beta 2014.01.18 13:23

1 files changed, 144 insertions, 124 deletions

diff --git a/metapost/context/base/mp-grap.mpiv b/metapost/context/base/mp-grap.mpiv
index 417bfbe69..6d69c0b1e 100644
--- a/metapost/context/base/mp-grap.mpiv
+++ b/metapost/context/base/mp-grap.mpiv
@@ -52,11 +52,11 @@ fi
 % endgraph                       end of graph--the result is a picture
 
 % option `plot <picture>'        draws picture at each path knot, turns off pen
-% Gtemplate.<tickcmd>            template paths for tick marks and grid lines
+% graph_template.<tickcmd>            template paths for tick marks and grid lines
 % graph_margin_fraction.low,
 % graph_margin_fraction.high     fractions determining margins when no setrange
-% Glmarks[], Gumarks, Gemarks    loop text strings used by auto.<x or y>
-% Gmarks, Gminlog                numeric parameters used by auto.<x or y>
+% graph_log_marks[], graph_lin_marks, graph_exp_marks    loop text strings used by auto.<x or y>
+% graph_minimum_number_of_marks, graph_log_minimum                numeric parameters used by auto.<x or y>
 % Autoform                       is the format string used by autogrid
 % Autoform_X, Autoform_Y         if defined, are used instead
 
@@ -65,22 +65,26 @@ fi
 % with `graph_'
 
 % Depends on :
+
 input string.mp
 
 % Private version of a few marith macros, fixed for double math...
-newinternal Mzero;           Mzero := -16384; % Anything at least this small is treated as zero
-newinternal mlogten ;        mlogten        := mlog(10) ;
-newinternal singleinfinity ; singleinfinity := 2**128 ;
-newinternal doubleinfinity ; doubleinfinity := 2**1024 ;
-% Note that we get arithmetic overflows if we set to -doubleinfinity below.
-% (but "only on odd days"...)
+
+newinternal Mzero ;           Mzero := -16384; % Anything at least this small is treated as zero
+newinternal mlogten ;         mlogten         := mlog(10) ;
+newinternal largestmantissa ; largestmantissa := 2**52 ; % internal double warningcheck
+newinternal singleinfinity ;  singleinfinity  := 2**128 ;
+newinternal doubleinfinity ;  doubleinfinity  := 2**1024 ;
+Mzero := -largestmantissa ; % Note that we get arithmetic overflows if we set to -doubleinfinity
 
 % Safely convert a number to mlog form, trapping zero.
+
 vardef graph_mlog primary x =
   if unknown x: whatever
   elseif x=0: Mzero
   else: mlog(abs x) fi
 enddef ;
+
 vardef graph_exp  primary x =
   if unknown x: whatever
   elseif x<=Mzero: 0
@@ -89,21 +93,25 @@ enddef ;
 
 % and add the following for utility/completeness
 % (replacing the definitions in mp-tool.mpiv).
+
 vardef logten primary x =
   if unknown x: whatever
   elseif x=0: Mzero
   else: mlog(abs x)/mlog(10) fi
 enddef ;
+
 vardef ln     primary x =
   if unknown x: whatever
   elseif x=0: Mzero
   else: mlog(abs x)/256 fi
 enddef ;
+
 vardef exp    primary x =
   if unknown x: whatever
   elseif x<= Mzero: 0
   else: (mexp 256)**x fi
 enddef ;
+
 vardef powten primary x =
   if unknown x: whatever
   elseif x<= Mzero: 0
@@ -112,6 +120,7 @@ enddef ;
 
 % Convert x from mlog form into a pair whose xpart gives a mantissa and whose
 % ypart gives a power of ten.
+
 vardef graph_Meform(expr x) =
   if x<=Mzero : origin
   else :
@@ -122,6 +131,7 @@ vardef graph_Meform(expr x) =
 enddef ;
 
 % Modified from above.
+
 vardef graph_Feform(expr x) =
   interim warningcheck :=0 ;
   if x=0 : origin
@@ -146,6 +156,7 @@ def graph_suffix(suffix $) = % convert from x or y to X_ or Y_
 enddef ;
 
 % New :
+
 save graph_background ; color graph_background ; % if defined, fill the frame.
 save graph_close_file ; boolean graph_close_file ; graph_close_file = false ;
 
@@ -200,17 +211,20 @@ enddef ;
 % user to alter the behavior of these macros.
 % Not very modifiable :  log, linear,
 %                        graph_frame_pair_a, graph_frame_pair_b, graph_margin_pair
-% Modifiable :           Gtemplate.suffix, Glmarks[], Gumarks, Gemarks, Gmarks,
-%                        Gminlog, Autoform
+% Modifiable :           graph_template.suffix,
+%                        graph_log_marks[], graph_lin_marks, graph_exp_marks,
+%                        graph_minimum_number_of_marks,
+%                        graph_log_minimum, Autoform
 
 
 newinternal log, linear ;        % coordinate system codes
 log :=1 ; linear :=2;
+
 % note that mp-tool.mpiv defines log as log10.
 
