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author | Hans Hagen <pragma@wxs.nl> | 2022-09-16 15:53:42 +0200 |
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committer | Context Git Mirror Bot <phg@phi-gamma.net> | 2022-09-16 15:53:42 +0200 |
commit | c161b7d6fe142231346cc1844e6e27c0ab7718c1 (patch) | |
tree | 3fd877b8986137703e987e4651a2db8e946a0f72 /source/luametatex/source/libraries/decnumber/decNumber.c | |
parent | e94fa4dc30ec28a6727aa85e17aaac18b76aeadb (diff) | |
download | context-c161b7d6fe142231346cc1844e6e27c0ab7718c1.tar.gz |
2022-09-16 14:41:00
Diffstat (limited to 'source/luametatex/source/libraries/decnumber/decNumber.c')
-rw-r--r-- | source/luametatex/source/libraries/decnumber/decNumber.c | 8145 |
1 files changed, 8145 insertions, 0 deletions
diff --git a/source/luametatex/source/libraries/decnumber/decNumber.c b/source/luametatex/source/libraries/decnumber/decNumber.c new file mode 100644 index 000000000..8b8dd0d4b --- /dev/null +++ b/source/luametatex/source/libraries/decnumber/decNumber.c @@ -0,0 +1,8145 @@ +/* ------------------------------------------------------------------ */ +/* Decimal Number arithmetic module */ +/* ------------------------------------------------------------------ */ +/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ +/* */ +/* This software is made available under the terms of the */ +/* ICU License -- ICU 1.8.1 and later. */ +/* */ +/* The description and User's Guide ("The decNumber C Library") for */ +/* this software is called decNumber.pdf. This document is */ +/* available, together with arithmetic and format specifications, */ +/* testcases, and Web links, on the General Decimal Arithmetic page. */ +/* */ +/* Please send comments, suggestions, and corrections to the author: */ +/* mfc@uk.ibm.com */ +/* Mike Cowlishaw, IBM Fellow */ +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for arbitrary-precision General */ +/* Decimal Arithmetic as defined in the specification which may be */ +/* found on the General Decimal Arithmetic pages. It implements both */ +/* the full ('extended') arithmetic and the simpler ('subset') */ +/* arithmetic. */ +/* */ +/* Usage notes: */ +/* */ +/* 1. This code is ANSI C89 except: */ +/* */ +/* a) C99 line comments (double forward slash) are used. (Most C */ +/* compilers accept these. If yours does not, a simple script */ +/* can be used to convert them to ANSI C comments.) */ +/* */ +/* b) Types from C99 stdint.h are used. If you do not have this */ +/* header file, see the User's Guide section of the decNumber */ +/* documentation; this lists the necessary definitions. */ +/* */ +/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ +/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ +/* and DECDPUN<=4 (see documentation). */ +/* */ +/* The code also conforms to C99 restrictions; in particular, */ +/* strict aliasing rules are observed. */ +/* */ +/* 2. The decNumber format which this library uses is optimized for */ +/* efficient processing of relatively short numbers; in particular */ +/* it allows the use of fixed sized structures and minimizes copy */ +/* and move operations. It does, however, support arbitrary */ +/* precision (up to 999,999,999 digits) and arbitrary exponent */ +/* range (Emax in the range 0 through 999,999,999 and Emin in the */ +/* range -999,999,999 through 0). Mathematical functions (for */ +/* example decNumberExp) as identified below are restricted more */ +/* tightly: digits, emax, and -emin in the context must be <= */ +/* DEC_MAX_MATH (999999), and their operand(s) must be within */ +/* these bounds. */ +/* */ +/* 3. Logical functions are further restricted; their operands must */ +/* be finite, positive, have an exponent of zero, and all digits */ +/* must be either 0 or 1. The result will only contain digits */ +/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ +/* */ +/* 4. Operands to operator functions are never modified unless they */ +/* are also specified to be the result number (which is always */ +/* permitted). Other than that case, operands must not overlap. */ +/* */ +/* 5. Error handling: the type of the error is ORed into the status */ +/* flags in the current context (decContext structure). The */ +/* SIGFPE signal is then raised if the corresponding trap-enabler */ +/* flag in the decContext is set (is 1). */ +/* */ +/* It is the responsibility of the caller to clear the status */ +/* flags as required. */ +/* */ +/* The result of any routine which returns a number will always */ +/* be a valid number (which may be a special value, such as an */ +/* Infinity or NaN). */ +/* */ +/* 6. The decNumber format is not an exchangeable concrete */ +/* representation as it comprises fields which may be machine- */ +/* dependent (packed or unpacked, or special length, for example). */ +/* Canonical conversions to and from strings are provided; other */ +/* conversions are available in separate modules. */ +/* */ +/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ +/* to 1 for extended operand checking (including NULL operands). */ +/* Results are undefined if a badly-formed structure (or a NULL */ +/* pointer to a structure) is provided, though with DECCHECK */ +/* enabled the operator routines are protected against exceptions. */ +/* (Except if the result pointer is NULL, which is unrecoverable.) */ +/* */ +/* However, the routines will never cause exceptions if they are */ +/* given well-formed operands, even if the value of the operands */ +/* is inappropriate for the operation and DECCHECK is not set. */ +/* (Except for SIGFPE, as and where documented.) */ +/* */ +/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ +/* ------------------------------------------------------------------ */ +/* Implementation notes for maintenance of this module: */ +/* */ +/* 1. Storage leak protection: Routines which use malloc are not */ +/* permitted to use return for fastpath or error exits (i.e., */ +/* they follow strict structured programming conventions). */ +/* Instead they have a do{}while(0); construct surrounding the */ +/* code which is protected -- break may be used to exit this. */ +/* Other routines can safely use the return statement inline. */ +/* */ +/* Storage leak accounting can be enabled using DECALLOC. */ +/* */ +/* 2. All loops use the for(;;) construct. Any do construct does */ +/* not loop; it is for allocation protection as just described. */ +/* */ +/* 3. Setting status in the context must always be the very last */ +/* action in a routine, as non-0 status may raise a trap and hence */ +/* the call to set status may not return (if the handler uses long */ +/* jump). Therefore all cleanup must be done first. In general, */ +/* to achieve this status is accumulated and is only applied just */ +/* before return by calling decContextSetStatus (via decStatus). */ +/* */ +/* Routines which allocate storage cannot, in general, use the */ +/* 'top level' routines which could cause a non-returning */ +/* transfer of control. The decXxxxOp routines are safe (do not */ +/* call decStatus even if traps are set in the context) and should */ +/* be used instead (they are also a little faster). */ +/* */ +/* 4. Exponent checking is minimized by allowing the exponent to */ +/* grow outside its limits during calculations, provided that */ +/* the decFinalize function is called later. Multiplication and */ +/* division, and intermediate calculations in exponentiation, */ +/* require more careful checks because of the risk of 31-bit */ +/* overflow (the most negative valid exponent is -1999999997, for */ +/* a 999999999-digit number with adjusted exponent of -999999999). */ +/* */ +/* 5. Rounding is deferred until finalization of results, with any */ +/* 'off to the right' data being represented as a single digit */ +/* residue (in the range -1 through 9). This avoids any double- */ +/* rounding when more than one shortening takes place (for */ +/* example, when a result is subnormal). */ +/* */ +/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ +/* during many operations, so whole Units are handled and exact */ +/* accounting of digits is not needed. The correct digits value */ +/* is found by decGetDigits, which accounts for leading zeros. */ +/* This must be called before any rounding if the number of digits */ +/* is not known exactly. */ +/* */ +/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ +/* numbers up to four digits, using appropriate constants. This */ +/* is not useful for longer numbers because overflow of 32 bits */ +/* would lead to 4 multiplies, which is almost as expensive as */ +/* a divide (unless a floating-point or 64-bit multiply is */ +/* assumed to be available). */ +/* */ +/* 8. Unusual abbreviations that may be used in the commentary: */ +/* lhs -- left hand side (operand, of an operation) */ +/* lsd -- least significant digit (of coefficient) */ +/* lsu -- least significant Unit (of coefficient) */ +/* msd -- most significant digit (of coefficient) */ +/* msi -- most significant item (in an array) */ +/* msu -- most significant Unit (of coefficient) */ +/* rhs -- right hand side (operand, of an operation) */ +/* +ve -- positive */ +/* -ve -- negative */ +/* ** -- raise to the power */ +/* ------------------------------------------------------------------ */ + +#include <stdlib.h> // for malloc, free, etc. +#include <stdio.h> // for printf [if needed] +#include <string.h> // for strcpy +#include <ctype.h> // for lower +#include "decNumber.h" // base number library +#include "decNumberLocal.h" // decNumber local types, etc. + +/* Constants */ +// Public lookup table used by the D2U macro +const uByte d2utable[DECMAXD2U+1]=D2UTABLE; + +#define DECVERB 1 // set to 1 for verbose DECCHECK +#define powers DECPOWERS // old internal name + +// Local constants +#define DIVIDE 0x80 // Divide operators +#define REMAINDER 0x40 // .. +#define DIVIDEINT 0x20 // .. +#define REMNEAR 0x10 // .. +#define COMPARE 0x01 // Compare operators +#define COMPMAX 0x02 // .. +#define COMPMIN 0x03 // .. +#define COMPTOTAL 0x04 // .. +#define COMPNAN 0x05 // .. [NaN processing] +#define COMPSIG 0x06 // .. [signaling COMPARE] +#define COMPMAXMAG 0x07 // .. +#define COMPMINMAG 0x08 // .. + +#define DEC_sNaN 0x40000000 // local status: sNaN signal +#define BADINT (Int)0x80000000 // most-negative Int; error indicator +// Next two indicate an integer >= 10**6, and its parity (bottom bit) +#define BIGEVEN (Int)0x80000002 +#define BIGODD (Int)0x80000003 + +static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing + +/* Granularity-dependent code */ +#if DECDPUN<=4 + #define eInt Int // extended integer + #define ueInt uInt // unsigned extended integer + // Constant multipliers for divide-by-power-of five using reciprocal + // multiply, after removing powers of 2 by shifting, and final shift + // of 17 [we only need up to **4] + static const uInt multies[]={131073, 26215, 5243, 1049, 210}; + // QUOT10 -- macro to return the quotient of unit u divided by 10**n + #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) +#else + // For DECDPUN>4 non-ANSI-89 64-bit types are needed. + #if !DECUSE64 + #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 + #endif + #define eInt Long // extended integer + #define ueInt uLong // unsigned extended integer +#endif + +/* Local routines */ +static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, + decContext *, uByte, uInt *); +static Flag decBiStr(const char *, const char *, const char *); +static uInt decCheckMath(const decNumber *, decContext *, uInt *); +static void decApplyRound(decNumber *, decContext *, Int, uInt *); +static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); +static decNumber * decCompareOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + Flag, uInt *); +static void decCopyFit(decNumber *, const decNumber *, decContext *, + Int *, uInt *); +static decNumber * decDecap(decNumber *, Int); +static decNumber * decDivideOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, uInt *); +static decNumber * decExpOp(decNumber *, const decNumber *, + decContext *, uInt *); +static void decFinalize(decNumber *, decContext *, Int *, uInt *); +static Int decGetDigits(Unit *, Int); +static Int decGetInt(const decNumber *); +static decNumber * decLnOp(decNumber *, const decNumber *, + decContext *, uInt *); +static decNumber * decMultiplyOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + uInt *); +static decNumber * decNaNs(decNumber *, const decNumber *, + const decNumber *, decContext *, uInt *); +static decNumber * decQuantizeOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, + uInt *); +static void decReverse(Unit *, Unit *); +static void decSetCoeff(decNumber *, decContext *, const Unit *, + Int, Int *, uInt *); +static void decSetMaxValue(decNumber *, decContext *); +static void decSetOverflow(decNumber *, decContext *, uInt *); +static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); +static Int decShiftToLeast(Unit *, Int, Int); +static Int decShiftToMost(Unit *, Int, Int); +static void decStatus(decNumber *, uInt, decContext *); +static void decToString(const decNumber *, char[], Flag); +static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); +static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, + Unit *, Int); +static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); + +#if !DECSUBSET +/* decFinish == decFinalize when no subset arithmetic needed */ +#define decFinish(a,b,c,d) decFinalize(a,b,c,d) +#else +static void decFinish(decNumber *, decContext *, Int *, uInt *); +static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); +#endif + +/* Local macros */ +// masked special-values bits +#define SPECIALARG (rhs->bits & DECSPECIAL) +#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) + +/* Diagnostic macros, etc. */ +#if DECALLOC +// Handle malloc/free accounting. If enabled, our accountable routines +// are used; otherwise the code just goes straight to the system malloc +// and free routines. +#define malloc(a) decMalloc(a) +#define free(a) decFree(a) +#define DECFENCE 0x5a // corruption detector +// 'Our' malloc and free: +static void *decMalloc(size_t); +static void decFree(void *); +uInt decAllocBytes=0; // count of bytes allocated +// Note that DECALLOC code only checks for storage buffer overflow. +// To check for memory leaks, the decAllocBytes variable must be +// checked to be 0 at appropriate times (e.g., after the test +// harness completes a set of tests). This checking may be unreliable +// if the testing is done in a multi-thread environment. +#endif + +# include "../../utilities/auxmemory.h" +# define malloc lmt_memory_malloc +# define free lmt_memory_free + +#if DECCHECK +// Optional checking routines. Enabling these means that decNumber +// and decContext operands to operator routines are checked for +// correctness. This roughly doubles the execution time of the +// fastest routines (and adds 600+ bytes), so should not normally be +// used in 'production'. +// decCheckInexact is used to check that inexact results have a full +// complement of digits (where appropriate -- this is not the case +// for Quantize, for example) +#define DECUNRESU ((decNumber *)(void *)0xffffffff) +#define DECUNUSED ((const decNumber *)(void *)0xffffffff) +#define DECUNCONT ((decContext *)(void *)(0xffffffff)) +static Flag decCheckOperands(decNumber *, const decNumber *, + const decNumber *, decContext *); +static Flag decCheckNumber(const decNumber *); +static void decCheckInexact(const decNumber *, decContext *); +#endif + +#if DECTRACE || DECCHECK +// Optional trace/debugging routines (may or may not be used) +void decNumberShow(const decNumber *); // displays the components of a number +static void decDumpAr(char, const Unit *, Int); +#endif + +/* ================================================================== */ +/* Conversions */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* from-int32 -- conversion from Int or uInt */ +/* */ +/* dn is the decNumber to receive the integer */ +/* in or uin is the integer to be converted */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromInt32(decNumber *dn, Int in) { + uInt unsig; + if (in>=0) unsig=in; + else { // negative (possibly BADINT) + if (in==BADINT) unsig=(uInt)1073741824*2; // special case + else unsig=-in; // invert + } + // in is now positive + decNumberFromUInt32(dn, unsig); + if (in<0) dn->bits=DECNEG; // sign needed + return dn; + } // decNumberFromInt32 + +decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { + Unit *up; // work pointer + decNumberZero(dn); // clean + if (uin==0) return dn; // [or decGetDigits bad call] + for (up=dn->lsu; uin>0; up++) { + *up=(Unit)(uin%(DECDPUNMAX+1)); + uin=uin/(DECDPUNMAX+1); + } + dn->digits=decGetDigits(dn->lsu, up-dn->lsu); + return