:
                            {
                                mp_number ret;
                                new_number(ret);
                                make_scaled(ret, cur_exp_value_number, v_n);
                                mp_set_cur_exp_value_number(mp, &ret);
                                free_number(ret);
                            }
                            break;
                        case mp_pair_type:
                            {
                                mp_dep_div(mp, (mp_value_node) mp_x_part(mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_y_part(mp_get_value_node(cur_exp_node)), &v_n);
                            }
                            break;
                        case mp_color_type:
                            {
                                mp_dep_div(mp, (mp_value_node) mp_red_part  (mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_green_part(mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_blue_part (mp_get_value_node(cur_exp_node)), &v_n);
                            }
                            break;
                        case mp_cmykcolor_type:
                            {
                                mp_dep_div(mp, (mp_value_node) mp_cyan_part   (mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_magenta_part(mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_yellow_part (mp_get_value_node(cur_exp_node)), &v_n);
                                mp_dep_div(mp, (mp_value_node) mp_black_part  (mp_get_value_node(cur_exp_node)), &v_n);
                            }
                            break;
                        default:
                            {
                                mp_dep_div(mp, NULL, &v_n);
                            }
                            break;
                    }
                }
                free_number(v_n);
                mp_finish_binary(mp, old_p, old_exp);
                return;
            }
            break;
        case mp_power_operation:
            if ((mp->cur_exp.type == mp_known_type) && (mp_type(p) == mp_known_type)) {
                mp_number r;
                new_number(r);
                power_of(r, mp_get_value_number(p), cur_exp_value_number);
                check_arith();
                mp_set_cur_exp_value_number(mp, &r);
                free_number(r);
            } else
                mp_bad_binary(mp, p, (int) c);
            break;
        case mp_pythag_add_operation:
        case mp_pythag_sub_operation:
            if ((mp->cur_exp.type == mp_known_type) && (mp_type(p) == mp_known_type)) {
                mp_number r;
                new_number(r);
                if (c == mp_pythag_add_operation) {
                    pyth_add(r, mp_get_value_number(p), cur_exp_value_number);
                } else {
                    pyth_sub(r, mp_get_value_number(p), cur_exp_value_number);
                }
                mp_set_cur_exp_value_number(mp, &r);
                free_number(r);
            } else
                mp_bad_binary(mp, p, (int) c);
            break;
        case mp_rotated_operation:
        case mp_slanted_operation:
        case mp_scaled_operation:
        case mp_shifted_operation:
        case mp_transformed_operation:
        case mp_x_scaled_operation:
        case mp_y_scaled_operation:
        case mp_z_scaled_operation:
            /*
                The next few sections of the program deal with affine transformations
                of coordinate data.
            */
            switch (mp_type(p)) {
                case mp_path_type:
                    mp_set_up_known_trans(mp, (int) c);
                    mp_unstash_cur_exp(mp, p);
                    mp_do_path_trans(mp, cur_exp_knot);
                    mp_finish_binary(mp, old_p, old_exp);
                    return;
                case mp_pen_type:
                    mp_set_up_known_trans(mp, (int) c);
                    mp_unstash_cur_exp(mp, p);
                    mp_do_pen_trans(mp, cur_exp_knot);
                    /* rounding error could destroy convexity */
                    mp_set_cur_exp_knot(mp, mp_convex_hull(mp, cur_exp_knot));
                    mp_finish_binary(mp, old_p, old_exp);
                    return;
                case mp_nep_type:
                    mp_set_up_known_trans(mp, (int) c);
                    mp_unstash_cur_exp(mp, p);
                    mp_do_pen_trans(mp, cur_exp_knot);
                    mp_set_cur_exp_knot(mp, cur_exp_knot);
                    mp_finish_binary(mp, old_p, old_exp);
                    return;
                case mp_pair_type:
                case mp_transform_type:
                    mp_big_trans(mp, p, (int) c);
                    break;
                case mp_picture_type:
                    mp_do_edges_trans(mp, p, (int) c);
                    mp_finish_binary(mp, old_p, old_exp);
                    return;
                default:
                    mp_bad_binary(mp, p, (int) c);
                    break;
            }
            break;
        case mp_concatenate_operation:
        case mp_just_append_operation:
            if ((mp->cur_exp.type == mp_string_type) && (mp_type(p) == mp_string_type)) {
                mp_string str = mp_cat(mp, mp_get_value_str(p), cur_exp_str);
                delete_str_ref(cur_exp_str) ;
                mp_set_cur_exp_str(mp, str);
            } else {
                mp_bad_binary(mp, p, c);
            }
            break;
        case mp_substring_operation:
            if (mp_nice_pair(mp, p, mp_type(p)) && (mp->cur_exp.type == mp_string_type)) {
                mp_string str = mp_chop_string (mp,
                    cur_exp_str,
                    round_unscaled(mp_get_value_number(mp_x_part(mp_get_value_node(p)))),
                    round_unscaled(mp_get_value_number(mp_y_part(mp_get_value_node(p))))
                 );
                delete_str_ref(cur_exp_str) ;
                mp_set_cur_exp_str(mp, str);
            } else {
                mp_bad_binary(mp, p, mp_substring_operation);
            }
            break;
        case mp_subpath_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if (mp_nice_pair(mp, p, mp_type(p)) && (mp->cur_exp.type == mp_path_type)) {
                mp_chop_path(mp, mp_get_value_node(p));
            } else {
                mp_bad_binary(mp, p, mp_subpath_operation);
            }
            break;
        case mp_point_operation:
        case mp_precontrol_operation:
        case mp_postcontrol_operation:
        case mp_direction_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && (mp_type(p) == mp_known_type)) {
                mp_find_point(mp, &(mp_get_value_number(p)), (int) c);
            } else {
                mp_bad_binary(mp, p, c);
            }
            break;
        case mp_pen_offset_operation:
            if ((mp->cur_exp.type == mp_pen_type || mp->cur_exp.type == mp_nep_type) && mp_nice_pair(mp, p, mp_type(p))) {
                mp_set_up_offset(mp, mp_get_value_node(p));
            } else {
                mp_bad_binary(mp, p, mp_pen_offset_operation);
            }
            break;
        case mp_direction_time_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && mp_nice_pair(mp, p, mp_type(p))) {
                mp_set_up_direction_time(mp, mp_get_value_node(p));
            } else {
                mp_bad_binary(mp, p, mp_direction_time_operation);
            }
            break;
        case mp_envelope_operation:
            if ((mp_type(p) != mp_pen_type && mp_type(p) != mp_nep_type) || (mp->cur_exp.type != mp_path_type)) {
                mp_bad_binary(mp, p, mp_envelope_operation);
            } else {
                mp_set_up_envelope(mp, p);
            }
            break;
        case mp_boundingpath_operation:
            if ((mp_type(p) != mp_pen_type && mp_type(p) != mp_nep_type) || (mp->cur_exp.type != mp_path_type)) {
                mp_bad_binary(mp, p, mp_boundingpath_operation);
            } else {
                mp_set_up_boundingpath(mp, p);
            }
            break;
        case mp_arc_time_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && (mp_type(p) == mp_known_type)) {
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_get_arc_time(mp, &new_expr.data.n, cur_exp_knot, &(mp_get_value_number(p)), 0);
                mp_flush_cur_exp(mp, new_expr);
            } else {
                mp_bad_binary(mp, p, (int) c);
            }
            break;
        case mp_arc_point_operation:
            /* todo: make a function */
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && (mp_type(p) == mp_known_type || mp_type(p) == mp_pair_type)) {
                mp_knot k;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                if (mp_type(p) == mp_pair_type) {
                    mp_knot f = cur_exp_knot;
                    mp_node q = mp_get_value_node(p);
                    mp_number x;
                    new_number_clone(x, mp_get_value_number(mp_x_part(q)));
                    if (number_greater(x, zero_t)) {
                        while (number_greater(x, zero_t)) {
                            f = mp_next_knot(f);
                            number_subtract(x, unity_t);
                        }
                    } else {
                        while (number_less(x, zero_t)) {
                            f = mp_next_knot(f);
                            number_add(x, unity_t);
                        }
                    }
                    k = mp_get_arc_time(mp, &new_expr.data.n, f, &(mp_get_value_number(mp_y_part(q))), 1);
                    free_number(x);
                } else {
                    k = mp_get_arc_time(mp, &new_expr.data.n, cur_exp_knot, &(mp_get_value_number(p)), 1);
                }
                if (k) {
                    int toss = 0;
                    if (number_equal(new_expr.data.n, unity_t)) {
                        k = mp_next_knot(k);
                    } else if (! number_equal(new_expr.data.n, zero_t)) {
                        convert_scaled_to_fraction(new_expr.data.n);
                        k = mp_split_cubic_knot(mp, k, &new_expr.data.n);
                        toss = 1;
                    }
                    mp_pair_value(mp, &(k->x_coord), &(k->y_coord));
                    if (toss) {
                        mp_toss_knot(mp, k);
                    }
                } else {
                    mp_bad_unary(mp, mp_arc_point_operation);
                }
            } else {
                mp_bad_unary(mp, mp_arc_point_operation);
            }
            break;
        case mp_arc_point_list_operation:
            /* todo: make a function */
            /*
                vardef arcpoints_a(expr thepath, cnt) =
                    numeric len ; len := length thepath ;
                    numeric aln ; aln := arclength thepath ;
                    numeric seg ; seg := 0 ;
                    numeric tot ; tot := 0 ;
                    numeric tim ; tim := 0 ;
                    numeric stp ; stp := aln / cnt;
                    numeric acc ; acc := subarclength (0,1) of thepath ;
                    point 0 of thepath
                    for tot = stp step stp until aln :
                        hide(
                            forever :
                                exitif tot < acc ;
                                seg := seg + 1 ;
                                tim := acc ;
                                acc := acc + subarclength (seg,seg+1) of thepath ;
                            endfor ;
                        )
                        -- (arcpoint (seg,tot-tim) of thepath)
                    endfor if cycle thepath : -- cycle fi
                enddef ;
            */
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && mp_type(p) == mp_known_type) {
                // we can consider using ints as we have discrete points
                mp_knot cur = cur_exp_knot;
                mp_number len, aln, seg, tot, tim, stp, acc, tmp;
                mp_knot last = NULL;
                mp_knot list = NULL;
                int iscycle = mp_left_type(cur_exp_knot) == mp_explicit_knot;
                new_number(len);
                mp_path_length(mp, &len);
                new_number(aln);
                mp_get_arc_length(mp, &aln, cur_exp_knot);
                new_number(seg);
                new_number(tot);
                new_number(tim);
                new_number(stp);
                set_number_from_div(stp, aln, mp_get_value_number(p));
                new_number(acc);
                mp_get_subarc_length(mp, &acc, cur_exp_knot, &zero_t, &unity_t);
                /* */
                new_number(tmp);
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                /* first point */
                list = mp_complex_knot(mp, cur_exp_knot);
                mp_prev_knot(list) = list;
                mp_next_knot(list) = list;
                last = list;
                /* second and following points */
                number_clone(tot, stp);
                while (number_lessequal(tot, aln)) {
                    mp_knot k;
                    while (1) {
                        if (number_lessequal(tot, acc)) {
                            break;
                        } else {
                            number_add(seg, unity_t);
                            number_clone(tim, acc);
                            cur = mp_next_knot(cur);
                            mp_get_subarc_length(mp, &tmp, cur, &zero_t, &unity_t);
                            number_add(acc, tmp) ;
                        }
                    }
                    /* still from the start, can be improved with offset */
                    number_clone(tmp, tot);
                    number_subtract(tmp, tim);
                    k = mp_get_arc_time(mp, &new_expr.data.n, cur, &tmp, 1);
                    /* */
                    if (k) {
                        int toss = 0;
                        mp_knot kk;
                        if (number_equal(new_expr.data.n, unity_t)) {
                            k = mp_next_knot(k);
                        } else if (! number_equal(new_expr.data.n, zero_t)) {
                            convert_scaled_to_fraction(new_expr.data.n);
                            k = mp_split_cubic_knot(mp, k, &new_expr.data.n);
                            toss = 1;
                        }
                        kk = mp_complex_knot(mp, k);
                        mp_prev_knot(list) = kk;
                        mp_next_knot(kk) = list;
                        mp_prev_knot(kk) = last;
                        mp_next_knot(last) = kk;
                        last = kk;
                        if (toss) {
                            mp_toss_knot(mp, k);
                        }
                        number_add(tot, stp);
                    } else {
                        break;
                    }
                }

                free_number(len);
                free_number(aln);
                free_number(seg);
                free_number(tot);
                free_number(tim);
                free_number(stp);
                free_number(acc);
                free_number(tmp);
                if (list) {
                    if (iscycle) {
                        mp_left_type(list) = mp_explicit_knot;
                        mp_right_type(last) = mp_explicit_knot;
                    } else {
                        mp_left_type(list) = mp_endpoint_knot;
                        mp_right_type(last) = mp_endpoint_knot;
                    }
                    mp->cur_exp.type = mp_path_type;
                    mp_set_cur_exp_knot(mp, list);
                } else {
                    mp_bad_unary(mp, mp_arc_point_list_operation);
                }
            } else {
                mp_bad_unary(mp, mp_arc_point_list_operation);
            }
            break;
        case mp_subarc_length_operation:
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && mp_type(p) == mp_pair_type) {
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_node q = mp_get_value_node(p);
                mp_get_subarc_length(mp, &new_expr.data.n, cur_exp_knot, &(mp_get_value_number(mp_x_part(q))), &(mp_get_value_number(mp_y_part(q))));
                mp_flush_cur_exp(mp, new_expr);
            } else {
                mp_bad_unary(mp, mp_subarc_length_operation);
            }
            break;
        case mp_intertimes_operation:
        case mp_intertimes_list_operation:
            if (mp_type(p) == mp_pair_type) {
                mp_node q = mp_stash_cur_exp(mp);
                mp_unstash_cur_exp(mp, p);
                mp_pair_to_path(mp);
                p = mp_stash_cur_exp(mp);
                mp_unstash_cur_exp(mp, q);
            }
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if ((mp->cur_exp.type == mp_path_type) && (mp_type(p) == mp_path_type)) {
                if (c == mp_intertimes_operation) {
                 // mp_number arg1, arg2;
                 // mp_path_intersection(mp, mp_get_value_knot(p), cur_exp_knot, 0, NULL);
                 // new_number_clone(arg1, mp->cur_t);
                 // new_number_clone(arg2, mp->cur_tt);
                 // mp_pair_value(mp, &arg1, &arg2);
                 // free_number(arg1);
                 // free_number(arg2);
                    mp_path_intersection(mp, mp_get_value_knot(p), cur_exp_knot, 0, NULL);
                    mp_pair_value(mp, &mp->cur_t, &mp->cur_tt);
                } else {
                    mp_knot last = NULL;
                    mp_knot list = mp_path_intersection(mp, mp_get_value_knot(p), cur_exp_knot, 1, &last);
                    mp_left_type(list) = mp_endpoint_knot;
                    mp_right_type(last) = mp_endpoint_knot;
                    mp->cur_exp.type = mp_path_type;
                    mp_set_cur_exp_knot(mp, list);
                }
            } else {
                mp_bad_binary(mp, p, c);
            }
            break;
    }
    mp_recycle_value(mp, p);
    mp_free_value_node(mp, p); /* |return| to avoid this */
    mp_finish_binary(mp, old_p, old_exp);
}

@ @<Declare binary action...@>=
static void mp_bad_binary (MP mp, mp_node p, int c)
{
    char msg[256];
    mp_string sname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    if (c >= mp_min_of_operation) {
        mp_print_op(mp, c);
    }
    mp_print_known_or_unknown_type(mp, mp_type(p), p);
    if (c >= mp_min_of_operation) {
        mp_print_str(mp, "of");
    } else {
        mp_print_op(mp, c);
    }
    mp_print_known_or_unknown_type(mp, mp->cur_exp.type, cur_exp_node);
    sname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "Not implemented: %s", mp_str(mp, sname));
    @.Not implemented...@>
    delete_str_ref(sname);
    mp_disp_err(mp, p);
    mp_disp_err(mp, NULL);
    mp_back_error(
        mp,
        msg,
        "I'm afraid I don't know how to apply that operation to that combination of types.\n"
        "Continue, and I'll return the second argument (see above) as the result of the"
        "operation."
    );
    mp_get_x_next(mp);
}

static void mp_bad_envelope_pen (MP mp)
{
    mp_disp_err(mp, NULL);
    mp_disp_err(mp, NULL);
    mp_back_error(
        mp,
        "Not implemented: 'envelope(elliptical pen) of (path)'",
        "I'm afraid I don't know how to apply that operation to that combination of types.\n"
        "Continue, and I'll return the second argument (see above) as the result of the\n"
        "operation."
    );
    @.Not implemented...@>
    mp_get_x_next(mp);
}

@ @<Declare binary action...@>=
static mp_node mp_tarnished (MP mp, mp_node p)
{
    mp_node q = mp_get_value_node(p);
    (void) mp;
    switch (mp_type(p)) {
        case mp_pair_type:
            return (
                (mp_type(mp_x_part(q)) == mp_independent_type) ||
                (mp_type(mp_y_part(q)) == mp_independent_type)
            ) ? MP_VOID : NULL;
        case mp_color_type:
            return (
                (mp_type(mp_red_part(q))   == mp_independent_type) ||
                (mp_type(mp_green_part(q)) == mp_independent_type) ||
                (mp_type(mp_blue_part(q))  == mp_independent_type)
            ) ? MP_VOID : NULL;
        case mp_cmykcolor_type:
            return (
                (mp_type(mp_cyan_part(q))    == mp_independent_type) ||
                (mp_type(mp_magenta_part(q)) == mp_independent_type) ||
                (mp_type(mp_yellow_part(q))  == mp_independent_type) ||
                (mp_type(mp_black_part(q))   == mp_independent_type)
            ) ? MP_VOID : NULL;
        case mp_transform_type:
            return (
                (mp_type(mp_tx_part(q)) == mp_independent_type) ||
                (mp_type(mp_ty_part(q)) == mp_independent_type) ||
                (mp_type(mp_xx_part(q)) == mp_independent_type) ||
                (mp_type(mp_xy_part(q)) == mp_independent_type) ||
                (mp_type(mp_yx_part(q)) == mp_independent_type) ||
                (mp_type(mp_yy_part(q)) == mp_independent_type)
            ) ? MP_VOID : NULL;
        default:
            return NULL;
    }
}

@ The first argument to |add_or_subtract| is the location of a value node in a
capsule or pair node that will soon be recycled. The second argument is either a
location within a pair or transform node of |cur_exp|, or it is NULL (which means
that |cur_exp| itself should be the second argument). The third argument is
either |plus| or |minus|.

The sum or difference of the numeric quantities will replace the second operand.
Arithmetic overflow may go undetected; users aren't supposed to be monkeying
around with really big values. @^overflow in arithmetic@>

@<Declare binary action...@>=
@<Declare the procedure called |dep_finish|@>
static void mp_add_or_subtract (MP mp, mp_node p, mp_node q, int c)
{
    mp_variable_type s, t;  /* operand types */
    mp_value_node r;        /* dependency list traverser */
    mp_value_node v = NULL; /* second operand value for dep lists */
    mp_number vv;           /* second operand value for known values */
    new_number(vv);
    if (q == NULL) {
        t = mp->cur_exp.type;
        if (t < mp_dependent_type) {
            number_clone(vv, cur_exp_value_number);
        } else {
            v = (mp_value_node) mp_get_dep_list((mp_value_node) cur_exp_node);
        }
    } else {
        t = mp_type(q);
        if (t < mp_dependent_type) {
            number_clone(vv, mp_get_value_number(q));
        } else {
            v = (mp_value_node) mp_get_dep_list((mp_value_node) q);
        }
    }
    if (t == mp_known_type) {
        mp_value_node qq = (mp_value_node) q;
        if (c == mp_minus_operation) {
            number_negate(vv);
        }
        if (mp_type(p) == mp_known_type) {
            slow_add(vv, mp_get_value_number(p), vv);
            if (q == NULL) {
                mp_set_cur_exp_value_number(mp, &vv);
            } else {
                mp_set_value_number(q, vv);
            }
            free_number(vv);
            return;
        } else {
            /* Add a known value to the constant term of |mp_get_dep_list(p)| */
            r = (mp_value_node) mp_get_dep_list((mp_value_node) p);
            while (mp_get_dep_info(r) != NULL) {
                r = (mp_value_node) mp_link(r);
            }
            slow_add(vv, mp_get_dep_value(r), vv);
            mp_set_dep_value(r, vv);
            if (qq == NULL) {
                qq = mp_get_dep_node(mp);
                mp_set_cur_exp_node(mp, (mp_node) qq);
                mp->cur_exp.type = mp_type(p);
                mp_name_type(qq) = mp_capsule_operation;
                /* clang: never read: |q = (mp_node) qq;| */
            }
            mp_set_dep_list(qq, mp_get_dep_list((mp_value_node) p));
            mp_type(qq) = mp_type(p);
            mp_set_prev_dep(qq, mp_get_prev_dep((mp_value_node) p));
            mp_link(mp_get_prev_dep((mp_value_node) p)) = (mp_node) qq;
            mp_type(p) = mp_known_type; /* this will keep the recycler from collecting non-garbage */
        }
    } else {
        if (c == mp_minus_operation) {
            mp_negate_dep_list(mp, v);
        }
        /*
            Add operand |p| to the dependency list |v|. We prefer |dependent| lists to
            |mp_proto_dependent| ones, because it is nice to retain the extra accuracy
            of |fraction| coefficients. But we have to handle both kinds, and mixtures
            too.
        */
        if (mp_type(p) == mp_known_type) {
            /* Add the known |value(p)| to the constant term of |v| */
            while (mp_get_dep_info(v) != NULL) {
                v = (mp_value_node) mp_link(v);
            }
            slow_add(vv, mp_get_value_number(p), mp_get_dep_value(v));
            mp_set_dep_value(v, vv);
        } else {
            s = mp_type(p);
            r = (mp_value_node) mp_get_dep_list((mp_value_node) p);
            if (t == mp_dependent_type) {
                if (s == mp_dependent_type) {
                    int b;
                    mp_number ret1, ret2;
                    new_fraction(ret1);
                    new_fraction(ret2);
                    mp_max_coef(mp, &ret1, r);
                    mp_max_coef(mp, &ret2, v);
                    number_add(ret1, ret2);
                    b = number_less(ret1, coef_bound_k);
                    free_number(ret1);
                    free_number(ret2);
                    if (b) {
                        v = mp_p_plus_q(mp, v, r, mp_dependent_type);
                        goto DONE;
                    }
                } /* |fix_needed| will necessarily be false */
                t = mp_proto_dependent_type;
                v = mp_p_over_v(mp, v, &unity_t, mp_dependent_type, mp_proto_dependent_type);
            }
            if (s == mp_proto_dependent_type) {
                v = mp_p_plus_q(mp, v, r, mp_proto_dependent_type);
            } else {
                v = mp_p_plus_fq(mp, v, &unity_t, r, mp_proto_dependent_type, mp_dependent_type);
            }
          DONE:
            /* Output the answer, |v| (which might have become |known|) */
            if (q != NULL) {
                mp_dep_finish(mp, v, (mp_value_node) q, t);
            } else {
                mp->cur_exp.type = t;
                mp_dep_finish(mp, v, NULL, t);
            }
        }
    }
    free_number(vv);
}

@ Here's the current situation: The dependency list |v| of type |t| should either
be put into the current expression (if |q=NULL|) or into location |q| within a
pair node (otherwise). The destination (|cur_exp| or |q|) formerly held a
dependency list with the same final pointer as the list |v|.

@<Declare the procedure called |dep_finish|@>=
static void mp_dep_finish (MP mp, mp_value_node v, mp_value_node q, int t)
{
    mp_value_node p = (q == NULL) ? (mp_value_node) cur_exp_node : q; /* the destination */
    mp_set_dep_list(p, v);
    mp_type(p) = t;
    if (mp_get_dep_info(v) == NULL) {
        mp_number vv; /* the value, if it is |known| */
        new_number_clone(vv, mp_get_value_number(v));
        if (q == NULL) {
            mp_value new_expr;
            memset(&new_expr, 0, sizeof(mp_value));
            new_number_clone(new_expr.data.n, vv);
            mp_flush_cur_exp(mp, new_expr);
        } else {
            mp_recycle_value(mp, (mp_node) p);
            mp_type(q) = mp_known_type;
            mp_set_value_number(q, vv);
        }
        free_number(vv);
    } else if (q == NULL) {
        mp->cur_exp.type = t;
    }
    if (mp->fix_needed) {
        mp_fix_dependencies(mp);
    }
}

@ @<Declare binary action...@>=
static void mp_dep_mult (MP mp, mp_value_node p, mp_number *v, int v_is_scaled)
{
    mp_value_node q; /* the dependency list being multiplied by |v| */
    int s, t;        /* its type, before and after */
    if (p == NULL) {
        q = (mp_value_node) cur_exp_node;
    } else if (mp_type(p) != mp_known_type) {
        q = p;
    } else {
        mp_number r1, arg1;
        new_number_clone(arg1, mp_get_dep_value(p));
        if (v_is_scaled) {
            new_number(r1);
            take_scaled(r1, arg1, *v);
        } else {
            new_fraction(r1);
            take_fraction(r1, arg1, *v);
        }
        mp_set_dep_value(p, r1);
        free_number(r1);
        free_number(arg1);
        return;
    }
    t = mp_type(q);
    q = (mp_value_node) mp_get_dep_list(q);
    s = t;
    if (t == mp_dependent_type && v_is_scaled) {
        mp_number arg1, arg2;
        new_fraction(arg1);
        mp_max_coef(mp, &arg1, q);
        new_number_abs(arg2, *v);
        if (ab_vs_cd(arg1, arg2, coef_bound_minus_1, unity_t) >= 0) {
            t = mp_proto_dependent_type;
        }
        free_number(arg1);
        free_number(arg2);
    }
    q = mp_p_times_v(mp, q, v, s, t, v_is_scaled);
    mp_dep_finish(mp, q, p, t);
}

@ Here is a routine that is similar to |times|; but it is invoked only
internally, when |v| is a |fraction| whose magnitude is at most~1, and when
|cur_type >= mp_color_type|.

@c
static void mp_frac_mult (MP mp, mp_number *n, mp_number *d)
{
    /* multiplies |cur_exp| by |n/d| */
    mp_node old_exp; /* a capsule to recycle */
    mp_number v;     /* |n/d| */
    new_fraction(v);
    if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
        @<Trace the fraction multiplication@>
    }
    switch (mp->cur_exp.type) {
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
            old_exp = mp_tarnished(mp, cur_exp_node);
            break;
        case mp_independent_type:
            old_exp = MP_VOID;
            break;
        default:
            old_exp = NULL;
            break;
    }
    if (old_exp != NULL) {
        old_exp = cur_exp_node;
        mp_make_exp_copy(mp, old_exp);
    }
    make_fraction(v, *n, *d);
    switch (mp->cur_exp.type) {
        case mp_known_type:
            {
                mp_number r1, arg1;
                new_fraction(r1);
                new_number_clone(arg1, cur_exp_value_number);
                take_fraction(r1, arg1, v);
                mp_set_cur_exp_value_number(mp, &r1);
                free_number(r1);
                free_number(arg1);
            }
            break;
        case mp_pair_type:
            {
                mp_dep_mult(mp, (mp_value_node) mp_x_part(mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_y_part(mp_get_value_node(cur_exp_node)), &v, 0);
            }
            break;
        case mp_color_type:
            {
                mp_dep_mult(mp, (mp_value_node) mp_red_part  (mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_green_part(mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_blue_part (mp_get_value_node(cur_exp_node)), &v, 0);
            }
            break;
        case mp_cmykcolor_type:
            {
                mp_dep_mult(mp, (mp_value_node) mp_cyan_part   (mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_magenta_part(mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_yellow_part (mp_get_value_node(cur_exp_node)), &v, 0);
                mp_dep_mult(mp, (mp_value_node) mp_black_part  (mp_get_value_node(cur_exp_node)), &v, 0);
            }
            break;
        default:
            {
                mp_dep_mult(mp, NULL, &v, 0);
            }
            break;
    }
    if (old_exp != NULL) {
        mp_recycle_value(mp, old_exp);
        mp_free_value_node(mp, old_exp);
    }
    free_number(v);
}

@ @<Trace the fraction multiplication@>=
mp_begin_diagnostic(mp);
mp_print_nl(mp, "{(");
print_number(*n);
mp_print_chr(mp, '/');
print_number(*d);
mp_print_str(mp, ")*(");
mp_print_exp(mp, NULL, 0);
mp_print_str(mp, ")}");
mp_end_diagnostic(mp, 0);

@ The |hard_times| routine multiplies a nice color or pair by a dependency list.