 %%%%%%%%%%%%%%%%%%%%%% Coordinates : setcoords, setrange %%%%%%%%%%%%%%%%%%%%%%
 
-% Graph-related usr input is `user graph coordinates' as specified by arguments
+% Graph-related user input is `user graph coordinates' as specified by arguments
 % to setcoords.
 % `Internal graph coordinates' are used for graph_current_graph, graph_current_bb, Z_.low, Z_.high.
 % Their meaning depends on the appropriate component of Z_.graph_coordinate_type :
@@ -227,14 +241,15 @@ vardef graph_set_default_bounds =         % Set default Z_.low, Z_.high
           graph_margin_pair$ ;
   endfor
 enddef ;
+
 pair graph_margin_pair.low, graph_margin_pair.high ;
 graph_margin_pair.high = -graph_margin_pair.low = (.00002,.00002) ;
 
+% Set $, $$, $$$ so that shifting by $ then transforming by $$ and then $$$ maps
+% the essential bounding box of graph_current_graph into (0,0)..Z_.graph_dimensions.
+% The `essential bounding box' is either what Z_.low and Z_.high imply
+% or the result of ignoring pen widths in graph_current_graph.
 
-% Set $, $$, $$$ so that shifting by $ then transforming by $$ and then $$$
-% maps the essential bounding box of graph_current_graph into (0,0)..Z_.graph_dimensions.  The
-% `essential bounding box' is either what Z_.low and Z_.high imply or the
-% result of ignoring pen widths in graph_current_graph.
 vardef graph_remap(suffix $,$$,$$$) =
   save p_ ;
   graph_set_default_bounds ;
@@ -245,10 +260,10 @@ vardef graph_remap(suffix $,$$,$$$) =
   (Z_.high+$) transformed $$ = p_ ;
   p_ transformed $$$ = Z_.graph_dimensions ;
 enddef ;
+
 graph_margin_fraction.low=-.07 ;         % bbox fraction for default range start
 graph_margin_fraction.high=1.07 ;        % bbox fraction for default range stop
 
-
 def graph_with_pen_and_color(expr q) =
   withpen penpart q withcolor
   if colormodel q=1 :
@@ -268,7 +283,7 @@ enddef ;
 % Pair o is the value of p that makes tp (0,0).  This implements the trick
 % whereby using 1 instead of 0 for the width or height or the setbounds path
 % for a label picture suppresses shifting in x or y.
-%
+
 %vardef graph_picture_conversion@#(expr q, o)(text tp) =
 %  save p ;
 %  if stroked q :
@@ -284,8 +299,9 @@ enddef ;
 %    addto @# also q shifted ((tp)-llcorner q) ;
 %  fi
 %enddef ;
-%
+
 % This new version makes gdraw clip the result to the window defined with setrange
+
 vardef graph_picture_conversion@#(expr q, o)(text tp) =
   save p ;
   save do_clip, tp_clipped ; boolean do_clip ; do_clip := true ;
@@ -315,12 +331,11 @@ enddef ;
 
 def graph_coordinate_multiplication(expr a,b) = (xpart a*xpart b, ypart a*ypart b) enddef ;
 
-
 vardef graph_clear_bounds@# =  numeric @#.low, @#.high ;  enddef;
 
-
 % Finalize anything drawn in the present coordinate system and set up a new
 % system as requested
+
 vardef setcoords(expr tx, ty) =
   interim warningcheck :=0 ;
   if length graph_current_graph>0 :
@@ -335,10 +350,10 @@ vardef setcoords(expr tx, ty) =
   X_.graph_coordinate_type := tx ; Y_.graph_coordinate_type := ty;
 enddef ;
 
-
 % Set Z_.low and Z_.high to correspond to given range of user graph
 % coordinates.  The text argument should be a sequence of pairs and/or strings
 % with 4 components in all.
+
 vardef setrange(text t) =
   interim warningcheck :=0 ;
   save r_ ; r_=0;
@@ -353,8 +368,8 @@ vardef setrange(text t) =
   endfor
 enddef ;
 