dn; + } // decNumberFromUInt32 + +/* ------------------------------------------------------------------ */ +/* to-int32 -- conversion to Int or uInt */ +/* */ +/* dn is the decNumber to convert */ +/* set is the context for reporting errors */ +/* returns the converted decNumber, or 0 if Invalid is set */ +/* */ +/* Invalid is set if the decNumber does not have exponent==0 or if */ +/* it is a NaN, Infinite, or out-of-range. */ +/* ------------------------------------------------------------------ */ +Int decNumberToInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + // special or too many digits, or bad exponent + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad + else { // is a finite integer with 10 or fewer digits + Int d; // work + const Unit *up; // .. + uInt hi=0, lo; // .. + up=dn->lsu; // -> lsu + lo=*up; // get 1 to 9 digits + #if DECDPUN>1 // split to higher + hi=lo/10; + lo=lo%10; + #endif + up++; + // collect remaining Units, if any, into hi + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + // now low has the lsd, hi the remainder + if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range? + // most-negative is a reprieve + if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; + // bad -- drop through + } + else { // in-range always + Int i=X10(hi)+lo; + if (dn->bits&DECNEG) return -i; + return i; + } + } // integer + decContextSetStatus(set, DEC_Invalid_operation); // [may not return] + return 0; + } // decNumberToInt32 + +uInt decNumberToUInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + // special or too many digits, or bad exponent, or negative (<0) + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 + || (dn->bits&DECNEG && !ISZERO(dn))); // bad + else { // is a finite integer with 10 or fewer digits + Int d; // work + const Unit *up; // .. + uInt hi=0, lo; // .. + up=dn->lsu; // -> lsu + lo=*up; // get 1 to 9 digits + #if DECDPUN>1 // split to higher + hi=lo/10; + lo=lo%10; + #endif + up++; + // collect remaining Units, if any, into hi + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + + // now low has the lsd, hi the remainder + if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible + else return X10(hi)+lo; + } // integer + decContextSetStatus(set, DEC_Invalid_operation); // [may not return] + return 0; + } // decNumberToUInt32 + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decNumberToString(dn, string); */ +/* decNumberToEngString(dn, string); */ +/* */ +/* dn is the decNumber to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decNumberToString(const decNumber *dn, char *string){ + decToString(dn, string, 0); + return string; + } // DecNumberToString + +char * decNumberToEngString(const decNumber *dn, char *string){ + decToString(dn, string, 1); + return string; + } // DecNumberToEngString + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decNumberFromString -- convert string to decNumber */ +/* dn -- the number structure to fill */ +/* chars[] -- the string to convert ('\0' terminated) */ +/* set -- the context used for processing any error, */ +/* determining the maximum precision available */ +/* (set.digits), determining the maximum and minimum */ +/* exponent (set.emax and set.emin), determining if */ +/* extended values are allowed, and checking the */ +/* rounding mode if overflow occurs or rounding is */ +/* needed. */ +/* */ +/* The length of the coefficient and the size of the exponent are */ +/* checked by this routine, so the correct error (Underflow or */ +/* Overflow) can be reported or rounding applied, as necessary. */ +/* */ +/* If bad syntax is detected, the result will be a quiet NaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromString(decNumber *dn, const char chars[], + decContext *set) { + Int exponent=0; // working exponent [assume 0] + uByte bits=0; // working flags [assume +ve] + Unit *res; // where result will be built + Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary + // [+9 allows for ln() constants] + Unit *allocres=NULL; // -> allocated result, iff allocated + Int d=0; // count of digits found in decimal part + const char *dotchar=NULL; // where dot was found + const char *cfirst=chars; // -> first character of decimal part + const char *last=NULL; // -> last digit of decimal part + const char *c; // work + Unit *up; // .. + #if DECDPUN>1 + Int cut, out; // .. + #endif + Int residue; // rounding residue + uInt status=0; // error code + + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) + return decNumberZero(dn); + #endif + + do { // status & malloc protection + for (c=chars;; c++) { // -> input character + if (*c>='0' && *c<='9') { // test for Arabic digit + last=c; + d++; // count of real digits + continue; // still in decimal part + } + if (*c=='.' && dotchar==NULL) { // first '.' + dotchar=c; // record offset into decimal part + if (c==cfirst) cfirst++; // first digit must follow + continue;} + if (c==chars) { // first in string... + if (*c=='-') { // valid - sign + cfirst++; + bits=DECNEG; + continue;} + if (*c=='+') { // valid + sign + cfirst++; + continue;} + } + // *c is not a digit, or a valid +, -, or '.' + break; + } // c + + if (last==NULL) { // no digits yet + status=DEC_Conversion_syntax;// assume the worst + if (*c=='\0') break; // and no more to come... + #if DECSUBSET + // if subset then infinities and NaNs are not allowed + if (!set->extended) break; // hopeless + #endif + // Infinities and NaNs are possible, here + if (dotchar!=NULL) break; // .. unless had a dot + decNumberZero(dn); // be optimistic + if (decBiStr(c, "infinity", "INFINITY") + || decBiStr(c, "inf", "INF")) { + dn->bits=bits | DECINF; + status=0; // is OK + break; // all done + } + // a NaN expected + // 2003.09.10 NaNs are now permitted to have a sign + dn->bits=bits | DECNAN; // assume simple NaN + if (*c=='s' || *c=='S') { // looks like an sNaN + c++; + dn->bits=bits | DECSNAN; + } + if (*c!='n' && *c!='N') break; // check caseless "NaN" + c++; + if (*c!='a' && *c!='A') break; // .. + c++; + if (*c!='n' && *c!='N') break; // .. + c++; + // now either nothing, or nnnn payload, expected + // -> start of integer and skip leading 0s [including plain 0] + for (cfirst=c; *cfirst=='0';) cfirst++; + if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s + status=0; // it's good + break; // .. + } + // something other than 0s; setup last and d as usual [no dots] + for (c=cfirst;; c++, d++) { + if (*c<'0' || *c>'9') break; // test for Arabic digit + last=c; + } + if (*c!='\0') break; // not all digits + if (d>set->digits-1) { + // [NB: payload in a decNumber can be full length unless + // clamped, in which case can only be digits-1] + if (set->clamp) break; + if (d>set->digits) break; + } // too many digits? + // good; drop through to convert the integer to coefficient + status=0; // syntax is OK + bits=dn->bits; // for copy-back + } // last==NULL + + else if (*c!='\0') { // more to process... + // had some digits; exponent is only valid sequence now + Flag nege; // 1=negative exponent + const char *firstexp; // -> first significant exponent digit + status=DEC_Conversion_syntax;// assume the worst + if (*c!='e' && *c!='E') break; + /* Found 'e' or 'E' -- now process explicit exponent */ + // 1998.07.11: sign no longer required + nege=0; + c++; // to (possible) sign + if (*c=='-') {nege=1; c++;} + else if (*c=='+') c++; + if (*c=='\0') break; + + for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros + firstexp=c; // save exponent digit place + for (; ;c++) { + if (*c<'0' || *c>'9') break; // not a digit + exponent=X10(exponent)+(Int)*c-(Int)'0'; + } // c + // if not now on a '\0', *c must not be a digit + if (*c!='\0') break; + + // (this next test must be after the syntax checks) + // if it was too long the exponent may have wrapped, so check + // carefully and set it to a certain overflow if wrap possible + if (c>=firstexp+9+1) { + if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; + // [up to 1999999999 is OK, for example 1E-1000000998] + } + if (nege) exponent=-exponent; // was negative + status=0; // is OK + } // stuff after digits + + // Here when whole string has been inspected; syntax is good + // cfirst->first digit (never dot), last->last digit (ditto) + + // strip leading zeros/dot [leave final 0 if all 0's] + if (*cfirst=='0') { // [cfirst has stepped over .] + for (c=cfirst; c<last; c++, cfirst++) { + if (*c=='.') continue; // ignore dots + if (*c!='0') break; // non-zero found + d--; // 0 stripped + } // c + #if DECSUBSET + // make a rapid exit for easy zeros if !extended + if (*cfirst=='0' && !set->extended) { + decNumberZero(dn); // clean result + break; // [could be return] + } + #endif + } // at least one leading 0 + + // Handle decimal point... + if (dotchar!=NULL && dotchar<last) // non-trailing '.' found? + exponent-=(last-dotchar); // adjust exponent + // [we can now ignore the .] + + // OK, the digits string is good. Assemble in the decNumber, or in + // a temporary units array if rounding is needed + if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber + else { // rounding needed + Int needbytes=D2U(d)*sizeof(Unit);// bytes needed + res=resbuff; // assume use local buffer + if (needbytes>(Int)sizeof(resbuff)) { // too big for local + allocres=(Unit *)malloc(needbytes); + if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} + res=allocres; + } + } + // res now -> number lsu, buffer, or allocated storage for Unit array + + // Place the coefficient into the selected Unit array + // [this is often 70% of the cost of this function when DECDPUN>1] + #if DECDPUN>1 + out=0; // accumulator + up=res+D2U(d)-1; // -> msu + cut=d-(up-res)*DECDPUN; // digits in top unit + for (c=cfirst;; c++) { // along the digits + if (*c=='.') continue; // ignore '.' [don't decrement cut] + out=X10(out)+(Int)*c-(Int)'0'; + if (c==last) break; // done [never get to trailing '.'] + cut--; + if (cut>0) continue; // more for this unit + *up=(Unit)out; // write unit + up--; // prepare for unit below.. + cut=DECDPUN; // .. + out=0; // .. + } // c + *up=(Unit)out; // write lsu + + #else + // DECDPUN==1 + up=res; // -> lsu + for (c=last; c>=cfirst; c--) { // over each character, from least + if (*c=='.') continue; // ignore . [don't step up] + *up=(Unit)((Int)*c-(Int)'0'); + up++; + } // c + #endif + + dn->bits=bits; + dn->exponent=exponent; + dn->digits=d; + + // if not in number (too long) shorten into the number + if (d>set->digits) { + residue=0; + decSetCoeff(dn, set, res, d, &residue, &status); + // always check for overflow or subnormal and round as needed + decFinalize(dn, set, &residue, &status); + } + else { // no rounding, but may still have overflow or subnormal + // [these tests are just for performance; finalize repeats them] + if ((dn->exponent-1<set->emin-dn->digits) + || (dn->exponent-1>set->emax-set->digits)) { + residue=0; + decFinalize(dn, set, &residue, &status); + } + } + // decNumberShow(dn); + } while(0); // [for break] + + if (allocres!=NULL) free(allocres); // drop any storage used + if (status!=0) decStatus(dn, status, set); + return dn; + } /* decNumberFromString */ + +/* ================================================================== */ +/* Operators */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberAbs -- absolute value operator */ +/* */ +/* This computes C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyAbs for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This has the same effect as decNumberPlus unless A is negative, */ +/* in which case it has the same effect as decNumberMinus. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; // for 0 + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // set 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberAbs + +/* ------------------------------------------------------------------ */ +/* decNumberAdd -- add two Numbers */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This just calls the routine shared with Subtract */ +decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decAddOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberAdd + +/* ------------------------------------------------------------------ */ +/* decNumberAnd -- AND two Numbers, digitwise */ +/* */ +/* This computes C = A & B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + *uc=0; // can now write back + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i<DECDPUN; i++) { + if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // both OK + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberAnd + +/* ------------------------------------------------------------------ */ +/* decNumberCompare -- compare two Numbers */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPARE, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompare + +/* ------------------------------------------------------------------ */ +/* decNumberCompareSignal -- compare, signalling on all NaNs */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPSIG, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareSignal + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotal -- compare two Numbers, using total ordering */ +/* */ +/* This computes C = A ? B, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareTotal + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ +/* */ +/* This computes C = |A| ? |B|, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + uInt needbytes; // for space calculations + decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0 + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber bufb[D2N(DECBUFFER+1)]; + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *a, *b; // temporary pointers + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + // if either is negative, take a copy and absolute + if (decNumberIsNegative(lhs)) { // lhs<0 + a=bufa; + needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + decNumberCopy(a, lhs); // copy content + a->bits&=~DECNEG; // .. and clear the sign + lhs=a; // use copy from here on + } + if (decNumberIsNegative(rhs)) { // rhs<0 + b=bufb; + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + decNumberCopy(b, rhs); // copy content + b->bits&=~DECNEG; // .. and clear the sign + rhs=b; // use copy from here on + } + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareTotalMag + +/* ------------------------------------------------------------------ */ +/* decNumberDivide -- divide one number by another */ +/* */ +/* This computes C = A / B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, DIVIDE, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberDivide + +/* ------------------------------------------------------------------ */ +/* decNumberDivideInteger -- divide and return integer quotient */ +/* */ +/* This computes C = A # B, where # is the integer divide operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberDivideInteger + +/* ------------------------------------------------------------------ */ +/* decNumberExp -- exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decExpOp which can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-a) where a can be the tiniest number (Ntiny). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberExp(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; these restrictions ensure that if h=8 (see + // decExpOp) then the result will either overflow or underflow to 0. + // Other math functions restrict the input range, too, for inverses. + // If not violated then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect allocation + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + decExpOp(res, rhs, set, &status); + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberExp + +/* ------------------------------------------------------------------ */ +/* decNumberFMA -- fused multiply add */ +/* */ +/* This computes D = (A * B) + C with only one rounding */ +/* */ +/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ +/* lhs is A */ +/* rhs is B */ +/* fhs is C [far hand side] */ +/* set is the context */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, + const decNumber *rhs, const decNumber *fhs, + decContext *set) { + uInt status=0; // accumulator + decContext dcmul; // context for the multiplication + uInt needbytes; // for space calculations + decNumber bufa[D2N(DECBUFFER*2+1)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *acc; // accumulator pointer + decNumber dzero; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { // [undefined if subset] + status|=DEC_Invalid_operation; + break;} + #endif + // Check math restrictions [these ensure no overflow or underflow] + if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) + || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) + || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; + // set up context for multiply + dcmul=*set; + dcmul.digits=lhs->digits+rhs->digits; // just enough + // [The above may be an over-estimate for subset arithmetic, but that's OK] + dcmul.emax=DEC_MAX_EMAX; // effectively unbounded .. + dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions] + // set up decNumber space to receive the result of the multiply + acc=bufa; // may fit + needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + acc=allocbufa; // use the allocated space + } + // multiply with extended range and necessary precision + //printf("emin=%ld\n", dcmul.emin); + decMultiplyOp(acc, lhs, rhs, &dcmul, &status); + // Only Invalid operation (from sNaN or Inf * 0) is possible in + // status; if either is seen than ignore fhs (in case it is + // another sNaN) and set acc to NaN unless we had an sNaN + // [decMultiplyOp leaves that to caller] + // Note sNaN has to go through addOp to shorten payload if + // necessary + if ((status&DEC_Invalid_operation)!