@<Declare binary action procedures@>=
static void mp_hard_times (MP mp, mp_node p)
{
    mp_value_node q;  /* a copy of the dependent variable |p| */
    mp_value_node pp; /* for typecasting p */
    mp_number v;      /* the known value for |r| */
    new_number(v);
    if (mp_type(p) <= mp_pair_type) {
        q = (mp_value_node) mp_stash_cur_exp(mp);
        mp_unstash_cur_exp(mp, p);
        p = (mp_node) q;
    }
    /* now |cur_type=mp_pair_type| or |cur_type=mp_color_type| or |cur_type=mp_cmykcolor_type| */
    pp = (mp_value_node) p;
    switch (mp->cur_exp.type) {
        case mp_pair_type:
            {
                mp_node r = mp_x_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_y_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
            }
            break;
        case mp_color_type:
            {
                mp_node r = mp_red_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_green_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_blue_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
            }
            break;
        case mp_cmykcolor_type:
            {
                mp_node r = mp_cyan_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_yellow_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_magenta_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
                r = mp_black_part(mp_get_value_node(cur_exp_node));
                number_clone(v, mp_get_value_number(r));
                mp_new_dep(mp, r, mp_type(pp), mp_copy_dep_list(mp, (mp_value_node) mp_get_dep_list(pp)));
                mp_dep_mult(mp, (mp_value_node) r, &v, 1);
            }
            break;
        default:
            break;
    }
    free_number(v);
}

@ @<Declare binary action...@>=
static void mp_dep_div (MP mp, mp_value_node p, mp_number *v)
{
    mp_value_node q; /* the dependency list being divided by |v| */
    int s, t;        /* its type, before and after */
    if (p == NULL) {
        q = (mp_value_node) cur_exp_node;
    } else if (mp_type(p) != mp_known_type) {
        q = p;
    } else {
        mp_number ret;
        new_number(ret);
        make_scaled(ret, mp_get_value_number(p), *v);
        mp_set_value_number(p, ret);
        free_number(ret);
        return;
    }
    t = mp_type(q);
    q = (mp_value_node) mp_get_dep_list(q);
    s = t;
    if (t == mp_dependent_type) {
        mp_number arg1, arg2;
        new_number(arg2);
        new_fraction(arg1);
        mp_max_coef(mp, &arg1, q);
        number_abs_clone(arg2, *v);
        if (ab_vs_cd(arg1, unity_t, coef_bound_minus_1, arg2) >= 0) {
            t = mp_proto_dependent_type;
        }
        free_number(arg1);
        free_number(arg2);
    }
    q = mp_p_over_v(mp, q, v, s, t);
    mp_dep_finish(mp, q, p, t);
}

@ Let |c| be one of the eight transform operators. The procedure call
|set_up_trans(c)| first changes |cur_exp| to a transform that corresponds to |c|
and the original value of |cur_exp|. (In particular, |cur_exp| doesn't change at
all if |c=transformed_by|.)

Then, if all components of the resulting transform are |known|, they are moved to
the global variables |txx|, |txy|, |tyx|, |tyy|, |tx|, |ty|; and |cur_exp| is
changed to the known value zero.

@<Declare binary action...@>=
static void mp_set_up_trans (MP mp, int c)
{
    mp_node p, q, r; /* list manipulation registers */
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    if ((c != mp_transformed_operation) || (mp->cur_exp.type != mp_transform_type)) {
        /* Put the current transform into |cur_exp| */
        p = mp_stash_cur_exp(mp);
        mp_set_cur_exp_node(mp, mp_id_transform(mp));
        mp->cur_exp.type = mp_transform_type;
        q = mp_get_value_node(cur_exp_node);
        @<For each of the eight cases, change the relevant fields of |cur_exp| and |goto done|; but do nothing if capsule |p| doesn't have  the appropriate type@>
        mp_disp_err(mp, p);
        mp_back_error(
            mp,
            "Improper transformation argument",
            "The expression shown above has the wrong type, so I can't transform anything\n"
            "using it. Proceed, and I'll omit the transformation."
         );
        mp_get_x_next(mp);
      DONE:
        mp_recycle_value(mp, p);
        mp_free_value_node(mp, p);
    }
    /*
        If the current transform is entirely known, stash it in global variables;
        otherwise |return|
    */
    q = mp_get_value_node(cur_exp_node);
    if ( (mp_type(mp_tx_part(q)) == mp_known_type) &&
         (mp_type(mp_ty_part(q)) == mp_known_type) &&
         (mp_type(mp_xx_part(q)) == mp_known_type) &&
         (mp_type(mp_xy_part(q)) == mp_known_type) &&
         (mp_type(mp_yx_part(q)) == mp_known_type) &&
         (mp_type(mp_yy_part(q)) == mp_known_type) ) {
        number_clone(mp->txx, mp_get_value_number(mp_xx_part(q)));
        number_clone(mp->txy, mp_get_value_number(mp_xy_part(q)));
        number_clone(mp->tyx, mp_get_value_number(mp_yx_part(q)));
        number_clone(mp->tyy, mp_get_value_number(mp_yy_part(q)));
        number_clone(mp->tx,  mp_get_value_number(mp_tx_part(q)));
        number_clone(mp->ty,  mp_get_value_number(mp_ty_part(q)));
        new_number(new_expr.data.n);
        mp_flush_cur_exp(mp, new_expr);
    }
}

@ @<Glob...@>=
mp_number txx;
mp_number txy;
mp_number tyx;
mp_number tyy;
mp_number tx;
mp_number ty;      /* current transform coefficients */

@ @<Initialize table...@>=
new_number(mp->txx);
new_number(mp->txy);
new_number(mp->tyx);
new_number(mp->tyy);
new_number(mp->tx);
new_number(mp->ty);

@ @<Free table...@>=
free_number(mp->txx);
free_number(mp->txy);
free_number(mp->tyx);
free_number(mp->tyy);
free_number(mp->tx);
free_number(mp->ty);

@ @<For each of the eight cases...@>=
switch (c) {
    case mp_rotated_operation:
        if (mp_type(p) == mp_known_type) {
            @<Install sines and cosines, then |goto done|@>
        }
        break;
    case mp_slanted_operation:
        if (mp_type(p) > mp_pair_type) {
            mp_install(mp, mp_xy_part(q), p);
            goto DONE;
        }
        break;
    case mp_scaled_operation:
        if (mp_type(p) > mp_pair_type) {
            mp_install(mp, mp_xx_part(q), p);
            mp_install(mp, mp_yy_part(q), p);
            goto DONE;
        }
        break;
    case mp_shifted_operation:
        if (mp_type(p) == mp_pair_type) {
            r = mp_get_value_node(p);
            mp_install(mp, mp_tx_part(q), mp_x_part(r));
            mp_install(mp, mp_ty_part(q), mp_y_part(r));
            goto DONE;
        }
        break;
    case mp_x_scaled_operation:
        if (mp_type(p) > mp_pair_type) {
            mp_install(mp, mp_xx_part(q), p);
            goto DONE;
        }
        break;
    case mp_y_scaled_operation:
        if (mp_type(p) > mp_pair_type) {
            mp_install(mp, mp_yy_part(q), p);
            goto DONE;
        }
        break;
    case mp_z_scaled_operation:
        if (mp_type(p) == mp_pair_type) {
            @<Install a complex multiplier, then |goto done|@>
        }
        break;
    case mp_transformed_operation:
        break;
}

@ @<Install sines and cosines, then |goto done|@>=
mp_number n_sin, n_cos, arg1, arg2;
new_fraction(n_sin);
new_fraction(n_cos); /* results computed by |n_sin_cos| */
new_number_clone(arg2, unity_t);
new_number_clone(arg1, mp_get_value_number(p));
number_multiply_int(arg2, 360);
number_modulo(arg1, arg2);
convert_scaled_to_angle(arg1);
n_sin_cos(arg1, n_cos, n_sin);
fraction_to_round_scaled(n_sin);
fraction_to_round_scaled(n_cos);
mp_set_value_number(mp_xx_part(q), n_cos);
mp_set_value_number(mp_yx_part(q), n_sin);
mp_set_value_number(mp_xy_part(q), mp_get_value_number(mp_yx_part(q)));
number_negate(mp_get_value_number(mp_xy_part(q)));
mp_set_value_number(mp_yy_part(q), mp_get_value_number(mp_xx_part(q)));
free_number(arg1);
free_number(arg2);
free_number(n_sin);
free_number(n_cos);
goto DONE;

@ @<Install a complex multiplier, then |goto done|@>=
{
    r = mp_get_value_node(p);
    mp_install(mp, mp_xx_part(q), mp_x_part(r));
    mp_install(mp, mp_yy_part(q), mp_x_part(r));
    mp_install(mp, mp_yx_part(q), mp_y_part(r));
    if (mp_type(mp_y_part(r)) == mp_known_type) {
        mp_set_value_number(mp_y_part(r), mp_get_value_number(mp_y_part(r)));
        number_negate(mp_get_value_number(mp_y_part(r)));
    } else {
        mp_negate_dep_list(mp, (mp_value_node) mp_get_dep_list((mp_value_node) mp_y_part(r)));
    }
    mp_install(mp, mp_xy_part(q), mp_y_part(r));
    goto DONE;
}

@ Procedure |set_up_known_trans| is like |set_up_trans|, but it
insists that the transformation be entirely known.

@<Declare binary action...@>=
static void mp_set_up_known_trans (MP mp, int c)
{
    mp_set_up_trans(mp, c);
    if (mp->cur_exp.type != mp_known_type) {
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Transform components aren't all known",
            "I'm unable to apply a partially specified transformation except to a fully known\n"
            "pair or transform. Proceed, and I'll omit the transformation."
        );
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
        set_number_to_unity(mp->txx);
        set_number_to_zero(mp->txy);
        set_number_to_zero(mp->tyx);
        set_number_to_unity(mp->tyy);
        set_number_to_zero(mp->tx);
        set_number_to_zero(mp->ty);
    }
}

@ Here's a procedure that applies the transform |txx..ty| to a pair of
coordinates in locations |p| and~|q|.

@<Declare binary action...@>=
static void mp_number_trans (MP mp, mp_number *p, mp_number *q)
{
    mp_number r1, r2, v;
    new_number(r1);
    new_number(r2);
    new_number(v);
    take_scaled(r1, *p, mp->txx);
    take_scaled(r2, *q, mp->txy);
    number_add(r1, r2);
    set_number_from_addition(v, r1, mp->tx);
    take_scaled(r1, *p, mp->tyx);
    take_scaled(r2, *q, mp->tyy);
    number_add(r1, r2);
    set_number_from_addition(*q, r1, mp->ty);
    number_clone(*p,v);
    free_number(r1);
    free_number(r2);
    free_number(v);
}

@ The simplest transformation procedure applies a transform to all
coordinates of a path.  The |path_trans(c)(p)| macro applies
a transformation defined by |cur_exp| and the transform operator |c|
to the path~|p|. The macro was used only once and has been inlined.

@<Declare binary action...@>=
static void mp_do_path_trans (MP mp, mp_knot p)
{
    mp_knot q = p;
    do {
        if (mp_left_type(q) != mp_endpoint_knot) {
            mp_number_trans(mp, &q->left_x, &q->left_y);
        }
        mp_number_trans(mp, &q->x_coord, &q->y_coord);
        if (mp_right_type(q) != mp_endpoint_knot) {
            mp_number_trans(mp, &q->right_x, &q->right_y);
        }
        q = mp_next_knot(q);
    } while (q != p);
}

@ Transforming a pen is very similar, except that there are no |mp_left_type|
and |mp_right_type| fields.

@<Declare binary action...@>=
static void mp_do_pen_trans (MP mp, mp_knot p)
{
    mp_knot q = p; /* list traverser */
    if (mp_pen_is_elliptical(p)) {
        mp_number_trans(mp, &p->left_x, &p->left_y);
        mp_number_trans(mp, &p->right_x, &p->right_y);
    }
    do {
        mp_number_trans(mp, &q->x_coord, &q->y_coord);
        q = mp_next_knot(q);
    } while (q != p);
}

@ Note that the shift parameters |(tx,ty)| apply only to the path being stroked.
The |dashscale| has to be adjusted to scale the dash lengths in |mp_dash_ptr(q)|
since the \ps\ output procedures will try to compensate for the transformation we
are applying to |mp_pen_ptr(q)|. Since this compensation is based on the square
root of the determinant, |sqdet| is the appropriate factor.

@<Declare binary action...@>=
static void mp_do_path_pen_trans (MP mp, mp_shape_node p, mp_number *sqdet, int sgndet)
{
    mp_number sx, sy;
    if (mp_pen_ptr(p) != NULL) {
        new_number_clone(sx, mp->tx);
        new_number_clone(sy, mp->ty);
        set_number_to_zero(mp->tx);
        set_number_to_zero(mp->ty);
        mp_do_pen_trans(mp, mp_pen_ptr(p));
        if (number_nonzero(*sqdet) && ((mp_type(p) == mp_stroked_node_type) && (mp_dash_ptr(p) != NULL))) {
            mp_number ret;
            new_number(ret);
            take_scaled(ret, ((mp_shape_node) p)->dashscale, *sqdet);
            number_clone(((mp_shape_node) p)->dashscale, ret);
            free_number(ret);
        }
        if (! mp_pen_is_elliptical(mp_pen_ptr(p)) && sgndet < 0) {
            mp_pen_ptr(p) = mp_make_pen(mp, mp_copy_path(mp, mp_pen_ptr(p)), 1);
        }
        number_clone(mp->tx, sx);
        number_clone(mp->ty, sy);
        free_number(sx);
        free_number(sy);
    }
}

@ The next transformation procedure applies to edge structures. It will do any
transformation, but the results may be substandard if the picture contains text
that uses downloaded bitmap fonts. The binary action procedure is
|do_edges_trans|, but we also need a function that just scales a picture. That
routine is |scale_edges|. Both it and the underlying routine |edges_trans| should
be thought of as procedures that update an edge structure |h|, except that they
have to return a (possibly new) structure because of the need to call
|private_edges|.

@<Declare binary action...@>=
static mp_edge_header_node mp_edges_trans (MP mp, mp_edge_header_node h)
{
    mp_node q;         /* the object being transformed */
    mp_dash_node r, s; /* for list manipulation */
    mp_number sqdet;   /* square root of determinant for |dashscale| */
    int sgndet;  /* sign of the determinant */
    h = mp_private_edges(mp, h);
    new_number(sqdet);
    mp_sqrt_det(mp, &sqdet, &(mp->txx), &(mp->txy), &(mp->tyx), &(mp->tyy));
    sgndet = ab_vs_cd(mp->txx, mp->tyy, mp->txy, mp->tyx);
    if (mp_get_dash_list(h) != mp->null_dash) {
        @<Try to transform the dash list of |h|@>
    }
    @<Make the bounding box of |h| unknown if it can't be updated properly without scanning the whole structure@>
    q = mp_link(mp_edge_list(h));
    while (q != NULL) {
        @<Transform graphical object |q|@>
        q = mp_link(q);
    }
    free_number(sqdet);
    return h;
}

static void mp_do_edges_trans (MP mp, mp_node p, int c)
{
    mp_set_up_known_trans (mp, c);
    mp_set_value_node(p, (mp_node) mp_edges_trans(mp, (mp_edge_header_node) mp_get_value_node(p)));
    mp_unstash_cur_exp(mp, p);
}

static mp_edge_header_node mp_scale_edges (MP mp, mp_number *se_sf, mp_edge_header_node se_pic)
{
    number_clone(mp->txx, *se_sf);
    number_clone(mp->tyy, *se_sf);
    set_number_to_zero(mp->txy);
    set_number_to_zero(mp->tyx);
    set_number_to_zero(mp->tx);
    set_number_to_zero(mp->ty);
    return mp_edges_trans(mp, se_pic);
}

@ @<Try to transform the dash list of |h|@>=
if (number_nonzero(mp->txy) || number_nonzero(mp->tyx) || number_nonzero(mp->ty) || number_nonequalabs(mp->txx, mp->tyy)) {
    mp_flush_dash_list(mp, h);
} else {
    mp_number abs_tyy, ret;
    new_number(abs_tyy);
    if (number_negative(mp->txx)) {
        @<Reverse the dash list of |h|@>
    }
    @<Scale the dash list by |txx| and shift it by |tx|@>
    number_abs_clone(abs_tyy, mp->tyy);
    new_number(ret);
    take_scaled(ret, h->dash_y, abs_tyy);
    number_clone(h->dash_y, ret);
    free_number(ret);
    free_number(abs_tyy);
}

@ @<Reverse the dash list of |h|@>=
{
    r = mp_get_dash_list(h);
    mp_set_dash_list(h, mp->null_dash);
    while (r != mp->null_dash) {
        s = r;
        r = (mp_dash_node) mp_link(r);
        number_swap(s->start_x, s->stop_x );
        mp_link(s) = (mp_node) mp_get_dash_list(h);
        mp_set_dash_list(h, s);
    }
}

@ @<Scale the dash list by |txx| and shift it by |tx|@>=
r = mp_get_dash_list(h);
{
    mp_number arg1;
    new_number(arg1);
    while (r != mp->null_dash) {
        take_scaled(arg1, r->start_x, mp->txx);
        set_number_from_addition(r->start_x, arg1, mp->tx);
        take_scaled(arg1, r->stop_x, mp->txx);
        set_number_from_addition(r->stop_x, arg1, mp->tx);
        r = (mp_dash_node) mp_link(r);
    }
    free_number(arg1);
}

@ @<Make the bounding box of |h| unknown if it can't be updated properly...@>=
if (number_zero(mp->txx) && number_zero(mp->tyy)) {
    @<Swap the $x$ and $y$ parameters in the bounding box of |h|@>
} else if (number_nonzero(mp->txy) || number_nonzero(mp->tyx)) {
    mp_init_bbox(mp, h);
    goto DONE1;
}
if (number_lessequal(h->minx, h->maxx)) {
    @<Scale the bounding box by |txx+txy| and |tyx+tyy|; then shift by |(tx,ty)|@>
}
DONE1:

@ @<Swap the $x$ and $y$ parameters in the bounding box of |h|@>=
number_swap(h->minx, h->miny);
number_swap(h->maxx, h->maxy);

@ The sum |txx+txy| is whichever of |txx| or |txy| is nonzero. The other sum
is similar.

@<Scale the bounding box by |txx+txy| and |tyx+tyy|; then shift...@>=
mp_number tot, ret;
new_number(tot);
new_number(ret);
set_number_from_addition(tot,mp->txx,mp->txy);
take_scaled(ret, h->minx, tot);
set_number_from_addition(h->minx,ret, mp->tx);
take_scaled(ret, h->maxx, tot);
set_number_from_addition(h->maxx,ret, mp->tx);

set_number_from_addition(tot,mp->tyx,mp->tyy);
take_scaled(ret, h->miny, tot);
set_number_from_addition(h->miny, ret, mp->ty);
take_scaled(ret, h->maxy, tot);
set_number_from_addition(h->maxy, ret, mp->ty);
set_number_from_addition(tot, mp->txx, mp->txy);
if (number_negative(tot)) {
    number_swap(h->minx, h->maxx);
}
set_number_from_addition(tot, mp->tyx, mp->tyy);
if (number_negative(tot)) {
    number_swap(h->miny, h->maxy);
}
free_number(ret);
free_number(tot);

@ Now we ready for the main task of transforming the graphical objects in edge
structure~|h|.

@<Transform graphical object |q|@>=
switch (mp_type(q)) {
    case mp_fill_node_type:
    case mp_stroked_node_type:
        mp_do_path_trans(mp, mp_path_ptr((mp_shape_node) q));
        mp_do_path_pen_trans(mp, (mp_shape_node) q, &sqdet, sgndet);
        break;
    case mp_start_clip_node_type:
    case mp_start_group_node_type:
    case mp_start_bounds_node_type:
        mp_do_path_trans(mp, mp_path_ptr((mp_start_node) q));
        break;
    case mp_stop_clip_node_type:
    case mp_stop_group_node_type:
    case mp_stop_bounds_node_type:
        break;
    default:
        break;
}

@ The hard cases of transformation occur when big nodes are involved, and when
some of their components are unknown.

@<Declare binary action...@>=
@<Declare subroutines needed by |big_trans|@>
static void mp_big_trans (MP mp, mp_node p, int c)
{
    mp_node q = mp_get_value_node(p);
    if (mp_type(q) == mp_pair_node_type) {
        if (mp_type(mp_x_part(q)) != mp_known_type || mp_type(mp_y_part(q)) != mp_known_type) {
            goto UNKNOWN;
        }
    } else if (mp_type(mp_tx_part(q)) != mp_known_type || mp_type(mp_ty_part(q)) != mp_known_type ||
               mp_type(mp_xx_part(q)) != mp_known_type || mp_type(mp_xy_part(q)) != mp_known_type ||
               mp_type(mp_yx_part(q)) != mp_known_type || mp_type(mp_yy_part(q)) != mp_known_type) {
        goto UNKNOWN;
    }
    {
        @<Transform a known big node@>
        return;
    }
  UNKNOWN:
    {
        @<Transform an unknown big node and |return|@>
        return;
    }
}

@ @<Transform an unknown big node and |return|@>=
mp_node r;
mp_set_up_known_trans(mp, c);
mp_make_exp_copy(mp, p);
r = mp_get_value_node(cur_exp_node);
if (mp->cur_exp.type == mp_transform_type) {
    mp_bilin1(mp, mp_yy_part(r), &(mp->tyy), mp_xy_part(q), &(mp->tyx), &zero_t);
    mp_bilin1(mp, mp_yx_part(r), &(mp->tyy), mp_xx_part(q), &(mp->tyx), &zero_t);
    mp_bilin1(mp, mp_xy_part(r), &(mp->txx), mp_yy_part(q), &(mp->txy), &zero_t);
    mp_bilin1(mp, mp_xx_part(r), &(mp->txx), mp_yx_part(q), &(mp->txy), &zero_t);
}
mp_bilin1(mp, mp_y_part(r), &(mp->tyy), mp_x_part(q), &(mp->tyx), &(mp->ty));
mp_bilin1(mp, mp_x_part(r), &(mp->txx), mp_y_part(q), &(mp->txy), &(mp->tx));

@ Let |p| point to a value field inside a big node of |cur_exp|, and let |q|
point to a another value field. The |bilin1| procedure replaces |p| by $p\cdot
t+q\cdot u+\delta$.

@<Declare subroutines needed by |big_trans|@>=
static void mp_bilin1 (MP mp, mp_node p, mp_number *t, mp_node q, mp_number *u, mp_number *delta_orig)
{
    mp_number delta;
    new_number_clone(delta, *delta_orig);
    if (! number_equal(*t, unity_t)) {
        mp_dep_mult(mp, (mp_value_node) p, t, 1);
    }
    if (number_nonzero(*u)) {
        if (mp_type(q) == mp_known_type) {
            mp_number tmp;
            new_number(tmp);
            take_scaled(tmp, mp_get_value_number(q), *u);
            number_add(delta, tmp);
            free_number(tmp);
        } else {
            /* Ensure that |type(p)=mp_proto_dependent| */
            if (mp_type(p) != mp_proto_dependent_type) {
                if (mp_type(p) == mp_known_type) {
                    mp_new_dep(mp, p, mp_type(p), mp_const_dependency(mp, &(mp_get_value_number(p))));
                } else {
                    mp_set_dep_list((mp_value_node) p,
                        mp_p_times_v(mp,
                            (mp_value_node) mp_get_dep_list((mp_value_node) p), &unity_t,
                            mp_dependent_type, mp_proto_dependent_type, 1));
                }
                mp_type(p) = mp_proto_dependent_type;
            }
            mp_set_dep_list((mp_value_node) p,
                mp_p_plus_fq(mp,
                    (mp_value_node) mp_get_dep_list((mp_value_node) p), u,
                    (mp_value_node) mp_get_dep_list((mp_value_node) q),
                    mp_proto_dependent_type, mp_type(q)));
        }
    }
    if (mp_type(p) == mp_known_type) {
        mp_set_value_number(p, mp_get_value_number(p));
        number_add(mp_get_value_number(p), delta);
    } else {
        mp_number tmp;
        mp_value_node r = (mp_value_node) mp_get_dep_list((mp_value_node) p);
        while (mp_get_dep_info(r) != NULL) {
            r = (mp_value_node) mp_link(r);
        }
        new_number_clone(tmp, mp_get_value_number(r));
        number_add(delta, tmp);
     // number_add(delta, mp_get_value_number(r));
        if (r != (mp_value_node) mp_get_dep_list((mp_value_node) p)) {
            mp_set_value_number(r, delta);
        } else {
            mp_recycle_value(mp, p);
            mp_type(p) = mp_known_type;
            mp_set_value_number(p, delta);
        }
        free_number(tmp);
    }
    if (mp->fix_needed) {
        mp_fix_dependencies(mp);
    }
    free_number(delta);
}

@ @<Transform a known big node@>=
mp_node r, pp, qq; /* list manipulation registers */
mp_set_up_trans(mp, c);
if (mp->cur_exp.type == mp_known_type) {
    /* Transform known by known */
    mp_make_exp_copy(mp, p);
    r = mp_get_value_node(cur_exp_node);
    if (mp->cur_exp.type == mp_transform_type) {
        mp_bilin3(mp, mp_yy_part(r), &(mp->tyy), &(mp_get_value_number(mp_xy_part(q))), &(mp->tyx), &zero_t);
        mp_bilin3(mp, mp_yx_part(r), &(mp->tyy), &(mp_get_value_number(mp_xx_part(q))), &(mp->tyx), &zero_t);
        mp_bilin3(mp, mp_xy_part(r), &(mp->txx), &(mp_get_value_number(mp_yy_part(q))), &(mp->txy), &zero_t);
        mp_bilin3(mp, mp_xx_part(r), &(mp->txx), &(mp_get_value_number(mp_yx_part(q))), &(mp->txy), &zero_t);
    }
    mp_bilin3(mp, mp_y_part(r), &(mp->tyy), &(mp_get_value_number(mp_x_part(q))), &(mp->tyx), &(mp->ty));
    mp_bilin3(mp, mp_x_part(r), &(mp->txx), &(mp_get_value_number(mp_y_part(q))), &(mp->txy), &(mp->tx));
} else {
    pp = mp_stash_cur_exp(mp);
    qq = mp_get_value_node(pp);
    mp_make_exp_copy(mp, p);
    r = mp_get_value_node(cur_exp_node);
    if (mp->cur_exp.type == mp_transform_type) {
        mp_bilin2(mp, mp_yy_part(r), mp_yy_part(qq), &(mp_get_value_number(mp_xy_part(q))), mp_yx_part(qq), NULL);
        mp_bilin2(mp, mp_yx_part(r), mp_yy_part(qq), &(mp_get_value_number(mp_xx_part(q))), mp_yx_part(qq), NULL);
        mp_bilin2(mp, mp_xy_part(r), mp_xx_part(qq), &(mp_get_value_number(mp_yy_part(q))), mp_xy_part(qq), NULL);
        mp_bilin2(mp, mp_xx_part(r), mp_xx_part(qq), &(mp_get_value_number(mp_yx_part(q))), mp_xy_part(qq), NULL);
    }
    mp_bilin2(mp, mp_y_part(r), mp_yy_part(qq), &(mp_get_value_number(mp_x_part(q))), mp_yx_part(qq), mp_y_part(qq));
    mp_bilin2(mp, mp_x_part(r), mp_xx_part(qq), &(mp_get_value_number(mp_y_part(q))), mp_xy_part(qq), mp_x_part(qq));
    mp_recycle_value(mp, pp);
    mp_free_value_node(mp, pp);
}

@ Let |p| be a |mp_proto_dependent| value whose dependency list ends at
|dep_final|. The following procedure adds |v| times another numeric quantity
to~|p|.