-
 % @# is X_ or Y_ ; l and h are numeric or string
+
 vardef graph_set_bounds@#(expr l, h) =
   graph_clear_bounds@# ;
   if @#graph_coordinate_type>0 :
@@ -382,15 +397,12 @@ vardef graph_set_bounds@#(expr l, h) =
   fi
 enddef ;
 
-
-
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%% Converting path coordinates %%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Find the result of scanning path p and using macros tx and ty to adjust the
 % x and y parts of each coordinate pair.  Boolean parameter c tells whether to
 % force the result to be polygonal.
+
 vardef graph_scan_path(expr p, c)(suffix tx, ty) =
   if (str tx="") and (str ty="") :  p
   else :
@@ -409,10 +421,11 @@ vardef graph_scan_path(expr p, c)(suffix tx, ty) =
     if pair p : point 0 of fi r_
   fi
 enddef ;
-vardef graph_pair_adjust(expr p)(suffix tx, ty) = (tx xpart p, ty ypart p) enddef ;
 
+vardef graph_pair_adjust(expr p)(suffix tx, ty) = (tx xpart p, ty ypart p) enddef ;
 
 % Convert path p from user graph coords to internal graph coords.
+
 vardef graph_convert_user_path_to_internal primary p =
   interim warningcheck :=0 ;
   graph_scan_path(p,
@@ -424,11 +437,11 @@ vardef graph_convert_user_path_to_internal primary p =
       if Y_.graph_coordinate_type<0 : yscaled -1 fi)
 enddef ;
 
-
 % Convert label location t_ from user graph coords to internal graph coords.
 % The label location should be a pair, or two numbers/strings.  If t_ is empty
 % or a single item of non-pair type, just return t_.  Unknown coordinates
 % produce unknown components in the result.
+
 vardef graph_label_convert_user_to_internal(text t_) =
   save n_ ; n_=0;
   interim warningcheck :=0 ;
@@ -448,13 +461,12 @@ vardef graph_label_convert_user_to_internal(text t_) =
   fi
 enddef ;
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Reading data files %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Read a line from file f, extract whitespace-separated tokens ignoring any
 % initial "%", and return true if at least one token is found.  The tokens
 % are stored in @#1, @#2, .. with "" in the last @#[] entry.
+
 vardef graph_read_line@#(expr f) =
   save n_, s_ ; string s_;
   s_ = readfrom f ;
@@ -472,9 +484,9 @@ vardef graph_read_line@#(expr f) =
   fi
 enddef ;
 
-
 % Execute c for each line of data read from file f, and stop at the first
 % line with no data.  Commands c can use line number i and tokens $1, $2, ...
+
 def gdata(expr f)(suffix $)(text c) =
   boolean flag ;
   for i=1 upto infinity :
@@ -486,8 +498,8 @@ def gdata(expr f)(suffix $)(text c) =
   fi
 enddef ;
 
-
 % Read a path from file f. The path is terminated by blank line or EOF.
+
 vardef graph_readpath(expr f) =
   interim warningcheck :=0 ;
   save s ;
@@ -497,9 +509,9 @@ vardef graph_readpath(expr f) =
   )
 enddef ;
 
-
 % Append coordinates t to polygonal path @#.  The coordinates can be numerics,
 % strings, or a single pair.
+
 vardef augment@#(text t) =
   interim warningcheck := 0 ;
   if not path begingroup @# endgroup :
@@ -513,12 +525,11 @@ vardef augment@#(text t) =
   fi
 enddef ;
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Drawing and filling %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Unknown pair components are set to 0 because glabel and gdotlabel understand
 % unknown coordinates as `0 in absolute units'.
+
 vardef graph_unknown_pair_bbox(expr p) =
   interim warningcheck:=0 ;
   if known p : addto graph_current_bb doublepath p ;
@@ -535,6 +546,7 @@ enddef ;
 % Initiate a gdraw or gfill command.  This must be done before scanning the
 % argument, because that could invoke the `if known graph_plot_picture' test in a following
 % plot option .
+
 def graph_addto =
   def graph_errorbar_text = enddef ;
   color graph_foreground ;
@@ -542,8 +554,8 @@ def graph_addto =
   graph_last_drawn := graph_plot_picture := nullpicture ; addto graph_last_drawn
 enddef;
 
+% Handle the part of a gdraw command that uses path or data file p.
 