=0) { + if (!(status&DEC_sNaN)) { // but be true invalid + decNumberZero(res); // acc not yet set + res->bits=DECNAN; + break; + } + decNumberZero(&dzero); // make 0 (any non-NaN would do) + fhs=&dzero; // use that + } + #if DECCHECK + else { // multiply was OK + if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); + } + #endif + // add the third operand and result -> res, and all is done + decAddOp(res, acc, fhs, set, 0, &status); + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberFMA + +/* ------------------------------------------------------------------ */ +/* decNumberInvert -- invert a Number, digitwise */ +/* */ +/* This computes C = ~A */ +/* */ +/* res is C, the result. C may be A (e.g., X=~X) */ +/* rhs is A */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, + decContext *set) { + const Unit *ua, *msua; // -> operand and its msu + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operand is valid + ua=rhs->lsu; // bottom-up + uc=res->lsu; // .. + msua=ua+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, uc++) { // Unit loop + Unit a; // extract unit + Int i, j; // work + if (ua>msua) a=0; + else a=*ua; + *uc=0; // can now write back + // always need to examine all bits in rhs + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i<DECDPUN; i++) { + if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT + j=a%10; + a=a/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberInvert + +/* ------------------------------------------------------------------ */ +/* decNumberLn -- natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decLnOp which can handle the slightly wider */ +/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ +/* to calculate at p+e+2). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLn(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; this is a math function; if not violated + // then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect allocation + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + // special check in subset for rhs=0 + if (ISZERO(rhs)) { // +/- zeros -> error + status|=DEC_Invalid_operation; + break;} + } // extended=0 + #endif + decLnOp(res, rhs, set, &status); + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberLn + +/* ------------------------------------------------------------------ */ +/* decNumberLogB - get adjusted exponent, by 754 rules */ +/* */ +/* This computes C = adjustedexponent(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context, used only for digits and status */ +/* */ +/* For an unrounded result, digits may need to be 10 (A might have */ +/* 10**9 digits and an exponent of +999999999, or one digit and an */ +/* exponent of -1999999999). */ +/* */ +/* This returns the adjusted exponent of A after (in theory) padding */ +/* with zeros on the right to set->digits digits while keeping the */ +/* same value. The exponent is not limited by emin/emax. */ +/* */ +/* Notable cases: */ +/* A<0 -> Use |A| */ +/* A=0 -> -Infinity (Division by zero) */ +/* A=Infinite -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* NaNs are propagated as usual */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // NaNs as usual; Infinities return +Infinity; 0->oops + if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); + else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); + else if (decNumberIsZero(rhs)) { + decNumberZero(res); // prepare for Infinity + res->bits=DECNEG|DECINF; // -Infinity + status|=DEC_Division_by_zero; // as per 754 + } + else { // finite non-zero + Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent + if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out + else { + decNumber buft[D2N(10)]; // temporary number + decNumber *t=buft; // .. + decNumberFromInt32(t, ae); // lay it out + decNumberPlus(res, t, set); // round as necessary + } + } + + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberLogB + +/* ------------------------------------------------------------------ */ +/* decNumberLog10 -- logarithm in base 10 */ +/* */ +/* This computes C = log10(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=10**n (if n is an integer) -> n (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This calculates ln(A)/ln(10) using appropriate precision. For */ +/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ +/* requested digits and t is the number of digits in the exponent */ +/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ +/* fastpath in decLnOp. The final division is done to the requested */ +/* precision. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0, ignore=0; // status accumulators + uInt needbytes; // for space calculations + Int p; // working precision + Int t; // digits in exponent of A + + // buffers for a and b working decimals + // (adjustment calculator, same size) + decNumber bufa[D2N(DECBUFFER+2)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // temporary a + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *b=bufb; // temporary b + decNumber bufw[D2N(10)]; // working 2-10 digit number + decNumber *w=bufw; // .. + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + decContext aset; // working context + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; this is a math function; if not violated + // then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect malloc + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + // special check in subset for rhs=0 + if (ISZERO(rhs)) { // +/- zeros -> error + status|=DEC_Invalid_operation; + break;} + } // extended=0 + #endif + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context + + // handle exact powers of 10; only check if +ve finite + if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { + Int residue=0; // (no residue) + uInt copystat=0; // clean status + + // round to a single digit... + aset.digits=1; + decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten + // if exact and the digit is 1, rhs is a power of 10 + if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { + // the exponent, conveniently, is the power of 10; making + // this the result needs a little care as it might not fit, + // so first convert it into the working number, and then move + // to res + decNumberFromInt32(w, w->exponent); + residue=0; + decCopyFit(res, w, set, &residue, &status); // copy & round + decFinish(res, set, &residue, &status); // cleanup/set flags + break; + } // not a power of 10 + } // not a candidate for exact + + // simplify the information-content calculation to use 'total + // number of digits in a, including exponent' as compared to the + // requested digits, as increasing this will only rarely cost an + // iteration in ln(a) anyway + t=6; // it can never be >6 + + // allocate space when needed... + p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + aset.digits=p; // as calculated + aset.emax=DEC_MAX_MATH; // usual bounds + aset.emin=-DEC_MAX_MATH; // .. + aset.clamp=0; // and no concrete format + decLnOp(a, rhs, &aset, &status); // a=ln(rhs) + + // skip the division if the result so far is infinite, NaN, or + // zero, or there was an error; note NaN from sNaN needs copy + if (status&DEC_NaNs && !(status&DEC_sNaN)) break; + if (a->bits&DECSPECIAL || ISZERO(a)) { + decNumberCopy(res, a); // [will fit] + break;} + + // for ln(10) an extra 3 digits of precision are needed + p=set->digits+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + decNumberZero(w); // set up 10... + #if DECDPUN==1 + w->lsu[1]=1; w->lsu[0]=0; // .. + #else + w->lsu[0]=10; // .. + #endif + w->digits=2; // .. + + aset.digits=p; + decLnOp(b, w, &aset, &ignore); // b=ln(10) + + aset.digits=set->digits; // for final divide + decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result + } while(0); // [for break] + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberLog10 + +/* ------------------------------------------------------------------ */ +/* decNumberMax -- compare two Numbers and return the maximum */ +/* */ +/* This computes C = A ? B, returning the maximum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMax(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMAX, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMax + +/* ------------------------------------------------------------------ */ +/* decNumberMaxMag -- compare and return the maximum by magnitude */ +/* */ +/* This computes C = A ? B, returning the maximum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMaxMag + +/* ------------------------------------------------------------------ */ +/* decNumberMin -- compare two Numbers and return the minimum */ +/* */ +/* This computes C = A ? B, returning the minimum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMin(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMIN, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMin + +/* ------------------------------------------------------------------ */ +/* decNumberMinMag -- compare and return the minimum by magnitude */ +/* */ +/* This computes C = A ? B, returning the minimum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMinMag + +/* ------------------------------------------------------------------ */ +/* decNumberMinus -- prefix minus operator */ +/* */ +/* This computes C = 0 - A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyNegate for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* Simply use AddOp for the subtract, which will do the necessary. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // make 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMinus + +/* ------------------------------------------------------------------ */ +/* decNumberNextMinus -- next towards -Infinity */ +/* */ +/* This computes C = A - infinitesimal, rounded towards -Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754 NextDown. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // +Infinity is the special case + if ((rhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); // is +ve + // there is no status to set + return res; + } + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + workset.round=DEC_ROUND_FLOOR; + decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); + status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextMinus + +/* ------------------------------------------------------------------ */ +/* decNumberNextPlus -- next towards +Infinity */ +/* */ +/* This computes C = A + infinitesimal, rounded towards +Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754 NextUp. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // -Infinity is the special case + if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; // negative + // there is no status to set + return res; + } + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + workset.round=DEC_ROUND_CEILING; + decAddOp(res, rhs, &dtiny, &workset, 0, &status); + status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextPlus + +/* ------------------------------------------------------------------ */ +/* decNumberNextToward -- next towards rhs */ +/* */ +/* This computes C = A +/- infinitesimal, rounded towards */ +/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ +/* modified during revision but dropped from 754-2008. */ +/* */ +/* res is C, the result. C may be A or B. */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* This is a generalization of 754-1985 NextAfter. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + Int result; // .. + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { + decNaNs(res, lhs, rhs, set, &status); + } + else { // Is numeric, so no chance of sNaN Invalid, etc. + result=decCompare(lhs, rhs, 0); // sign matters + if (result==BADINT) status|=DEC_Insufficient_storage; // rare + else { // valid compare + if (result==0) decNumberCopySign(res, lhs, rhs); // easy + else { // differ: need NextPlus or NextMinus + uByte sub; // add or subtract + if (result<0) { // lhs<rhs, do nextplus + // -Infinity is the special case + if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; // negative + return res; // there is no status to set + } + workset.round=DEC_ROUND_CEILING; + sub=0; // add, please + } // plus + else { // lhs>rhs, do nextminus + // +Infinity is the special case + if ((lhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); + return res; // there is no status to set + } + workset.round=DEC_ROUND_FLOOR; + sub=DECNEG; // subtract, please + } // minus + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or - + // turn off exceptions if the result is a normal number + // (including Nmin), otherwise let all status through + if (decNumberIsNormal(res, set)) status=0; + } // unequal + } // compare OK + } // numeric + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextToward + +/* ------------------------------------------------------------------ */ +/* decNumberOr -- OR two Numbers, digitwise */ +/* */ +/* This computes C = A | B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberOr(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i<DECDPUN; i++) { + if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // non-zero + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberOr + +/* ------------------------------------------------------------------ */ +/* decNumberPlus -- prefix plus operator */ +/* */ +/* This computes C = 0 + A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopy for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This simply uses AddOp; Add will take fast path after preparing A. */ +/* Performance is a concern here, as this routine is often used to */ +/* check operands and apply rounding and overflow/underflow testing. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // make 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberPlus + +/* ------------------------------------------------------------------ */ +/* decNumberMultiply -- multiply two Numbers */ +/* */ +/* This computes C = A x B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decMultiplyOp(res, lhs, rhs, set, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMultiply + +/* ------------------------------------------------------------------ */ +/* decNumberPower -- raise a number to a power */ +/* */ +/* This computes C = A ** B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* However, if 1999999997<=B<=999999999 and B is an integer then the */ +/* restrictions on A and the context are relaxed to the usual bounds, */ +/* for compatibility with the earlier (integer power only) version */ +/* of this function. */ +/* */ +/* When B is an integer, the result may be exact, even if rounded. */ +/* */ +/* The final result is rounded according to the context; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPower(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + decNumber *allocdac=NULL; // -> allocated acc buffer, iff used + decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used + Int reqdigits=set->digits; // requested DIGITS + Int n; // rhs in binary + Flag rhsint=0; // 1 if rhs is an integer + Flag useint=0; // 1 if can use integer calculation + Flag isoddint=0; // 1 if rhs is an integer and odd + Int i; // work + #if DECSUBSET + Int dropped; // .. + #endif + uInt needbytes; // buffer size needed + Flag seenbit; // seen a bit while powering + Int residue=0; // rounding residue + uInt status=0; // accumulators + uByte bits=0; // result sign if errors + decContext aset; // working context + decNumber dnOne; // work value 1... + // local accumulator buffer [a decNumber, with digits+elength+1 digits] + decNumber dacbuff[D2N(DECBUFFER+9)]; + decNumber *dac=dacbuff; // -> result accumulator + // same again for possible 1/lhs calculation + decNumber invbuff[D2N(DECBUFFER+9)]; + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { // reduce operands and set status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, &status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // handle NaNs and rhs Infinity (lhs infinity is harder) + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs + decNaNs(res, lhs, rhs, set, &status); + break;} + if (decNumberIsInfinite(rhs)) { // rhs Infinity + Flag rhsneg=rhs->bits&DECNEG; // save rhs sign + if (decNumberIsNegative(lhs) // lhs<0 + && !decNumberIsZero(lhs)) // .. + status|=DEC_Invalid_operation; + else { // lhs >=0 + decNumberZero(&dnOne); // set up 1 + dnOne.lsu[0]=1; + decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1 + decNumberZero(res); // prepare for 0/1/Infinity + if (decNumberIsNegative(dac)) { // lhs<1 + if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0] + } + else if (dac->lsu[0]==0) { // lhs=1 + // 1**Infinity is inexact, so return fully-padded 1.0000 + Int shift=set->digits-1; + *res->lsu=1; // was 0, make int 1 + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; // make 1.0000... + status|=DEC_Inexact|DEC_Rounded; // deemed inexact + } + else { // lhs>1 + if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0] + } + } // lhs>=0 + break;} + // [lhs infinity drops through] + } // specials + + // Original rhs may be an integer that fits and is in range + n=decGetInt(rhs); + if (n!