@<Declare subroutines needed by |big_trans|@>=
static void mp_add_mult_dep (MP mp, mp_value_node p, mp_number *v, mp_node r)
{
    if (mp_type(r) == mp_known_type) {
        mp_number ret;
        new_number(ret);
        take_scaled(ret, mp_get_value_number(r), *v);
        mp_set_dep_value(mp->dep_final, mp_get_dep_value(mp->dep_final));
        number_add(mp_get_dep_value(mp->dep_final), ret);
        free_number(ret);
    } else {
        mp_set_dep_list(p, mp_p_plus_fq(mp, (mp_value_node) mp_get_dep_list(p), v, (mp_value_node) mp_get_dep_list((mp_value_node) r), mp_proto_dependent_type, mp_type(r)));
        if (mp->fix_needed) {
            mp_fix_dependencies(mp);
        }
    }
}

@ The |bilin2| procedure is something like |bilin1|, but with known and unknown
quantities reversed. Parameter |p| points to a value field within the big node
for |cur_exp|; and |type(p)=mp_known|. Parameters |t| and~|u| point to value
fields elsewhere; so does parameter~|q|, unless it is |NULL| (which stands for
zero). Location~|p| will be replaced by $p\cdot t+v\cdot u+q$.

@<Declare subroutines needed by |big_trans|@>=
static void mp_bilin2 (MP mp, mp_node p, mp_node t, mp_number *v, mp_node u, mp_node q)
{
    mp_number vv; /* temporary storage for |value(p)| */
    new_number_clone(vv, mp_get_value_number(p));
    mp_new_dep(mp, p, mp_proto_dependent_type, mp_const_dependency(mp, &zero_t));    /* this sets |dep_final| */
    if (number_nonzero(vv)) {
        mp_add_mult_dep(mp, (mp_value_node) p, &vv, t); /* |dep_final| doesn't change */
    }
    if (number_nonzero(*v)) {
        mp_number arg1;
        new_number_clone(arg1, *v);
        mp_add_mult_dep(mp, (mp_value_node) p, &arg1, u);
        free_number(arg1);
    }
    if (q != NULL) {
        mp_add_mult_dep(mp, (mp_value_node) p, &unity_t, q);
    }
    if (mp_get_dep_list((mp_value_node) p) == (mp_node) mp->dep_final) {
        number_clone(vv, mp_get_dep_value(mp->dep_final));
        mp_recycle_value(mp, p);
        mp_type(p) = mp_known_type;
        mp_set_value_number(p, vv);
    }
    free_number(vv);
}

@ Finally, in |bilin3| everything is |known|.

@<Declare subroutines needed by |big_trans|@>=
static void mp_bilin3 (MP mp, mp_node p, mp_number *t, mp_number *v, mp_number *u, mp_number *delta_orig)
{
    mp_number delta;
    mp_number tmp;
    new_number(tmp);
    new_number_clone(delta, *delta_orig);
    if (! number_equal(*t, unity_t)) {
        take_scaled(tmp, mp_get_value_number(p), *t);
    } else {
        number_clone(tmp, mp_get_value_number(p));
    }
    number_add(delta, tmp);
    if (number_nonzero(*u)) {
        mp_number ret;
        new_number(ret);
        take_scaled(ret, *v, *u);
        mp_set_value_number(p, delta);
        number_add(mp_get_value_number(p), ret);
        free_number(ret);
    } else {
        mp_set_value_number(p, delta);
    }
    free_number(tmp);
    free_number(delta);
}

@ @<Declare binary action...@>=
static void mp_chop_path (MP mp, mp_node p)
{
    mp_knot q;      /* a knot in the original path */
    mp_knot pp, qq; /* link variables for copies of path nodes */
    mp_number a, b; /* indices for chopping */
    mp_number l;
    int reversed;   /* was |a>b|? */
    new_number(l);
    mp_path_length(mp, &l);
    new_number_clone(a, mp_get_value_number(mp_x_part(p)));
    new_number_clone(b, mp_get_value_number(mp_y_part(p)));
    if (number_lessequal(a, b)) {
        reversed = 0;
    } else {
        reversed = 1;
        number_swap (a, b);
    }
    /* Dispense with the cases |a<0| and/or |b>l| */
    if (number_negative(a)) {
        if (mp_left_type(cur_exp_knot) == mp_endpoint_knot) {
            set_number_to_zero(a);
            if (number_negative(b)) {
                set_number_to_zero(b);
            }
        } else {
            do {
                number_add(a, l);
                number_add(b, l);
            } while (number_negative(a)); /* a cycle always has length |l>0| */
        }
    }
    if (number_greater(b, l)) {
        if (mp_left_type(cur_exp_knot) == mp_endpoint_knot) {
            number_clone(b, l);
            if (number_greater(a, l)) {
                number_clone(a, l);
            }
        } else {
            while (number_greaterequal(a, l)) {
                number_subtract(a, l);
                number_subtract(b, l);
            }
        }
    }
    q = cur_exp_knot;
    while (number_greaterequal(a, unity_t)) {
        q = mp_next_knot(q);
        number_subtract(a, unity_t);
        number_subtract(b, unity_t);
    }
    if (number_equal(b, a)) {
        /* Construct a path from |pp| to |qq| of length zero */
        if (number_positive(a)) {
            mp_number arg1;
            new_number_clone(arg1, a);
            convert_scaled_to_fraction(arg1);
            mp_split_cubic(mp, q, &arg1);
            free_number(arg1);
            q = mp_next_knot(q);
        }
        pp = mp_copy_knot(mp, q);
        qq = pp;
    } else {
        /* Construct a path from |pp| to |qq| of length $\lceil b\rceil$ */
        mp_knot rr;
        pp = mp_copy_knot(mp, q);
        qq = pp;
        do {
            q = mp_next_knot(q);
            rr = qq;
            qq = mp_copy_knot(mp, q);
            mp_prev_knot(qq) = rr;
            mp_next_knot(rr) = qq;
            number_subtract(b, unity_t);
        } while (number_positive(b));
        if (number_positive(a)) {
            mp_knot ss = pp;
            mp_number arg1;
            new_number_clone(arg1, a);
            convert_scaled_to_fraction(arg1);
            mp_split_cubic(mp, ss, &arg1);
            free_number(arg1);
            pp = mp_next_knot(ss);
            mp_toss_knot(mp, ss);
            if (rr == ss) {
                mp_number arg1, arg2;
                new_number(arg1);
                set_number_from_subtraction(arg1, unity_t, a);
                new_number_clone(arg2, b);
                make_scaled(b, arg2, arg1);
                free_number(arg1);
                free_number(arg2);
                rr = pp;
            }
        }
        if (number_negative(b)) {
            mp_number arg1;
            new_number(arg1);
            set_number_from_addition(arg1, b, unity_t);
            convert_scaled_to_fraction(arg1);
            mp_split_cubic(mp, rr, &arg1);
            free_number(arg1);
            mp_toss_knot(mp, qq);
            qq = mp_next_knot(rr);
        }
    }
    mp_left_type(pp) = mp_endpoint_knot;
    mp_right_type(qq) = mp_endpoint_knot;
    mp_prev_knot(pp) = qq;
    mp_next_knot(qq) = pp;
    mp_toss_knot_list(mp, cur_exp_knot);
    if (reversed) {
        mp_set_cur_exp_knot(mp, mp_next_knot(mp_htap_ypoc(mp, pp)));
        mp_toss_knot_list(mp, pp);
    } else {
        mp_set_cur_exp_knot(mp, pp);
    }
    free_number(l);
    free_number(a);
    free_number(b);
}

@ @<Declare binary action...@>=
static void mp_set_up_offset (MP mp, mp_node p)
{
    mp_find_offset(mp, &(mp_get_value_number(mp_x_part(p))), &(mp_get_value_number(mp_y_part(p))), cur_exp_knot);
    mp_pair_value(mp, &(mp->cur_x), &(mp->cur_y));
}

static void mp_set_up_direction_time (MP mp, mp_node p)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_find_direction_time(mp, &new_expr.data.n, &(mp_get_value_number(mp_x_part(p))), &(mp_get_value_number(mp_y_part(p))), cur_exp_knot);
    mp_flush_cur_exp(mp, new_expr);
}

static void mp_set_up_envelope (MP mp, mp_node p)
{
    mp_knot q = mp_copy_path(mp, cur_exp_knot); /* the original path */
    /* TODO: accept elliptical pens for straight paths */
    /* TODO: quite some duplicate code here: maybe make some helpers */
    if (mp_pen_is_elliptical(mp_get_value_knot(p))) {
        mp_bad_envelope_pen(mp);
        mp_set_cur_exp_knot(mp, q);
        mp->cur_exp.type = mp_path_type;
    } else {
        int linejoin = mp_mitered_linejoin_code;
        int linecap = mp_butt_linecap_code;
        mp_number miterlimit;
        new_number(miterlimit);
        if (number_greater(internal_value(mp_linejoin_internal), unity_t)) {
            linejoin = mp_beveled_linejoin_code;
        } else if (number_positive(internal_value(mp_linejoin_internal))) {
            linejoin = mp_rounded_linejoin_code;
        }
        if (number_greater(internal_value(mp_linecap_internal), unity_t)) {
            linecap = mp_squared_linecap_code;
        } else if (number_positive(internal_value(mp_linecap_internal))) {
            linecap = mp_rounded_linecap_code;
        }
        if (number_less(internal_value(mp_miterlimit_internal), unity_t)) {
            set_number_to_unity(miterlimit);
        } else {
            number_clone(miterlimit, internal_value(mp_miterlimit_internal));
        }
        mp_set_cur_exp_knot(mp, mp_make_envelope(mp, q, mp_get_value_knot(p), linejoin, linecap, &miterlimit));
        mp->cur_exp.type = mp_path_type;
    }
}

static void mp_set_up_boundingpath (MP mp, mp_node p)
{
    mp_number miterlimit;
    mp_knot q = mp_copy_path(mp, cur_exp_knot); /* the original path */
    mp_knot qq;
    int linejoin = mp_mitered_linejoin_code;
    int linecap = mp_butt_linecap_code;
    mp_knot pen = mp_get_value_knot(p);
    new_number(miterlimit);
    /*
        Accept elliptical pens for s paths using |mp_make_path| to convert an
        elliptical pen to a polygonal one. The approximation of 8 knots should be
        good enough.
    */
    if (mp_pen_is_elliptical(mp_get_value_knot(p))) {
        mp_knot kp, kq;
        pen = mp_copy_pen(mp, mp_get_value_knot(p));
        mp_make_path(mp, pen);
        kq = pen;
        do {
            kp = kq;
            kq = mp_next_knot(kq);
            mp_prev_knot(kq) = kp;
        } while (kq != pen);
        mp_close_path_cycle(mp, kp, pen);
    }
    if (number_greater(internal_value(mp_linejoin_internal), unity_t)) {
        linejoin = mp_beveled_linejoin_code;
    } else if (number_positive(internal_value(mp_linejoin_internal))) {
        linejoin = mp_rounded_linejoin_code;
    }
    if (number_greater(internal_value(mp_linecap_internal), unity_t)) {
        linecap = mp_squared_linecap_code;
    } else if (number_positive(internal_value(mp_linecap_internal))) {
        linecap = mp_rounded_linecap_code;
    }
    if (number_less(internal_value(mp_miterlimit_internal), unity_t)) {
        set_number_to_unity(miterlimit);
    } else {
        number_clone(miterlimit, internal_value(mp_miterlimit_internal));
    }
    qq = mp_make_envelope(mp, q, pen, linejoin, linecap, &miterlimit);
    mp_set_cur_exp_knot(mp, qq);
    mp->cur_exp.type = mp_path_type;
    if (! mp_get_cur_bbox(mp)) {
        mp_bad_binary(mp, p, mp_boundingpath_operation);
        mp_set_cur_exp_knot(mp, q);
        mp->cur_exp.type = mp_path_type;
        return;
    } else {
        mp_knot ll = mp_new_knot(mp);
        mp_knot lr = mp_new_knot(mp);
        mp_knot ur = mp_new_knot(mp);
        mp_knot ul = mp_new_knot(mp);
        if (ll == NULL || lr == NULL || ur == NULL || ul == NULL){
            mp_bad_binary(mp, p, mp_boundingpath_operation);
            mp_set_cur_exp_knot(mp, q);
            mp->cur_exp.type = mp_path_type;
            return;
        } else {
            mp_left_type(ll) = mp_endpoint_knot;
            mp_right_type(ll) = mp_endpoint_knot;
            mp_originator(ll) = mp_program_code;
            mp_knotstate(ll) = mp_regular_knot;
            number_clone(ll->x_coord, mp_minx);
            number_clone(ll->y_coord, mp_miny);
            mp_originator(lr) = mp_program_code;
            mp_knotstate(lr) = mp_regular_knot;
            number_clone(lr->x_coord, mp_maxx);
            number_clone(lr->y_coord, mp_miny);
            mp_originator(ur) = mp_program_code;
            mp_knotstate(ur) = mp_regular_knot;
            number_clone(ur->x_coord, mp_maxx);
            number_clone(ur->y_coord, mp_maxy);
            mp_originator(ul) = mp_program_code;
            mp_knotstate(ul) = mp_regular_knot;
            number_clone(ul->x_coord, mp_minx);
            number_clone(ul->y_coord, mp_maxy);
            mp_prev_knot(lr) = ll;
            mp_next_knot(ll) = lr;
            mp_prev_knot(ur) = lr;
            mp_next_knot(lr) = ur;
            mp_prev_knot(ul) = ur;
            mp_next_knot(ur) = ul;
            mp_close_path_cycle(mp, ul, ll);
            mp_make_path(mp,ll);
            mp->cur_exp.type = mp_path_type;
            mp_set_cur_exp_knot(mp, ll);
            mp_free_path(mp,qq);
        }
    }
}

@ @<Declare binary action...@>=
static void mp_find_point (MP mp, mp_number *v_orig, int c)
{
    mp_knot p;   /* the path */
    mp_number n; /* its length */
    mp_number v;
    new_number(n);
    new_number_clone(v, *v_orig);
    p = cur_exp_knot;
    if (mp_left_type(p) == mp_endpoint_knot) {
        set_number_to_unity(n);
        number_negate(n);
    }
    do {
        p = mp_next_knot(p);
        number_add(n, unity_t);
    } while (p != cur_exp_knot);
    if (number_zero(n)) {
        set_number_to_zero(v);
    } else if (number_negative(v)) {
        if (mp_left_type(p) == mp_endpoint_knot) {
            set_number_to_zero(v);
        } else    {
            /* |v = n - 1 - ((-v - 1) % n) == - ((-v - 1) % n) - 1 + n| */
            number_negate(v);
            number_add_scaled(v, -1);
            number_modulo(v, n);
            number_negate(v);
            number_add_scaled(v, -1);
            number_add(v, n);
        }
    } else if (number_greater(v, n)) {
        if (mp_left_type(p) == mp_endpoint_knot) {
            number_clone(v, n);
        } else {
            number_modulo(v, n);
        }
    }
    p = cur_exp_knot;
    while (number_greaterequal(v, unity_t)) {
        p = mp_next_knot(p);
        number_subtract(v, unity_t);
    }
    if (number_nonzero(v)) {
        /* Insert a fractional node by splitting the cubic */
        convert_scaled_to_fraction(v);
        mp_split_cubic(mp, p, &v);
        p = mp_next_knot(p);
    }
    /* Set the current expression to the desired path coordinates */
    push_of_path_result(mp, c - mp_point_operation, p);
    free_number(v);
    free_number(n);
}

@* Statements and commands.

The chief executive of \MP\ is the |do_statement| routine, which contains the
master switch that causes all the various pieces of \MP\ to do their things, in
the right order.

In a sense, this is the grand climax of the program: It applies all the tools
that we have worked so hard to construct. In another sense, this is the messiest
part of the program: It necessarily refers to other pieces of code all over the
place, so that a person can't fully understand what is going on without paging
back and forth to be reminded of conventions that are defined elsewhere. We are
now at the hub of the web.

The structure of |do_statement| itself is quite simple. The first token of the
statement is fetched using |get_x_next|. If it can be the first token of an
expression, we look for an equation, an assignment, or a title. Otherwise we use
a |case| construction to branch at high speed to the appropriate routine for
various and sundry other types of commands, each of which has an \quote {action
procedure} that does the necessary work.

The program uses the fact that

$$\hbox{|min_primary_command=max_statement_command=type_name|}$$

to interpret a statement that starts with, e.g., |string|, as a type
declaration rather than a boolean expression.

@c
static void worry_about_bad_statement (MP mp);

static void flush_unparsable_junk_after_statement (MP mp);

void mp_do_statement (MP mp)
{
    /* governs \MP's activities */
    mp->cur_exp.type = mp_vacuous_type;
    mp_get_x_next(mp);
    if (cur_cmd > mp_max_primary_command) {
        worry_about_bad_statement(mp);
    } else if (cur_cmd > mp_max_statement_command) {
        /*
            Do an equation, assignment, title, or
            `$\langle\,$expression$\,\rangle\,$|endgroup|'; The most important
            statements begin with expressions
        */
        mp_value new_expr;
        mp->var_flag = mp_assignment_command;
        mp_scan_expression(mp);
        if (cur_cmd < mp_end_group_command) {
            if (cur_cmd == mp_equals_command) {
                mp_do_equation(mp);
            } else if (cur_cmd == mp_assignment_command) {
                mp_do_assignment(mp);
            } else if (mp->cur_exp.type == mp_string_type) {
                /* Do a title */
                if (number_positive(internal_value(mp_tracing_titles_internal))) {
                    mp_print_nl(mp, "");
                    mp_print_mp_str(mp, cur_exp_str);
                    update_terminal();
                }
            } else if (mp->cur_exp.type != mp_vacuous_type) {
                mp_disp_err(mp, NULL);
                mp_back_error(
                    mp,
                    "Isolated expression",
                    "I couldn't find an '=' or ':=' after the expression that is shown above this\n"
                    "error message, so I guess I'll just ignore it and carry on."
                );
                mp_get_x_next(mp);
            }
            memset(&new_expr, 0, sizeof(mp_value));
            new_number(new_expr.data.n);
            mp_flush_cur_exp(mp, new_expr);
            mp->cur_exp.type = mp_vacuous_type;
        }
    } else {
        /*
            Do a statement that doesn't begin with an expression. If |do_statement|
            ends with |cur_cmd=end_group|, we should have |cur_type=mp_vacuous| unless
            the statement was simply an expression; in the latter case, |cur_type| and
            |cur_exp| should represent that expression.
        */
        if (number_positive(internal_value(mp_tracing_commands_internal))) {
            mp_show_cmd_mod(mp, cur_cmd, cur_mod);
        }
        switch (cur_cmd) {
            case mp_type_name_command:
                mp_do_type_declaration(mp);
                break;
            case mp_macro_def_command:
                switch (cur_mod) {
                    case mp_def_code:
                    case mp_var_def_code:
                        mp_scan_def(mp, cur_mod);
                        break;
                    case mp_primary_def_code:
                    case mp_secondary_def_code:
                    case mp_tertiary_def_code:
                        mp_make_op_def(mp, cur_mod);
                        break;
                }
                break;
            case mp_only_set_command:
                switch (cur_mod) {
                    case mp_random_seed_code:
                        mp_do_random_seed(mp);
                        break;
                    case mp_max_knot_pool_code:
                        mp_do_max_knot_pool(mp);
                        break;
                }
                break;
            case mp_mode_command:
                mp_print_ln(mp);
                mp->interaction = cur_mod;
                mp->selector = mp->interaction == mp_batch_mode ? mp_log_only_selector : mp_term_and_log_selector;
                mp_get_x_next(mp);
                break;
            case mp_protection_command:
                mp_do_protection(mp);
                break;
            case mp_property_command:
                mp_do_property(mp);
                break;
            case mp_delimiters_command:
                mp_def_delims(mp);
                break;
            case mp_save_command:
                do {
                    mp_get_symbol(mp);
                    mp_save_variable(mp, cur_sym);
                    mp_get_x_next(mp);
                } while (cur_cmd == mp_comma_command);
                break;
            case mp_interim_command:
                mp_do_interim(mp);
                break;
            case mp_let_command:
                mp_do_let(mp);
                break;
            case mp_new_internal_command:
                mp_do_new_internal(mp);
                break;
            case mp_show_command:
                mp_do_show_whatever(mp);
                break;
            case mp_add_to_command:
                mp_do_add_to(mp);
                break;
            case mp_bounds_command:
                mp_do_bounds(mp);
                break;
            case mp_ship_out_command:
                mp_do_ship_out(mp);
                break;
            case mp_every_job_command:
                mp_get_symbol(mp);
                mp->every_job_sym = cur_sym;
                mp_get_x_next(mp);
                break;
            case mp_message_command:
                mp_do_message(mp);
                break;
            case mp_write_command:
                mp_do_write(mp);
                break;
            default:
                break;
        }
        mp->cur_exp.type = mp_vacuous_type;
    }
    if (cur_cmd < mp_semicolon_command) {
        flush_unparsable_junk_after_statement(mp);
    }
    mp->error_count = 0;
}

@ @<Declarations@>=
@<Declare action procedures for use by |do_statement|@>

@ The only command codes |>max_primary_command| that can be present at the
beginning of a statement are |semicolon| and higher; these occur when the
statement is null.

@c
static void worry_about_bad_statement (MP mp)
{
  if (cur_cmd < mp_semicolon_command) {
    char msg[256];
    mp_string sname;
    int selector = mp->selector;
    mp->selector = mp_new_string_selector;
    mp_print_cmd_mod(mp, cur_cmd, cur_mod);
    sname = mp_make_string(mp);
    mp->selector = selector;
    mp_snprintf(msg, 256, "A statement can't begin with '%s'", mp_str(mp, sname));
    delete_str_ref(sname);
    mp_back_error(
        mp,
        msg,
        "I was looking for the beginning of a new statement. If you just proceed without\n"
        "changing anything, I'll ignore everything up to the next ';'."
    );
    mp_get_x_next(mp);
  }
}

@ The help message printed here says that everything is flushed up to
a semicolon, but actually the commands |end_group| and |stop| will
also terminate a statement.

@c
static void flush_unparsable_junk_after_statement (MP mp)
{
    mp_back_error(
        mp,
        "Extra tokens will be flushed",
        "I've just read as much of that statement as I could fathom, so a semicolon should\n"
        "have been next. It's very puzzling ... but I'll try to get myself back together,\n"
        "by ignoring everything up to the next ';'."
    );
    mp->scanner_status = mp_flushing_state;
    do {
        get_t_next(mp);
        if (cur_cmd == mp_string_command) {
            delete_str_ref(cur_mod_str);
        }
    } while (! mp_end_of_statement); /* |cur_cmd=semicolon|, |end_group|, or |stop| */
    mp->scanner_status = mp_normal_state;
}

@ Equations and assignments are performed by the pair of mutually recursive
@^recursion@> routines |do_equation| and |do_assignment|. These routines are
called when |cur_cmd=equals| and when |cur_cmd=assignment|, respectively; the
left-hand side is in |cur_type| and |cur_exp|, while the right-hand side is yet
to be scanned. After the routines are finished, |cur_type| and |cur_exp| will be
equal to the right-hand side (which will normally be equal to the left-hand
side).