-% Handle the part of a Gdraw command that uses path or data file p.
 def graph_draw expr p =
   if string p :    hide(graph_last_path := graph_readpath(p) ;)
                    graph_convert_user_path_to_internal graph_last_path
@@ -556,8 +568,8 @@ def graph_draw expr p =
   withpen currentpen graph_withlist _op_
 enddef ;
 
+% Handle the part of a gdraw command that uses path or data file p.
 
-% Handle the part of a Gdraw command that uses path or data file p.
 def graph_fill expr p =
   if string p :    hide(graph_last_path := graph_readpath(p) --cycle ;)
                    graph_convert_user_path_to_internal graph_last_path
@@ -571,8 +583,8 @@ enddef ;
 def gdraw = graph_addto doublepath graph_draw enddef ;
 def gfill = graph_addto contour graph_fill enddef ;
 
-
 % This is used in graph_draw and graph_fill to allow postprocessing graph_last_drawn
+
 def graph_withlist text t_ = t_ ; graph_post_draw; enddef;
 
 def witherrorbars(text t) text options =
@@ -584,6 +596,8 @@ def witherrorbars(text t) text options =
     options
 enddef ;
 
+% new feature: graph_errorbars
+
 picture graph_errorbar_picture ; graph_errorbar_picture := image(draw (left--right) scaled .5 ;) ;
 %picture graph_xbar_picture ;    graph_xbar_picture := image(draw (down--up)    scaled .5 ;) ;
 %picture graph_ybar_picture ;    graph_ybar_picture := image(draw (left--right) scaled .5 ;) ;
@@ -646,6 +660,7 @@ enddef ;
 
 % Set graph_plot_picture so the postprocessing step will plot picture p at each path knot.
 % Also select nullpen to suppress stroking.
+
 def plot expr p =
   if known graph_plot_picture :
     withpen nullpen
@@ -657,20 +672,19 @@ def plot expr p =
 enddef ;
 
 % This hides a semicolon that could prematurely end graph_withlist's text argument
+
 def graph_addto_currentpicture primary p = addto currentpicture also p ; enddef;
 def graph_setbounds = setbounds currentpicture to enddef ;
 
-
-def gdrawarrow = graph_number_of_arrowheads :=1 ; gdraw enddef;
-def gdrawdblarrow = graph_number_of_arrowheads :=2 ; gdraw enddef;
-
+def gdrawarrow =    graph_number_of_arrowheads := 1 ; gdraw enddef;
+def gdrawdblarrow = graph_number_of_arrowheads := 2 ; gdraw enddef;
 
 % Post-process the filled or stroked picture graph_last_drawn as follows : (1) update
 % the bounding box information ; (2) transfer it to graph_current_graph unless the pen has
 % been set to nullpen to disable stroking ; (3) plot graph_plot_picture at each knot.
+
 vardef graph_post_draw =
-  save p ;
-  path p ; p=pathpart graph_last_drawn;
+  save p ; path p ; p = pathpart graph_last_drawn ;
   graph_unknown_pair_bbox(p) ;
   if filled graph_last_drawn or not graph_is_null(penpart graph_last_drawn) :
     addto graph_current_graph also graph_last_drawn ;
@@ -687,17 +701,23 @@ vardef graph_post_draw =
     if graph_number_of_arrowheads>1 :
       graph_draw_arrowhead(reverse p, graph_with_pen_and_color(graph_last_drawn)) ;
     fi
-    graph_number_of_arrowheads :=0 ;
+    graph_number_of_arrowheads := 0 ;
   fi
 enddef ;
-vardef graph_is_null(expr p) = (urcorner p=origin) and (llcorner p=origin) enddef ;
 
+vardef graph_is_null(expr p) = (urcorner p=origin) and (llcorner p=origin) enddef ;
 
 vardef graph_draw_arrowhead(expr p)(text w) = % Draw arrowhead for path p, with list w
+  %save r ; r := angle(precontrol infinity of p shifted -point infinity of p) ;
   addto graph_current_graph also
-    image(filldraw arrowhead(
-            graph_arrowhead_extent(precontrol infinity of p, point infinity of p)) w ;
-        graph_setbounds point infinity of p..cycle) ;
+    image(fill arrowhead (graph_arrowhead_extent(precontrol infinity of p,point infinity of p)) w ;
+          draw arrowhead (graph_arrowhead_extent(precontrol infinity of p,point infinity of p)) w
+            undashed ;
+%if (r mod 90 <> 0) : % orientation can be wrong due to remapping
+%  draw textext("\tfxx " & decimal r) shifted point infinity of p withcolor blue ;
+%fi
+          graph_setbounds point infinity of p..cycle ;
+    ) ; % rotatedabout(point infinity of p,-r) ;
 enddef ;
 