=BADINT) { // it is an integer + rhsint=1; // record the fact for 1**n + isoddint=(Flag)n&1; // [works even if big] + if (n!=BIGEVEN && n!=BIGODD) // can use integer path? + useint=1; // looks good + } + + if (decNumberIsNegative(lhs) // -x .. + && isoddint) bits=DECNEG; // .. to an odd power + + // handle LHS infinity + if (decNumberIsInfinite(lhs)) { // [NaNs already handled] + uByte rbits=rhs->bits; // save + decNumberZero(res); // prepare + if (n==0) *res->lsu=1; // [-]Inf**0 => 1 + else { + // -Inf**nonint -> error + if (!rhsint && decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; // -Inf**nonint is error + break;} + if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n + // [otherwise will be 0 or -0] + res->bits=bits; + } + break;} + + // similarly handle LHS zero + if (decNumberIsZero(lhs)) { + if (n==0) { // 0**0 => Error + #if DECSUBSET + if (!set->extended) { // [unless subset] + decNumberZero(res); + *res->lsu=1; // return 1 + break;} + #endif + status|=DEC_Invalid_operation; + } + else { // 0**x + uByte rbits=rhs->bits; // save + if (rbits & DECNEG) { // was a 0**(-n) + #if DECSUBSET + if (!set->extended) { // [bad if subset] + status|=DEC_Invalid_operation; + break;} + #endif + bits|=DECINF; + } + decNumberZero(res); // prepare + // [otherwise will be 0 or -0] + res->bits=bits; + } + break;} + + // here both lhs and rhs are finite; rhs==0 is handled in the + // integer path. Next handle the non-integer cases + if (!useint) { // non-integral rhs + // any -ve lhs is bad, as is either operand or context out of + // bounds + if (decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; + break;} + if (decCheckMath(lhs, set, &status) + || decCheckMath(rhs, set, &status)) break; // variable status + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context + aset.emax=DEC_MAX_MATH; // usual bounds + aset.emin=-DEC_MAX_MATH; // .. + aset.clamp=0; // and no concrete format + + // calculate the result using exp(ln(lhs)*rhs), which can + // all be done into the accumulator, dac. The precision needed + // is enough to contain the full information in the lhs (which + // is the total digits, including exponent), or the requested + // precision, if larger, + 4; 6 is used for the exponent + // maximum length, and this is also used when it is shorter + // than the requested digits as it greatly reduces the >0.5 ulp + // cases at little cost (because Ln doubles digits each + // iteration so a few extra digits rarely causes an extra + // iteration) + aset.digits=MAXI(lhs->digits, set->digits)+6+4; + } // non-integer rhs + + else { // rhs is in-range integer + if (n==0) { // x**0 = 1 + // (0**0 was handled above) + decNumberZero(res); // result=1 + *res->lsu=1; // .. + break;} + // rhs is a non-zero integer + if (n<0) n=-n; // use abs(n) + + aset=*set; // clone the context + aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced + // calculate the working DIGITS + aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; + #if DECSUBSET + if (!set->extended) aset.digits--; // use classic precision + #endif + // it's an error if this is more than can be handled + if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} + } // integer path + + // aset.digits is the count of digits for the accumulator needed + // if accumulator is too long for local storage, then allocate + needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); + // [needbytes also used below if 1/lhs needed] + if (needbytes>sizeof(dacbuff)) { + allocdac=(decNumber *)malloc(needbytes); + if (allocdac==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + dac=allocdac; // use the allocated space + } + // here, aset is set up and accumulator is ready for use + + if (!useint) { // non-integral rhs + // x ** y; special-case x=1 here as it will otherwise always + // reduce to integer 1; decLnOp has a fastpath which detects + // the case of x=1 + decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs) + // [no error possible, as lhs 0 already handled] + if (ISZERO(dac)) { // x==1, 1.0, etc. + // need to return fully-padded 1.0000 etc., but rhsint->1 + *dac->lsu=1; // was 0, make int 1 + if (!rhsint) { // add padding + Int shift=set->digits-1; + dac->digits=decShiftToMost(dac->lsu, 1, shift); + dac->exponent=-shift; // make 1.0000... + status|=DEC_Inexact|DEC_Rounded; // deemed inexact + } + } + else { + decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs + decExpOp(dac, dac, &aset, &status); // dac=exp(dac) + } + // and drop through for final rounding + } // non-integer rhs + + else { // carry on with integer + decNumberZero(dac); // acc=1 + *dac->lsu=1; // .. + + // if a negative power the constant 1 is needed, and if not subset + // invert the lhs now rather than inverting the result later + if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] + decNumber *inv=invbuff; // asssume use fixed buffer + decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later] + #if DECSUBSET + if (set->extended) { // need to calculate 1/lhs + #endif + // divide lhs into 1, putting result in dac [dac=1/dac] + decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); + // now locate or allocate space for the inverted lhs + if (needbytes>sizeof(invbuff)) { + allocinv=(decNumber *)malloc(needbytes); + if (allocinv==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + inv=allocinv; // use the allocated space + } + // [inv now points to big-enough buffer or allocated storage] + decNumberCopy(inv, dac); // copy the 1/lhs + decNumberCopy(dac, &dnOne); // restore acc=1 + lhs=inv; // .. and go forward with new lhs + #if DECSUBSET + } + #endif + } + + // Raise-to-the-power loop... + seenbit=0; // set once a 1-bit is encountered + for (i=1;;i++){ // for each bit [top bit ignored] + // abandon if had overflow or terminal underflow + if (status & (DEC_Overflow|DEC_Underflow)) { // interesting? + if (status&DEC_Overflow || ISZERO(dac)) break; + } + // [the following two lines revealed an optimizer bug in a C++ + // compiler, with symptom: 5**3 -> 25, when n=n+n was used] + n=n<<1; // move next bit to testable position + if (n<0) { // top bit is set + seenbit=1; // OK, significant bit seen + decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x + } + if (i==31) break; // that was the last bit + if (!seenbit) continue; // no need to square 1 + decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square] + } /*i*/ // 32 bits + + // complete internal overflow or underflow processing + if (status & (DEC_Overflow|DEC_Underflow)) { + #if DECSUBSET + // If subset, and power was negative, reverse the kind of -erflow + // [1/x not yet done] + if (!set->extended && decNumberIsNegative(rhs)) { + if (status & DEC_Overflow) + status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; + else { // trickier -- Underflow may or may not be set + status&=~(DEC_Underflow | DEC_Subnormal); // [one or both] + status|=DEC_Overflow; + } + } + #endif + dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign + // round subnormals [to set.digits rather than aset.digits] + // or set overflow result similarly as required + decFinalize(dac, set, &residue, &status); + decNumberCopy(res, dac); // copy to result (is now OK length) + break; + } + + #if DECSUBSET + if (!set->extended && // subset math + decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] + // so divide result into 1 [dac=1/dac] + decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); + } + #endif + } // rhs integer path + + // reduce result to the requested length and copy to result + decCopyFit(res, dac, set, &residue, &status); + decFinish(res, set, &residue, &status); // final cleanup + #if DECSUBSET + if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros + #endif + } while(0); // end protected + + if (allocdac!=NULL) free(allocdac); // drop any storage used + if (allocinv!=NULL) free(allocinv); // .. + #if DECSUBSET + if (alloclhs!=NULL) free(alloclhs); // .. + if (allocrhs!=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberPower + +/* ------------------------------------------------------------------ */ +/* decNumberQuantize -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has exponent of B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the number with exponent to match */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to that of B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decQuantizeOp(res, lhs, rhs, set, 1, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberQuantize + +/* ------------------------------------------------------------------ */ +/* decNumberReduce -- remove trailing zeros */ +/* */ +/* This computes C = 0 + A, and normalizes the result */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +// Previously known as Normalize +decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, + decContext *set) { + return decNumberReduce(res, rhs, set); + } // decNumberNormalize + +decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, + decContext *set) { + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + uInt status=0; // as usual + Int residue=0; // as usual + Int dropped; // work + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // Infinities copy through; NaNs need usual treatment + if (decNumberIsNaN(rhs)) { + decNaNs(res, rhs, NULL, set, &status); + break; + } + + // reduce result to the requested length and copy to result + decCopyFit(res, rhs, set, &residue, &status); // copy & round + decFinish(res, set, &residue, &status); // cleanup/set flags + decTrim(res, set, 1, 0, &dropped); // normalize in place + // [may clamp] + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set);// then report status + return res; + } // decNumberReduce + +/* ------------------------------------------------------------------ */ +/* decNumberRescale -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decQuantizeOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberRescale + +/* ------------------------------------------------------------------ */ +/* decNumberRemainder -- divide and return remainder */ +/* */ +/* This computes C = A % B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, REMAINDER, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberRemainder + +/* ------------------------------------------------------------------ */ +/* decNumberRemainderNear -- divide and return remainder from nearest */ +/* */ +/* This computes C = A % B, where % is the IEEE remainder operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, REMNEAR, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberRemainderNear + +/* ------------------------------------------------------------------ */ +/* decNumberRotate -- rotate the coefficient of a Number left/right */ +/* */ +/* This computes C = A rot B (in base ten and rotating set->digits */ +/* digits). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ +/* lhs is A */ +/* rhs is B, the number of digits to rotate (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are rotated to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. If lhs->digits is less than */ +/* set->digits the coefficient is padded with zeros on the left */ +/* before the rotate. Any leading zeros in the result are removed */ +/* as usual. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + Int rotate; // rhs as an Int + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // NaNs propagate as normal + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { // both numeric, rhs is an integer + rotate=decGetInt(rhs); // [cannot fail] + if (rotate==BADINT // something bad .. + || rotate==BIGODD || rotate==BIGEVEN // .. very big .. + || abs(rotate)>set->digits) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); + // convert -ve rotate to equivalent positive rotation + if (rotate<0) rotate=set->digits+rotate; + if (rotate!=0 && rotate!=set->digits // zero or full rotation + && !decNumberIsInfinite(res)) { // lhs was infinite + // left-rotate to do; 0 < rotate < set->digits + uInt units, shift; // work + uInt msudigits; // digits in result msu + Unit *msu=res->lsu+D2U(res->digits)-1; // current msu + Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu + for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0 + res->digits=set->digits; // now full-length + msudigits=MSUDIGITS(res->digits); // actual digits in msu + + // rotation here is done in-place, in three steps + // 1. shift all to least up to one unit to unit-align final + // lsd [any digits shifted out are rotated to the left, + // abutted to the original msd (which may require split)] + // + // [if there are no whole units left to rotate, the + // rotation is now complete] + // + // 2. shift to least, from below the split point only, so that + // the final msd is in the right place in its Unit [any + // digits shifted out will fit exactly in the current msu, + // left aligned, no split required] + // + // 3. rotate all the units by reversing left part, right + // part, and then whole + // + // example: rotate right 8 digits (2 units + 2), DECDPUN=3. + // + // start: 00a bcd efg hij klm npq + // + // 1a 000 0ab cde fgh|ijk lmn [pq saved] + // 1b 00p qab cde fgh|ijk lmn + // + // 2a 00p qab cde fgh|00i jkl [mn saved] + // 2b mnp qab cde fgh|00i jkl + // + // 3a fgh cde qab mnp|00i jkl + // 3b fgh cde qab mnp|jkl 00i + // 3c 00i jkl mnp qab cde fgh + + // Step 1: amount to shift is the partial right-rotate count + rotate=set->digits-rotate; // make it right-rotate + units=rotate/DECDPUN; // whole units to rotate + shift=rotate%DECDPUN; // left-over digits count + if (shift>0) { // not an exact number of units + uInt save=res->lsu[0]%powers[shift]; // save low digit(s) + decShiftToLeast(res->lsu, D2U(res->digits), shift); + if (shift>msudigits) { // msumax-1 needs >0 digits + uInt rem=save%powers[shift-msudigits];// split save + *msumax=(Unit)(save/powers[shift-msudigits]); // and insert + *(msumax-1)=*(msumax-1) + +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // .. + } + else { // all fits in msumax + *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1] + } + } // digits shift needed + + // If whole units to rotate... + if (units>0) { // some to do + // Step 2: the units to touch are the whole ones in rotate, + // if any, and the shift is DECDPUN-msudigits (which may be + // 0, again) + shift=DECDPUN-msudigits; + if (shift>0) { // not an exact number of units + uInt save=res->lsu[0]%powers[shift]; // save low digit(s) + decShiftToLeast(res->lsu, units, shift); + *msumax=*msumax+(Unit)(save*powers[msudigits]); + } // partial shift needed + + // Step 3: rotate the units array using triple reverse + // (reversing is easy and fast) + decReverse(res->lsu+units, msumax); // left part + decReverse(res->lsu, res->lsu+units-1); // right part + decReverse(res->lsu, msumax); // whole + } // whole units to rotate + // the rotation may have left an undetermined number of zeros + // on the left, so true length needs to be calculated + res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); + } // rotate needed + } // rhs OK + } // numerics + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberRotate + +/* ------------------------------------------------------------------ */ +/* decNumberSameQuantum -- test for equal exponents */ +/* */ +/* res is the result number, which will contain either 0 or 1 */ +/* lhs is a number to test */ +/* rhs is the second (usually a pattern) */ +/* */ +/* No errors are possible and no context is needed. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + Unit ret=0; // return value + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; + #endif + + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; + else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; + // [anything else with a special gives 0] + } + else if (lhs->exponent==rhs->exponent) ret=1; + + decNumberZero(res); // OK to overwrite an operand now + *res->lsu=ret; + return res; + } // decNumberSameQuantum + +/* ------------------------------------------------------------------ */ +/* decNumberScaleB -- multiply by a power of 10 */ +/* */ +/* This computes C = A x 10**B where B is an integer (q=0) with */ +/* maximum magnitude 2*(emax+digits) */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested power of ten to use */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* The result may underflow or overflow. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Int reqexp; // requested exponent change [B] + uInt status=0; // accumulator + Int residue; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // Handle special values except lhs infinite + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { + // lhs is a number; rhs is a finite with q==0 + reqexp=decGetInt(rhs); // [cannot fail] + // maximum range is larger than getInt can handle, so this is + // more restrictive than the specification + if (reqexp==BADINT // something bad .. + || reqexp==BIGODD || reqexp==BIGEVEN // it was huge + || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); // all done if infinite lhs + if (!decNumberIsInfinite(res)) { // prepare to scale + Int exp=res->exponent; // save for overflow test + res->exponent+=reqexp; // adjust the exponent + if (((exp^reqexp)>=0) // same sign ... + && ((exp^res->exponent)<0)) { // .. but result had different + // the calculation overflowed, so force right treatment + if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS; + else res->exponent=DEC_MAX_EMAX+1; + } + residue=0; + decFinalize(res, set, &residue, &status); // final check + } // finite LHS + } // rhs OK + } // rhs finite + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberScaleB + +/* ------------------------------------------------------------------ */ +/* decNumberShift -- shift the coefficient of a Number left or right */ +/* */ +/* This computes C = A << B or C = A >> -B (in base ten). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ +/* lhs is A */ +/* rhs is B, the number of digits to shift (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are shifted to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberShift(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + Int shift; // rhs as an Int + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // NaNs propagate as normal + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { // both numeric, rhs is an integer + shift=decGetInt(rhs); // [cannot fail] + if (shift==BADINT // something bad .. + || shift==BIGODD || shift==BIGEVEN // .. very big .. + || abs(shift)>set->digits) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); + if (shift!=0 && !decNumberIsInfinite(res)) { // something to do + if (shift>0) { // to left + if (shift==set->digits) { // removing all + *res->lsu=0; // so place 0 + res->digits=1; // .. + } + else { // + // first remove leading digits if necessary + if (res->digits+shift>set->digits) { + decDecap(res, res->digits+shift-set->digits); + // that updated res->digits; may have gone to 1 (for a + // single digit or for zero + } + if (res->digits>1 || *res->lsu) // if non-zero.. + res->digits=decShiftToMost(res->lsu, res->digits, shift); + } // partial left + } // left + else { // to right + if (-shift>=res->digits) { // discarding all + *res->lsu=0; // so place 0 + res->digits=1; // .. + } + else { + decShiftToLeast(res->lsu, D2U(res->digits), -shift); + res->digits-=(-shift); + } + } // to right + } // non-0 non-Inf shift + } // rhs OK + } // numerics + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberShift + +/* ------------------------------------------------------------------ */ +/* decNumberSquareRoot -- square root operator */ +/* */ +/* This computes C = squareroot(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This uses the following varying-precision algorithm in: */ +/* */ +/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ +/* pp229-237, ACM, September 1985. */ +/* */ +/* The square-root is calculated using Newton's method, after which */ +/* a check is made to ensure the result is correctly rounded. */ +/* */ +/* % [Reformatted original Numerical Turing source code follows.] */ +/* function sqrt(x : real) : real */ +/* % sqrt(x) returns the properly rounded approximation to the square */ +/* % root of x, in the precision of the calling environment, or it */ +/* % fails if x < 0. */ +/* % t e hull and a abrham, august, 1984 */ +/* if x <= 0 then */ +/* if x < 0 then */ +/* assert false */ +/* else */ +/* result 0 */ +/* end if */ +/* end if */ +/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ +/* var e := getexp(x) % exponent part of x */ +/* var approx : real */ +/* if e mod 2 = 0 then */ +/* approx := .259 + .819 * f % approx to root of f */ +/* else */ +/* f := f/l0 % adjustments */ +/* e := e + 1 % for odd */ +/* approx := .0819 + 2.59 * f % exponent */ +/* end if */ +/* */ +/* var p:= 3 */ +/* const maxp := currentprecision + 2 */ +/* loop */ +/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ +/* precision p */ +/* approx := .5 * (approx + f/approx) */ +/* exit when p = maxp */ +/* end loop */ +/* */ +/* % approx is now within 1 ulp of the properly rounded square root */ +/* % of f; to ensure proper rounding, compare squares of (approx - */ +/* % l/2 ulp) and (approx + l/2 ulp) with f. */ +/* p := currentprecision */ +/* begin */ +/* precision p + 2 */ +/* const approxsubhalf := approx - setexp(.5, -p) */ +/* if mulru(approxsubhalf, approxsubhalf) > f then */ +/* approx := approx - setexp(.l, -p + 1) */ +/* else */ +/* const approxaddhalf := approx + setexp(.5, -p) */ +/* if mulrd(approxaddhalf, approxaddhalf) < f then */ +/* approx := approx + setexp(.l, -p + 1) */ +/* end if */ +/* end if */ +/* end */ +/* result setexp(approx, e div 2) % fix exponent */ +/* end sqrt */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset, approxset; // work contexts + decNumber dzero; // used for constant zero + Int maxp; // largest working precision + Int workp; // working precision + Int residue=0; // rounding residue + uInt status=0, ignore=0; // status accumulators + uInt rstatus; // .. + Int exp; // working exponent + Int ideal; // ideal (preferred) exponent + Int needbytes; // work + Int dropped; // .. + + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + // buffer for f [needs +1 in case DECBUFFER 0] + decNumber buff[D2N(DECBUFFER+1)]; + // buffer for a [needs +2 to match likely maxp] + decNumber bufa[D2N(DECBUFFER+2)]; + // buffer for temporary, b [must be same size as a] + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbuff=NULL; // -> allocated buff, iff allocated + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *f=buff; // reduced fraction + decNumber *a=bufa; // approximation to result + decNumber *b=bufb; // intermediate result + // buffer for temporary variable, up to 3 digits + decNumber buft[D2N(3)]; + decNumber *t=buft; // up-to-3-digit constant or work + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + // [Note: 'f' allocation below could reuse this buffer if + // used, but as this is rare they are kept separate for clarity.] + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // handle infinities and NaNs + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); // +Infinity + } + else decNaNs(res, rhs, NULL, set, &status); // a NaN + break; + } + + // calculate the ideal (preferred) exponent [floor(exp/2)] + // [It would be nicer to write: ideal=rhs->exponent>>1, but this + // generates a compiler warning. Generated code is the same.] + ideal=(rhs->exponent&~1)/2; // target + + // handle zeros + if (ISZERO(rhs)) { + decNumberCopy(res, rhs); // could be 0 or -0 + res->exponent=ideal; // use the ideal [safe] + // use decFinish to clamp any out-of-range exponent, etc. + decFinish(res, set, &residue, &status); + break; + } + + // any other -x is an oops + if (decNumberIsNegative(rhs)) { + status|=DEC_Invalid_operation; + break; + } + + // space is needed for three working variables + // f -- the same precision as the RHS, reduced to 0.01->0.99... + // a -- Hull's approximation -- precision, when assigned, is + // currentprecision+1 or the input argument precision, + // whichever is larger (+2 for use as temporary) + // b -- intermediate temporary result (same size as a) + // if any is too long for local storage, then allocate + workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision + workp=MAXI(workp, 7); // at least 7 for low cases + maxp=workp+2; // largest working precision + + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(buff)) { + allocbuff=(decNumber *)malloc(needbytes); + if (allocbuff==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + f=allocbuff; // use the allocated space + } + // a and b both need to be able to hold a maxp-length number + needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(bufa)) { // [same applies to b] + allocbufa=(decNumber *)malloc(needbytes); + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufa==NULL || allocbufb==NULL) { // hopeless + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated spaces + b=allocbufb; // .. + } + + // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 + decNumberCopy(f, rhs); + exp=f->exponent+f->digits; // adjusted to Hull rules + f->exponent=-(f->digits); // to range + + // set up working context + decContextDefault(&workset, DEC_INIT_DECIMAL64); + workset.emax=DEC_MAX_EMAX; + workset.emin=DEC_MIN_EMIN; + + // [Until further notice, no error is possible and status bits + // (Rounded, etc.) should be ignored, not accumulated.] + + // Calculate initial approximation, and allow for odd exponent + workset.digits=workp; // p for initial calculation + t->bits=0; t->digits=3; + a->bits=0; a->digits=3; + if ((exp & 1)==0) { // even exponent + // Set t=0.259, a=0.819 + t->exponent=-3; + a->exponent=-3; + #if DECDPUN>=3 + t->lsu[0]=259; + a->lsu[0]=819; + #elif DECDPUN==2 + t->lsu[0]=59; t->lsu[1]=2; + a->lsu[0]=19; a->lsu[1]=8; + #else + t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; + a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; + #endif + } + else { // odd exponent + // Set t=0.0819, a=2.59 + f->exponent--; // f=f/10 + exp++; // e=e+1 + t->exponent=-4; + a->exponent=-2; + #if DECDPUN>=3 + t->lsu[0]=819; + a->lsu[0]=259; + #elif DECDPUN==2 + t->lsu[0]=19; t->lsu[1]=8; + a->lsu[0]=59; a->lsu[1]=2; + #else + t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; + a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; + #endif + } + + decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f + decAddOp(a, a, t, &workset, 0, &ignore); // ..+t + // [a is now the initial approximation for sqrt(f), calculated with + // currentprecision, which is also a's precision.] + + // the main calculation loop + decNumberZero(&dzero); // make 0 + decNumberZero(t); // set t = 0.5 + t->lsu[0]=5; // .. + t->exponent=-1; // .. + workset.digits=3; // initial p + for (; workset.digits<maxp;) { + // set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] + workset.digits=MINI(workset.digits*2-2, maxp); + // a = 0.5 * (a + f/a) + // [calculated at p then rounded to currentprecision] + decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a + decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a + decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5 + } // loop + + // Here, 0.1 <= a < 1 [Hull], and a has maxp digits + // now reduce to length, etc.; this needs to be done with a + // having the correct exponent so as to handle subnormals + // correctly + approxset=*set; // get emin, emax, etc. + approxset.round=DEC_ROUND_HALF_EVEN; + a->exponent+=exp/2; // set correct exponent + rstatus=0; // clear status + residue=0; // .. and accumulator + decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed) + decFinish(a, &approxset, &residue, &rstatus); // clean and finalize + + // Overflow was possible if the input exponent was out-of-range, + // in which case quit + if (rstatus&DEC_Overflow) { + status=rstatus; // use the status as-is + decNumberCopy(res, a); // copy to result + break; + } + + // Preserve status except Inexact/Rounded + status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); + + // Carry out the Hull correction + a->exponent-=exp/2; // back to 0.1->1 + + // a is now at final precision and within 1 ulp of the properly + // rounded square root of f; to ensure proper rounding, compare + // squares of (a - l/2 ulp) and (a + l/2 ulp) with f. + // Here workset.digits=maxp and t=0.5, and a->digits determines + // the ulp + workset.digits--; // maxp-1 is OK now + t->exponent=-a->digits-1; // make 0.5 ulp + decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp + workset.round=DEC_ROUND_UP; + decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b) + decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed + if (decNumberIsNegative(b)) { // f < b [i.e., b > f] + // this is the more common adjustment, though both are rare + t->exponent++; // make 1.0 ulp + t->lsu[0]=1; // .. + decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp + // assign to approx [round to length] + approxset.emin-=exp/2; // adjust to match a + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + else { + decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp + workset.round=DEC_ROUND_DOWN; + decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b) + decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f + if (decNumberIsNegative(b)) { // b < f + t->exponent++; // make 1.0 ulp + t->lsu[0]=1; // .. + decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp + // assign to approx [round to length] + approxset.emin-=exp/2; // adjust to match a + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + } + // [no errors are possible in the above, and rounding/inexact during + // estimation are irrelevant, so status was not accumulated] + + // Here, 0.1 <= a < 1 (still), so adjust back + a->exponent+=exp/2; // set correct exponent + + // count droppable zeros [after any subnormal rounding] by + // trimming a copy + decNumberCopy(b, a); + decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros] + + // Set Inexact and Rounded. The answer can only be exact if + // it is short enough so that squaring it could fit in workp + // digits, so this is the only (relatively rare) condition that + // a careful check is needed + if (b->digits*2-1 > workp) { // cannot fit + status|=DEC_Inexact|DEC_Rounded; + } + else { // could be exact/unrounded + uInt mstatus=0; // local status + decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply + if (mstatus&DEC_Overflow) { // result just won't fit + status|=DEC_Inexact|DEC_Rounded; + } + else { // plausible + decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs + if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal + else { // is Exact + // here, dropped is the count of trailing zeros in 'a' + // use closest exponent to ideal... + Int todrop=ideal-a->exponent; // most that can be dropped + if (todrop<0) status|=DEC_Rounded; // ideally would add 0s + else { // unrounded + // there are some to drop, but emax may not allow all + Int maxexp=set->emax-set->digits+1; + Int maxdrop=maxexp-a->exponent; + if (todrop>maxdrop && set->clamp) { // apply clamping + todrop=maxdrop; + status|=DEC_Clamped; + } + if (dropped<todrop) { // clamp to those available + todrop=dropped; + status|=DEC_Clamped; + } + if (todrop>0) { // have some to drop + decShiftToLeast(a->lsu, D2U(a->digits), todrop); + a->exponent+=todrop; // maintain numerical value + a->digits-=todrop; // new length + } + } + } + } + } + + // double-check Underflow, as perhaps the result could not have + // been subnormal (initial argument too big), or it is now Exact + if (status&DEC_Underflow) { + Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent + // check if truly subnormal + #if DECEXTFLAG // DEC_Subnormal too + if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); + #else + if (ae>=set->emin*2) status&=~DEC_Underflow; + #endif + // check if truly inexact + if (!(status&DEC_Inexact)) status&=~DEC_Underflow; + } + + decNumberCopy(res, a); // a is now the result + } while(0); // end protected + + if (allocbuff!=NULL) free(allocbuff); // drop any storage used + if (allocbufa!=NULL) free(allocbufa); // .. + if (allocbufb!