@<Declarations@>=
@<Declare the procedure called |make_eq|@>
static void mp_do_equation (MP mp);

@ @c
static void trace_equation (MP mp, mp_node lhs)
{
    mp_begin_diagnostic(mp);
    mp_print_nl(mp, "{(");
    mp_print_exp(mp, lhs, 0);
    mp_print_str(mp, ")=(");
    mp_print_exp(mp, NULL, 0);
    mp_print_str(mp, ")}");
    mp_end_diagnostic(mp, 0);
}

void mp_do_equation (MP mp)
{
    mp_node lhs = mp_stash_cur_exp(mp); /* capsule for the left-hand side */
    mp_get_x_next(mp);
    mp->var_flag = mp_assignment_command;
    mp_scan_expression(mp);
    if (cur_cmd == mp_equals_command) {
        mp_do_equation(mp);
    } else if (cur_cmd == mp_assignment_command) {
        mp_do_assignment(mp);
    }
    if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
        trace_equation(mp, lhs);
    }
    if (mp->cur_exp.type == mp_unknown_path_type) {
        if (mp_type(lhs) == mp_pair_type) {
            mp_node p; /* temporary register */
            p = mp_stash_cur_exp(mp);
            mp_unstash_cur_exp(mp, lhs);
            lhs = p;
        }
        /* in this case |make_eq| will change the pair to a path */
    }
    mp_make_eq(mp, lhs); /* equate |lhs| to |(cur_type,cur_exp)| */
}

@ And |do_assignment| is similar to |do_equation|:

@<Declarations@>=
static void mp_do_assignment (MP mp);

@ @c
static void bad_lhs (MP mp)
{
    mp_disp_err(mp, NULL);
    mp_error(
        mp,
        "Improper ':=' will be changed to '='",
        "I didn't find a variable name at the left of the ':=', so I'm going to pretend\n"
        "that you said '=' instead."
    );
    mp_do_equation(mp);
}

static void bad_internal_assignment (MP mp, mp_node lhs)
{
    char msg[256];
    mp_disp_err(mp, NULL);
    if (internal_type(mp_get_sym_info(lhs)) == mp_known_type) {
        mp_snprintf(msg, 256,
            "Internal quantity '%s' must receive a known numeric value",
            internal_name(mp_get_sym_info(lhs))
        );
        mp_back_error(
            mp,
            msg,
            "I can't set this internal quantity to anything but a known numeric value, so I'll\n"
            "have to ignore this assignment."
        );
    } else if (internal_type(mp_get_sym_info(lhs)) == mp_boolean_type) {
        mp_snprintf(msg, 256,
            "Internal quantity '%s' must receive a known boolean value",
            internal_name(mp_get_sym_info(lhs))
        );
        mp_back_error(
            mp,
            msg,
            "I can't set this internal quantity to anything but a known boolean value, so I'll\n"
            "have to ignore this assignment."
        );
    } else {
        mp_snprintf(msg, 256,
            "Internal quantity '%s' must receive a known string",
            internal_name(mp_get_sym_info(lhs))
        );
        mp_back_error(
            mp,
            msg,
            "I can't set this internal quantity to anything but a known string value, so I'll\n"
            "have to ignore this assignment."
        );
    }
    mp_get_x_next(mp);
}

static void forbidden_internal_assignment (MP mp, mp_node lhs)
{
    char msg[256];
    mp_snprintf(msg, 256,"Internal quantity '%s' is read-only", internal_name(mp_get_sym_info(lhs)));
    mp_back_error(
        mp,
        msg,
        "I can't set this internal quantity to anything just yet (it is read-only), so\n"
        "I'll have to ignore this assignment."
    );
    mp_get_x_next(mp);
}

static void bad_internal_assignment_precision (MP mp, mp_node lhs, mp_number *min, mp_number *max)
{
    char msg[256];
    char hlp[256];
    mp_snprintf(msg, 256,
        "Bad '%s' has been ignored",
        internal_name(mp_get_sym_info(lhs)));
    mp_snprintf(hlp, 256,
        "Precision values are limited by the current numbersystem.\n"
        "Currently I am using '%s'; the allowed precision range is [%s,%s].",
        mp_str(mp, internal_string(mp_number_system_internal)), number_tostring(*min), number_tostring(*max));
    mp_back_error(mp, msg, hlp);
    mp_get_x_next(mp);
}

static void bad_expression_assignment (MP mp, mp_node lhs)
{
    char *msg = mp_obliterated(mp, lhs);
    mp_back_error(
        mp,
        msg,
        "It seems you did a nasty thing --- probably by accident, but nevertheless you\n"
        "nearly hornswoggled me ... While I was evaluating the right-hand side of this\n"
        "command, something happened, and the left-hand side is no longer a variable! So I\n"
        "won't change anything."
    );
    mp_memory_free(msg);
    mp_get_x_next(mp);
}

static void trace_assignment (MP mp, mp_node lhs)
{
    mp_begin_diagnostic(mp);
    mp_print_nl(mp, "{");
    if (mp_name_type(lhs) == mp_internal_operation) {
        mp_print_str(mp, internal_name(mp_get_sym_info(lhs)));
    } else {
        mp_show_token_list(mp, lhs, NULL);
    }
    mp_print_str(mp, ":=");
    mp_print_exp(mp, NULL, 0);
    mp_print_chr(mp, '}');
    mp_end_diagnostic(mp, 0);
}

void mp_do_assignment (MP mp)
{
    if (mp->cur_exp.type != mp_token_list_type) {
        bad_lhs(mp);
    } else {
        mp_node lhs = cur_exp_node; /* token list for the left-hand side */
        mp->cur_exp.type = mp_vacuous_type;
        mp_get_x_next(mp);
        mp->var_flag = mp_assignment_command;
        mp_scan_expression(mp);
        if (cur_cmd == mp_equals_command) {
            mp_do_equation(mp);
        } else if (cur_cmd == mp_assignment_command) {
            mp_do_assignment(mp);
        }
        if (number_greater(internal_value(mp_tracing_commands_internal), two_t)) {
            trace_assignment (mp, lhs);
        }
        if (mp_name_type(lhs) == mp_internal_operation) {
            /* Assign the current expression to an internal variable */
            switch (mp->cur_exp.type) {
                case mp_known_type:
                case mp_string_type:
                case mp_boolean_type:
                    if (internal_type(mp_get_sym_info(lhs)) == mp->cur_exp.type) {
                        switch (mp_get_sym_info(lhs)) {
                            case mp_number_system_internal:
                                forbidden_internal_assignment(mp, lhs);
                                break;
                         // case mp_tracing_online_internal:
                         //     number_clone(internal_value(mp_get_sym_info(lhs)), cur_exp_value_number);
                         //     mp->run_internal(mp, 3, mp->int_ptr, number_to_int(internal_value(mp_get_sym_info(lhs))), internal_name(mp_get_sym_info(lhs)));
                         //     break;
                            case mp_number_precision_internal:
                                if (mp->cur_exp.type == mp_known_type
                                      && (! number_less   (cur_exp_value_number, precision_min))
                                      && (! number_greater(cur_exp_value_number, precision_max))
                                    ) {
                                     if (internal_type(mp_get_sym_info(lhs)) == mp_string_type) {
                                         add_str_ref(cur_exp_str);
                                         set_internal_string(mp_get_sym_info(lhs), cur_exp_str);
                                     } else {
                                         number_clone(internal_value(mp_get_sym_info(lhs)), cur_exp_value_number);
                                     }
                                     set_precision();
                                } else {
                                    bad_internal_assignment_precision(mp, lhs, &precision_min, &precision_max);
                                }
                            default:
                                if (internal_type(mp_get_sym_info(lhs)) == mp_string_type) {
                                    add_str_ref(cur_exp_str);
                                    set_internal_string(mp_get_sym_info(lhs), cur_exp_str);
                                } else {
                                    number_clone(internal_value(mp_get_sym_info(lhs)), cur_exp_value_number);
                                }
                                break;
                        }
                    } else {
                        bad_internal_assignment(mp, lhs);
                    }
                    break;
                default:
                    bad_internal_assignment(mp, lhs);
                }
        } else {
            /* Assign the current expression to the variable |lhs| */
            mp_node p = mp_find_variable(mp, lhs); /* where the left-hand value is stored */
            if (p != NULL) {
                mp_node q = mp_stash_cur_exp(mp); /* temporary capsule for the right-hand value */
                mp->cur_exp.type = mp_und_type(mp, p);
                mp_recycle_value(mp, p);
                mp_type(p) = mp->cur_exp.type;
                mp_set_value_number(p, zero_t);
                mp_make_exp_copy(mp, p);
                p = mp_stash_cur_exp(mp);
                mp_unstash_cur_exp(mp, q);
                mp_make_eq(mp, p);
            } else {
                bad_expression_assignment(mp, lhs);
            }
        }
        mp_flush_node_list(mp, lhs);
    }
}

@ And now we get to the nitty-gritty. The |make_eq| procedure is given a pointer
to a capsule that is to be equated to the current expression.

@<Declare the procedure called |make_eq|@>=
static void mp_make_eq (MP mp, mp_node lhs);

@ @c
static void announce_bad_equation (MP mp, mp_node lhs)
{
    char msg[256];
    mp_snprintf(msg, 256,
        "Equation cannot be performed (%s=%s)",
        (mp_type(lhs) <= mp_pair_type ? mp_type_string(mp_type(lhs)) : "numeric"),
        (mp->cur_exp.type <= mp_pair_type ? mp_type_string(mp->cur_exp.type) : "numeric"));
    mp_disp_err(mp, lhs);
    mp_disp_err(mp, NULL);
    mp_back_error(
        mp,
        msg,
        "I'm sorry, but I don't know how to make such things equal. (See the two\n"
        "expressions just above the error message.)"
    );
    mp_get_x_next(mp);
}

static void mp_exclaim_inconsistent_equation (MP mp)
{
    mp_back_error(
        mp,
        "Inconsistent equation",
        "The equation I just read contradicts what was said before. But don't worry;\n"
        "continue and I'll just ignore it."
    );
    mp_get_x_next(mp);
}

static void mp_exclaim_redundant_or_inconsistent_equation (MP mp)
{
    mp_back_error(
        mp,
        "Redundant or inconsistent equation",
        "An equation between already-known quantities can't help. But don't worry;\n"
        "continue and I'll just ignore it."
    );
    mp_get_x_next(mp);
}

static void report_redundant_or_inconsistent_equation (MP mp, mp_node lhs, mp_number *v)
{
    if (mp->cur_exp.type <= mp_string_type) {
        if (mp->cur_exp.type == mp_string_type) {
            if (mp_str_vs_str(mp, mp_get_value_str(lhs), cur_exp_str) != 0) {
                mp_exclaim_inconsistent_equation(mp);
            } else {
                mp_exclaim_redundant_equation(mp);
            }
        } else if (number_equal(*v, cur_exp_value_number)) {
            mp_exclaim_redundant_equation(mp);
        } else {
            mp_exclaim_inconsistent_equation(mp);
        }
    } else {
        mp_exclaim_redundant_or_inconsistent_equation(mp);
    }
}

void mp_make_eq (MP mp, mp_node lhs)
{
    mp_value new_expr;
    mp_variable_type t; /* type of the left-hand side */
    mp_number v;        /* value of the left-hand side */
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(v);
  RESTART:
    t = mp_type(lhs);
    if (t <= mp_pair_type) {
        number_clone(v, mp_get_value_number(lhs));
    }
    /*
        For each type |t|, make an equation or complain if |cur_type| is
        incompatible with~|t|
    */
    switch (t) {
        case mp_boolean_type:
        case mp_string_type:
        case mp_pen_type:
        case mp_nep_type:
        case mp_path_type:
        case mp_picture_type:
            if (mp->cur_exp.type == t + unknown_tag) {
                new_number(new_expr.data.n);
                switch (t) {
                    case mp_boolean_type:
                        number_clone(new_expr.data.n, v);
                        break;
                    case mp_string_type:
                        new_expr.data.str = mp_get_value_str(lhs);
                        break;
                    case mp_picture_type:
                        new_expr.data.node = mp_get_value_node(lhs);
                        break;
                    default:
                        /* pen or path */
                        new_expr.data.p = mp_get_value_knot(lhs);
                        break;
                }
                mp_nonlinear_eq(mp, new_expr, cur_exp_node, 0);
                mp_unstash_cur_exp(mp, cur_exp_node);
            } else if (mp->cur_exp.type == t) {
                report_redundant_or_inconsistent_equation(mp, lhs, &v);
            } else {
                announce_bad_equation(mp, lhs);
            }
            break;
        case mp_unknown_boolean_type:
        case mp_unknown_string_type:
        case mp_unknown_pen_type:
        case mp_unknown_nep_type:
        case mp_unknown_path_type:
        case mp_unknown_picture_type:
            if (mp->cur_exp.type == t - unknown_tag) {
                mp_nonlinear_eq(mp, mp->cur_exp, lhs, 1);
            } else if (mp->cur_exp.type == t) {
                mp_ring_merge (mp, lhs, cur_exp_node);
            } else if (mp->cur_exp.type == mp_pair_type) {
                if (t == mp_unknown_path_type) {
                    mp_pair_to_path(mp);
                    goto RESTART;
                }
            } else {
                announce_bad_equation(mp, lhs);
            }
            break;
        case mp_transform_type:
        case mp_color_type:
        case mp_cmykcolor_type:
        case mp_pair_type:
            if (mp->cur_exp.type == t) {
                /* Do multiple equations */
                mp_node q = mp_get_value_node(cur_exp_node);
                mp_node p = mp_get_value_node(lhs);
                switch (t) {
                    case mp_transform_type:
                        mp_try_eq(mp, mp_yy_part(p), mp_yy_part(q));
                        mp_try_eq(mp, mp_yx_part(p), mp_yx_part(q));
                        mp_try_eq(mp, mp_xy_part(p), mp_xy_part(q));
                        mp_try_eq(mp, mp_xx_part(p), mp_xx_part(q));
                        mp_try_eq(mp, mp_ty_part(p), mp_ty_part(q));
                        mp_try_eq(mp, mp_tx_part(p), mp_tx_part(q));
                        break;
                    case mp_color_type:
                        mp_try_eq(mp, mp_blue_part(p),  mp_blue_part(q));
                        mp_try_eq(mp, mp_green_part(p), mp_green_part(q));
                        mp_try_eq(mp, mp_red_part(p),   mp_red_part(q));
                        break;
                    case mp_cmykcolor_type:
                        mp_try_eq(mp, mp_black_part(p),   mp_black_part(q));
                        mp_try_eq(mp, mp_yellow_part(p),  mp_yellow_part(q));
                        mp_try_eq(mp, mp_magenta_part(p), mp_magenta_part(q));
                        mp_try_eq(mp, mp_cyan_part(p),    mp_cyan_part(q));
                        break;
                    case mp_pair_type:
                        mp_try_eq(mp, mp_y_part(p), mp_y_part(q));
                        mp_try_eq(mp, mp_x_part(p), mp_x_part(q));
                        break;
                    default:
                        break;
                }
            } else {
                announce_bad_equation(mp, lhs);
            }
            break;
        case mp_known_type:
        case mp_dependent_type:
        case mp_proto_dependent_type:
        case mp_independent_type:
            if (mp->cur_exp.type >= mp_known_type) {
                mp_try_eq(mp, lhs, NULL);
            } else {
                announce_bad_equation(mp, lhs);
            }
            break;
        case mp_vacuous_type:
            announce_bad_equation(mp, lhs);
            break;
        default:
            announce_bad_equation(mp, lhs);
            break;
    }
    check_arith();
    mp_recycle_value(mp, lhs);
    free_number(v);
    mp_free_value_node(mp, lhs);
}

@ The first argument to |try_eq| is the location of a value node in a capsule
that will soon be recycled. The second argument is either a location within a
pair or transform node pointed to by |cur_exp|, or it is |NULL| (which means that
|cur_exp| itself serves as the second argument). The idea is to leave |cur_exp|
unchanged, but to equate the two operands.


@<Declarations@>=
static void mp_try_eq (MP mp, mp_node l, mp_node r);

@d equation_threshold_k mp->math->md_equation_threshold_t

@ @c
static void deal_with_redundant_or_inconsistent_equation (MP mp, mp_value_node p, mp_node r)
{
    mp_number absp;
    new_number_abs(absp, mp_get_value_number(p));
    if (number_greater(absp, equation_threshold_k)) {   /* off by .001 or more */
        char msg[256];
        mp_snprintf(msg, 256, "Inconsistent equation (off by %s)", number_tostring (mp_get_value_number(p)));
        mp_back_error(
            mp,
            msg,
            "The equation I just read contradicts what was said before. But don't worry;\n"
            "continue and I'll just ignore it."
        );
        mp_get_x_next(mp);
    } else if (r == NULL) {
        mp_exclaim_redundant_equation(mp);
    }
    free_number(absp);
    mp_free_dep_node(mp, p);
}

void mp_try_eq (MP mp, mp_node l, mp_node r)
{
    mp_value_node p;     /* dependency list for right operand minus left operand */
    mp_value_node q;     /* the constant term of |p| is here */
    mp_value_node pp;    /* dependency list for right operand */
    mp_variable_type tt; /* the type of list |pp| */
    int copied;          /* have we copied a list that ought to be recycled? */
    /*
        Remove the left operand from its container, negate it, and put it into
        dependency list~|p| with constant term~|q|
    */
    mp_variable_type t = mp_type(l); /* the type of list |p| */
    switch (t) {
        case mp_known_type:
            {
                mp_number arg1;
                new_number(arg1);
                number_negated_clone(arg1, mp_get_value_number(l));
                t = mp_dependent_type;
                p = mp_const_dependency(mp, &arg1);
                q = p;
                free_number(arg1);
            }
            break;
        case mp_independent_type:
            {
                t = mp_dependent_type;
                p = mp_single_dependency(mp, l);
                number_negate(mp_get_dep_value(p));
                q = mp->dep_final;
            }
            break;
        default:
            {
                mp_value_node ll = (mp_value_node) l;
                p = (mp_value_node) mp_get_dep_list(ll);
                q = p;
                while (1) {
                    number_negate(mp_get_dep_value(q));
                    if (mp_get_dep_info(q) == NULL) {
                        break;
                    } else {
                        q = (mp_value_node) mp_link(q);
                    }
                }
                mp_link(mp_get_prev_dep(ll)) = mp_link(q);
                mp_set_prev_dep((mp_value_node) mp_link(q), mp_get_prev_dep(ll));
                mp_type(ll) = mp_known_type;
            }
            break;
    }
    /* Add the right operand to list |p| */
    if (r == NULL) {
        if (mp->cur_exp.type == mp_known_type) {
            number_add(mp_get_value_number(q), cur_exp_value_number);
            goto DONE1;
        } else {
            tt = mp->cur_exp.type;
            if (tt == mp_independent_type) {
                pp = mp_single_dependency(mp, cur_exp_node);
            } else {
                pp = (mp_value_node) mp_get_dep_list((mp_value_node) cur_exp_node);
            }
        }
    } else if (mp_type(r) == mp_known_type) {
        number_add(mp_get_dep_value(q), mp_get_value_number(r));
        goto DONE1;
    } else {
        tt = mp_type(r);
        if (tt == mp_independent_type) {
            pp = mp_single_dependency(mp, r);
        } else {
            pp = (mp_value_node) mp_get_dep_list((mp_value_node) r);
        }
    }
    if (tt != mp_independent_type) {
        copied = 0;
    } else {
        copied = 1;
        tt = mp_dependent_type;
    }
    /* Add dependency list |pp| of type |tt| to dependency list~|p| of type~|t| */
    mp->watch_coefs = 0;
    if (t == tt) {
        p = mp_p_plus_q(mp, p, pp, (int) t);
    } else if (t == mp_proto_dependent_type) {
        p = mp_p_plus_fq(mp, p, &unity_t, pp, mp_proto_dependent_type, mp_dependent_type);
    } else {
        mp_number x;
        new_number(x);
        q = p;
        while (mp_get_dep_info(q) != NULL) {
            number_clone(x, mp_get_dep_value(q));
            fraction_to_round_scaled(x);
            mp_set_dep_value(q, x);
            q = (mp_value_node) mp_link(q);
        }
        free_number(x);
        t = mp_proto_dependent_type;
        p = mp_p_plus_q(mp, p, pp, (int) t);
    }
    mp->watch_coefs = 1;
    if (copied) {
        mp_flush_node_list(mp, (mp_node) pp);
    }
  DONE1:
    if (mp_get_dep_info(p) == NULL) {
        deal_with_redundant_or_inconsistent_equation(mp, p, r);
    } else {
        mp_linear_eq(mp, p, (int) t);
        if (r == NULL && mp->cur_exp.type != mp_known_type && mp_type(cur_exp_node) == mp_known_type) {
            mp_node pp = cur_exp_node;
            mp_set_cur_exp_value_number(mp, &(mp_get_value_number(pp)));
            mp->cur_exp.type = mp_known_type;
            mp_free_value_node(mp, pp);
        }
    }
}

@ Our next goal is to process type declarations. For this purpose it's convenient
to have a procedure that scans a $\langle\,$declared variable$\,\rangle$ and
returns the corresponding token list. After the following procedure has acted,
the token after the declared variable will have been scanned, so it will appear
in |cur_cmd|, |cur_mod|, and~|cur_sym|.

@<Declarations@>=
static mp_node mp_scan_declared_variable (MP mp);

@ @c
mp_node mp_scan_declared_variable (MP mp)
{
    mp_sym x;     /* hash address of the variable's root */
    mp_node h, t; /* head and tail of the token list to be returned */
    mp_get_symbol(mp);
    x = cur_sym;
    if (cur_cmd != mp_tag_command) {
        mp_clear_symbol(mp, x, 0);
    }
    h = mp_new_symbolic_node(mp);
    mp_set_sym_sym(h, x);
    t = h;
    while (1) {
        mp_get_x_next(mp);
        if (cur_sym == NULL) {
            break;
        } else if (cur_cmd != mp_tag_command) {
            /* could be smarter: */
            if (cur_cmd != mp_internal_command) {
                if (cur_cmd == mp_left_bracket_command) {
                    /*
                        Descend past a collective subscript If the subscript
                        isn't collective, we don't accept it as part of the
                        declared variable.
                    */
                    mp_sym ll = cur_sym; /* hash address of left bracket */
                    mp_get_x_next(mp);
                    if (cur_cmd == mp_right_bracket_command) {
                        set_cur_sym(mp_collective_subscript);
                    } else {
                        mp_back_input(mp);
                        set_cur_sym(ll);
                        set_cur_cmd(mp_left_bracket_command);
                        break;
                    }
                } else {
                    break;
                }
          }
        }
        mp_link(t) = mp_new_symbolic_node(mp);
        t = mp_link(t);
        mp_set_sym_sym(t, cur_sym);
        mp_name_type(t) = cur_sym_mod;
    }
    if (eq_property(x) != 0) {
        mp_check_overload(mp, x);
    }
 // if ((eq_type(x) % mp_outer_tag_command) != mp_tag_command) {
    if (eq_type(x) != mp_tag_command) {
        mp_clear_symbol(mp, x, 0);
    }
    if (equiv_node(x) == NULL) {
        mp_new_root (mp, x);
    }
    return h;
}

@ Type declarations are introduced by the following primitive operations.

@ @<Put each...@>=
mp_primitive(mp, "numeric", mp_type_name_command, mp_numeric_type_operation);
@:numeric_}{|numeric| primitive@>
mp_primitive(mp, "string", mp_type_name_command, mp_string_type_operation);
@:string_}{|string| primitive@>
mp_primitive(mp, "boolean", mp_type_name_command, mp_boolean_type_operation);
@:boolean_}{|boolean| primitive@>
mp_primitive(mp, "path", mp_type_name_command, mp_path_type_operation);
@:path_}{|path| primitive@>
mp_primitive(mp, "pen", mp_type_name_command, mp_pen_type_operation);
@:pen_}{|pen| primitive@>
mp_primitive(mp, "nep", mp_type_name_command, mp_nep_type_operation);
@:nep_}{|nep| primitive@>
mp_primitive(mp, "picture", mp_type_name_command, mp_picture_type_operation);
@:picture_}{|picture| primitive@>
mp_primitive(mp, "transform", mp_type_name_command, mp_transform_type_operation);
@:transform_}{|transform| primitive@>
mp_primitive(mp, "color", mp_type_name_command, mp_color_type_operation);
@:color_}{|color| primitive@>
mp_primitive(mp, "rgbcolor", mp_type_name_command, mp_color_type_operation);
@:color_}{|rgbcolor| primitive@>
mp_primitive(mp, "cmykcolor", mp_type_name_command, mp_cmykcolor_type_operation);
@:color_}{|cmykcolor| primitive@>
mp_primitive(mp, "pair", mp_type_name_command, mp_pair_type_operation);
@:pair_}{|pair| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_type_name_command:
 /* return mp_type_string(mp, m): */
    return "";

@ Now we are ready to handle type declarations, assuming that a |type_name| has
just been scanned. We don't use the type to operation mix here, we just have
am extra set of operations and a switch that maps on type.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_type_declaration (MP mp);

@ @c
static void flush_spurious_symbols_after_declared_variable (MP mp);

void mp_do_type_declaration (MP mp)
{
    int t = mp_numeric_type; /* cur_mod >= mp_transform_type ? cur_mod : cur_mod + unknown_tag; */ /* the type being declared */
    switch (cur_mod) {
        case mp_string_type_operation:    t = mp_unknown_string_type; break;
        case mp_boolean_type_operation:   t = mp_unknown_boolean_type; break;
        case mp_path_type_operation:      t = mp_unknown_path_type; break;
        case mp_pen_type_operation:       t = mp_unknown_pen_type; break;
        case mp_nep_type_operation:       t = mp_unknown_nep_type; break;
        case mp_picture_type_operation:   t = mp_unknown_picture_type; break;
        case mp_transform_type_operation: t = mp_transform_type;  break;
        case mp_color_type_operation:     t = mp_color_type; break;
        case mp_cmykcolor_type_operation: t = mp_cmykcolor_type; break;
        case mp_pair_type_operation:      t = mp_pair_type; break;
        case mp_numeric_type_operation:   t = mp_numeric_type; break;
    }

    do {
        mp_node p = mp_scan_declared_variable(mp); /* token list for a declared variable */
        mp_node q;                                 /* value node for the variable */
        mp_flush_variable(mp, equiv_node(mp_get_sym_sym(p)), mp_link(p), 0);
        q = mp_find_variable(mp, p);
        if (q != NULL) {
            mp_type(q) = t;
            mp_set_value_number(q, zero_t); /* todo: this was |null| */
        } else {
            mp_back_error(
                mp,
                "Declared variable conflicts with previous vardef",
                "You can't use, e.g., 'numeric foo[]' after 'vardef foo'. Proceed, and I'll ignore\n"
                "the illegal redeclaration."
            );
            mp_get_x_next(mp);
        }
        mp_flush_node_list(mp, p);
        if (cur_cmd < mp_comma_command) {
            flush_spurious_symbols_after_declared_variable(mp);
        }
    } while (! mp_end_of_statement);
}

@
@c
static void flush_spurious_symbols_after_declared_variable (MP mp)
{
    const char *hlp = NULL;
    if (cur_cmd == mp_numeric_command) {
        hlp =
            "Variables in declarations must consist entirely of names and explicit subscripts\n"
            "like 'x15a' aren't permitted. I'm going to discard the junk I found here, up to the\n"
            "next comma or the end of the declaration.";
    } else {
        hlp =
            "Variables in declarations must consist entirely of names and collective\n"
            "subscripts, e.g., 'x[]a'. Are you trying to use a reserved word in a variable\n"
            "name? I'm going to discard the junk I found here, up to the next comma or the end\n"
            "of the declaration.";
    }
    mp_back_error(
        mp,
        "Illegal suffix of declared variable will be flushed",
        hlp
    );
    mp_get_x_next(mp);
    mp->scanner_status = mp_flushing_state;
    do {
        get_t_next(mp);
        @<Decrease the string reference count...@>
    } while (cur_cmd < mp_comma_command); /* break on either |end_of_statement| or |comma| */
    mp->scanner_status = mp_normal_state;
}

@ \MP's |main_control| procedure just calls |do_statement| repeatedly until
coming to the end of the user's program. Each execution of |do_statement|
concludes with |cur_cmd=semicolon|, |end_group|, or |stop|.

@c
static void mp_main_control (MP mp) {
    do {
        mp_do_statement(mp);
        if (cur_cmd == mp_end_group_command) {
            mp_value new_expr;
            memset(&new_expr, 0, sizeof(mp_value));
            new_number(new_expr.data.n);
            mp_error(
                mp,
                "Extra 'endgroup'",
                "I'm not currently working on a 'begingroup', so I had better not try to end\n"
                "anything."
            );
            mp_flush_cur_exp(mp, new_expr);
        }
    } while (cur_cmd != mp_stop_command);
}

int mp_run (MP mp)
{
    if (mp->history < mp_fatal_error_stop) {
        mp_memory_free(mp->jump_buf);
        mp->jump_buf = mp_memory_allocate(sizeof(jmp_buf));
        if (mp->jump_buf == NULL || setjmp (*(mp->jump_buf)) != 0) {
            return mp->history;
        }
        mp_main_control(mp);  /* come to life */
        mp_final_cleanup(mp); /* prepare for death */
        mp_close_files_and_terminate(mp);
    }
    return mp->history;
}

@ This function allows setting of internals from an external source (like the
command line or a controlling application).

It accepts two |char *|'s, even for numeric assignments when it calls |atoi| to
get an integer from the start of the string.

@c
void mp_set_internal (MP mp, char *n, char *v, int isstring)
{
    size_t l = strlen(n);
    char err[256];
    const char *errid = NULL;
    if (l > 0) {
        mp_sym p = mp_id_lookup(mp, n, l, 0);
        if (p == NULL) {
            errid = "variable does not exist";
        } else if (eq_type(p) != mp_internal_command) {
            errid = "variable is not an internal";
        } else if ((internal_type(equiv(p)) == mp_string_type) && (isstring)) {
            set_internal_string(equiv(p), mp_rts(mp, v));
        } else if ((internal_type(equiv(p)) == mp_known_type) && (! isstring)) {
            int test = atoi(v);
            if (test > 16383 && mp->math_mode == mp_math_scaled_mode) {
                errid = "value is too large";
            } else if (test < -16383 && mp->math_mode == mp_math_scaled_mode) {
                errid = "value is too small";
            } else {
                number_clone(internal_value(equiv(p)), unity_t);
                number_multiply_int(internal_value(equiv(p)), test);
            }
        } else {
            errid = "value has the wrong type";
        }
    }
    if (errid != NULL) {
        if (isstring) {
            mp_snprintf(err, 256, "%s=\"%s\": %s, assignment ignored.", n, v, errid);
        } else {
            mp_snprintf(err, 256, "%s=%d: %s, assignment ignored.", n, atoi (v), errid);
        }
        mp_warn(mp, err);
    }
}

@ @<Exported function headers@>=
void mp_set_internal (MP mp, char *n, char *v, int isstring);

@ For |mp_execute|, we need to define a structure to store the redirected input
and output. This structure holds the five relevant streams: the three
informational output streams, the PostScript generation stream, and the input
stream. These streams have many things in common, so it makes sense to give them
their own structure definition.

\item{fptr} is a virtual file pointer
\item{data} is the data this stream holds
\item{cur}  is a cursor pointing into |data|
\item{size} is the allocated length of the data stream
\item{used} is the actual length of the data stream

There are small differences between input and output: |term_in| never uses
|used|, whereas the other four never use |cur|.