 vardef graph_arrowhead_extent(expr p, q) =
@@ -705,8 +725,6 @@ vardef graph_arrowhead_extent(expr p, q) =
   q
 enddef ;
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Drawing labels %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Argument c is a drawing command that needs an additional argument p that gives
@@ -714,6 +732,7 @@ enddef ;
 % path. Unknown components of p cause the setbounds path to have width or height 1 instead of 0.
 % Then graph_unknown_pair_bbox sets these components to 0 and graph_picture_conversion
 % suppresses subsequent repositioning.
+
 def graph_draw_label(expr p)(suffix $)(text c) =
   save sdim_ ; pair sdim_;
   sdim_ := (if unknown xpart p : 1+ fi 0, if unknown ypart p : 1+ fi 0) ;
@@ -722,14 +741,13 @@ def graph_draw_label(expr p)(suffix $)(text c) =
     image(c(p) ; graph_setbounds p--p+sdim_--cycle) _op_
 enddef ;
 
-
 % Stash the result drawing command c in the graph_label table using with list w and
 % an index based on angle mfun_laboff$.
+
 vardef graph_stash_label(suffix $)(text c) text w =
   graph_label[1.5+angle mfun_laboff$ /90] = image(c(origin) w) ;
 enddef ;
 
-
 def graph_label_location primary p =
   if pair p : graph_draw_label(p)
   elseif numeric p : graph_draw_label(point p of pathpart graph_last_drawn)
@@ -737,33 +755,31 @@ def graph_label_location primary p =
   fi
 enddef ;
 
-
 % Place label p at user graph coords t using with list w. (t is a time, a pair
 % or 2 numerics or strings).
+
 vardef glabel@#(expr p)(text t) text w  =
   graph_label_location graph_label_convert_user_to_internal(t)  (@#,label@#(p)) w ; enddef;
 
-
 % Place label p at user graph coords t using with list w and draw a dot there.
 % (t is a time, a pair, or 2 numerics or strings).
+
 vardef gdotlabel@#(expr p)(text t) text w =
   graph_label_location graph_label_convert_user_to_internal(t)  (@#,dotlabel@#(p)) w ; enddef;
 
-
 def OUT = enddef ;       % location text for outside labels
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%% Grid lines, ticks, etc. %%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Grid lines and tick marks are transformed versions of the templates below.
 % In the template paths, (0,0) is on the edge of the frame and inward is to
 % the right.
-path Gtemplate.tick, Gtemplate.itick, Gtemplate.otick, Gtemplate.grid ;
-Gtemplate.tick  = (-3.5bp,0)--(3.5bp,0) ;
-Gtemplate.itick = origin--(7bp,0) ;
-Gtemplate.otick = (-7bp,0)--origin ;
-Gtemplate.grid  = origin--(1,0) ;
+
+path graph_template.tick, graph_template.itick, graph_template.otick, graph_template.grid ;
+graph_template.tick  = (-3.5bp,0)--(3.5bp,0) ;
+graph_template.itick = origin--(7bp,0) ;
+graph_template.otick = (-7bp,0)--origin ;
+graph_template.grid  = origin--(1,0) ;
 
 vardef  tick@#(expr f,u) text w =  graph_tick_label(@#,@,false,f,u,w) ;  enddef;
 
@@ -774,75 +790,82 @@ vardef otick@#(expr f,u) text w =  graph_tick_label(@#,@,false,f,u,w) ;  enddef;
 vardef  grid@#(expr f,u) text w =  graph_tick_label(@#,@,true,f,u,w) ;  enddef;
 
 
-% Produce a tick or grid mark for label suffix $, Gtemplate suffix $$,
-% coordinate value u, and with list w.  Boolean c tells whether Gtemplate$$
+% Produce a tick or grid mark for label suffix $, graph_template suffix $$,
+% coordinate value u, and with list w.  Boolean c tells whether graph_template$$
 % needs scaling by X_.graph_dimensions or Y_.graph_dimensions,
 % and f gives a format string or a label picture.
+
 def graph_tick_label(suffix $,$$)(expr c, f, u)(text w) =
-  graph_draw_label(graph_label_convert_user_to_internal(graph_generate_label_position($,u)),,draw graph_gridline_picture$($$,c,f,u,w) shifted)
+  graph_draw_label(graph_label_convert_user_to_internal(graph_generate_label_position($,u)),,
+                   draw graph_gridline_picture$($$,c,f,u,w) shifted)
 enddef ;
 