=NULL) free(allocbufb); // .. + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set);// then report status + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberSquareRoot + +/* ------------------------------------------------------------------ */ +/* decNumberSubtract -- subtract two Numbers */ +/* */ +/* This computes C = A - B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + + decAddOp(res, lhs, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberSubtract + +/* ------------------------------------------------------------------ */ +/* decNumberToIntegralExact -- round-to-integral-value with InExact */ +/* decNumberToIntegralValue -- round-to-integral-value */ +/* */ +/* res is the result */ +/* rhs is input number */ +/* set is the context */ +/* */ +/* res must have space for any value of rhs. */ +/* */ +/* This implements the IEEE special operators and therefore treats */ +/* special values as valid. For finite numbers it returns */ +/* rescale(rhs, 0) if rhs->exponent is <0. */ +/* Otherwise the result is rhs (so no error is possible, except for */ +/* sNaN). */ +/* */ +/* The context is used for rounding mode and status after sNaN, but */ +/* the digits setting is ignored. The Exact version will signal */ +/* Inexact if the result differs numerically from rhs; the other */ +/* never signals Inexact. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dn; + decContext workset; // working context + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // handle infinities and NaNs + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity + else decNaNs(res, rhs, NULL, set, &status); // a NaN + } + else { // finite + // have a finite number; no error possible (res must be big enough) + if (rhs->exponent>=0) return decNumberCopy(res, rhs); + // that was easy, but if negative exponent there is work to do... + workset=*set; // clone rounding, etc. + workset.digits=rhs->digits; // no length rounding + workset.traps=0; // no traps + decNumberZero(&dn); // make a number with exponent 0 + decNumberQuantize(res, rhs, &dn, &workset); + status|=workset.status; + } + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberToIntegralExact + +decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset=*set; // working context + workset.traps=0; // no traps + decNumberToIntegralExact(res, rhs, &workset); + // this never affects set, except for sNaNs; NaN will have been set + // or propagated already, so no need to call decStatus + set->status|=workset.status&DEC_Invalid_operation; + return res; + } // decNumberToIntegralValue + +/* ------------------------------------------------------------------ */ +/* decNumberXor -- XOR two Numbers, digitwise */ +/* */ +/* This computes C = A ^ B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberXor(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i<DECDPUN; i++) { + if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // non-zero + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberXor + + +/* ================================================================== */ +/* Utility routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberClass -- return the decClass of a decNumber */ +/* dn -- the decNumber to test */ +/* set -- the context to use for Emin */ +/* returns the decClass enum */ +/* ------------------------------------------------------------------ */ +enum decClass decNumberClass(const decNumber *dn, decContext *set) { + if (decNumberIsSpecial(dn)) { + if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; + if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; + // must be an infinity + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; + return DEC_CLASS_POS_INF; + } + // is finite + if (decNumberIsNormal(dn, set)) { // most common + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; + return DEC_CLASS_POS_NORMAL; + } + // is subnormal or zero + if (decNumberIsZero(dn)) { // most common + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; + return DEC_CLASS_POS_ZERO; + } + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; + return DEC_CLASS_POS_SUBNORMAL; + } // decNumberClass + +/* ------------------------------------------------------------------ */ +/* decNumberClassToString -- convert decClass to a string */ +/* */ +/* eclass is a valid decClass */ +/* returns a constant string describing the class (max 13+1 chars) */ +/* ------------------------------------------------------------------ */ +const char *decNumberClassToString(enum decClass eclass) { + if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; + if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; + if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; + if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; + if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; + if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; + if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; + if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; + if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; + if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; + return DEC_ClassString_UN; // Unknown + } // decNumberClassToString + +/* ------------------------------------------------------------------ */ +/* decNumberCopy -- copy a number */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* returns dest */ +/* */ +/* (dest==src is allowed and is a no-op) */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { + + #if DECCHECK + if (src==NULL) return decNumberZero(dest); + #endif + + if (dest==src) return dest; // no copy required + + // Use explicit assignments here as structure assignment could copy + // more than just the lsu (for small DECDPUN). This would not affect + // the value of the results, but could disturb test harness spill + // checking. + dest->bits=src->bits; + dest->exponent=src->exponent; + dest->digits=src->digits; + dest->lsu[0]=src->lsu[0]; + if (src->digits>DECDPUN) { // more Units to come + const Unit *smsup, *s; // work + Unit *d; // .. + // memcpy for the remaining Units would be safe as they cannot + // overlap. However, this explicit loop is faster in short cases. + d=dest->lsu+1; // -> first destination + smsup=src->lsu+D2U(src->digits); // -> source msu+1 + for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; + } + return dest; + } // decNumberCopy + +/* ------------------------------------------------------------------ */ +/* decNumberCopyAbs -- quiet absolute value operator */ +/* */ +/* This sets C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberAbs for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits&=~DECNEG; // turn off sign + return res; + } // decNumberCopyAbs + +/* ------------------------------------------------------------------ */ +/* decNumberCopyNegate -- quiet negate value operator */ +/* */ +/* This sets C = negate(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberMinus for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits^=DECNEG; // invert the sign + return res; + } // decNumberCopyNegate + +/* ------------------------------------------------------------------ */ +/* decNumberCopySign -- quiet copy and set sign operator */ +/* */ +/* This sets C = A with the sign of B */ +/* */ +/* res is C, the result. C may be A */ +/* lhs is A */ +/* rhs is B */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + uByte sign; // rhs sign + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + sign=rhs->bits & DECNEG; // save sign bit + decNumberCopy(res, lhs); + res->bits&=~DECNEG; // clear the sign + res->bits|=sign; // set from rhs + return res; + } // decNumberCopySign + +/* ------------------------------------------------------------------ */ +/* decNumberGetBCD -- get the coefficient in BCD8 */ +/* dn is the source decNumber */ +/* bcd is the uInt array that will receive dn->digits BCD bytes, */ +/* most-significant at offset 0 */ +/* returns bcd */ +/* */ +/* bcd must have at least dn->digits bytes. No error is possible; if */ +/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ +/* ------------------------------------------------------------------ */ +uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) { + uByte *ub=bcd+dn->digits-1; // -> lsd + const Unit *up=dn->lsu; // Unit pointer, -> lsu + + #if DECDPUN==1 // trivial simple copy + for (; ub>=bcd; ub--, up++) *ub=*up; + #else // chopping needed + uInt u=*up; // work + uInt cut=DECDPUN; // downcounter through unit + for (; ub>=bcd; ub--) { + *ub=(uByte)(u%10); // [*6554 trick inhibits, here] + u=u/10; + cut--; + if (cut>0) continue; // more in this unit + up++; + u=*up; + cut=DECDPUN; + } + #endif + return bcd; + } // decNumberGetBCD + +/* ------------------------------------------------------------------ */ +/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ +/* dn is the target decNumber */ +/* bcd is the uInt array that will source n BCD bytes, most- */ +/* significant at offset 0 */ +/* n is the number of digits in the source BCD array (bcd) */ +/* returns dn */ +/* */ +/* dn must have space for at least n digits. No error is possible; */ +/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ +/* and bcd[0] zero. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { + Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer] + const uByte *ub=bcd; // -> source msd + + #if DECDPUN==1 // trivial simple copy + for (; ub<bcd+n; ub++, up--) *up=*ub; + #else // some assembly needed + // calculate how many digits in msu, and hence first cut + Int cut=MSUDIGITS(n); // [faster than remainder] + for (;up>=dn->lsu; up--) { // each Unit from msu + *up=0; // will take <=DECDPUN digits + for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; + cut=DECDPUN; // next Unit has all digits + } + #endif + dn->digits=n; // set digit count + return dn; + } // decNumberSetBCD + +/* ------------------------------------------------------------------ */ +/* decNumberIsNormal -- test normality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ +/* ------------------------------------------------------------------ */ +Int decNumberIsNormal(const decNumber *dn, decContext *set) { + Int ae; // adjusted exponent + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + if (decNumberIsSpecial(dn)) return 0; // not finite + if (decNumberIsZero(dn)) return 0; // not non-zero + + ae=dn->exponent+dn->digits-1; // adjusted exponent + if (ae<set->emin) return 0; // is subnormal + return 1; + } // decNumberIsNormal + +/* ------------------------------------------------------------------ */ +/* decNumberIsSubnormal -- test subnormality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ +/* ------------------------------------------------------------------ */ +Int decNumberIsSubnormal(const decNumber *dn, decContext *set) { + Int ae; // adjusted exponent + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + if (decNumberIsSpecial(dn)) return 0; // not finite + if (decNumberIsZero(dn)) return 0; // not non-zero + + ae=dn->exponent+dn->digits-1; // adjusted exponent + if (ae<set->emin) return 1; // is subnormal + return 0; + } // decNumberIsSubnormal + +/* ------------------------------------------------------------------ */ +/* decNumberTrim -- remove insignificant zeros */ +/* */ +/* dn is the number to trim */ +/* returns dn */ +/* */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. The */ +/* zeros are removed unconditionally. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberTrim(decNumber *dn) { + Int dropped; // work + decContext set; // .. + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; + #endif + decContextDefault(&set, DEC_INIT_BASE); // clamp=0 + return decTrim(dn, &set, 0, 1, &dropped); + } // decNumberTrim + +/* ------------------------------------------------------------------ */ +/* decNumberVersion -- return the name and version of this module */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +const char * decNumberVersion(void) { + return DECVERSION; + } // decNumberVersion + +/* ------------------------------------------------------------------ */ +/* decNumberZero -- set a number to 0 */ +/* */ +/* dn is the number to set, with space for one digit */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +// Memset is not used as it is much slower in some environments. +decNumber * decNumberZero(decNumber *dn) { + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + dn->bits=0; + dn->exponent=0; + dn->digits=1; + dn->lsu[0]=0; + return dn; + } // decNumberZero + +/* ================================================================== */ +/* Local routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decToString -- lay out a number into a string */ +/* */ +/* dn is the number to lay out */ +/* string is where to lay out the number */ +/* eng is 1 if Engineering, 0 if Scientific */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* No error is possible. */ +/* */ +/* Note that this routine can generate a -0 or 0.000. These are */ +/* never generated in subset to-number or arithmetic, but can occur */ +/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ +/* ------------------------------------------------------------------ */ +// If DECCHECK is enabled the string "?" is returned if a number is +// invalid. +static void decToString(const decNumber *dn, char *string, Flag eng) { + Int exp=dn->exponent; // local copy + Int e; // E-part value + Int pre; // digits before the '.' + Int cut; // for counting digits in a Unit + char *c=string; // work [output pointer] + const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer] + uInt u, pow; // work + + #if DECCHECK + if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { + strcpy(string, "?"); + return;} + #endif + + if (decNumberIsNegative(dn)) { // Negatives get a minus + *c='-'; + c++; + } + if (dn->bits&DECSPECIAL) { // Is a special value + if (decNumberIsInfinite(dn)) { + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return;} + // a NaN + if (dn->bits&DECSNAN) { // signalling NaN + *c='s'; + c++; + } + strcpy(c, "NaN"); + c+=3; // step past + // if not a clean non-zero coefficient, that's all there is in a + // NaN string + if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; + // [drop through to add integer] + } + + // calculate how many digits in msu, and hence first cut + cut=MSUDIGITS(dn->digits); // [faster than remainder] + cut--; // power of ten for digit + + if (exp==0) { // simple integer [common fastpath] + for (;up>=dn->lsu; up--) { // each Unit from msu + u=*up; // contains DECDPUN digits to lay out + for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); + cut=DECDPUN-1; // next Unit has all digits + } + *c='\0'; // terminate the string + return;} + + /* non-0 exponent -- assume plain form */ + pre=dn->digits+exp; // digits before '.' + e=0; // no E + if ((exp>0) || (pre<-5)) { // need exponential form + e=exp+dn->digits-1; // calculate E value + pre=1; // assume one digit before '.' + if (eng && (e!=0)) { // engineering: may need to adjust + Int adj; // adjustment + // The C remainder operator is undefined for negative numbers, so + // a positive remainder calculation must be used here + if (e<0) { + adj=(-e)%3; + if (adj!=0) adj=3-adj; + } + else { // e>0 + adj=e%3; + } + e=e-adj; + // if dealing with zero still produce an exponent which is a + // multiple of three, as expected, but there will only be the + // one zero before the E, still. Otherwise note the padding. + if (!ISZERO(dn)) pre+=adj; + else { // is zero + if (adj!=0) { // 0.00Esnn needed + e=e+3; + pre=-(2-adj); + } + } // zero + } // eng + } // need exponent + + /* lay out the digits of the coefficient, adding 0s and . as needed */ + u=*up; + if (pre>0) { // xxx.xxx or xx00 (engineering) form + Int n=pre; + for (; pre>0; pre--, c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits (pre>digits) + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + if (n<dn->digits) { // more to come, after '.' + *c='.'; c++; + for (;; c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed + } + else { // 0.xxx or 0.000xxx form + *c='0'; c++; + *c='.'; c++; + for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.' + for (; ; c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + + /* Finally add the E-part, if needed. It will never be 0, has a + base maximum and minimum of +999999999 through -999999999, but + could range down to -1999999998 for anormal numbers */ + if (e!