@<Exported types@>=
# undef term_in
# undef term_out

typedef struct mp_run_data
{
    void                  *term_in; /* dummy pointer */
    struct mp_edge_object *edges;
} mp_run_data;

@ We need a function to clear an output stream, this is called at the beginning
of |mp_execute|. We also need one for destroying an output stream, this is called
just before a stream is (re)opened.

@ The global instance contains a pointer instead of the actual structure even
though it is essentially static, because that makes it is easier to move the
object around.

@<Global ...@>=
mp_run_data run_data;

@ Another type is needed: the indirection will overload some of the file pointer
objects in the instance (but not all). For clarity, an indirect object is used
that wraps a |FILE *|.

@<Types ... @>=
typedef struct File {
    FILE *f;
} File;

@ Here are all of the functions that need to be overloaded for |mp_execute|.

@<Exported function headers@>=
void  mplib_shipout_backend (MP mp, void *h);

@ This is where we fill them all in.

@<Set default function pointers@>=
mp->find_file       = mp_find_file;
mp->open_file       = mp_open_file;
mp->close_file      = mp_close_file;
mp->write_file      = mp_write_file;
mp->read_file       = mp_read_file;
mp->run_script      = mp_run_script;
mp->run_internal    = mp_run_internal;
mp->run_logger      = mp_run_logger;
mp->run_overload    = mp_run_overload;
mp->run_error       = mp_run_error;
mp->run_warning     = mp_run_warning;
mp->make_text       = mp_make_text;
mp->shipout_backend = mp_shipout_backend;

mp->find_file_id    = 0;
mp->run_script_id   = 0;
mp->run_logger_id   = 0;
mp->run_error_id    = 0;
mp->run_warning_id  = 0;
mp->run_overload_id = 0;
mp->make_text_id    = 0;
mp->open_file_id    = 0;

@ This might change too.

@c
void mplib_shipout_backend (MP mp, void *voidh)
{
    mp_edge_header_node h = (mp_edge_header_node) voidh;
    mp_edge_object *hh = mp_gr_export (mp, h);
    if (hh) {
        mp_run_data *run = mp_rundata(mp);
        if (run->edges == NULL) {
            run->edges = hh;
        } else {
            mp_edge_object *p = run->edges;
            while (p->next != NULL) {
                p = p->next;
            }
            p->next = hh;
        }
    }
}

@ Perhaps this is the most important API function in the library.

@<Exported function ...@>=
extern mp_run_data *mp_rundata (MP mp);

@ @c
mp_run_data *mp_rundata (MP mp) {
    return &(mp->run_data);
}

@ @<Finish non-interactive use@>=
mp_memory_free(mp->term_in);
mp->term_in = NULL;

@ @<Start non-interactive work@>=
@<Initialize the output routines@>
mp->input_ptr = 0;
mp->max_in_stack = mp_file_bottom_text;
mp->in_open = mp_file_bottom_text;
mp->open_parens = 0;
mp->max_buf_stack = 0;
mp->param_ptr = 0;
mp->max_param_stack = 0;
start = loc = 0;
iindex = mp_file_bottom_text;
nloc = nstart = NULL;
mp->first = 0;
line = 0;
name = is_term;
mp->force_eof = 0;
if (mp->term_in == NULL) {
    mp->term_in = (mp->open_file)(mp,"terminal", "r", mp_filetype_terminal);
}
mp->last = 0;
mp->scanner_status = mp_normal_state;
mp_fix_date_and_time(mp);
if (mp->random_seed == 0) {
    mp->random_seed = (number_to_scaled(internal_value(mp_time_internal))/number_to_scaled(unity_t))
        + number_to_scaled(internal_value(mp_day_internal));
}
init_randoms(mp->random_seed);
mp->selector = mp->interaction == mp_batch_mode ? mp_no_print_selector : mp_term_only_selector;
mp->history = mp_spotless;
if (mp->every_job_sym != NULL) {
    set_cur_sym(mp->every_job_sym);
    mp_back_input(mp);
}

@ @c
int mp_execute (MP mp, const char *s, size_t l)
{
    (void) l;
    if (mp->finished) {
        return mp->history;
    } else if (mp->history < mp_fatal_error_stop) {
        mp_memory_free(mp->jump_buf);
        mp->jump_buf = mp_memory_allocate(sizeof(jmp_buf));
        if (mp->jump_buf == NULL || setjmp (*(mp->jump_buf)) != 0) {
            return mp->history;
        } else {
            mp->term_offset = 0;
            mp->file_offset = 0;
            if (mp->term_in == NULL) {
                mp->term_in = (mp->open_file)(mp,"terminal", "r", mp_filetype_terminal);
                mp->last = 0;
            }
            if (s && l > 0) {
                (mp->write_file)(mp, mp->term_in, s);
            } else {
                /* we already filled the terminal buffer, so no longer: */
                /*
                    mp_final_cleanup(mp);
                    mp_close_files_and_terminate(mp);
                    return mp->history;
                */
            }
            if (mp->run_state == 0) {
             /* mp->selector = mp_term_only_selector; */
                @<Start non-interactive work@>
            }
            mp->run_state = 1;
            /* we grab one line */
            mp_input_ln(mp, mp->term_in);
            mp_firm_up_the_line(mp);
            mp->buffer[limit] = '%';
            mp->first = (size_t) (limit + 1);
            loc = start;
            do {
                mp_do_statement(mp);
            } while (cur_cmd != mp_stop_command);
            mp_final_cleanup(mp);
            mp_close_files_and_terminate(mp);
        }
    }
    return mp->history;
}

@ This function cleans up

@c
int mp_finish (MP mp)
{
    int history = 0;
    if (mp->finished || mp->history >= mp_fatal_error_stop) {
        history = mp->history;
        mp_free(mp);
    } else {
        mp_memory_free(mp->jump_buf);
        mp->jump_buf = mp_memory_allocate(sizeof(jmp_buf));
        if (mp->jump_buf == NULL || setjmp (*(mp->jump_buf)) != 0) {
            history = mp->history;
        } else {
            history = mp->history;
            mp_final_cleanup(mp); /* prepare for death */
        }
        mp_close_files_and_terminate(mp);
        mp_free(mp);
    }
    return history;
}

@ People may want to know the library version
@c
char *mp_metapost_version(void) {
    return mp_strdup(metapost_version);
}

@ @<Exported function headers@>=
int   mp_run              (MP mp);
int   mp_execute          (MP mp, const char *s, size_t l);
int   mp_finish           (MP mp);
char *mp_metapost_version (void);

@ @<Put each...@>=
mp_primitive(mp, "end", mp_stop_command, 0);
@:end_}{|end| primitive@>
mp_primitive(mp, "dump", mp_stop_command, 1);
mp->frozen_dump = mp_frozen_primitive (mp, "dump", mp_stop_command, 1);
@:dump_}{|dump| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_stop_command:
    return cur_mod == 0 ? "end" : "dump";

@* Commands.

Let's turn now to statements that are classified as \quote {commands} because of their
imperative nature. We'll begin with simple ones, so that it will be clear how to
hook command processing into the |do_statement| routine; then we'll tackle the
tougher commands.

Here's one of the simplest (when we have more seters thsi will change into one
function and a genericmessage).

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_max_knot_pool (MP mp);

@ @c
void mp_do_max_knot_pool (MP mp)
{
    /* similar to the random seed setter */
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_get_x_next(mp);
    if (cur_cmd != mp_assignment_command) {
        mp_back_error(
            mp,
            "Missing ':=' has been inserted",
            "Always say 'maxknotpool := <numeric expression>'."
        );
        @.Missing `:='@>
    };
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_known_type) {
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Unknown value will be ignored",
            "Your expression was too random for me to handle, so I won't change the maximum\n"
            "seed just now."
        );
        @.Unknown value...ignored@>
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    } else {
        /* the action */
        int p = (int) number_to_scaled (cur_exp_value_number) / 65536;
        if (p > mp->max_knot_nodes) {
            mp->max_knot_nodes = p;
        } else if (p > max_num_knot_nodes) {
            /* not now: flush excess nodes */
        } else {
            /* we always keep the minimum */
        }
    }
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_random_seed (MP mp);

@ @c
void mp_do_random_seed (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_get_x_next(mp);
    if (cur_cmd != mp_assignment_command) {
        mp_back_error(
            mp,
            "Missing ':=' has been inserted",
            "Always say 'randomseed := <numeric expression>'."
        );
        @.Missing `:='@>
    };
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_known_type) {
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Unknown value will be ignored",
            "Your expression was too random for me to handle, so I won't change the random\n"
            "seed just now."
        );
        @.Unknown value...ignored@>
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    } else {
        @<Initialize the random seed to |cur_exp|@>
    }
}

@ @<Initialize the random seed to |cur_exp|@>=
init_randoms(number_to_scaled(cur_exp_value_number));
if (mp->interaction < mp_silent_mode && (mp->selector == mp_log_only_selector || mp->selector == mp_term_and_log_selector)) {
    int selector = mp->selector;
    mp->selector = mp_log_only_selector;
    mp_print_nl(mp, "{randomseed:=");
    print_number(cur_exp_value_number);
    mp_print_chr(mp, '}');
    mp_print_nl(mp, "");
    mp->selector = selector;
}

@ And here's another simple one (somewhat different in flavor):

@ @<Put each...@>=
mp_primitive(mp, "batchmode", mp_mode_command, mp_batch_mode);
@:mp_batch_mode_}{|batchmode| primitive@>
mp_primitive(mp, "nonstopmode", mp_mode_command, mp_nonstop_mode);
@:mp_nonstop_mode_}{|nonstopmode| primitive@>
mp_primitive(mp, "scrollmode", mp_mode_command, mp_scroll_mode);
@:mp_scroll_mode_}{|scrollmode| primitive@>
mp_primitive(mp, "errorstopmode", mp_mode_command, mp_error_stop_mode);
@:mp_error_stop_mode_}{|errorstopmode| primitive@>
mp_primitive(mp, "silentmode", mp_mode_command, mp_silent_mode);
@:mp_silent_mode_}{|silentmode| primitive@>

@ @<Cases of |print_cmd_mod|...@>=
case mp_mode_command:
    switch (m) {
        case mp_batch_mode     : return "batchmode";
        case mp_nonstop_mode   : return "nonstopmode";
        case mp_scroll_mode    : return "scrollmode";
        case mp_error_stop_mode: return "errorstopmode";
        default                : return "silentmode";
    }
break;

@ The |inner| and |outer| commands are only slightly harder.

@ @<Put each...@>=
mp_primitive(mp, "inner", mp_protection_command, 0);
@:inner_}{|inner| primitive@>
mp_primitive(mp, "outer", mp_protection_command, 1);
@:outer_}{|outer| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_protection_command:
    switch (m) {
        case 0: return "inner";
        case 1: return "outer";
    }
    break;

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_protection (MP mp);

@ @c
void mp_do_protection (MP mp)
{
//  int m = cur_mod; /* 0 to unprotect, 1 to protect */
    do {
//      int t; /* the |eq_type| before we change it */
        mp_get_symbol(mp);
//        t = eq_type(cur_sym);
//        switch(m) {
//            case 0:
//                if (t >= mp_outer_tag_command) {
//                    set_eq_type(cur_sym, (t - mp_outer_tag_command));
//                }
//                break;
//            case 1:
//                if (t < mp_outer_tag_command) {
//                    set_eq_type(cur_sym, (t + mp_outer_tag_command));
//                }
//                break;
//        }
        mp_get_x_next(mp);
    } while (cur_cmd == mp_comma_command);
}

@ The |setproperty| command expects a numeric, followed by a color and then
a list of symbols (names) that get that numeric value as property value. We use
a plural because one can use bitsets. This property, when larger than zero, can
trigger a callback when |overloadmode| is other than zero. This mechanism is
quite experimental and used in \CONTEXT\ for protecting definitions.

@ @<Put each...@>=
mp_primitive(mp, "setproperty", mp_property_command, 1);
@:setproperty_}{|setproperty| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_property_command:
    return "setproperty";

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_property (MP mp);

@ @c
// mp_scan_numeric_value(mp, 0, &p);

void mp_do_property (MP mp)
{
   int p = 0;
   mp_get_x_next(mp);
   mp_scan_primary(mp);
   switch (mp->cur_exp.type) {
        case mp_numeric_type:
        case mp_known_type:
            {
                mp_back_input(mp);
                p = (int) number_to_scaled (cur_exp_value_number) / 65536; // hm
            }
            break;
        default:
            mp_back_error(mp, "Bad property value", NULL);
            break;
    }
    mp_get_x_next(mp);
    if (cur_cmd == mp_colon_command) {
        do {
            mp_get_symbol(mp);
            set_eq_property(cur_sym, p);
            mp_get_x_next(mp);
        } while (cur_cmd == mp_comma_command);
    } else {
        mp_back_error(mp, "Bad property specification, colon expected", NULL);
    }
}

@ \MP\ never defines the tokens |(| and |)| to be primitives, but plain \MP\
begins with the declaration `|delimiters| |()|'. Such a declaration assigns
the command code |left_delimiter| to |(| and |right_delimiter| to |)|;
the |equiv| of each delimiter is the hash address of its mate.

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_def_delims (MP mp);

@ @c
void mp_def_delims (MP mp)
{
    mp_sym l_delim, r_delim; /* the new delimiter pair */
    mp_get_clear_symbol(mp);
    l_delim = cur_sym;
    mp_get_clear_symbol(mp);
    r_delim = cur_sym;
    set_eq_type(l_delim, mp_left_delimiter_command);
    set_equiv_sym(l_delim, r_delim);
    set_eq_type(r_delim, mp_right_delimiter_command);
    set_equiv_sym(r_delim, l_delim);
    mp_get_x_next(mp);
}

@ Here is a procedure that is called when \MP\ has reached a point where some
right delimiter is mandatory.

@<Declarations@>=
static void mp_check_delimiter (MP mp, mp_sym l_delim, mp_sym r_delim);

@ @c
void mp_check_delimiter (MP mp, mp_sym l_delim, mp_sym r_delim)
{
    if (cur_cmd == mp_right_delimiter_command && equiv_sym(cur_sym) == l_delim) {
        return;
    } else if (cur_sym != r_delim) {
        char msg[256];
        mp_snprintf(msg, 256, "Missing '%s' has been inserted", mp_str(mp, text(r_delim)));
        @.Missing `)'@>
        mp_back_error(
            mp,
            msg,
            "I found no right delimiter to match a left one. So I've put one in, behind the\n"
            "scenes; this may fix the problem."
        );
    } else {
        char msg[256];
        mp_snprintf(msg, 256, "The token '%s' is no longer a right delimiter", mp_str(mp, text(r_delim)));
        @.The token...delimiter@>
        mp_error(
            mp,
            msg,
            "Strange: This token has lost its former meaning! I'll read it as a right\n"
            "delimiter this time; but watch out, I'll probably miss it later."
        );
    }
}

@ The next four commands save or change the values associated with tokens.

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_statement (MP mp);
static void mp_do_interim   (MP mp);

@ @c
void mp_do_interim (MP mp) {
    mp_get_x_next(mp);
    if (cur_cmd != mp_internal_command) {
        char msg[256];
        mp_snprintf(msg, 256,
            "The token '%s' isn't an internal quantity",
            (cur_sym == NULL ? "(%CAPSULE)" : mp_str(mp, text(cur_sym)))
        );
        @.The token...quantity@>
        mp_back_error(mp, msg, "Something like 'tracingonline' should follow 'interim'.");
    } else {
        mp_save_internal(mp, cur_mod);
        mp_back_input(mp);
    }
    mp_do_statement(mp);
}

@ The following procedure is careful not to undefine the left-hand symbol too
soon, lest commands like `{\tt let x=x}' have a surprising effect.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_let (MP mp);

@ @c
void mp_do_let (MP mp)
{
    mp_sym l; /* hash location of the left-hand symbol */
    mp_get_symbol(mp);
    l = cur_sym;
    mp_get_x_next(mp);
    if (cur_cmd != mp_equals_command && cur_cmd != mp_assignment_command) {
        mp_back_error(
            mp,
            "Missing '=' has been inserted",
            "You should have said 'let symbol = something'. But don't worry; I'll pretend that\n"
            "an equals sign was present. The next token I read will be 'something'."
        );
        @.Missing `='@>
    }
    mp_get_symbol(mp);
    switch (cur_cmd) {
        case mp_defined_macro_command:
        case mp_primary_def_command:
        case mp_secondary_def_command:
        case mp_tertiary_def_command:
            mp_add_mac_ref(cur_mod_node);
            break;
        default:
            break;
    }
    mp_clear_symbol(mp, l, 0);
    set_eq_type(l, cur_cmd);
    switch (cur_cmd) {
        case mp_tag_command:
            set_equiv(l, 0); /* todo: this was |null| */
            break;
        case mp_defined_macro_command:
        case mp_primary_def_command:
        case mp_secondary_def_command:
        case mp_tertiary_def_command:
            set_equiv_node(l, cur_mod_node);
            break;
        case mp_left_delimiter_command:
        case mp_right_delimiter_command:
            set_equiv_sym(l, equiv_sym(cur_sym));
            break;
        default:
            set_equiv(l, cur_mod);
            break;
    }
    mp_get_x_next(mp);
}

@ @<Declarations@>=
static void mp_do_new_internal (MP mp);

@ @<Internal library ...@>=
void mp_grow_internals (MP mp, int l);

@ @c
void mp_grow_internals (MP mp, int l)
{
    if (l > max_halfword) {
        mp_confusion(mp, "out of memory"); /* can't be reached */
    } else {
        mp_internal *internal = mp_memory_allocate((size_t) (l + 1) * sizeof(mp_internal));
        for (int k = 0; k <= l; k++) {
            if (k <= mp->max_internal) {
                memcpy(internal + k, mp->internal + k, sizeof(mp_internal));
            } else {
                memset(internal + k, 0, sizeof(mp_internal));
                new_number(((mp_internal *)(internal + k))->v.data.n);
            }
        }
        mp_memory_free(mp->internal);
        mp->internal = internal;
        mp->max_internal = l;
    }
}


/* newinternal [numeric|string|boolean] [runscript] | [runscript] */

/* 0:allocate 1:push 2:pop 3:pushlogging 4:poplogging */

void mp_do_new_internal (MP mp)
{
    int the_type = mp_known_type;
    int run_script = 0;
    mp_get_next(mp); /* not mp_get_next(mp) because we don't want to expand runscript */
    if (cur_cmd == mp_type_name_command && cur_mod == mp_string_type_operation) {
        the_type = mp_string_type;
    } else if (cur_cmd == mp_type_name_command && cur_mod == mp_boolean_type_operation) {
        the_type = mp_boolean_type;
    } else if (cur_cmd == mp_type_name_command && cur_mod == mp_numeric_type_operation) {
        the_type = mp_numeric_type;
    } else if (! (cur_cmd == mp_type_name_command && cur_mod == mp_numeric_type_operation)) {
        mp_back_input(mp);
    }
    if (mp_numeric_type == mp_known_type) {
        /* We do as traditional MP does. */
    } else {
        /* We have an explicit type and check for run_internal. */
        if (the_type == mp_numeric_type) {
            the_type = mp_known_type;
        }
        mp_get_next(mp); /* not mp_get_next(mp) because we don't want to expand runscript */
        if (cur_cmd == mp_runscript_command) {
            run_script = 1; /* run_internal */
        } else {
            mp_back_input(mp);
        }
    }
    do {
        if (mp->int_ptr == mp->max_internal) {
            mp_grow_internals(mp, (mp->max_internal + (mp->max_internal / 4)));
        }
        mp_get_clear_symbol(mp);
        ++mp->int_ptr;
        set_eq_type(cur_sym, mp_internal_command);
        set_equiv(cur_sym, mp->int_ptr);
        mp_memory_free(internal_name(mp->int_ptr));
        set_internal_name(mp->int_ptr, mp_strdup(mp_str(mp, text(cur_sym))));
        if (the_type == mp_string_type) {
            set_internal_string(mp->int_ptr, mp_rts(mp,""));
        } else {
            set_number_to_zero(internal_value(mp->int_ptr));
        }
        set_internal_type(mp->int_ptr, the_type);
        set_internal_run(mp->int_ptr, run_script);
        if (run_script) {
           mp->run_internal(mp, 0, mp->int_ptr, the_type, internal_name(mp->int_ptr));
        }
        mp_get_x_next(mp);
  } while (cur_cmd == mp_comma_command);
}

@ @<Dealloc variables@>=
for (int k = 0; k <= mp->max_internal; k++) {
    free_number(mp->internal[k].v.data.n);
    mp_memory_free(internal_name(k));
}
mp_memory_free(mp->internal);

@ The various |show| commands are distinguished by modifier fields in the
usual way.

@<Enumeration types@>=
typedef enum mp_show_codes {
    mp_show_token_code,        /* show the meaning of a single token */
    mp_show_stats_code,        /* show current memory and string usage */
    mp_show_code,              /* show a list of expressions */
    mp_show_var_code,          /* show a variable and its descendents */
    mp_show_dependencies_code, /* show dependent variables in terms of independents */
} mp_show_codes;

@ @<Put each...@>=
mp_primitive(mp, "showtoken", mp_show_command, mp_show_token_code);
@:show_token_}{|showtoken| primitive@>
mp_primitive(mp, "showstats", mp_show_command, mp_show_stats_code);
@:show_stats_}{|showstats| primitive@>
mp_primitive(mp, "show", mp_show_command, mp_show_code);
@:show_}{|show| primitive@>
mp_primitive(mp, "showvariable", mp_show_command, mp_show_var_code);
@:show_var_}{|showvariable| primitive@>
mp_primitive(mp, "showdependencies", mp_show_command, mp_show_dependencies_code);
@:show_dependencies_}{|showdependencies| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_show_command:
    switch (m) {
        case mp_show_token_code       : return "showtoken";
        case mp_show_stats_code       : return "showstats";
        case mp_show_code             : return "show";
        case mp_show_var_code         : return "showvariable";
        case mp_show_dependencies_code: return "showdependencies";
    }
    break;

@ The value of |cur_mod| controls the |verbosity| in the |print_exp| routine: if
it's |show_code|, complicated structures are abbreviated, otherwise they aren't.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_show (MP mp);

@ @c
void mp_do_show (MP mp)
{
    do {
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_get_x_next(mp);
        mp_scan_expression(mp);
        mp_print_nl(mp, ">> ");
        @.>>@>
        mp_print_exp(mp, NULL, 2);
        mp_flush_cur_exp(mp, new_expr);
    } while (cur_cmd == mp_comma_command);
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_disp_token (MP mp);

@ @c
void mp_disp_token (MP mp)
{
    mp_print_nl(mp, "> ");
    @.>\relax@>
    if (cur_sym == NULL) {
        /* Show a numeric or string or capsule token */
        switch (cur_cmd) {
            case mp_numeric_command:
                print_number(cur_mod_number);
                break;
            case mp_capsule_command:
                mp_print_capsule(mp, cur_mod_node);
                break;
            default:
                mp_print_chr(mp, '"');
                mp_print_mp_str(mp, cur_mod_str);
                mp_print_chr(mp, '"');
                delete_str_ref(cur_mod_str);
                break;
        }
    } else {
        mp_print_mp_str(mp,text(cur_sym));
        mp_print_chr(mp, '=');
     // if (eq_type(cur_sym) >= mp_outer_tag_command) {
     //     mp_print_str(mp, "(outer) ");
     // }
        mp_print_cmd_mod(mp, cur_cmd, cur_mod);
        if (cur_cmd == mp_defined_macro_command) {
            mp_print_ln(mp);
            mp_show_macro (mp, cur_mod_node, NULL);
        }
        /* this avoids recursion between |show_macro| and |print_cmd_mod| */
        @^recursion@>
    }
}

@ The following cases of |print_cmd_mod| might arise in connection with
|disp_token|, although they don't necessarily correspond to primitive tokens.

@<Cases of |print_cmd_...@>=
case mp_left_delimiter_command:
case mp_right_delimiter_command:
    return c == mp_left_delimiter_command ? "left delimiter" : "right delimiter";
case mp_tag_command:
    return m == 0 ? "tag" : "variable";
case mp_defined_macro_command:
    return "macro:";
case mp_primary_def_command:
    return "primarydef";
case mp_secondary_def_command:
    return "secondarydef";
case mp_tertiary_def_command:
    return "tertiarydef";
case mp_repeat_loop_command:
    return "[repeat the loop]";
case mp_internal_command:
    return internal_name(m);

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_show_token (MP mp);

@ @c
void mp_do_show_token (MP mp)
{
    do {
        get_t_next(mp);
        mp_disp_token(mp);
        mp_get_x_next(mp);
    } while (cur_cmd == mp_comma_command);
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_show_stats (MP mp);

@ @c
void mp_do_show_stats (MP mp)
{
    mp_print_nl(mp, "Memory usage ");
    @.Memory usage...@>
    mp_print_int(mp, (int) mp->var_used);
    mp_print_ln(mp);
    mp_print_nl(mp, "String usage ");
    mp_print_int(mp, (int) mp->strs_in_use);
    mp_print_chr(mp, '&');
    mp_print_int(mp, (int) mp->pool_in_use);
    mp_print_ln(mp);
    mp_get_x_next(mp);
}

@ Here's a recursive procedure that gives an abbreviated account of a variable,
for use by |do_show_var|.

@<Declare action procedures for use by |do_statement|@>=
static void mp_disp_var (MP mp, mp_node p);

@ @c
void mp_disp_var (MP mp, mp_node p)
{
    if (mp_type(p) == mp_structured_type) {
        /* Descend the structure */
        mp_node q = mp_get_attribute_head(p);
        do {
            mp_disp_var(mp, q);
            q = mp_link(q);
        } while (q != mp->end_attr);
        q = mp_get_subscr_head(p);
        while (mp_name_type(q) == mp_subscript_operation) {
            mp_disp_var(mp, q);
            q = mp_link(q);
        }
    } else if (mp_type(p) >= mp_unsuffixed_macro_type) {
        /* Display a variable macro */
        mp_print_nl(mp, "");
        mp_print_variable_name(mp, p);
        if (mp_type(p) > mp_unsuffixed_macro_type) {
            mp_print_str(mp, "@@#"); /* |suffixed_macro| */
        }
        mp_print_str(mp, "=macro:");
        mp_show_macro(mp, mp_get_value_node(p), NULL);
    } else if (mp_type(p) != mp_undefined_type) {
        mp_print_nl(mp, "");
        mp_print_variable_name(mp, p);
        mp_print_chr(mp, '=');
        mp_print_exp(mp, p, 0);
    }
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_show_var (MP mp);

@ @c
void mp_do_show_var (MP mp)
{
    do {
        get_t_next(mp);
        if (cur_sym != NULL && cur_sym_mod == 0 && cur_cmd == mp_tag_command) {
            if (cur_mod != 0 || cur_mod_node != NULL) {
                mp_disp_var(mp, cur_mod_node);
                goto DONE;
            }
        }
        mp_disp_token(mp);
      DONE:
        mp_get_x_next(mp);
    } while (cur_cmd == mp_comma_command);
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_show_dependencies (MP mp);

@ @c
void mp_do_show_dependencies (MP mp)
{
    /* link that runs through all dependencies */
    mp_value_node p = (mp_value_node) mp_link(mp->dep_head);
    while (p != mp->dep_head) {
        if (mp_interesting(mp, (mp_node) p)) {
            mp_print_nl(mp, "");
            mp_print_variable_name(mp, (mp_node) p);
            if (mp_type(p) == mp_dependent_type) {
                mp_print_chr(mp, '=');
            } else {
                mp_print_str(mp, " = "); /* extra spaces imply proto-dependency */
            }
            mp_print_dependency(mp, (mp_value_node) mp_get_dep_list(p), mp_type(p));
        }
        p = (mp_value_node) mp_get_dep_list(p);
        while (mp_get_dep_info(p) != NULL)
            p = (mp_value_node) mp_link(p);
        p = (mp_value_node) mp_link(p);
    }
    mp_get_x_next(mp);
}

@ Finally we are ready for the procedure that governs all of the show commands.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_show_whatever (MP mp);

@ @c
void mp_do_show_whatever (MP mp)
{
    if (mp->interaction == mp_error_stop_mode) {
        wake_up_terminal();
    }
    switch (cur_mod) {
        case mp_show_token_code:
            mp_do_show_token(mp);
            break;
        case mp_show_stats_code:
            mp_do_show_stats(mp);
            break;
        case mp_show_code:
            mp_do_show(mp);
            break;
        case mp_show_var_code:
            mp_do_show_var(mp);
            break;
        case mp_show_dependencies_code:
            mp_do_show_dependencies(mp);
            break;
    }
    if (number_positive(internal_value(mp_showstopping_internal))) {
        const char *hlp = NULL;
        if (mp->interaction < mp_error_stop_mode) {
            --mp->error_count;
        } else {
            hlp = "This isn't an error message; I'm just showing something.";
        }
        if (cur_cmd == mp_semicolon_command) {
            mp_error(mp, "OK", hlp);
        } else {
            mp_back_error(mp, "OK", hlp);
            mp_get_x_next(mp);
        }
        @.OK@>
    }
}

@ We have all kind of with variants.