-
 % Generate label positioning arguments appropriate for label suffix $ and
 % coordinate u.
+
 def graph_generate_label_position(suffix $)(expr u) =
-  if xpart mfun_laboff.$=0 : u,whatever else : whatever,u fi
+  if pair u : u elseif xpart mfun_laboff.$=0 : u,whatever else : whatever,u fi
 enddef ;
 
-
 % Generate a picture of a grid line labeled with coordinate value u, picture
 % or format string f, and with list w.  Suffix @# is bot, top, lft, or rt,
-% suffix $ identifies entries in the Gtemplate table, and boolean c tells
-% whether to scale Gtemplate$.
+% suffix $ identifies entries in the graph_template table, and boolean c tells
+% whether to scale graph_template$.
+
 vardef graph_gridline_picture@#(suffix $)(expr c, f, u)(text w) =
   if unknown u : graph_error(u,"Label coordinate should be known") ; nullpicture
   else :
     save p ; path p;
     interim warningcheck :=0 ;
     graph_autogrid_needed :=false ;
-    p = Gtemplate$ zscaled -mfun_laboff@#
-        if c : Gxyscale fi
-        shifted (((.5 + mfun_laboff@# dotprod (.5,.5)) * mfun_laboff@#) Gxyscale) ;
+    p = graph_template$ zscaled -mfun_laboff@#
+        if c : graph_xyscale fi
+        shifted (((.5 + mfun_laboff@# dotprod (.5,.5)) * mfun_laboff@#) graph_xyscale) ;
     image(draw p w ;
         label@#(if string f : format(f,u) else : f fi, point 0 of p))
   fi
 enddef ;
-def Gxyscale = xscaled X_.graph_dimensions yscaled Y_.graph_dimensions enddef ;
 
+def graph_xyscale = xscaled X_.graph_dimensions yscaled Y_.graph_dimensions enddef ;
 
 % Draw the frame or the part corresponding to label suffix @# using with list w.
+
 vardef frame@# text w =
   graph_frame_needed :=false ;
   picture p_ ;
   p_ = image(draw
     if str@#<>"" :  subpath round(angle mfun_laboff@#*graph_frame_pair_a+graph_frame_pair_b) of  fi
-    unitsquare Gxyscale  w) ;
+    unitsquare graph_xyscale  w) ;
   graph_draw_label((whatever,whatever),,draw p_ shifted) ;
 enddef ;
-pair graph_frame_pair_a ; graph_frame_pair_a=(1,1)/90;     % unitsquare subpath is linear in label angle
-pair graph_frame_pair_b ; graph_frame_pair_b=(.75,2.25);
-
-
 
+pair graph_frame_pair_a ; graph_frame_pair_a=(1,1)/90; % unitsquare subpath is linear in label angle
+pair graph_frame_pair_b ; graph_frame_pair_b=(.75,2.25);
 
 %%%%%%%%%%%%%%%%%%%%%%%%%% Automatic grid selection %%%%%%%%%%%%%%%%%%%%%%%%%%
 
-string Glmarks[] ;       % marking options per decade for logarithmic scales
-string Gumarks ;         % mark spacing options per decade for linear scales
-string Gemarks ;         % exponent spacing options for logarithmic scales
-newinternal Gmarks, Gminlog ;
-Gmarks  := 4 ;           % minimum number marks generated by auto.x or auto.y
-Gminlog := mlog 3 ;      % revert to uniform marks when largest/smallest < this
+string graph_log_marks[] ;           % marking options per decade for logarithmic scales
+string graph_lin_marks ;             % mark spacing options per decade for linear scales
+string graph_exp_marks ;             % exponent spacing options for logarithmic scales
+newinternal graph_minimum_number_of_marks, graph_log_minimum ;
+graph_minimum_number_of_marks := 4 ; % minimum number marks generated by auto.x or auto.y
+graph_log_minimum := mlog 3 ;        % revert to uniform marks when largest/smallest < this
 
-def Gfor(text t) = for i=t endfor enddef ;  % to shorten the mark templates below
-Glmarks[1]="1,2,5" ;
-Glmarks[2]="1,1.5,2,3,4,5,7" ;
-Glmarks[3]="1Gfor(6upto10 :,i/5)Gfor(5upto10 :,i/2)Gfor(6upto9 :,i)" ;
-Glmarks[4]="1Gfor(11upto20 :,i/10)Gfor(11upto25 :,i/5)Gfor(11upto19 :,i/2)" ;
-Glmarks[5]="1Gfor(21upto40 :,i/20)Gfor(21upto50 :,i/10)Gfor(26upto49 :,i/5)" ;
-Gumarks="10,5,2" ;       % start with 10 and go down; a final `,1' is appended
-Gemarks="20,10,5,2,1" ;
+def Gfor(text t) = for i=t endfor enddef ; % to shorten the mark templates below
 