=0) { + Flag had=0; // 1=had non-zero + *c='E'; c++; + *c='+'; c++; // assume positive + u=e; // .. + if (e<0) { + *(c-1)='-'; // oops, need - + u=-e; // uInt, please + } + // lay out the exponent [_itoa or equivalent is not ANSI C] + for (cut=9; cut>=0; cut--) { + TODIGIT(u, cut, c, pow); + if (*c=='0' && !had) continue; // skip leading zeros + had=1; // had non-0 + c++; // step for next + } // cut + } + *c='\0'; // terminate the string (all paths) + return; + } // decToString + +/* ------------------------------------------------------------------ */ +/* decAddOp -- add/subtract operation */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* negate is DECNEG if rhs should be negated, or 0 otherwise */ +/* status accumulates status for the caller */ +/* */ +/* C must have space for set->digits digits. */ +/* Inexact in status must be 0 for correct Exact zero sign in result */ +/* ------------------------------------------------------------------ */ +/* If possible, the coefficient is calculated directly into C. */ +/* However, if: */ +/* -- a digits+1 calculation is needed because the numbers are */ +/* unaligned and span more than set->digits digits */ +/* -- a carry to digits+1 digits looks possible */ +/* -- C is the same as A or B, and the result would destructively */ +/* overlap the A or B coefficient */ +/* then the result must be calculated into a temporary buffer. In */ +/* this case a local (stack) buffer is used if possible, and only if */ +/* too long for that does malloc become the final resort. */ +/* */ +/* Misalignment is handled as follows: */ +/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ +/* BPad: Apply the padding by a combination of shifting (whole */ +/* units) and multiplication (part units). */ +/* */ +/* Addition, especially x=x+1, is speed-critical. */ +/* The static buffer is larger than might be expected to allow for */ +/* calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decAddOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uByte negate, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Int rhsshift; // working shift (in Units) + Int maxdigits; // longest logical length + Int mult; // multiplier + Int residue; // rounding accumulator + uByte bits; // result bits + Flag diffsign; // non-0 if arguments have different sign + Unit *acc; // accumulator for result + Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many + // allocations when called from + // other operations, notable exp] + Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated + Int reqdigits=set->digits; // local copy; requested DIGITS + Int padding; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // note whether signs differ [used all paths] + diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN + decNaNs(res, lhs, rhs, set, status); + else { // one or two infinities + if (decNumberIsInfinite(lhs)) { // LHS is infinity + // two infinities with different signs is invalid + if (decNumberIsInfinite(rhs) && diffsign) { + *status|=DEC_Invalid_operation; + break; + } + bits=lhs->bits & DECNEG; // get sign from LHS + } + else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity + bits|=DECINF; + decNumberZero(res); + res->bits=bits; // set +/- infinity + } // an infinity + break; + } + + // Quick exit for add 0s; return the non-0, modified as need be + if (ISZERO(lhs)) { + Int adjust; // work + Int lexp=lhs->exponent; // save in case LHS==RES + bits=lhs->bits; // .. + residue=0; // clear accumulator + decCopyFit(res, rhs, set, &residue, status); // copy (as needed) + res->bits^=negate; // flip if rhs was negated + #if DECSUBSET + if (set->extended) { // exponents on zeros count + #endif + // exponent will be the lower of the two + adjust=lexp-res->exponent; // adjustment needed [if -ve] + if (ISZERO(res)) { // both 0: special IEEE 754 rules + if (adjust<0) res->exponent=lexp; // set exponent + // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 + if (diffsign) { + if (set->round!=DEC_ROUND_FLOOR) res->bits=0; + else res->bits=DECNEG; // preserve 0 sign + } + } + else { // non-0 res + if (adjust<0) { // 0-padding needed + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; // to fit exactly + *status|=DEC_Rounded; // [but exact] + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // set the exponent. + } + } // non-0 res + #if DECSUBSET + } // extended + #endif + decFinish(res, set, &residue, status); // clean and finalize + break;} + + if (ISZERO(rhs)) { // [lhs is non-zero] + Int adjust; // work + Int rexp=rhs->exponent; // save in case RHS==RES + bits=rhs->bits; // be clean + residue=0; // clear accumulator + decCopyFit(res, lhs, set, &residue, status); // copy (as needed) + #if DECSUBSET + if (set->extended) { // exponents on zeros count + #endif + // exponent will be the lower of the two + // [0-0 case handled above] + adjust=rexp-res->exponent; // adjustment needed [if -ve] + if (adjust<0) { // 0-padding needed + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; // to fit exactly + *status|=DEC_Rounded; // [but exact] + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // set the exponent. + } + #if DECSUBSET + } // extended + #endif + decFinish(res, set, &residue, status); // clean and finalize + break;} + + // [NB: both fastpath and mainpath code below assume these cases + // (notably 0-0) have already been handled] + + // calculate the padding needed to align the operands + padding=rhs->exponent-lhs->exponent; + + // Fastpath cases where the numbers are aligned and normal, the RHS + // is all in one unit, no operand rounding is needed, and no carry, + // lengthening, or borrow is needed + if (padding==0 + && rhs->digits<=DECDPUN + && rhs->exponent>=set->emin // [some normals drop through] + && rhs->exponent<=set->emax-set->digits+1 // [could clamp] + && rhs->digits<=reqdigits + && lhs->digits<=reqdigits) { + Int partial=*lhs->lsu; + if (!diffsign) { // adding + partial+=*rhs->lsu; + if ((partial<=DECDPUNMAX) // result fits in unit + && (lhs->digits>=DECDPUN || // .. and no digits-count change + partial<(Int)powers[lhs->digits])) { // .. + if (res!=lhs) decNumberCopy(res, lhs); // not in place + *res->lsu=(Unit)partial; // [copy could have overwritten RHS] + break; + } + // else drop out for careful add + } + else { // signs differ + partial-=*rhs->lsu; + if (partial>0) { // no borrow needed, and non-0 result + if (res!=lhs) decNumberCopy(res, lhs); // not in place + *res->lsu=(Unit)partial; + // this could have reduced digits [but result>0] + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + break; + } + // else drop out for careful subtract + } + } + + // Now align (pad) the lhs or rhs so they can be added or + // subtracted, as necessary. If one number is much larger than + // the other (that is, if in plain form there is a least one + // digit between the lowest digit of one and the highest of the + // other) padding with up to DIGITS-1 trailing zeros may be + // needed; then apply rounding (as exotic rounding modes may be + // affected by the residue). + rhsshift=0; // rhs shift to left (padding) in Units + bits=lhs->bits; // assume sign is that of LHS + mult=1; // likely multiplier + + // [if padding==0 the operands are aligned; no padding is needed] + if (padding!=0) { + // some padding needed; always pad the RHS, as any required + // padding can then be effected by a simple combination of + // shifts and a multiply + Flag swapped=0; + if (padding<0) { // LHS needs the padding + const decNumber *t; + padding=-padding; // will be +ve + bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS + t=lhs; lhs=rhs; rhs=t; + swapped=1; + } + + // If, after pad, rhs would be longer than lhs by digits+1 or + // more then lhs cannot affect the answer, except as a residue, + // so only need to pad up to a length of DIGITS+1. + if (rhs->digits+padding > lhs->digits+reqdigits+1) { + // The RHS is sufficient + // for residue use the relative sign indication... + Int shift=reqdigits-rhs->digits; // left shift needed + residue=1; // residue for rounding + if (diffsign) residue=-residue; // signs differ + // copy, shortening if necessary + decCopyFit(res, rhs, set, &residue, status); + // if it was already shorter, then need to pad with zeros + if (shift>0) { + res->digits=decShiftToMost(res->lsu, res->digits, shift); + res->exponent-=shift; // adjust the exponent. + } + // flip the result sign if unswapped and rhs was negated + if (!swapped) res->bits^=negate; + decFinish(res, set, &residue, status); // done + break;} + + // LHS digits may affect result + rhsshift=D2U(padding+1)-1; // this much by Unit shift .. + mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication + } // padding needed + + if (diffsign) mult=-mult; // signs differ + + // determine the longer operand + maxdigits=rhs->digits+padding; // virtual length of RHS + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + + // Decide on the result buffer to use; if possible place directly + // into result. + acc=res->lsu; // assume add direct to result + // If destructive overlap, or the number is too long, or a carry or + // borrow to DIGITS+1 might be possible, a buffer must be used. + // [Might be worth more sophisticated tests when maxdigits==reqdigits] + if ((maxdigits>=reqdigits) // is, or could be, too large + || (res==rhs && rhsshift>0)) { // destructive overlap + // buffer needed, choose it; units for maxdigits digits will be + // needed, +1 Unit for carry or borrow + Int need=D2U(maxdigits)+1; + acc=accbuff; // assume use local buffer + if (need*sizeof(Unit)>sizeof(accbuff)) { + // printf("malloc add %ld %ld\n", need, sizeof(accbuff)); + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; + } + } + + res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite.. + res->exponent=lhs->exponent; // .. operands (even if aliased) + + #if DECTRACE + decDumpAr('A', lhs->lsu, D2U(lhs->digits)); + decDumpAr('B', rhs->lsu, D2U(rhs->digits)); + printf(" :h: %ld %ld\n", rhsshift, mult); + #endif + + // add [A+B*m] or subtract [A+B*(-m)] + res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhsshift, acc, mult) + *DECDPUN; // [units -> digits] + if (res->digits<0) { // borrowed... + res->digits=-res->digits; + res->bits^=DECNEG; // flip the sign + } + #if DECTRACE + decDumpAr('+', acc, D2U(res->digits)); + #endif + + // If a buffer was used the result must be copied back, possibly + // shortening. (If no buffer was used then the result must have + // fit, so can't need rounding and residue must be 0.) + residue=0; // clear accumulator + if (acc!=res->lsu) { + #if DECSUBSET + if (set->extended) { // round from first significant digit + #endif + // remove leading zeros that were added due to rounding up to + // integral Units -- before the test for rounding. + if (res->digits>reqdigits) + res->digits=decGetDigits(acc, D2U(res->digits)); + decSetCoeff(res, set, acc, res->digits, &residue, status); + #if DECSUBSET + } + else { // subset arithmetic rounds from original significant digit + // May have an underestimate. This only occurs when both + // numbers fit in DECDPUN digits and are padding with a + // negative multiple (-10, -100...) and the top digit(s) become + // 0. (This only matters when using X3.274 rules where the + // leading zero could be included in the rounding.) + if (res->digits<maxdigits) { + *(acc+D2U(res->digits))=0; // ensure leading 0 is there + res->digits=maxdigits; + } + else { + // remove leading zeros that added due to rounding up to + // integral Units (but only those in excess of the original + // maxdigits length, unless extended) before test for rounding. + if (res->digits>reqdigits) { + res->digits=decGetDigits(acc, D2U(res->digits)); + if (res->digits<maxdigits) res->digits=maxdigits; + } + } + decSetCoeff(res, set, acc, res->digits, &residue, status); + // Now apply rounding if needed before removing leading zeros. + // This is safe because subnormals are not a possibility + if (residue!=0) { + decApplyRound(res, set, residue, status); + residue=0; // did what needed to be done + } + } // subset + #endif + } // used buffer + + // strip leading zeros [these were left on in case of subset subtract] + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + + // apply checks and rounding + decFinish(res, set, &residue, status); + + // "When the sum of two operands with opposite signs is exactly + // zero, the sign of that sum shall be '+' in all rounding modes + // except round toward -Infinity, in which mode that sign shall be + // '-'." [Subset zeros also never have '-', set by decFinish.] + if (ISZERO(res) && diffsign + #if DECSUBSET + && set->extended + #endif + && (*status&DEC_Inexact)==0) { + if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign - + else res->bits&=~DECNEG; // sign + + } + } while(0); // end protected + + if (allocacc!=NULL) free(allocacc); // drop any storage used + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decAddOp + +/* ------------------------------------------------------------------ */ +/* decDivideOp -- division operation */ +/* */ +/* This routine performs the calculations for all four division */ +/* operators (divide, divideInteger, remainder, remainderNear). */ +/* */ +/* C=A op B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* The underlying algorithm of this routine is the same as in the */ +/* 1981 S/370 implementation, that is, non-restoring long division */ +/* with bi-unit (rather than bi-digit) estimation for each unit */ +/* multiplier. In this pseudocode overview, complications for the */ +/* Remainder operators and division residues for exact rounding are */ +/* omitted for clarity. */ +/* */ +/* Prepare operands and handle special values */ +/* Test for x/0 and then 0/x */ +/* Exp =Exp1 - Exp2 */ +/* Exp =Exp +len(var1) -len(var2) */ +/* Sign=Sign1 * Sign2 */ +/* Pad accumulator (Var1) to double-length with 0's (pad1) */ +/* Pad Var2 to same length as Var1 */ +/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ +/* have=0 */ +/* Do until (have=digits+1 OR residue=0) */ +/* if exp<0 then if integer divide/residue then leave */ +/* this_unit=0 */ +/* Do forever */ +/* compare numbers */ +/* if <0 then leave inner_loop */ +/* if =0 then (* quick exit without subtract *) do */ +/* this_unit=this_unit+1; output this_unit */ +/* leave outer_loop; end */ +/* Compare lengths of numbers (mantissae): */ +/* If same then tops2=msu2pair -- {units 1&2 of var2} */ +/* else tops2=msu2plus -- {0, unit 1 of var2} */ +/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ +/* mult=tops1/tops2 -- Good and safe guess at divisor */ +/* if mult=0 then mult=1 */ +/* this_unit=this_unit+mult */ +/* subtract */ +/* end inner_loop */ +/* if have\=0 | this_unit\=0 then do */ +/* output this_unit */ +/* have=have+1; end */ +/* var2=var2/10 */ +/* exp=exp-1 */ +/* end outer_loop */ +/* exp=exp+1 -- set the proper exponent */ +/* if have=0 then generate answer=0 */ +/* Return (Result is defined by Var1) */ +/* */ +/* ------------------------------------------------------------------ */ +/* Two working buffers are needed during the division; one (digits+ */ +/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ +/* long subtractions. These are acc and var1 respectively. */ +/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ +/* The static buffers may be larger than might be expected to allow */ +/* for calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decDivideOp(decNumber *res, + const decNumber *lhs, const decNumber *rhs, + decContext *set, Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer + Unit *acc=accbuff; // -> accumulator array for result + Unit *allocacc=NULL; // -> allocated buffer, iff allocated + Unit *accnext; // -> where next digit will go + Int acclength; // length of acc needed [Units] + Int accunits; // count of units accumulated + Int accdigits; // count of digits accumulated + + Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1 + Unit *var1=varbuff; // -> var1 array for long subtraction + Unit *varalloc=NULL; // -> allocated buffer, iff used + Unit *msu1; // -> msu of var1 + + const Unit *var2; // -> var2 array + const Unit *msu2; // -> msu of var2 + Int msu2plus; // msu2 plus one [does not vary] + eInt msu2pair; // msu2 pair plus one [does not vary] + + Int var1units, var2units; // actual lengths + Int var2ulen; // logical length (units) + Int var1initpad=0; // var1 initial padding (digits) + Int maxdigits; // longest LHS or required acc length + Int mult; // multiplier for subtraction + Unit thisunit; // current unit being accumulated + Int residue; // for rounding + Int reqdigits=set->digits; // requested DIGITS + Int exponent; // working exponent + Int maxexponent=0; // DIVIDE maximum exponent if unrounded + uByte bits; // working sign + Unit *target; // work + const Unit *source; // .. + uInt const *pow; // .. + Int shift, cut; // .. + #if DECSUBSET + Int dropped; // work + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs + decNaNs(res, lhs, rhs, set, status); + break; + } + // one or two infinities + if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite + if (decNumberIsInfinite(rhs) || // two infinities are invalid .. + op & (REMAINDER | REMNEAR)) { // as is remainder of infinity + *status|=DEC_Invalid_operation; + break; + } + // [Note that infinity/0 raises no exceptions] + decNumberZero(res); + res->bits=bits|DECINF; // set +/- infinity + break; + } + else { // RHS (divisor) is infinite + residue=0; + if (op&(REMAINDER|REMNEAR)) { + // result is [finished clone of] lhs + decCopyFit(res, lhs, set, &residue, status); + } + else { // a division + decNumberZero(res); + res->bits=bits; // set +/- zero + // for DIVIDEINT the exponent is always 0. For DIVIDE, result + // is a 0 with infinitely negative exponent, clamped to minimum + if (op&DIVIDE) { + res->exponent=set->emin-set->digits+1; + *status|=DEC_Clamped; + } + } + decFinish(res, set, &residue, status); + break; + } + } + + // handle 0 rhs (x/0) + if (ISZERO(rhs)) { // x/0 is always exceptional + if (ISZERO(lhs)) { + decNumberZero(res); // [after lhs test] + *status|=DEC_Division_undefined;// 0/0 will become NaN + } + else { + decNumberZero(res); + if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; + else { + *status|=DEC_Division_by_zero; // x/0 + res->bits=bits|DECINF; // .. is +/- Infinity + } + } + break;} + + // handle 0 lhs (0/x) + if (ISZERO(lhs)) { // 0/x [x!