@<Enumeration types@>=
typedef enum mp_with_codes {
    mp_with_pen_code,
    mp_with_dashed_code,
    mp_with_pre_script_code,
    mp_with_post_script_code,
    mp_with_stacking_code,
    mp_with_no_model_code,
    mp_with_grey_model_code,
    mp_with_uninitialized_model_code,
    mp_with_rgb_model_code,
    mp_with_cmyk_model_code,
    mp_with_linecap_code,
    mp_with_linejoin_code,
    mp_with_miterlimit_code,
} mp_with_codes;

@ We use enums so that it looks better in the editor:

@<Enumeration types@>=
typedef enum mp_add_codes {
    mp_add_double_path_code, /* command modifier for |doublepath| */
    mp_add_contour_code,     /* command modifier for |contour| */
    mp_add_also_code,        /* command modifier for |also| */
} mp_add_codes ;

@ The |addto| command needs the following additional primitives:

@<Put each...@>=
mp_primitive(mp, "doublepath", mp_thing_to_add_command, mp_add_double_path_code);
@:double_path_}{|doublepath| primitive@>
mp_primitive(mp, "contour", mp_thing_to_add_command, mp_add_contour_code);
@:contour_}{|contour| primitive@>
mp_primitive(mp, "also", mp_thing_to_add_command, mp_add_also_code);
@:also_}{|also| primitive@>
mp_primitive(mp, "withpen", mp_with_option_command, mp_with_pen_code);
@:with_pen_}{|withpen| primitive@>
mp_primitive(mp, "dashed", mp_with_option_command, mp_with_dashed_code);
@:dashed_}{|dashed| primitive@>
mp_primitive(mp, "withprescript", mp_with_option_command, mp_with_pre_script_code);
@:with_mp_pre_script_}{|withprescript| primitive@>
mp_primitive(mp, "withpostscript", mp_with_option_command, mp_with_post_script_code);
@:with_mp_post_script_}{|withpostscript| primitive@>
mp_primitive(mp, "withstacking", mp_with_option_command, mp_with_stacking_code);
@:with_mp_stacking_}{|withstacking| primitive@>
mp_primitive(mp, "withlinecap", mp_with_option_command, mp_with_linecap_code);
@:with_mp_linecap_}{|withlinecap| primitive@>
mp_primitive(mp, "withlinejoin", mp_with_option_command, mp_with_linejoin_code);
@:with_mp_linejoin_}{|withlinejoin| primitive@>
mp_primitive(mp, "withmiterlimit", mp_with_option_command, mp_with_miterlimit_code);
@:with_mp_miterlimit_}{|withmiterlimit| primitive@>
mp_primitive(mp, "withoutcolor", mp_with_option_command, mp_with_no_model_code);
@:with_color_}{|withoutcolor| primitive@>
mp_primitive(mp, "withgreyscale", mp_with_option_command, mp_with_grey_model_code);
@:with_color_}{|withgreyscale| primitive@>
mp_primitive(mp, "withcolor", mp_with_option_command, mp_with_uninitialized_model_code);
@:with_color_}{|withcolor| primitive@>
mp_primitive(mp, "withrgbcolor", mp_with_option_command, mp_with_rgb_model_code);
@:with_color_}{|withrgbcolor| primitive@>
mp_primitive(mp, "withcmykcolor", mp_with_option_command, mp_with_cmyk_model_code);
@:with_color_}{|withcmykcolor| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_thing_to_add_command:
    switch (m) {
        case mp_add_contour_code    : return "contour";
        case mp_add_double_path_code: return "doublepath";
        case mp_add_also_code       : return "also";
    }
    break;

case mp_with_option_command:
    switch (m) {
        case mp_with_pen_code                : return "withpen";
        case mp_with_pre_script_code         : return "withprescript";
        case mp_with_post_script_code        : return "withpostscript";
        case mp_with_stacking_code           : return "withstacking";
        case mp_with_no_model_code           : return "withoutcolor";
        case mp_with_rgb_model_code          : return "withrgbcolor";
        case mp_with_uninitialized_model_code: return "withcolor";
        case mp_with_cmyk_model_code         : return "withcmykcolor";
        case mp_with_grey_model_code         : return "withgreyscale";
        case mp_with_linecap_code            : return "withlinecap";
        case mp_with_linejoin_code           : return "withlinejoin";
        case mp_with_miterlimit_code         : return "withmiterlimit";
        default                              : return "dashed";
    }
    break;

@ The |scan_with_list| procedure parses a $\langle$with list$\rangle$ and updates
the list of graphical objects starting at |p|. Each $\langle$with clause$\rangle$
updates all graphical objects whose |type| is compatible. Other objects are
ignored.

@<Declare action procedures for use by |do_statement|@>=
static void mp_scan_with_list (MP mp, mp_node p, mp_node pp);

@ Forcing the color to be between |0| and |unity| here guarantees that no picture
will ever contain a color outside the legal range for \ps\ graphics.

@d make_cp_a_colored_object(cp,p) do {
    cp = p;
    while (cp != NULL) {
        if (mp_has_color(cp)) {
            break;
        } else {
            cp = mp_link(cp);
        }
    }
} while (0)

@d set_color_val(A,B) do {
    if (number_negative(A)) {
        set_number_to_zero(A);
    } else if (number_greater(A,unity_t)) {
        set_number_to_unity(A);
    } else {
        number_clone(A, (B));
    }
} while (0)

@ @<Declarations@>=
/* void mp_clear_color (MP mp, void *n); */

@ @c
/* void mp_clear_color (MP mp, void *n)
{
    set_number_to_zero(((mp_shape_node) n)->cyan);
    set_number_to_zero(((mp_shape_node) n)->magenta);
    set_number_to_zero(((mp_shape_node) n)->yellow);
    set_number_to_zero(((mp_shape_node) n)->black);
    mp_color_model(n) = mp_uninitialized_model;
} */

@ @c
static void complain_invalid_with_list (MP mp, mp_variable_type t)
{
   /* Complain about improper type */
    mp_value new_expr;
    const char *hlp = NULL;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_disp_err(mp, NULL);
    switch (t) {
        case mp_with_pre_script_code:
            hlp =
                "Next time say 'withprescript <known string expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_post_script_code:
            hlp =
                "Next time say 'withpostscript <known string expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_stacking_code:
            hlp =
                "Next time say 'withstacking <known numeric expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_dashed_code:
            hlp =
                "Next time say 'dashed <known picture expression>'; I'll ignore the bad 'with'\n"
                "clause and look for another.";
            break;
        case mp_with_uninitialized_model_code:
            hlp =
                "Next time say 'withcolor <known color expression>'; I'll ignore the bad 'with'\n"
                "clause and look for another.";
            break;
        case mp_with_rgb_model_code:
            hlp =
                "Next time say 'withrgbcolor <known color expression>'; I'll ignore the bad 'with'\n"
                "clause and look for another.";
            break;
        case mp_with_cmyk_model_code:
            hlp =
                "Next time say 'withcmykcolor <known cmykcolor expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_grey_model_code:
            hlp =
                "Next time say 'withgreyscale <known numeric expression>'; I'll ignore the bad\n"
                " with' clause and look for another.";
            break;
        case mp_with_linecap_code:
            hlp =
                "Next time say 'withlinecap <known numeric expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_linejoin_code:
            hlp =
                "Next time say 'withlinejoin <known numeric expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        case mp_with_miterlimit_code:
            hlp =
                "Next time say 'miterlimit <known numeric expression>'; I'll ignore the bad\n"
                "'with' clause and look for another.";
            break;
        default:
            hlp =
                "Next time say 'withpen <known pen expression>'; I'll ignore the bad 'with' clause\n"
                "and look for another.";
            break;
    }
    mp_back_error(mp, "Improper type", hlp);
    mp_get_x_next(mp);
    mp_flush_cur_exp(mp, new_expr);
}

void mp_scan_with_list (MP mp, mp_node p, mp_node pstop)
{
    mp_node cp = MP_VOID; /* can't we reuse some? */
    mp_node pp = MP_VOID;
    mp_node dp = MP_VOID;
    mp_node ap = MP_VOID;
    mp_node bp = MP_VOID;
    mp_node sp = MP_VOID;
    mp_node spstop = MP_VOID;
    mp_number ml;
    int miterlimit = 0;
    int linecap = -1;
    int linejoin = -1;
    while (cur_cmd == mp_with_option_command) {
        /* |cur_mod| of the |with_option| (should match |cur_type|) */
        int t;
      CONTINUE:
        t = cur_mod;
        mp_get_x_next(mp);
        if (t != mp_with_no_model_code) {
            mp_scan_expression(mp);
        }
        switch (t) {
            case mp_with_uninitialized_model_code :
                switch (mp->cur_exp.type) {
                    case mp_cmykcolor_type:
                    case mp_color_type:
                    case mp_known_type:
                    case mp_boolean_type:
                        {
                            mp_value new_expr;
                            memset(&new_expr, 0, sizeof(mp_value));
                            new_number(new_expr.data.n);
                            if (cp == MP_VOID) {
                                make_cp_a_colored_object(cp, p);
                            }
                            if (cp != NULL) {
                                /* Transfer a color from the current expression to object~|cp| */
                                switch (mp->cur_exp.type) {
                                    case mp_color_type:
                                        {
                                            /* Transfer a rgbcolor from the current expression to object~|cp| */
                                            mp_node q = mp_get_value_node(cur_exp_node);
                                            mp_color_model(cp) = mp_rgb_model;
                                            set_color_val(mp_red_color(cp), mp_get_value_number(mp_red_part(q)));
                                            set_color_val(mp_green_color(cp), mp_get_value_number(mp_green_part(q)));
                                            set_color_val(mp_blue_color(cp), mp_get_value_number(mp_blue_part(q)));
                                            set_number_to_zero(mp_black_color(cp));
                                        }
                                        break;
                                    case mp_cmykcolor_type:
                                        {
                                            /* Transfer a cmykcolor from the current expression to object~|cp| */
                                            mp_node q = mp_get_value_node(cur_exp_node);
                                            mp_color_model(cp) = mp_cmyk_model;
                                            set_color_val(mp_cyan_color(cp), mp_get_value_number(mp_cyan_part(q)));
                                            set_color_val(mp_magenta_color(cp), mp_get_value_number(mp_magenta_part(q)));
                                            set_color_val(mp_yellow_color(cp), mp_get_value_number(mp_yellow_part(q)));
                                            set_color_val(mp_black_color(cp), mp_get_value_number(mp_black_part(q)));
                                        }
                                        break;
                                    case mp_known_type:
                                        {
                                            /* Transfer a greyscale from the current expression to object~|cp| */
                                         // mp_number qq;
                                         // new_number_clone(qq, cur_exp_value_number);
                                            mp_color_model(cp) = mp_grey_model;
                                            set_number_to_zero(mp_cyan_color(cp));
                                            set_number_to_zero(mp_magenta_color(cp));
                                            set_number_to_zero(mp_yellow_color(cp));
                                            set_color_val(mp_grey_color(cp), cur_exp_value_number);
                                         // set_color_val(mp_grey_color(cp), qq);
                                         // free_number(qq);
                                        }
                                        break;
                                    default:
                                        switch (cur_exp_value_boolean) {
                                            case mp_false_operation:
                                                /* Transfer a noncolor from the current expression to object~|cp| */
                                                mp_color_model(cp) = mp_no_model;
                                                break;
                                            case mp_true_operation:
                                                /* Transfer no color from the current expression to object~|cp| */
                                                mp_color_model(cp) = mp_uninitialized_model;
                                                break;
                                            default:
                                                break;
                                        }
                                        set_number_to_zero(mp_cyan_color(cp));
                                        set_number_to_zero(mp_magenta_color(cp));
                                        set_number_to_zero(mp_yellow_color(cp));
                                        set_number_to_zero(mp_black_color(cp));
                                        break;
                                }
                            }
                            mp_flush_cur_exp(mp, new_expr);
                        }
                        break;
                    default:
                        complain_invalid_with_list(mp, t);
                        goto CONTINUE;
                }
                break;
            case mp_with_rgb_model_code:
                if (mp->cur_exp.type != mp_color_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else {
                    mp_value new_expr;
                    memset(&new_expr, 0, sizeof(mp_value));
                    new_number(new_expr.data.n);
                    if (cp == MP_VOID) {
                        make_cp_a_colored_object(cp, p);
                    }
                    if (cp != NULL) {
                        /* Transfer a rgbcolor from the current expression to ob    ject~|cp| */
                        mp_node q = mp_get_value_node(cur_exp_node);
                        mp_color_model(cp) = mp_rgb_model;
                        set_color_val(mp_red_color(cp), mp_get_value_number(mp_red_part(q)));
                        set_color_val(mp_green_color(cp), mp_get_value_number(mp_green_part(q)));
                        set_color_val(mp_blue_color(cp), mp_get_value_number(mp_blue_part(q)));
                        set_number_to_zero(mp_black_color(cp));
                    }
                    mp_flush_cur_exp(mp, new_expr);
                }
                break;
            case mp_with_cmyk_model_code:
                if (mp->cur_exp.type != mp_cmykcolor_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else {
                    mp_value new_expr;
                    memset(&new_expr, 0, sizeof(mp_value));
                    new_number(new_expr.data.n);
                    if (cp == MP_VOID) {
                        make_cp_a_colored_object(cp, p);
                    }
                    if (cp != NULL) {
                        /* Transfer a cmykcolor from the current expression to object~|cp| */
                        mp_node q = mp_get_value_node(cur_exp_node);
                        mp_color_model(cp) = mp_cmyk_model;
                        set_color_val(mp_cyan_color(cp), mp_get_value_number(mp_cyan_part(q)));
                        set_color_val(mp_magenta_color(cp), mp_get_value_number(mp_magenta_part(q)));
                        set_color_val(mp_yellow_color(cp), mp_get_value_number(mp_yellow_part(q)));
                        set_color_val(mp_black_color(cp), mp_get_value_number(mp_black_part(q)));
                    }
                    mp_flush_cur_exp(mp, new_expr);
                }
                break;
            case mp_with_grey_model_code:
                if (mp->cur_exp.type != mp_known_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else {
                    mp_value new_expr;
                    memset(&new_expr, 0, sizeof(mp_value));
                    new_number(new_expr.data.n);
                    if (cp == MP_VOID) {
                        make_cp_a_colored_object(cp, p);
                    }
                    if (cp != NULL) {
                        /* Transfer a greyscale from the current expression to object~|cp| */
                     // mp_number qq;
                     // new_number_clone(qq, cur_exp_value_number);
                        mp_color_model(cp) = mp_grey_model;
                        set_number_to_zero(mp_cyan_color(cp));
                        set_number_to_zero(mp_magenta_color(cp));
                        set_number_to_zero(mp_yellow_color(cp));
                        set_color_val(mp_grey_color(cp), cur_exp_value_number);
                     // set_color_val(mp_grey_color(cp), qq);
                     // free_number(qq);
                    }
                    mp_flush_cur_exp(mp, new_expr);
                }
                break;
            case mp_with_no_model_code:
                if (cp == MP_VOID) {
                    make_cp_a_colored_object(cp, p);
                }
                if (cp != NULL) {
                    /* Transfer a noncolor from the current expression to object~|cp| */
                    mp_color_model(cp) = mp_no_model;
                    set_number_to_zero(mp_cyan_color(cp));
                    set_number_to_zero(mp_magenta_color(cp));
                    set_number_to_zero(mp_yellow_color(cp));
                    set_number_to_zero(mp_grey_color(cp));
                }
                break;
            case mp_with_pen_code:
                if (mp->cur_exp.type != mp_pen_type && mp->cur_exp.type != mp_nep_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else {
                    if (pp == MP_VOID) {
                        /* Make |pp| an object in list~|p| that needs a pen */
                        pp = p;
                        while (pp != NULL) {
                            if (mp_has_pen(pp)) {
                                break;
                            } else {
                                pp = mp_link(pp);
                            }
                        }
                    }
                    if (pp != NULL) {
                        switch (mp_type(pp)) {
                            case mp_fill_node_type:
                            case mp_stroked_node_type:
                                if (mp_pen_ptr((mp_shape_node) pp) != NULL) {
                                    mp_toss_knot_list(mp, mp_pen_ptr((mp_shape_node) pp));
                                }
                                mp_pen_ptr((mp_shape_node) pp) = cur_exp_knot;
                                mp_pen_type((mp_shape_node) pp) = mp->cur_exp.type == mp_nep_type;
                                break;
                            default:
                                break;
                        }
                        mp->cur_exp.type = mp_vacuous_type;
                    }
                }
                break;
            case mp_with_pre_script_code:
                if (mp->cur_exp.type != mp_string_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else if (cur_exp_str->len) {
                    if (ap == MP_VOID) {
                        ap = p;
                    }
                    while ((ap != NULL) && (! mp_has_script(ap))) {
                        ap = mp_link(ap);
                    }
                    if (ap != NULL) {
                        if (mp_pre_script(ap) != NULL) {
                            int selector = mp->selector;
                            mp_string s = mp_pre_script(ap); /* for string cleanup after combining */
                            mp->selector = mp_new_string_selector;
                            mp_str_room(mp, (int) (mp_pre_script(ap)->len + cur_exp_str->len + 2));
                            mp_print_mp_str(mp, cur_exp_str);
                            mp_str_room(mp, 1);
                            mp_append_char(mp, 13);
                            mp_print_mp_str(mp, mp_pre_script(ap));
                            mp_pre_script(ap) = mp_make_string(mp);
                            delete_str_ref(s);
                            mp->selector = selector;
                        } else {
                            mp_pre_script(ap) = cur_exp_str;
                        }
                        add_str_ref(mp_pre_script(ap));
                        mp->cur_exp.type = mp_vacuous_type;
                    }
                }
                break;
            case mp_with_post_script_code:
                if (mp->cur_exp.type != mp_string_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                } else if (cur_exp_str->len) {
                    if (bp == MP_VOID) {
                        bp = p;
                    }
                    while ((bp != NULL) && (! mp_has_script(bp))) {
                        bp = mp_link(bp);
                    }
                    if (bp != NULL) {
                        if (mp_post_script(bp) != NULL) {
                            int selector = mp->selector;
                            mp_string s = mp_post_script(bp); /* for string cleanup after combining */
                            mp->selector = mp_new_string_selector;
                            mp_str_room(mp, (int) (mp_post_script(bp)->len + cur_exp_str->len + 2));
                            mp_print_mp_str(mp, mp_post_script(bp));
                            mp_str_room(mp, 1);
                            mp_append_char(mp, 13);
                            mp_print_mp_str(mp, cur_exp_str);
                            mp_post_script(bp) = mp_make_string(mp);
                            delete_str_ref(s);
                            mp->selector = selector;
                        } else {
                            mp_post_script(bp) = cur_exp_str;
                        }
                        add_str_ref(mp_post_script(bp));
                        mp->cur_exp.type = mp_vacuous_type;
                    }
                }
                break;
            case mp_with_stacking_code:
                switch (mp->cur_exp.type) {
                    case mp_known_type:
                        {
                            if (sp == MP_VOID) {
                                sp = p;
                            }
                            if (pp && spstop == MP_VOID) {
                                spstop = pstop;
                            }
                            if (sp != NULL) {
                                mp_stacking(sp) = round_unscaled(cur_exp_value_number);
                            }
                            if (pp && spstop != NULL) {
                                mp_stacking(spstop) = round_unscaled(cur_exp_value_number);
                            }
                            /* free ? */
                            mp->cur_exp.type = mp_vacuous_type;
                        }
                        break;
                    case mp_pair_type:
                        {
                            if (pp && mp_nice_pair(mp, cur_exp_node, mp->cur_exp.type)) {
                                if (sp == MP_VOID) {
                                    sp = p;
                                }
                                if (spstop == MP_VOID) {
                                    spstop = pstop;
                                }
                                if (sp != NULL) {
                                    mp_stacking(sp) = round_unscaled(mp_get_value_number(mp_x_part(mp_get_value_node(cur_exp_node))));
                                }
                                if (spstop != NULL) {
                                    mp_stacking(spstop) = round_unscaled(mp_get_value_number(mp_y_part(mp_get_value_node(cur_exp_node))));
                                }
                                /* free ? */
                                mp->cur_exp.type = mp_vacuous_type;
                            } else {
                                complain_invalid_with_list(mp, t);
                                goto CONTINUE;
                            }
                        }
                        break;
                    default:
                        {
                            complain_invalid_with_list(mp, t);
                            goto CONTINUE;
                        }
                }
                break;
            case mp_with_linecap_code:
                switch (mp->cur_exp.type) {
                    case mp_known_type:
                        {
                            linecap = round_unscaled(cur_exp_value_number);
                            mp->cur_exp.type = mp_vacuous_type;
                            break;
                        }
                    default:
                        {
                            complain_invalid_with_list(mp, t);
                            goto CONTINUE;
                        }
                }
                break;
            case mp_with_linejoin_code:
                switch (mp->cur_exp.type) {
                    case mp_known_type:
                        {
                            linejoin = round_unscaled(cur_exp_value_number);
                            mp->cur_exp.type = mp_vacuous_type;
                            break;
                        }
                    default:
                        {
                            complain_invalid_with_list(mp, t);
                            goto CONTINUE;
                        }
                }
                break;
            case mp_with_miterlimit_code:
                switch (mp->cur_exp.type) {
                    case mp_known_type:
                        {
                            miterlimit = 1;
                            new_number_clone(ml, cur_exp_value_number);
                            mp->cur_exp.type = mp_vacuous_type;
                            break;
                        }
                    default:
                        {
                            complain_invalid_with_list(mp, t);
                            goto CONTINUE;
                        }
                }
                break;
            case mp_with_dashed_code:
                if (mp->cur_exp.type != mp_picture_type) {
                    complain_invalid_with_list(mp, t);
                    goto CONTINUE;
                }
                // fall through
            default:
                if (dp == MP_VOID) {
                    /* Make |dp| a stroked node in list~|p| */
                    dp = p;
                    while (dp != NULL) {
                        if (mp_type(dp) == mp_stroked_node_type) {
                            break;
                        } else {
                            dp = mp_link(dp);
                        }
                    }
                }
                if (dp != NULL) {
                    if (mp_dash_ptr(dp) != NULL) {
                        mp_delete_edge_ref(mp, mp_dash_ptr(dp));
                    }
                    mp_dash_ptr(dp) = (mp_node) mp_make_dashes(mp, (mp_edge_header_node) cur_exp_node);
                    set_number_to_unity(((mp_shape_node) dp)->dashscale);
                    mp->cur_exp.type = mp_vacuous_type;
                }
                break;
        }
    }
    /*
        Copy the information from objects |cp|, |pp|, and |dp| into the rest of
        the list. These were > MP_VOID tests but can we rely on that one being
        |1| which is hopefully not some used address.
    */
    if (cp > MP_VOID) {
        /* Copy |cp|'s color into the colored objects linked to~|cp| */
        mp_node q = mp_link(cp);
        while (q != NULL) {
            if (mp_has_color(q)) {
                mp_shape_node q0 = (mp_shape_node) q;
                mp_shape_node cp0 = (mp_shape_node) cp;
                number_clone(q0->red, cp0->red);
                number_clone(q0->green, cp0->green);
                number_clone(q0->blue, cp0->blue);
                number_clone(q0->black, cp0->black);
                mp_color_model(q) = mp_color_model(cp);
            }
            q = mp_link(q);
        }
    }
    if (pp > MP_VOID) {
        /* Copy |mp_pen_ptr(pp)| into stroked and filled nodes linked to |pp| */
        mp_node q = mp_link(pp);
        while (q != NULL) {
            if (mp_has_pen(q)) {
                switch (mp_type(q)) {
                    case mp_fill_node_type:
                    case mp_stroked_node_type:
                        if (mp_pen_ptr((mp_shape_node) q) != NULL) {
                            mp_toss_knot_list(mp, mp_pen_ptr((mp_shape_node) q));
                        }
                        mp_pen_ptr((mp_shape_node) q) = mp_copy_pen(mp, mp_pen_ptr((mp_shape_node) pp));
                        break;
                    default:
                        break;
                }
            }
            q = mp_link(q);
        }
    }
    if (dp > MP_VOID) {
        /* Make stroked nodes linked to |dp| refer to |mp_dash_ptr(dp)| */
        mp_node q = mp_link(dp);
        while (q != NULL) {
            if (mp_type(q) == mp_stroked_node_type) {
                if (mp_dash_ptr(q) != NULL) {
                    mp_delete_edge_ref(mp, mp_dash_ptr(q));
                }
                mp_dash_ptr(q) = mp_dash_ptr(dp);
                set_number_to_unity(((mp_shape_node) q)->dashscale);
                if (mp_dash_ptr(q) != NULL) {
                    mp_add_edge_ref(mp, mp_dash_ptr(q));
                }
            }
            q = mp_link(q);
        }
    }
    if (linecap >= 0 && linecap < mp_weird_linecap_code) {
        mp_node q = p;
        while (q != NULL) {
            switch (mp_type(q)) {
                case mp_fill_node_type:
                case mp_stroked_node_type:
                    mp_set_linecap(q, linecap);
                    break;
                default:
                    break;
            }
            q = mp_link(q);
        }
    }
    if (linejoin >= 0 && linejoin < mp_weird_linejoin_code) {
        mp_node q = p;
        while (q != NULL) {
            switch (mp_type(q)) {
                case mp_fill_node_type:
                case mp_stroked_node_type:
                    mp_set_linejoin(q, linejoin);
                    break;
                default:
                    break;
            }
            q = mp_link(q);
        }
    }
    if (miterlimit) {
        mp_node q = p;
        while (q != NULL) {
            switch (mp_type(q)) {
                case mp_fill_node_type:
                case mp_stroked_node_type:
                    number_clone(mp_miterlimit(q), ml);
                    break;
                default:
                    break;
            }
            q = mp_link(q);
        }
        free_number(ml);
    }
    if (! pp && sp > MP_VOID) {
        mp_node q = mp_link(sp);
        while (q != NULL) {
            mp_stacking(q) = mp_stacking(sp);
            q = mp_link(q);
        }
    }
}

@ One of the things we need to do when we've parsed an |addto| or similar
command is find the header of a supposed |picture| variable, given a token list
for that variable. Since the edge structure is about to be updated, we use
|private_edges| to make sure that this is possible.