+graph_log_marks[1]="1,2,5" ;
+graph_log_marks[2]="1,1.5,2,3,4,5,7" ;
+graph_log_marks[3]="1Gfor(6upto10 :,i/5)Gfor(5upto10 :,i/2)Gfor(6upto9 :,i)" ;
+graph_log_marks[4]="1Gfor(11upto20 :,i/10)Gfor(11upto25 :,i/5)Gfor(11upto19 :,i/2)" ;
+graph_log_marks[5]="1Gfor(21upto40 :,i/20)Gfor(21upto50 :,i/10)Gfor(26upto49 :,i/5)" ;
+graph_lin_marks="10,5,2" ;           % start with 10 and go down; a final `,1' is appended
+graph_exp_marks="20,10,5,2,1" ;
+
+Ten_to0 =     1 ;
+Ten_to1 =    10 ;
+Ten_to2 =   100 ;
+Ten_to3 =  1000 ;
+Ten_to4 = 10000 ;
 
 % Determine the X_ or Y_ bounds on the range to be covered by automatic grid
 % marks.  Suffix @# is X_ or Y_.  The result is log or linear to specify the
@@ -851,6 +874,7 @@ Gemarks="20,10,5,2,1" ;
 %  are upper and lower bounds in
 % `modified exponential form'.  In modified exponential form, (x,y) means
 % (x/1000)*10^y, where 1000<=abs x<10000.
+
 vardef graph_bounds@# =
   interim warningcheck :=0 ;
   save l, h ;
@@ -859,28 +883,29 @@ vardef graph_bounds@# =
   if abs @#graph_coordinate_type=log :
     graph_modified_lower  := graph_Meform(l)+graph_modified_bias ;
     graph_modified_higher := graph_Meform(h)+graph_modified_bias ;
-    if h-l >= Gminlog : log else : linear fi
+    if h-l >= graph_log_minimum : log else : linear fi
   else :
     graph_modified_lower  := graph_Feform(l)+graph_modified_bias ;
     graph_modified_higher := graph_Feform(h)+graph_modified_bias ;
     linear
   fi
 enddef ;
+
 pair graph_modified_bias ; graph_modified_bias=(0,3);
 pair graph_modified_lower, graph_modified_higher ;
 
+% Scan graph_log_marks[k] and evaluate tokens t for each m where l<=m<=h.
 
-% Scan Glmarks[k] and evaluate tokens t for each m where l<=m<=h.
 def graph_scan_marks(expr k, l, h)(text t) =
-  for m=scantokens Glmarks[k] :
+  for m=scantokens graph_log_marks[k] :
     exitif m>h ;
     if m>=l : t fi
   endfor
 enddef ;
 
-
-% Scan Gmark[k] and evaluate tokens t for each m and e where m*10^e belongs
+% Scan graph_log_marks[k] and evaluate tokens t for each m and e where m*10^e belongs
 % between l and h (inclusive), where both l and h are in modified exponent form.
+
 def graph_scan_mark(expr k, l, h)(text t) =
   for e=ypart l upto ypart h :
     graph_scan_marks(k, if e>ypart l : 1 else : xpart l/1000 fi,
@@ -888,27 +913,29 @@ def graph_scan_mark(expr k, l, h)(text t) =
   endfor
 enddef ;
 
-
 % Select a k for which graph_scan_mark(k,...) gives enough marks.
+
 vardef graph_select_mark =
   save k ;
   k = 0 ;
   forever :
-    exitif unknown Glmarks[k+1] ;
-    exitif 0 graph_scan_mark(incr k, graph_modified_lower, graph_modified_higher, +1) >= Gmarks ;
+    exitif unknown graph_log_marks[k+1] ;
+    exitif 0 graph_scan_mark(incr k, graph_modified_lower, graph_modified_higher, +1)
+           >= graph_minimum_number_of_marks ;
   endfor
   k
 enddef ;
 