@<Declare action procedures for use by |do_statement|@>=
static mp_edge_header_node mp_find_edges_var (MP mp, mp_node t);

@ @c
mp_edge_header_node mp_find_edges_var (MP mp, mp_node t)
{
    mp_edge_header_node cur_edges = NULL;
    mp_node p = mp_find_variable(mp, t);
    if (p == NULL) {
        char *msg = mp_obliterated(mp, t);
        mp_back_error(
            mp,
            msg,
            "It seems you did a nasty thing --- probably by accident, but nevertheless you\n"
            "nearly hornswoggled me ... While I was evaluating the right-hand side of thisn"
            "command, something happened, and the left-hand side is no longer a variable! So In"
            "won't change anything."
        );
        mp_memory_free(msg);
        mp_get_x_next(mp);
    } else if (mp_type(p) != mp_picture_type) {
        char msg[256];
        mp_string sname;
        int selector = mp->selector;
        mp->selector = mp_new_string_selector;
        mp_show_token_list(mp, t, NULL);
        sname = mp_make_string(mp);
        mp->selector = selector;
        mp_snprintf(msg, 256, "Variable %s is the wrong type(%s)", mp_str(mp, sname), mp_type_string(mp_type(p)));
        @.Variable x is the wrong type@>
        delete_str_ref(sname);
        mp_back_error(
            mp,
            msg,
            "I was looking for a 'known' picture variable. So I'll not change anything just\n"
            "now."
        );
        mp_get_x_next(mp);
    } else {
        mp_set_value_node(p, (mp_node) mp_private_edges(mp, (mp_edge_header_node) mp_get_value_node(p)));
        cur_edges = (mp_edge_header_node) mp_get_value_node(p);
    }
    mp_flush_node_list(mp, t);
    return cur_edges;
}

@ @<Put each...@>=
mp_primitive(mp, "clip", mp_bounds_command, mp_start_clip_node_type);
@:clip_}{|clip| primitive@>
mp_primitive(mp, "setgroup", mp_bounds_command, mp_start_group_node_type);
@:group_}{|group| primitive@>
mp_primitive(mp, "setbounds", mp_bounds_command, mp_start_bounds_node_type);
@:set_bounds_}{|setbounds| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_bounds_command:
    switch (m) {
        case mp_start_clip_node_type  : return "clip";
        case mp_start_group_node_type : return "setgroup";
        case mp_start_bounds_node_type: return "setbounds";
    }
    break;

@ The following function parses the beginning of an |addto| or |clip|
command: it expects a variable name followed by a token with |cur_cmd = sep| and
then an expression. The function returns the token list for the variable and
stores the command modifier for the separator token in the global variable
|last_add_type|. We must be careful because this variable might get overwritten
any time we call |get_x_next|.

@<Glob...@>=
int last_add_type; /* command modifier that identifies the last |addto| command */

@ @<Declare action procedures for use by |do_statement|@>=
static mp_node mp_start_draw_cmd (MP mp, int sep);

@ @c
mp_node mp_start_draw_cmd (MP mp, int sep)
{
    mp_node lhv = NULL; /* variable to add to left */
    int add_type = 0;   /* value to be returned in |last_add_type| */
    mp_get_x_next(mp);
    mp->var_flag = sep;
    mp_scan_primary(mp);
    if (mp->cur_exp.type != mp_token_list_type) {
        /* Abandon edges command because there's no variable */
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        new_number(new_expr.data.n);
        mp_disp_err(mp, NULL);
        mp_back_error(
            mp,
            "Not a suitable variable",
            "At this point I needed to see the name of a picture variable. (Or perhaps you\n"
            "have indeed presented me with one; I might have missed it, if it wasn't followed\n"
            "by the proper token.) So I'll not change anything just now.\n"
        );
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    } else {
        lhv = cur_exp_node;
        add_type = (int) cur_mod;
        mp->cur_exp.type = mp_vacuous_type;
        mp_get_x_next(mp);
        mp_scan_expression(mp);
    }
    mp->last_add_type = add_type;
    return lhv;
}

@ Here is an example of how to use |start_draw_cmd|.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_bounds (MP mp);

@ @c
void mp_do_bounds (MP mp)
{
    mp_edge_header_node lhe;
    /* initial value of |cur_mod| */
    int c = cur_cmd;
    int m = cur_mod;
    /* variable on left, the corresponding edge structure */
    mp_node lhv = mp_start_draw_cmd(mp, mp_to_command);
    if (lhv != NULL) {
        mp_value new_expr;
        memset(&new_expr, 0, sizeof(mp_value));
        lhe = mp_find_edges_var(mp, lhv);
        if (lhe == NULL) {
            new_number(new_expr.data.n);
            mp_flush_cur_exp(mp, new_expr);
        } else if (mp->cur_exp.type != mp_path_type) {
            char msg[256];
            mp_disp_err(mp, NULL);
            new_number(new_expr.data.n);
            mp_snprintf(msg, 256, "Improper '%s'", mp_cmd_mod_string(mp, c, m));
            mp_back_error(
                mp,
                msg,
                "This expression should have specified a known path. So I'll not change anything\n"
                "just now."
            );
            mp_get_x_next(mp);
            mp_flush_cur_exp(mp, new_expr);
        } else if (mp_left_type(cur_exp_knot) == mp_endpoint_knot) {
            /* Complain about a non-cycle */
            mp_back_error(
                mp,
                "Not a cycle",
                "That contour should have ended with '..cycle' or '&cycle'. So I'll not change\n"
                "anything just now."
            );
            mp_get_x_next(mp);
        } else {
            /* Make |cur_exp| into a |setbounds| or clipping path and add it to |lhe| */
            mp_node p = mp_new_bounds_node(mp, cur_exp_knot, (int) m);
            mp_node pp;
            int mm = 0;
            switch (m) {
                case mp_start_clip_node_type  : mm = mp_stop_clip_node_type; break;
                case mp_start_group_node_type : mm = mp_stop_group_node_type; break;
                case mp_start_bounds_node_type: mm = mp_stop_bounds_node_type; break;
            }
            pp = mp_new_bounds_node(mp, NULL, mm);
            mp_scan_with_list(mp, p, pp);
            mp_link(p) = mp_link(mp_edge_list(lhe));
            mp_link(mp_edge_list(lhe)) = p;
            if (mp_obj_tail(lhe) == mp_edge_list(lhe)) {
                mp_obj_tail(lhe) = p;
            }
            mp_link(mp_obj_tail(lhe)) = pp;
            mp_obj_tail(lhe) = pp;
            mp_init_bbox(mp, lhe);
        }
    }
}

@ The |do_add_to| procedure is a little like |do_clip| but there are a lot more
cases to deal with.

@<Declare action procedures for use by |do_statement|@>=
static void mp_do_add_to (MP mp);

@ @c
void mp_do_add_to (MP mp)
{
    mp_node lhv = mp_start_draw_cmd(mp, mp_thing_to_add_command);
    if (lhv != NULL) {
        mp_edge_header_node lhe;  /* variable on left, the corresponding edge structure */
        mp_node p;                /* the graphical object or list for |scan_with_list| to update */
        mp_edge_header_node e;    /* an edge structure to be merged */
        int add_type = mp->last_add_type; /* |also_code|, |contour_code|, or |double_path_code| */
        if (add_type == mp_add_also_code) {
            /*
                Make sure the current expression is a suitable picture and set
                |e| and |p| appropriately. Setting |p:=NULL| causes the
                $\langle$with list$\rangle$ to be ignored; setting |e:=NULL|
                prevents anything from being added to |lhe|.
            */
            p = NULL;
            e = NULL;
            if (mp->cur_exp.type != mp_picture_type) {
                mp_value new_expr;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_disp_err(mp, NULL);
                mp_back_error(
                    mp,
                    "Improper 'addto'",
                    "This expression should have specified a known picture. So I'll not change\n"
                    "anything just now."
                );
                mp_get_x_next(mp);
                mp_flush_cur_exp(mp, new_expr);
            } else {
                e = mp_private_edges(mp, (mp_edge_header_node) cur_exp_node);
                mp->cur_exp.type = mp_vacuous_type;
                p = mp_link(mp_edge_list(e));
            }
        } else {
            /*
                Create a graphical object |p| based on |add_type| and the current
                expression. In this case |add_type<>also_code| so setting
                |p:=NULL| suppresses future attempts to add to the edge
                structure.
            */
            e = NULL;
            p = NULL;
            if (mp->cur_exp.type == mp_pair_type) {
                mp_pair_to_path(mp);
            }
            if (mp->cur_exp.type != mp_path_type) {
                mp_value new_expr;
                memset(&new_expr, 0, sizeof(mp_value));
                new_number(new_expr.data.n);
                mp_disp_err(mp, NULL);
                mp_back_error(
                    mp,
                    "Improper 'addto'",
                    "This expression should have specified a known path. So I'll not change anything\n"
                    "just now."
                );
                mp_get_x_next(mp);
                mp_flush_cur_exp(mp, new_expr);
            } else if (add_type != mp_add_contour_code) {
                p = mp_new_shape_node(mp, cur_exp_knot, mp_stroked_node_type);
                mp->cur_exp.type = mp_vacuous_type;
            } else if (mp_left_type(cur_exp_knot) == mp_endpoint_knot) {
                /* Complain about a non-cycle */
                mp_back_error(
                    mp,
                    "Not a cycle",
                    "That contour should have ended with '.. cycle' or '& cycle'. So I'll not change\n"
                    "anything just now."
                );
                mp_get_x_next(mp);
            } else {
                p = mp_new_shape_node(mp, cur_exp_knot, mp_fill_node_type);
                mp->cur_exp.type = mp_vacuous_type;
            }
        }
        mp_scan_with_list(mp, p, NULL);
        /* Use |p|, |e|, and |add_type| to augment |lhv| as requested */
        lhe = mp_find_edges_var(mp, lhv);
        if (lhe == NULL) {
            if ((e == NULL) && (p != NULL)) {
                e = mp_toss_gr_object(mp, p);
            }
            if (e != NULL) {
                mp_delete_edge_ref(mp, e);
            }
        } else if (add_type == mp_add_also_code) {
            if (e != NULL) {
                /* Merge |e| into |lhe| and delete |e| */
                if (mp_link(mp_edge_list(e)) != NULL) {
                    mp_link(mp_obj_tail(lhe)) = mp_link(mp_edge_list(e));
                    mp_obj_tail(lhe) = mp_obj_tail(e);
                    mp_obj_tail(e) = mp_edge_list(e);
                    mp_link(mp_edge_list(e)) = NULL;
                    mp_flush_dash_list(mp, lhe);
                }
                mp_toss_edges(mp, e);
            }
        } else if (p != NULL) {
            mp_link(mp_obj_tail(lhe)) = p;
            mp_obj_tail(lhe) = p;
            if (add_type == mp_add_double_path_code) {
                if (mp_pen_ptr((mp_shape_node) p) == NULL) {
                    mp_pen_ptr((mp_shape_node) p) = mp_get_pen_circle(mp, &zero_t);
                }
            }
        }
    }
}

@ @<Declare action procedures for use by |do_statement|@>=
@<Declare the output procedures@>
static void mp_do_ship_out (MP mp);

@ @c
void mp_do_ship_out (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_picture_type) {
        mp_disp_err(mp, NULL);
        set_number_to_zero(new_expr.data.n);
        mp_back_error(mp, "Not a known picture", "I can only output known pictures.");
        mp_get_x_next(mp);
        mp_flush_cur_exp(mp, new_expr);
    } else {
        mp_ship_out(mp, cur_exp_node);
        set_number_to_zero(new_expr.data.n);
        mp_flush_cur_exp(mp, new_expr);
    }
}

@ The |everyjob| command simply assigns a nonzero value to the global variable
|every_job_sym|.

@ @<Glob...@>=
mp_sym every_job_sym;

@ @<Set init...@>=
mp->every_job_sym = NULL;

@ Finally, we have only the \quote {message} commands remaining.

@d message_code     0
@d err_message_code 1
@d err_help_code    2

@<Put each...@>=
mp_primitive(mp, "message", mp_message_command, message_code);
@:message_}{|message| primitive@>
mp_primitive(mp, "errmessage", mp_message_command, err_message_code);
@:err_message_}{|errmessage| primitive@>
mp_primitive(mp, "errhelp", mp_message_command, err_help_code);
@:err_help_}{|errhelp| primitive@>

@ @<Cases of |print_cmd...@>=
case mp_message_command:
    if (m < err_message_code) {
        return "message";
    } else if (m == err_message_code) {
        return "errmessage";
    } else {
        return "errhelp";
    }

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_message    (MP mp);
static void mp_no_string_err (MP mp, const char *s);

@ @c
void mp_do_message (MP mp)
{
    mp_value new_expr;
    int m = cur_mod; /* the type of message */
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_string_type) {
        mp_no_string_err(mp, "A message should be a known string expression.");
    } else {
        switch (m) {
            case message_code:
                mp_print_nl(mp, "");
                mp_print_mp_str(mp, cur_exp_str);
                break;
            case err_message_code:
                @<Print string |cur_exp| as an error message@>
                break;
            case err_help_code:
                @<Save string |cur_exp| as the |err_help|@>
                break;
        }
    }
    set_number_to_zero(new_expr.data.n);
    mp_flush_cur_exp(mp, new_expr);
}

static void mp_no_string_err (MP mp, const char *s)
{
    mp_disp_err(mp, NULL);
    mp_back_error(mp, "Not a string", s);
    @.Not a string@>
    mp_get_x_next(mp);
}

@ The global variable |err_help| is zero when the user has most recently given an
empty help string, or if none has ever been given.

@<Save string |cur_exp| as the |err_help|@>=
{
    if (mp->err_help != NULL) {
        delete_str_ref(mp->err_help);
    } if (cur_exp_str->len == 0) {
        mp->err_help = NULL;
    } else {
        mp->err_help = cur_exp_str;
        add_str_ref(mp->err_help);
    }
}

@ If |errmessage| occurs often in |mp_scroll_mode|, without user-defined
|errhelp|, we don't want to give a long help message each time. So we give a
verbose explanation only once.

@<Glob...@>=
int long_help_seen; /* has the long |\\errmessage| help been used? */

@ @<Set init...@>=
mp->long_help_seen = 0;

@ @<Print string |cur_exp| as an error message@>=
{
    char msg[256];
    mp_snprintf(msg, 256, "%s", mp_str(mp, cur_exp_str));
    if (mp->err_help != NULL) {
        mp->use_err_help = 1;
        mp_back_error(mp, msg, NULL);
    } else if (mp->long_help_seen) {
        mp_back_error(mp, msg, "(That was another 'errmessage'.)");
    } else {
        @^Marple, Jane@>
        if (mp->interaction < mp_error_stop_mode) {
            mp->long_help_seen = 1;
        }
        mp_back_error(
            mp,
            msg,
            "This error message was generated by an 'errmessage' command, so I can't give any\n"
            "explicit help. Pretend that you're Miss Marple: Examine all clues, and deduce the\n"
            "truth by inspired guesses."
        );
    }
    mp_get_x_next(mp);
    mp->use_err_help = 0;
}

@ @<Declare action procedures for use by |do_statement|@>=
static void mp_do_write        (MP mp);
static void mp_do_write_string (MP mp, mp_string t);

@ @c
void mp_do_write (MP mp)
{
    mp_value new_expr;
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    mp_get_x_next(mp);
    mp_scan_expression(mp);
    if (mp->cur_exp.type != mp_string_type) {
        mp_no_string_err(mp, "The text to be written should be a known string expression");
    } else if (cur_cmd != mp_to_command) {
        mp_back_error(mp, "Missing 'to' clause", "A write command should end with 'to <filename>'");
        mp_get_x_next(mp);
    } else {
        mp_string t = cur_exp_str; /* the line of text to be written */
        mp->cur_exp.type = mp_vacuous_type;
        mp_get_x_next(mp);
        mp_scan_expression(mp);
        if (mp->cur_exp.type != mp_string_type) {
            mp_no_string_err(mp, "I can\'t write to that file name. It isn't a known string");
        } else {
            mp_do_write_string(mp, t);
        }
    }
    set_number_to_zero(new_expr.data.n);
    mp_flush_cur_exp(mp, new_expr);
}

static void mp_do_write_string (MP mp, mp_string t)
{
    char *fn = mp_str(mp, cur_exp_str);
    int n = mp->write_files;
    int n0 = mp->write_files;
    while (mp_strcmp(fn, mp->wr_fname[n]) != 0) {
        if (n == 0) {
            /* bottom reached */
            if (n0 == mp->write_files) {
                if (mp->write_files < mp->max_write_files) {
                    ++mp->write_files;
                } else {
                    int l = mp->max_write_files + (mp->max_write_files / 4);
                    void **wr_file = mp_memory_allocate((size_t) (l + 1) * sizeof(void *));
                    char **wr_fname = mp_memory_allocate((size_t) (l + 1) * sizeof(char *));
                    for (int k = 0; k <= l; k++) {
                        if (k <= mp->max_write_files) {
                            wr_file[k] = mp->wr_file[k];
                            wr_fname[k] = mp->wr_fname[k];
                        } else {
                            wr_file[k] = 0;
                            wr_fname[k] = NULL;
                        }
                    }
                    mp_memory_free(mp->wr_file);
                    mp_memory_free(mp->wr_fname);
                    mp->max_write_files = l;
                    mp->wr_file = wr_file;
                    mp->wr_fname = wr_fname;
                }
            }
            n = n0;
            mp_open_write_file(mp, fn, n);
        } else {
            --n;
            if (mp->wr_fname[n] == NULL) {
                n0 = n;
            }
        }
    }
    if (mp_str_vs_str(mp, t, mp->eof_line) == 0) {
        (mp->close_file)(mp, mp->wr_file[n]);
        mp_memory_free(mp->wr_fname[n]);
        mp->wr_fname[n] = NULL;
        if (n == mp->write_files - 1) {
            mp->write_files = n;
        }
    } else {
        int selector = mp->selector;
        mp->selector = n + mp_first_file_selector;
        mp_print_mp_str(mp, t);
        mp_print_ln(mp);
        mp->selector = selector;
    }
}

@ @<Initialize table entries@>=
mp->inf_val = mp_new_value_node(mp);
mp_set_value_number(mp->inf_val, fraction_four_t);

@ @<Free table entries@>=
mp_free_value_node(mp, mp->inf_val);

@ The smallest |d| such that a given list can be covered with |m| intervals is
determined by the |threshold| routine, which is sort of an inverse to
|min_cover|. The idea is to increase the interval size rapidly until finding the
range, then to go sequentially until the exact borderline has been discovered.

@ Heights, depths, and italic corrections are different from widths not only
because their list length is more severely restricted, but also because zero
values do not need to be put into the list

@ @<Initialize table entries@>=
mp->zero_val = mp_new_value_node(mp);
mp_set_value_number(mp->zero_val, zero_t);

@ @<Free table entries@>=
mp_free_value_node(mp, mp->zero_val);

@ To print |scaled| value to PDF output we need some subroutines to ensure
accurary.

@d max_integer 0x7FFFFFFF /* $2^{31}-1$ */

@<Glob...@>=
int ten_pow[10]; /* $10^0..10^9$ */
int scaled_out;  /* amount of |scaled| that was taken out in |divide_scaled| */

@ @<Set init...@>=
mp->ten_pow[0] = 1;
for (int i = 1; i <= 9; i++) {
    mp->ten_pow[i] = 10 * mp->ten_pow[i - 1];
}

@* Shipping pictures out.

The |ship_out| procedure, to be described below, is given a pointer to an edge
structure. Originally teh output was targeted at \POSTSCRIPT\ but the library
has no backend. It privides the result as a structure that reflects the original
\POSTSCRIPT\ backend. We could use more direct methods but for now we follow the
route with an intermediate. Actually, it's that intermediate that is kind of
the standard output \API. We no longer report the shipped outfigure because the
backend can do that, but we keep the number.

@<Declare the output procedures@>=
static void mp_ship_out (MP mp, mp_node h);

@ Some of these types are already used earlier.

@<Exported types@>=
typedef struct mp_color {
    double a_val; /* r or c */
    double b_val; /* g or m */
    double c_val; /* b or y */
    double d_val; /*      k */
} mp_color;

typedef struct mp_dash_object {
    double  offset;
    double *array;
} mp_dash_object;

/*
    This mp_graphic_object gets cast onto the fill and stroke. For some reason
    we don't distinguish between start and stop here.
*/

typedef struct mp_graphic_object {
    int                       type;
    int                       stacking;
    struct mp_graphic_object *next;
} mp_graphic_object;

typedef struct mp_shape_object {
    int                       type;
    int                       stacking;
    struct mp_graphic_object *next;
    char                     *pre_script;
    char                     *post_script;
    size_t                    pre_length;
    size_t                    post_length;
    mp_color                  color;
    mp_gr_knot                path;
    mp_gr_knot                htap;
    mp_gr_knot                pen;
    double                    miterlimit;
    mp_dash_object           *dash;
    unsigned char             color_model;
    unsigned char             linejoin;
    unsigned char             linecap;
    unsigned char             padding; /* pen_type */
} mp_shape_object;

typedef struct mp_start_object {
    int                       type;
    int                       stacking;
    struct mp_graphic_object *next;
    char                     *pre_script;
    char                     *post_script;
    size_t                    pre_length;
    size_t                    post_length;
    mp_gr_knot                path;
} mp_start_object;

typedef struct mp_stop_object {
    int                       type;
    int                       stacking;
    struct mp_graphic_object *next;
    char                     *pre_script;
    char                     *post_script;
    size_t                    pre_length;
    size_t                    post_length;
    mp_gr_knot                path;
} mp_stop_object;

typedef struct mp_edge_object {
    struct mp_graphic_object *body;
    struct mp_edge_object    *next;
    MP                        parent;
    double                    minx;
    double                    miny;
    double                    maxx;
    double                    maxy;
    double                    width;
    double                    height;
    double                    depth;
    double                    italic;
    int                       charcode;
    int                       padding;
} mp_edge_object;

@d gr_next_knot(A)      (A)->next
@d gr_originator(A)     (A)->originator
@d mp_knotstate(A)      (A)->state
@d gr_type(A)           (A)->type
@d gr_link(A)           (A)->next
@d gr_color_model(A)    (A)->color_model
@d gr_red_val(A)        (A)->color.a_val
@d gr_green_val(A)      (A)->color.b_val
@d gr_blue_val(A)       (A)->color.c_val
@d gr_cyan_val(A)       (A)->color.a_val
@d gr_magenta_val(A)    (A)->color.b_val
@d gr_yellow_val(A)     (A)->color.c_val
@d gr_black_val(A)      (A)->color.d_val
@d gr_grey_val(A)       (A)->color.d_val
@d gr_path_ptr(A)       (A)->path
@d gr_htap_ptr(A)       (A)->htap
@d gr_pen_ptr(A)        (A)->pen
@d gr_linejoin_val(A)   (A)->linejoin
@d gr_linecap_val(A)    (A)->linecap
@d gr_stacking_val(A)   (A)->stacking
@d gr_miterlimit_val(A) (A)->miterlimit
@d gr_pre_script(A)     (A)->pre_script
@d gr_post_script(A)    (A)->post_script
@d gr_pre_length(A)     (A)->pre_length
@d gr_post_length(A)    (A)->post_length
@d gr_dash_ptr(A)       (A)->dash

@d mp_gr_export_color(q,p)
if (mp_color_model(p) == mp_uninitialized_model) {
    gr_color_model(q) = number_to_scaled(internal_value(mp_default_color_model_internal))/65536;
    gr_cyan_val(q)    = 0;
    gr_magenta_val(q) = 0;
    gr_yellow_val(q)  = 0;
    gr_black_val(q)   = gr_color_model(q) == mp_cmyk_model ? (number_to_scaled(unity_t)/65536.0) : 0;
} else {
    gr_color_model(q) = mp_color_model(p);
    gr_cyan_val(q)    = number_to_double(p->cyan);
    gr_magenta_val(q) = number_to_double(p->magenta);
    gr_yellow_val(q)  = number_to_double(p->yellow);
    gr_black_val(q)   = number_to_double(p->black);
}

@d mp_gr_export_scripts(q,p)
if (mp_pre_script (p)) {
    gr_pre_script(q) = mp_strndup((const char *) mp_pre_script(p)->str, mp_pre_script(p)->len);
    gr_pre_length(q) = mp_pre_script(p)->len;
}
if (mp_post_script(p)) {
    gr_post_script(q) = mp_strndup((const char *) mp_post_script(p)->str, mp_post_script(p)->len);
    gr_post_length(q) = mp_post_script(p)->len;
}

@ @c
struct mp_edge_object *mp_gr_export (MP mp, mp_edge_header_node h)
{
    mp_node p;                                                       /* the current graphical object */
    mp_edge_object *hh = mp_memory_allocate(sizeof(mp_edge_object)); /* the first graphical object */
    mp_graphic_object *hp = NULL;                                    /* the current graphical object */
    mp_set_bbox(mp, h, 1);
    hh->parent = mp;
    hh->body = NULL;
    hh->next = NULL;
    hh->minx = number_to_double(h->minx);
    hh->minx = fabs(hh->minx) < 0.00001 ? 0 : hh->minx;
    hh->miny = number_to_double(h->miny);
    hh->miny = fabs(hh->miny) < 0.00001 ? 0 : hh->miny;
    hh->maxx = number_to_double(h->maxx);
    hh->maxx = fabs(hh->maxx) < 0.00001 ? 0 : hh->maxx;
    hh->maxy = number_to_double(h->maxy);
    hh->maxy = fabs(hh->maxy) < 0.00001 ? 0 : hh->maxy;
    hh->charcode = round_unscaled(internal_value(mp_char_code_internal));
    hh->width = number_to_double(internal_value(mp_char_wd_internal));
    hh->height = number_to_double(internal_value(mp_char_ht_internal));
    hh->depth = number_to_double(internal_value(mp_char_dp_internal));
    hh->italic = number_to_double(internal_value(mp_char_ic_internal));
    p = mp_link(mp_edge_list(h));
    while (p != NULL) {
        mp_graphic_object *hq = mp_new_graphic_object(mp, (int) ((mp_type(p) - mp_fill_node_type) + 1));
        switch (mp_type(p)) {
            /* todo: share code between fill and stroked */
            case mp_fill_node_type:
                {
                    mp_number d_width; /* the current pen width */
                    mp_shape_node p0 = (mp_shape_node) p;
                    mp_shape_object *tf = (mp_shape_object *) hq;
                    gr_pen_ptr(tf) = mp_export_knot_list(mp, mp_pen_ptr(p0));
                    new_number(d_width);
                    mp_get_pen_scale(mp, &d_width, mp_pen_ptr(p0)); /* whats the point ? */
                    free_number(d_width);
                    if ((mp_pen_ptr(p0) == NULL) || mp_pen_is_elliptical(mp_pen_ptr(p0))) {
                        gr_path_ptr(tf) = mp_export_knot_list(mp, mp_path_ptr(p0));
                    } else {
                        mp_knot pc = mp_copy_path(mp, mp_path_ptr(p0));
                        mp_knot pp = mp_make_envelope(mp, pc, mp_pen_ptr(p0), p0->linejoin, 0, &(p0->miterlimit));
                        gr_path_ptr(tf) = mp_export_knot_list(mp, pp);
                        mp_toss_knot_list(mp, pp);
                        pc = mp_htap_ypoc(mp, mp_path_ptr(p0));
                        pp = mp_make_envelope(mp, pc, mp_pen_ptr((mp_shape_node) p), p0->linejoin, 0, &(p0->miterlimit));
                        gr_htap_ptr(tf) = mp_export_knot_list(mp, pp);
                        mp_toss_knot_list(mp, pp);
                    }
                    mp_gr_export_color(tf, p0);
                    mp_gr_export_scripts(tf, p);
                    gr_linejoin_val(tf) = p0->linejoin;
                    gr_stacking_val(tf) = p0->stacking;
                    gr_miterlimit_val(tf) = number_to_double(p0->miterlimit);
                }
                break;
            case mp_stroked_node_type:
                {
                    mp_number d_width; /* the current pen width */
                    mp_shape_node p0 = (mp_shape_node) p;
                    mp_shape_object *ts = (mp_shape_object *) hq;
                    gr_pen_ptr(ts) = mp_export_knot_list(mp, mp_pen_ptr(p0));
                    new_number(d_width);
                    mp_get_pen_scale(mp, &d_width, mp_pen_ptr(p0));
                    if (mp_pen_is_elliptical(mp_pen_ptr(p0))) {
                        gr_path_ptr(ts) = mp_export_knot_list(mp, mp_path_ptr(p0));
                    } else {
                        mp_knot pc = mp_copy_path(mp, mp_path_ptr(p0));
                        int t = p0->linecap;
                        if (mp_left_type(pc) != mp_endpoint_knot) {
                            mp_left_type(mp_insert_knot(mp, pc, &(pc->x_coord), &(pc->y_coord))) =  mp_endpoint_knot;
                            mp_right_type(pc) = mp_endpoint_knot;
                            pc = mp_next_knot(pc);
                            t = 1;
                        }
                        pc = mp_make_envelope(mp, pc, mp_pen_ptr(p0), p0->linejoin, (int) t, &(p0->miterlimit));
                        gr_path_ptr(ts) = mp_export_knot_list(mp, pc);
                        mp_toss_knot_list(mp, pc);
                    }
                    mp_gr_export_color(ts, p0);
                    mp_gr_export_scripts(ts, p);
                    gr_linejoin_val(ts) = p0->linejoin;
                    gr_miterlimit_val(ts) = number_to_double(p0->miterlimit);
                    gr_linecap_val(ts) = p0->linecap;
                    gr_stacking_val(ts) = p0->stacking;
                    gr_dash_ptr(ts) = mp_export_dashes(mp, p0, &d_width);
                    free_number(d_width);
                }
                break;
            case mp_start_clip_node_type:
            case mp_start_group_node_type:
            case mp_start_bounds_node_type:
                {
                    mp_start_node p0 = (mp_start_node) p;
                    mp_start_object *tb = (mp_start_object *) hq;
                    gr_path_ptr(tb) = mp_export_knot_list(mp, mp_path_ptr((mp_start_node) p));
                    gr_stacking_val(tb) = p0->stacking;
                    mp_gr_export_scripts(tb, p);
                }
                break;
            case mp_stop_clip_node_type:
            case mp_stop_group_node_type:
            case mp_stop_bounds_node_type:
                {
                    mp_stop_node p0 = (mp_stop_node) p;
                    mp_stop_object *tb = (mp_stop_object *) hq;
                    gr_stacking_val(tb) = p0->stacking;
                }
                break;
            default:
                break;
        }
        if (hh->body == NULL) {
            hh->body = hq;
        } else {
            gr_link(hp) = hq;
        }
        hp = hq;
        p = mp_link(p);
    }
    return hh;
}

@ The code here comes from the psout.w file and is part of the stipped down
library for \LUAMETATEX. There is no backend code in this subset. For that you
need the official \METAPOST\ distribution. One way of making a stand alone image
is to wrap the code in a small \CONTEXT\ file and process it to \PDF, which then
can be converted to another image format. You can blame me for errors.

@<MPlib export header stuff@>=
struct mp_edge_object *mp_gr_export          (MP mp, mp_edge_header_node h);
mp_graphic_object     *mp_new_graphic_object (MP mp, int type);
void                   mp_gr_toss_objects    (mp_edge_object *hh);
void                   mp_gr_toss_object     (mp_graphic_object *p);

@ @c
static void mp_do_gr_toss_dashes (mp_dash_object *dl) {
    if (dl) {
        mp_memory_free(dl->array);
        mp_memory_free(dl);
    }
}

@ @c
static void mp_do_gr_toss_knot_list (mp_gr_knot p)
{
    if (p) {
        mp_gr_knot q = p;
        do {
            mp_gr_knot r = gr_next_knot(q);
            mp_memory_free(q);
            q = r;
        } while (q != p);
    }
}

@ @c
mp_graphic_object *mp_new_graphic_object (MP mp, int type)
{
    mp_graphic_object *p;
    size_t size;
    (void) mp;
    switch (type) {
        case mp_fill_code:
        case mp_stroked_code:
            size = sizeof(mp_shape_object);
            break;
        case mp_start_clip_code:
        case mp_start_group_code:
        case mp_start_bounds_code:
            size = sizeof(mp_start_object);
            break;
        default:
            size = sizeof(mp_graphic_object);
            break;
    }
    p = (mp_graphic_object *) mp_memory_allocate(size);
    memset(p, 0, size);
    gr_type(p) = type;
    return p;
}

@ @c
void mp_gr_toss_object (mp_graphic_object *p)
{
    switch (gr_type(p)) {
        case mp_fill_code:
        case mp_stroked_code:
            {
                mp_shape_object *o = (mp_shape_object *) p;
                mp_memory_free(gr_pre_script(o));
                mp_memory_free(gr_post_script(o));
                mp_do_gr_toss_knot_list(gr_pen_ptr(o));
                mp_do_gr_toss_knot_list(gr_path_ptr(o));
                if (gr_htap_ptr(o)) {
                    mp_do_gr_toss_knot_list(gr_htap_ptr(o));
                }
                if (gr_dash_ptr(o)) {
                    mp_do_gr_toss_dashes(gr_dash_ptr(o));
                }
            }
            break;
        case mp_start_clip_code:
        case mp_start_group_code:
        case mp_start_bounds_code:
            {
                mp_start_object *o = (mp_start_object *) p;
                mp_memory_free(gr_pre_script(o));
                mp_memory_free(gr_post_script(o));
                mp_do_gr_toss_knot_list(gr_path_ptr(o));
            }
            break;
        case mp_stop_clip_code:
        case mp_stop_group_code:
        case mp_stop_bounds_code:
            break;
    }
    mp_memory_free(p);
}

@ @c
void mp_gr_toss_objects (mp_edge_object *hh)
{
    mp_graphic_object *p = hh->body;
    while (p) {
        mp_graphic_object *q = gr_link(p);
        mp_gr_toss_object(p);
        p = q;
    }
    mp_memory_free(hh);
}

@ This function is now nearly trivial.

@c
void mp_ship_out (MP mp, mp_node h) {
    (mp->shipout_backend)(mp, h);
}

@ @<Declarations@>=
static void mp_shipout_backend (MP mp, void *h);

@ We keep the template as comment:

@c
static void mp_shipout_backend (MP mp, void *voidh)
{
    (void) mp;
    (void) voidh;
}

@ @<Exported types@>=
typedef void (*mp_backend_writer) (MP, void *);

@ @<Option variables@>=
mp_backend_writer shipout_backend;

@* Some extensions.

Get a numeric value from \MP\ is not easy. We have to consider the macro and the
loops, as also the internal type (this is a first attempt, and more work is
needed). If we are inside a |for| loop, then the global |loop_ptr| is not null
and the other loops eventually nested are available by mean of |loop_ptr->link|.
The current numeric value is stored in |old_value|.

@ @<Exported function headers@>=
void mp_scan_next_value      (MP mp, int keep, int *token, int *mode, int *kind);
void mp_scan_expr_value      (MP mp, int keep, int *kind);
void mp_scan_token_value     (MP mp, int keep, int *token, int *mode, int *kind);
void mp_scan_symbol_value    (MP mp, int keep, char **s, int expand);
void mp_scan_property_value  (MP mp, int keep, int *kind, char **s, int *property, int *detail);

int  mp_skip_token_value     (MP mp, int token);

void mp_scan_numeric_value   (MP mp, int primary, double *d);
void mp_scan_boolean_value   (MP mp, int primary, int *b);
void mp_scan_string_value    (MP mp, int primary, char **s, size_t *l);
void mp_scan_pair_value      (MP mp, int primary, double *x, double *y);
void mp_scan_color_value     (MP mp, int primary, double *r, double *g, double *b);
void mp_scan_cmykcolor_value (MP mp, int primary, double *c, double *m, double *y, double *k);
void mp_scan_transform_value (MP mp, int primary, double *x, double *y, double *xx, double *xy, double *yx, double *yy);
void mp_scan_path_value      (MP mp, int primary, mp_knot *k);

void mp_push_numeric_value   (MP mp, double n);
void mp_push_integer_value   (MP mp, int i);
void mp_push_boolean_value   (MP mp, int b);
void mp_push_string_value    (MP mp, const char *s, int l);
void mp_push_pair_value      (MP mp, double x, double y);
void mp_push_color_value     (MP mp, double r, double g, double b);
void mp_push_cmykcolor_value (MP mp, double c, double m, double y, double k);
void mp_push_transform_value (MP mp, double x, double y, double xx, double xy, double yx, double yy);
void mp_push_path_value      (MP mp, mp_knot k);

@ This is a lightweight version, one that also omits the quotes around strings.
When we scan we check the type anyway. We don't really have a list either. So we
only serialize symbolic names, strings and single tokens.

@c
// void mp_scan_symbol_value (MP mp, int keep, char **s, int expand)
// {
//     if (mp->extensions) {
//         mp_node p;
//         unsigned char *r = NULL;
//         if (expand) {
//             mp_get_x_next(mp);
//         } else {
//             mp_get_next(mp);
//         }
//         if (keep) {
//             mp_back_input(mp);
//         }
//         *s = NULL;
//         p = mp_cur_tok(mp);
//         if (p) {
//             /* simplified mp_show_token_list */
//             if (mp_type(p) == mp_symbol_node_type) {
//             //    if (mp_name_type(p) != mp_expr_operation && mp_name_type(p) != mp_suffix_operation && mp_name_type(p) != mp_text_operation) {
//                     mp_sym sr = mp_get_sym_sym(p);
//             //        if (sr != mp_collective_subscript) {
//                         mp_string rr = text(sr);
//                         if (rr && rr->str) {
//                             r = rr->str;
//                         }
//             //        }
//             //    }
//             } else if (mp_name_type(p) == mp_token_operation) {
//                 if (mp_type(p) == mp_string_type) {
//                     r = mp_get_value_str(p)->str;
//                 }
//             }
//         }
//         if (r) {
//             *s = (char *) mp_strdup((char *) r);
//         } else {
//             *s = NULL;
//         }
//     }
// }

void mp_scan_symbol_value (MP mp, int keep, char **s, int expand)
{
    if (mp->extensions) {
        if (expand) {
            mp_get_x_next(mp);
        } else {
            mp_get_next(mp);
        }
        if (keep) {
            mp_back_input(mp);
        }
        if (cur_sym == NULL && (cur_sym_mod == 0 || cur_sym_mod == mp_normal_operation)) {
            *s = NULL;
        } else {
            unsigned char *r = NULL;
            mp_node p = mp_new_symbolic_node(mp);
            mp_set_sym_sym(p, cur_sym);
            mp_name_type(p) = cur_sym_mod;
            if (mp_type(p) == mp_symbol_node_type) {
                mp_sym sr = mp_get_sym_sym(p);
                mp_string rr = text(sr);
                if (rr && rr->str) {
                    r = rr->str;
                }
            } else if (mp_name_type(p) == mp_token_operation) {
                if (mp_type(p) == mp_string_type) {
                    r = mp_get_value_str(p)->str;
                }
            }
            mp_free_symbolic_node(mp, p);
            if (r) {
                *s = (char *) mp_strdup((char *) r);
            } else {
                *s = NULL;
            }
        }
    }
}

void mp_scan_property_value (MP mp, int keep, int *kind, char **str, int *property, int *detail)
{
    if (mp->extensions) {
        mp_symbol_entry *entry;
        mp_get_symbol(mp);
        entry = cur_sym;
        if (entry) {
            mp_node node = entry->type == mp_tag_command ? entry->v.data.node : NULL;
            *kind = entry->type;
            *str = (char *) mp_strdup((char *) entry->text->str);
            *property = entry->property;
            if (node) {
                *detail = node->type;
            }
            if (keep) {
                mp_back_input(mp);
            }
        }
    }
}

void mp_scan_next_value (MP mp, int keep, int *token, int *mode, int *kind)
{
    if (mp->extensions) {
        mp_get_next(mp);
        if (keep) {
            mp_back_input(mp);
        }
        *token = cur_cmd;
        *mode = cur_mod;
        *kind = mp->cur_exp.type;
    }
}

void mp_scan_expr_value (MP mp, int keep, int *kind)
{
    if (mp->extensions) {
        mp_get_next(mp);
        mp_scan_primary(mp);
        *kind = mp->cur_exp.type;
        if (keep) {
            mp_back_input(mp);
            mp_back_expr(mp);
        }
    }
}

void mp_scan_token_value (MP mp, int keep, int *token, int *mode, int *kind)
{
    if (mp->extensions) {
        mp_get_x_next(mp);
        if (keep) {
            mp_back_input(mp);
        }
        *token = cur_cmd;
        *mode = cur_mod;
        *kind = mp->cur_exp.type;
    }
}

int mp_skip_token_value (MP mp, int token)
{
    if (mp->extensions) {
        mp_get_x_next(mp);
        if (token == cur_cmd) {
            return 1;
        } else {
            mp_back_input(mp);
        }
    }
    return 0;
}

static void mp_scan_something (MP mp, int primary)
{
    mp_get_x_next(mp);
    switch (primary) {
        case 0:  mp_scan_expression(mp); break;
        case 1:  mp_scan_primary(mp);    break;
        case 2:  mp_scan_secondary(mp);  break;
        case 3:  mp_scan_tertiary(mp);   break;
        default: mp_scan_expression(mp); break;
    }
}

void mp_scan_numeric_value (MP mp, int primary, double *d)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_known_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_back_input(mp); /* hm */
            *d = number_to_double(cur_exp_value_number);
        }
    }
}

# define mp_set_double_value(mp,target,what) \
if (mp_type(what) == mp_known_type) { \
    *target = number_to_double(mp_get_value_number(what)); \
}

void mp_scan_pair_value (MP mp, int primary, double *x, double *y)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_pair_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_node p ;
            mp_back_input(mp); /* hm */
            p = mp_get_value_node(cur_exp_node);
            mp_set_double_value(mp, x, mp_x_part(p));
            mp_set_double_value(mp, y, mp_y_part(p));
        }
    }
}

void mp_scan_color_value (MP mp, int primary, double *r, double *g, double *b)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_color_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_node p ;
            mp_back_input(mp); /* hm */
            p = mp_get_value_node(cur_exp_node);
            mp_set_double_value(mp, r, mp_red_part(p));
            mp_set_double_value(mp, g, mp_green_part(p));
            mp_set_double_value(mp, b, mp_blue_part(p));
        }
    }
}

void mp_scan_cmykcolor_value (MP mp, int primary, double *c, double *m, double *y, double *k)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_cmykcolor_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_node p ;
            mp_back_input(mp); /* hm */
            p = mp_get_value_node(cur_exp_node);
            mp_set_double_value(mp, c, mp_cyan_part(p));
            mp_set_double_value(mp, m, mp_magenta_part(p));
            mp_set_double_value(mp, y, mp_yellow_part(p));
            mp_set_double_value(mp, k, mp_black_part(p));
        }
    }
}

void mp_scan_transform_value (MP mp, int primary, double *x, double *y, double *xx, double *xy, double *yx, double *yy)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_transform_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_node p ;
            mp_back_input(mp); /* hm */
            p = mp_get_value_node(cur_exp_node);
            mp_set_double_value(mp, x, mp_x_part(p));
            mp_set_double_value(mp, y, mp_y_part(p));
            mp_set_double_value(mp, xx, mp_xx_part(p));
            mp_set_double_value(mp, xy, mp_xy_part(p));
            mp_set_double_value(mp, yx, mp_yx_part(p));
            mp_set_double_value(mp, yy, mp_yy_part(p));
        }
    }
}

void mp_scan_path_value (MP mp, int primary, mp_knot *k)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_path_type && mp->cur_exp.type != mp_pen_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_back_input(mp); /* hm */
            *k = cur_exp_knot;
        }
    }
}

void mp_scan_boolean_value (MP mp, int primary, int *b)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_boolean_type) {
            mp_back_input(mp); /* hm */
        } else {
            mp_back_input(mp); /* hm */
            *b = cur_exp_value_boolean == mp_true_operation ? 1 : 0 ;
        }
    }
}

void mp_scan_string_value (MP mp, int primary, char **s, size_t *l)
{
    if (mp->extensions) {
        mp_scan_something(mp, primary);
        if (mp->cur_exp.type != mp_string_type) {
            mp_back_input(mp); /* hm */
            *s = NULL ;
            *l = 0;
        } else {
            mp_back_input(mp); /* hm */
            *s = (char *) cur_exp_str->str ;
            *l = cur_exp_str->len;
        }
    }
}

void mp_push_numeric_value (MP mp, double n)
{
    mp_number m;
    new_number_from_double(mp, m, n);
    mp->cur_exp.type = mp_known_type;
    mp_set_cur_exp_value_number(mp, &m);
    mp_back_expr(mp);
}

void mp_push_integer_value (MP mp, int i)
{
    mp_number m;
    new_number(m);
    set_number_from_int(m, i);
    mp->cur_exp.type = mp_known_type;
    mp_set_cur_exp_value_number(mp, &m);
    mp_back_expr(mp);
}

void mp_push_boolean_value (MP mp, int b)
{
    mp->cur_exp.type = mp_boolean_type;
    mp_set_cur_exp_value_boolean(mp, b ? mp_true_operation : mp_false_operation);
    mp_back_expr(mp);
}

void mp_push_string_value (MP mp, const char *s, int l)
{
    mp->cur_exp.type = mp_string_type;
    mp_set_cur_exp_str(mp, mp_rtsl(mp, (char *) s, l));
    mp_back_expr(mp);
}

void mp_push_pair_value (MP mp, double x, double y)
{
    /*
    mp_value new_expr;
    */
    mp_number px, py;
    mp_node p = mp_new_value_node(mp);
    mp_node v;
    mp_init_pair_node(mp, p);
    v = mp_get_value_node(p);
    new_number_from_double(mp, px, x);
    new_number_from_double(mp, py, y);
    mp_type(mp_x_part(v)) = mp_known_type;
    mp_type(mp_y_part(v)) = mp_known_type;
    mp_set_value_number(mp_x_part(v), px);
    mp_set_value_number(mp_y_part(v), py);
    free_number(px);
    free_number(py);
    /*
    memset(&new_expr, 0, sizeof(mp_value));
    new_number(new_expr.data.n);
    new_expr.type = mp_type(p);
    new_expr.data.node = p;
    mp_flush_cur_exp(mp, new_expr);
    mp->cur_exp.type = mp_pair_type;
    mp_name_type(p) = mp_capsule_operation;
    */
    mp_name_type(p) = mp_capsule_operation;
    mp->cur_exp.type = mp_pair_type;
    mp_set_cur_exp_node(mp, p);
    mp_back_expr(mp);
}

void mp_push_color_value (MP mp, double r, double g, double b)
{
    mp_number pr, pg, pb;
    mp_node p = mp_new_value_node(mp);
    mp_node v;
    mp_init_color_node(mp, p, mp_color_type);
    v = mp_get_value_node(p);
    new_number_from_double(mp, pr, r);
    new_number_from_double(mp, pg, g);
    new_number_from_double(mp, pb, b);
    mp_type(mp_red_part  (v)) = mp_known_type;
    mp_type(mp_green_part(v)) = mp_known_type;
    mp_type(mp_blue_part (v)) = mp_known_type;
    mp_set_value_number(mp_red_part  (v), pr);
    mp_set_value_number(mp_green_part(v), pg);
    mp_set_value_number(mp_blue_part (v), pb);
    free_number(pr);
    free_number(pg);
    free_number(pb);
    mp_name_type(p) = mp_capsule_operation;
    mp->cur_exp.type = mp_color_type;
    mp_set_cur_exp_node(mp, p);
    mp_back_expr(mp);
}

void mp_push_cmykcolor_value (MP mp, double c, double m, double y, double k)
{
    mp_number pc, pm, py, pk;
    mp_node p = mp_new_value_node(mp);
    mp_node v;
    mp_init_color_node(mp, p, mp_cmykcolor_type);
    v = mp_get_value_node(p);
    new_number_from_double(mp, pc, c);
    new_number_from_double(mp, pm, m);
    new_number_from_double(mp, py, y);
    new_number_from_double(mp, pk, k);
    mp_type(mp_cyan_part   (v)) = mp_known_type;
    mp_type(mp_magenta_part(v)) = mp_known_type;
    mp_type(mp_yellow_part (v)) = mp_known_type;
    mp_type(mp_black_part  (v)) = mp_known_type;
    mp_set_value_number(mp_cyan_part   (v), pc);
    mp_set_value_number(mp_magenta_part(v), pm);
    mp_set_value_number(mp_yellow_part (v), py);
    mp_set_value_number(mp_black_part  (v), pk);
    free_number(pc);
    free_number(pm);
    free_number(py);
    free_number(pk);
    mp_name_type(p) = mp_capsule_operation;
    mp->cur_exp.type = mp_cmykcolor_type;
    mp_set_cur_exp_node(mp, p);
    mp_back_expr(mp);
}

void mp_push_transform_value (MP mp, double x, double y, double xx, double xy, double yx, double yy)
{
    mp_number px, py, pxx, pxy, pyx, pyy ;
    mp_node p = mp_new_value_node(mp);
    mp_node v;
    mp_init_transform_node(mp, p);
    v = mp_get_value_node(p);
    new_number_from_double(mp, px, x);
    new_number_from_double(mp, py, y);
    new_number_from_double(mp, pxx, xx);
    new_number_from_double(mp, pxy, xy);
    new_number_from_double(mp, pyx, yx);
    new_number_from_double(mp, pyy, yy);
    mp_type(mp_x_part (v)) = mp_known_type;
    mp_type(mp_y_part (v)) = mp_known_type;
    mp_type(mp_xx_part(v)) = mp_known_type;
    mp_type(mp_xy_part(v)) = mp_known_type;
    mp_type(mp_yx_part(v)) = mp_known_type;
    mp_type(mp_yy_part(v)) = mp_known_type;
    mp_set_value_number(mp_x_part (v), px);
    mp_set_value_number(mp_y_part (v), py);
    mp_set_value_number(mp_xx_part(v), pxx);
    mp_set_value_number(mp_xy_part(v), pxy);
    mp_set_value_number(mp_yx_part(v), pyx);
    mp_set_value_number(mp_yy_part(v), pyy);
    free_number(px);
    free_number(py);
    free_number(pxx);
    free_number(pxy);
    free_number(pyx);
    free_number(pyy);
    mp_name_type(p) = mp_capsule_operation;
    mp->cur_exp.type = mp_transform_type;
    mp_set_cur_exp_node(mp, p);
    mp_back_expr(mp);
}

void mp_push_path_value (MP mp, mp_knot k)
{
    mp->cur_exp.type = mp_path_type;
    mp_set_cur_exp_knot(mp, k);
    mp_back_expr(mp);
}

@* The main program.

This is it: the part of \MP\ that executes all those procedures we have written.

Well---almost. We haven't put the parsing subroutines into the program yet; and
we'd better leave space for a few more routines that may have been forgotten.

@c
@<Declare the basic parsing subroutines@>
@<Declare miscellaneous procedures that were declared |forward|@>

@ Here we do whatever is needed to complete \MP's job gracefully on the local
operating system. The code here might come into play after a fatal error; it must
therefore consist entirely of \quote {safe} operations that cannot produce error
messages. For example, it would be a mistake to call |str_room| or |make_string|
at this time, because a call on |overflow| might lead to an infinite loop.
@^system dependencies@>

Watch out: we also close all files when we do a subrun (execute) so that's why
we have this static closer.

@ @<Declarations@>=
static void mp_close_files               (MP mp);
static void mp_close_files_and_terminate (MP mp);

@ @c
static void mp_close_files (MP mp)
{
    if (mp->rd_fname != NULL) {
        for (int k = 0; k < (int) mp->read_files; k++) {
            if (mp->rd_fname[k] != NULL) {
                (mp->close_file)(mp, mp->rd_file[k]);
                mp_memory_free(mp->rd_fname[k]);
                mp->rd_fname[k] = NULL;
            }
        }
    }
    if (mp->wr_fname != NULL) {
        for (int k = 0; k < (int) mp->write_files; k++) {
            if (mp->wr_fname[k] != NULL) {
                (mp->close_file)(mp, mp->wr_file[k]);
                mp_memory_free(mp->wr_fname[k]);
                mp->wr_fname[k] = NULL;
            }
        }
    }
}

void mp_close_files_and_terminate (MP mp)
{
    if (mp->finished) {
        return;
    } else {
        mp_close_files(mp);
        wake_up_terminal();
        mp_print_ln(mp);
        mp->finished = 1;
    }
}

@ @<Dealloc ...@>=
mp_close_files(mp);
if (mp->rd_fname != NULL) {
    mp_memory_free(mp->rd_file);
    mp_memory_free(mp->rd_fname);
    mp->rd_file = NULL;
    mp->rd_fname = NULL;
}
if (mp->wr_fname != NULL) {
    mp_memory_free(mp->wr_file);
    mp_memory_free(mp->wr_fname);
    mp->wr_file = NULL;
    mp->wr_fname = NULL;
}

@ We get to the |final_cleanup| routine when |end| or |dump| has been
scanned.

@c
void mp_final_cleanup (MP mp)
{
    while (mp->input_ptr > 0) {
        if (token_state) {
            mp_end_token_list(mp);
        } else {
            mp_end_file_reading(mp);
        }
    }
    while (mp->loop_ptr != NULL) {
        mp_stop_iteration(mp);
    }
    if (mp->interaction < mp_silent_mode) {
        while (mp->open_parens > 0) {
            mp_print_str(mp, " )");
            --mp->open_parens;
        }
    }
    while (mp->cond_ptr != NULL) {
        mp_print_nl(mp, "(end occurred when ");
        @.end occurred...@>
        mp_print_cmd_mod(mp, mp_fi_or_else_command, mp->cur_if);
        /* |if| or |elseif| or |else| */
        if (mp->if_line != 0) {
            mp_print_str(mp, " on line ");
            mp_print_int(mp, mp->if_line);
        }
        mp_print_str(mp, " was incomplete)");
        mp->if_line = mp_if_line_field(mp->cond_ptr);
        mp->cur_if = mp_name_type(mp->cond_ptr);
        mp->cond_ptr = mp_link(mp->cond_ptr);
    }
    if (mp->history != mp_spotless) {
        if (((mp->history == mp_warning_issued) || (mp->interaction < mp_error_stop_mode))) {
            if (mp->selector == mp_term_and_log_selector) {
                mp->selector = mp_term_only_selector;
                mp_print_nl(mp, "(see the transcript file for additional information)");
                @.see the transcript file...@>
                mp->selector = mp_term_and_log_selector;
            }
        }
    }
}

@ @<Declarations@>=
static void mp_final_cleanup (MP mp);
static void mp_init_prim     (MP mp);
static void mp_init_tab      (MP mp);

@ Initialize all the primitives.

@c void mp_init_prim (MP mp)
{
    @<Put each...@>
}

@ Initialize other tables:

@c void mp_init_tab (MP mp)
{
    @<Initialize table entries@>
}

@* Index.

Here is where you can find all uses of each identifier in the program, with
underlined entries pointing to where the identifier was defined. If the
identifier is only one letter long, however, you get to see only the underlined
entries. {\sl All references are to section numbers instead of page numbers.}

This index also lists error messages and other aspects of the program that you
might want to look up some day. For example, the entry for \quote {system
dependencies} lists all sections that should receive special attention from
people who are installing \MP\ in a new operating environment. A list of various
things that can't happen appears under ``this can't happen''. Approximately 25
sections are listed under \quote {inner loop}; these account for more than 60\pct! of
\MP's running time, exclusive of input and output.