-
-% Try to select an exponent spacing from Gemarks.  If successful, set @# and
+% Try to select an exponent spacing from graph_exp_marks.  If successful, set @# and
 % return true
+
 vardef graph_select_exponent_mark@# =
   numeric @# ;
-  for e=scantokens Gemarks :
+  for e=scantokens graph_exp_marks :
     @# = e ;
     exitif floor(ypart graph_modified_higher/e) -
-           floor(graph_modified_exponent_ypart(graph_modified_lower)/e) >= Gmarks ;
+           floor(graph_modified_exponent_ypart(graph_modified_lower)/e)
+           >= graph_minimum_number_of_marks ;
     numeric @# ;
   endfor
   known @#
@@ -916,17 +943,17 @@ enddef ;
 
 vardef graph_modified_exponent_ypart(expr p) = ypart p  if xpart p=1000 : -1 fi  enddef ;
 
-
 % Compute the mark spacing d between xpart graph_modified_lower and xpart graph_modified_higher.
+
 vardef graph_tick_mark_spacing =
   interim warningcheck :=0 ;
   save m, n, d ;
-  m = Gmarks ;
+  m = graph_minimum_number_of_marks ;
   n = 1 for i=1 upto
                 (mlog(xpart graph_modified_higher-xpart graph_modified_lower) - mlog m)/mlogten :
         *10 endfor ;
   if n<=1000 :
-    for x=scantokens Gumarks :
+    for x=scantokens graph_lin_marks :
       d = n*x ;
       exitif 0 graph_generate_numbers(d,+1)>=m ;
       numeric d ;
@@ -935,25 +962,24 @@ vardef graph_tick_mark_spacing =
   if known d : d else : n fi
 enddef ;
 
-
 def graph_generate_numbers(expr d)(text t) =
   for m = d*ceiling(xpart graph_modified_lower/d) step d until xpart graph_modified_higher :
     t
   endfor
 enddef ;
 
-
 % Evaluate tokens t for exponents e in multiples of d in the range determined
 % by graph_modified_lower and graph_modified_higher.
+
 def graph_generate_exponents(expr d)(text t) =
   for e = d*floor(graph_modified_exponent_ypart(graph_modified_lower)/d+1)
       step d until d*floor(ypart graph_modified_higher/d) :  t
   endfor
 enddef ;
 
-
 % Adjust graph_modified_lower and graph_modified_higher so their exponent parts match
 % and they are in true exponent form ((x,y) means x*10^y).  Return the new exponent.
+
 vardef graph_match_exponents =
   interim warningcheck := 0 ;
   save e ;
@@ -966,10 +992,10 @@ vardef graph_match_exponents =
   e
 enddef ;
 
-
 % Assume e is an integer and either m=0 or 1<=abs(m)<10000.  Find m*(10^e)
 % and represent the result as a string if its absolute value would be at least
 % 4096 or less than .1.  It is OK to return 0 as a string or a numeric.
+
 vardef graph_factor_and_exponent_to_string(expr m, e) =
   if (e>3)or(e<-4) :
     decimal m & "e" & decimal e
@@ -984,7 +1010,6 @@ vardef graph_factor_and_exponent_to_string(expr m, e) =
   fi
 enddef ;
 
-
 def auto suffix $ =
   hide(def graph_comma= hide(def graph_comma=,enddef) enddef)
   if graph_bounds.graph_suffix($)=log :
@@ -1002,7 +1027,6 @@ def auto suffix $ =
   fi
 enddef ;
 
-
 string Autoform ; Autoform = "%g";
 
 %vardef autogrid(suffix tx, ty) text w =
@@ -1053,12 +1077,11 @@ vardef autogrid(suffix tx, ty) text w =
     fi
 enddef ;
 
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% endgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 def endgraph =
   if graph_autogrid_needed : autogrid(otick.bot, otick.lft) ; fi
-  if graph_frame_needed :    frame ; fi
+  if    graph_frame_needed : frame ; fi
   setcoords(linear,linear) ;
   interim truecorners :=1 ;
   for  b=bbox graph_finished_graph :
@@ -1075,14 +1098,9 @@ enddef ;
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
+% We format in luatex (using \mathematics{}) ...
 % we could pass via variables and save escaping as that is inefficient
 
-Ten_to0 =     1 ;
-Ten_to1 =    10 ;
-Ten_to2 =   100 ;
-Ten_to3 =  1000 ;
-Ten_to4 = 10000 ;
-
 if unknown context_mlib :
 
     vardef escaped_format(expr s) =
@@ -1108,6 +1126,8 @@ if unknown context_mlib :
 
 fi ;
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 % A couple of extensions :
 
 % Define a function plotsymbol() returning a picture : 10 different shapes,