=0] + #if DECSUBSET + if (!set->extended) decNumberZero(res); + else { + #endif + if (op&DIVIDE) { + residue=0; + exponent=lhs->exponent-rhs->exponent; // ideal exponent + decNumberCopy(res, lhs); // [zeros always fit] + res->bits=bits; // sign as computed + res->exponent=exponent; // exponent, too + decFinalize(res, set, &residue, status); // check exponent + } + else if (op&DIVIDEINT) { + decNumberZero(res); // integer 0 + res->bits=bits; // sign as computed + } + else { // a remainder + exponent=rhs->exponent; // [save in case overwrite] + decNumberCopy(res, lhs); // [zeros always fit] + if (exponent<res->exponent) res->exponent=exponent; // use lower + } + #if DECSUBSET + } + #endif + break;} + + // Precalculate exponent. This starts off adjusted (and hence fits + // in 31 bits) and becomes the usual unadjusted exponent as the + // division proceeds. The order of evaluation is important, here, + // to avoid wrap. + exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); + + // If the working exponent is -ve, then some quick exits are + // possible because the quotient is known to be <1 + // [for REMNEAR, it needs to be < -1, as -0.5 could need work] + if (exponent<0 && !(op==DIVIDE)) { + if (op&DIVIDEINT) { + decNumberZero(res); // integer part is 0 + #if DECSUBSET + if (set->extended) + #endif + res->bits=bits; // set +/- zero + break;} + // fastpath remainders so long as the lhs has the smaller + // (or equal) exponent + if (lhs->exponent<=rhs->exponent) { + if (op&REMAINDER || exponent<-1) { + // It is REMAINDER or safe REMNEAR; result is [finished + // clone of] lhs (r = x - 0*y) + residue=0; + decCopyFit(res, lhs, set, &residue, status); + decFinish(res, set, &residue, status); + break; + } + // [unsafe REMNEAR drops through] + } + } // fastpaths + + /* Long (slow) division is needed; roll up the sleeves... */ + + // The accumulator will hold the quotient of the division. + // If it needs to be too long for stack storage, then allocate. + acclength=D2U(reqdigits+DECDPUN); // in Units + if (acclength*sizeof(Unit)>sizeof(accbuff)) { + // printf("malloc dvacc %ld units\n", acclength); + allocacc=(Unit *)malloc(acclength*sizeof(Unit)); + if (allocacc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; // use the allocated space + } + + // var1 is the padded LHS ready for subtractions. + // If it needs to be too long for stack storage, then allocate. + // The maximum units needed for var1 (long subtraction) is: + // Enough for + // (rhs->digits+reqdigits-1) -- to allow full slide to right + // or (lhs->digits) -- to allow for long lhs + // whichever is larger + // +1 -- for rounding of slide to right + // +1 -- for leading 0s + // +1 -- for pre-adjust if a remainder or DIVIDEINT + // [Note: unused units do not participate in decUnitAddSub data] + maxdigits=rhs->digits+reqdigits-1; + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + var1units=D2U(maxdigits)+2; + // allocate a guard unit above msu1 for REMAINDERNEAR + if (!(op&DIVIDE)) var1units++; + if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { + // printf("malloc dvvar %ld units\n", var1units+1); + varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); + if (varalloc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + var1=varalloc; // use the allocated space + } + + // Extend the lhs and rhs to full long subtraction length. The lhs + // is truly extended into the var1 buffer, with 0 padding, so a + // subtract in place is always possible. The rhs (var2) has + // virtual padding (implemented by decUnitAddSub). + // One guard unit was allocated above msu1 for rem=rem+rem in + // REMAINDERNEAR. + msu1=var1+var1units-1; // msu of var1 + source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array + for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; + for (; target>=var1; target--) *target=0; + + // rhs (var2) is left-aligned with var1 at the start + var2ulen=var1units; // rhs logical length (units) + var2units=D2U(rhs->digits); // rhs actual length (units) + var2=rhs->lsu; // -> rhs array + msu2=var2+var2units-1; // -> msu of var2 [never changes] + // now set up the variables which will be used for estimating the + // multiplication factor. If these variables are not exact, add + // 1 to make sure that the multiplier is never overestimated. + msu2plus=*msu2; // it's value .. + if (var2units>1) msu2plus++; // .. +1 if any more + msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair .. + if (var2units>1) { // .. [else treat 2nd as 0] + msu2pair+=*(msu2-1); // .. + if (var2units>2) msu2pair++; // .. +1 if any more + } + + // The calculation is working in units, which may have leading zeros, + // but the exponent was calculated on the assumption that they are + // both left-aligned. Adjust the exponent to compensate: add the + // number of leading zeros in var1 msu and subtract those in var2 msu. + // [This is actually done by counting the digits and negating, as + // lead1=DECDPUN-digits1, and similarly for lead2.] + for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; + for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; + + // Now, if doing an integer divide or remainder, ensure that + // the result will be Unit-aligned. To do this, shift the var1 + // accumulator towards least if need be. (It's much easier to + // do this now than to reassemble the residue afterwards, if + // doing a remainder.) Also ensure the exponent is not negative. + if (!(op&DIVIDE)) { + Unit *u; // work + // save the initial 'false' padding of var1, in digits + var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; + // Determine the shift to do. + if (exponent<0) cut=-exponent; + else cut=DECDPUN-exponent%DECDPUN; + decShiftToLeast(var1, var1units, cut); + exponent+=cut; // maintain numerical value + var1initpad-=cut; // .. and reduce padding + // clean any most-significant units which were just emptied + for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; + } // align + else { // is DIVIDE + maxexponent=lhs->exponent-rhs->exponent; // save + // optimization: if the first iteration will just produce 0, + // preadjust to skip it [valid for DIVIDE only] + if (*msu1<*msu2) { + var2ulen--; // shift down + exponent-=DECDPUN; // update the exponent + } + } + + // ---- start the long-division loops ------------------------------ + accunits=0; // no units accumulated yet + accdigits=0; // .. or digits + accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1] + for (;;) { // outer forever loop + thisunit=0; // current unit assumed 0 + // find the next unit + for (;;) { // inner forever loop + // strip leading zero units [from either pre-adjust or from + // subtract last time around]. Leave at least one unit. + for (; *msu1==0 && msu1>var1; msu1--) var1units--; + + if (var1units<var2ulen) break; // var1 too low for subtract + if (var1units==var2ulen) { // unit-by-unit compare needed + // compare the two numbers, from msu + const Unit *pv1, *pv2; + Unit v2; // units to compare + pv2=msu2; // -> msu + for (pv1=msu1; ; pv1--, pv2--) { + // v1=*pv1 -- always OK + v2=0; // assume in padding + if (pv2>=var2) v2=*pv2; // in range + if (*pv1!=v2) break; // no longer the same + if (pv1==var1) break; // done; leave pv1 as is + } + // here when all inspected or a difference seen + if (*pv1<v2) break; // var1 too low to subtract + if (*pv1==v2) { // var1 == var2 + // reach here if var1 and var2 are identical; subtraction + // would increase digit by one, and the residue will be 0 so + // the calculation is done; leave the loop with residue=0. + thisunit++; // as though subtracted + *var1=0; // set var1 to 0 + var1units=1; // .. + break; // from inner + } // var1 == var2 + // *pv1>v2. Prepare for real subtraction; the lengths are equal + // Estimate the multiplier (there's always a msu1-1)... + // Bring in two units of var2 to provide a good estimate. + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); + } // lengths the same + else { // var1units > var2ulen, so subtraction is safe + // The var2 msu is one unit towards the lsu of the var1 msu, + // so only one unit for var2 can be used. + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); + } + if (mult==0) mult=1; // must always be at least 1 + // subtraction needed; var1 is > var2 + thisunit=(Unit)(thisunit+mult); // accumulate + // subtract var1-var2, into var1; only the overlap needs + // processing, as this is an in-place calculation + shift=var2ulen-var2units; + #if DECTRACE + decDumpAr('1', &var1[shift], var1units-shift); + decDumpAr('2', var2, var2units); + printf("m=%ld\n", -mult); + #endif + decUnitAddSub(&var1[shift], var1units-shift, + var2, var2units, 0, + &var1[shift], -mult); + #if DECTRACE + decDumpAr('#', &var1[shift], var1units-shift); + #endif + // var1 now probably has leading zeros; these are removed at the + // top of the inner loop. + } // inner loop + + // The next unit has been calculated in full; unless it's a + // leading zero, add to acc + if (accunits!=0 || thisunit!=0) { // is first or non-zero + *accnext=thisunit; // store in accumulator + // account exactly for the new digits + if (accunits==0) { + accdigits++; // at least one + for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; + } + else accdigits+=DECDPUN; + accunits++; // update count + accnext--; // ready for next + if (accdigits>reqdigits) break; // have enough digits + } + + // if the residue is zero, the operation is done (unless divide + // or divideInteger and still not enough digits yet) + if (*var1==0 && var1units==1) { // residue is 0 + if (op&(REMAINDER|REMNEAR)) break; + if ((op&DIVIDE) && (exponent<=maxexponent)) break; + // [drop through if divideInteger] + } + // also done enough if calculating remainder or integer + // divide and just did the last ('units') unit + if (exponent==0 && !(op&DIVIDE)) break; + + // to get here, var1 is less than var2, so divide var2 by the per- + // Unit power of ten and go for the next digit + var2ulen--; // shift down + exponent-=DECDPUN; // update the exponent + } // outer loop + + // ---- division is complete --------------------------------------- + // here: acc has at least reqdigits+1 of good results (or fewer + // if early stop), starting at accnext+1 (its lsu) + // var1 has any residue at the stopping point + // accunits is the number of digits collected in acc + if (accunits==0) { // acc is 0 + accunits=1; // show have a unit .. + accdigits=1; // .. + *accnext=0; // .. whose value is 0 + } + else accnext++; // back to last placed + // accnext now -> lowest unit of result + + residue=0; // assume no residue + if (op&DIVIDE) { + // record the presence of any residue, for rounding + if (*var1!=0 || var1units>1) residue=1; + else { // no residue + // Had an exact division; clean up spurious trailing 0s. + // There will be at most DECDPUN-1, from the final multiply, + // and then only if the result is non-0 (and even) and the + // exponent is 'loose'. + #if DECDPUN>1 + Unit lsu=*accnext; + if (!(lsu&0x01) && (lsu!=0)) { + // count the trailing zeros + Int drop=0; + for (;; drop++) { // [will terminate because lsu!=0] + if (exponent>=maxexponent) break; // don't chop real 0s + #if DECDPUN<=4 + if ((lsu-QUOT10(lsu, drop+1) + *powers[drop+1])!=0) break; // found non-0 digit + #else + if (lsu%powers[drop+1]!=0) break; // found non-0 digit + #endif + exponent++; + } + if (drop>0) { + accunits=decShiftToLeast(accnext, accunits, drop); + accdigits=decGetDigits(accnext, accunits); + accunits=D2U(accdigits); + // [exponent was adjusted in the loop] + } + } // neither odd nor 0 + #endif + } // exact divide + } // divide + else /* op!=DIVIDE */ { + // check for coefficient overflow + if (accdigits+exponent>reqdigits) { + *status|=DEC_Division_impossible; + break; + } + if (op & (REMAINDER|REMNEAR)) { + // [Here, the exponent will be 0, because var1 was adjusted + // appropriately.] + Int postshift; // work + Flag wasodd=0; // integer was odd + Unit *quotlsu; // for save + Int quotdigits; // .. + + bits=lhs->bits; // remainder sign is always as lhs + + // Fastpath when residue is truly 0 is worthwhile [and + // simplifies the code below] + if (*var1==0 && var1units==1) { // residue is 0 + Int exp=lhs->exponent; // save min(exponents) + if (rhs->exponent<exp) exp=rhs->exponent; + decNumberZero(res); // 0 coefficient + #if DECSUBSET + if (set->extended) + #endif + res->exponent=exp; // .. with proper exponent + res->bits=(uByte)(bits&DECNEG); // [cleaned] + decFinish(res, set, &residue, status); // might clamp + break; + } + // note if the quotient was odd + if (*accnext & 0x01) wasodd=1; // acc is odd + quotlsu=accnext; // save in case need to reinspect + quotdigits=accdigits; // .. + + // treat the residue, in var1, as the value to return, via acc + // calculate the unused zero digits. This is the smaller of: + // var1 initial padding (saved above) + // var2 residual padding, which happens to be given by: + postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; + // [the 'exponent' term accounts for the shifts during divide] + if (var1initpad<postshift) postshift=var1initpad; + + // shift var1 the requested amount, and adjust its digits + var1units=decShiftToLeast(var1, var1units, postshift); + accnext=var1; + accdigits=decGetDigits(var1, var1units); + accunits=D2U(accdigits); + + exponent=lhs->exponent; // exponent is smaller of lhs & rhs + if (rhs->exponent<exponent) exponent=rhs->exponent; + + // Now correct the result if doing remainderNear; if it + // (looking just at coefficients) is > rhs/2, or == rhs/2 and + // the integer was odd then the result should be rem-rhs. + if (op&REMNEAR) { + Int compare, tarunits; // work + Unit *up; // .. + // calculate remainder*2 into the var1 buffer (which has + // 'headroom' of an extra unit and hence enough space) + // [a dedicated 'double' loop would be faster, here] + tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, + 0, accnext, 1); + // decDumpAr('r', accnext, tarunits); + + // Here, accnext (var1) holds tarunits Units with twice the + // remainder's coefficient, which must now be compared to the + // RHS. The remainder's exponent may be smaller than the RHS's. + compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), + rhs->exponent-exponent); + if (compare==BADINT) { // deep trouble + *status|=DEC_Insufficient_storage; + break;} + + // now restore the remainder by dividing by two; the lsu + // is known to be even. + for (up=accnext; up<accnext+tarunits; up++) { + Int half; // half to add to lower unit + half=*up & 0x01; + *up/=2; // [shift] + if (!half) continue; + *(up-1)+=(DECDPUNMAX+1)/2; + } + // [accunits still describes the original remainder length] + + if (compare>0 || (compare==0 && wasodd)) { // adjustment needed + Int exp, expunits, exprem; // work + // This is effectively causing round-up of the quotient, + // so if it was the rare case where it was full and all + // nines, it would overflow and hence division-impossible + // should be raised + Flag allnines=0; // 1 if quotient all nines + if (quotdigits==reqdigits) { // could be borderline + for (up=quotlsu; ; up++) { + if (quotdigits>DECDPUN) { + if (*up!=DECDPUNMAX) break;// non-nines + } + else { // this is the last Unit + if (*up==powers[quotdigits]-1) allnines=1; + break; + } + quotdigits-=DECDPUN; // checked those digits + } // up + } // borderline check + if (allnines) { + *status|=DEC_Division_impossible; + break;} + + // rem-rhs is needed; the sign will invert. Again, var1 + // can safely be used for the working Units array. + exp=rhs->exponent-exponent; // RHS padding needed + // Calculate units and remainder from exponent. + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + // subtract [A+B*(-m)]; the result will always be negative + accunits=-decUnitAddSub(accnext, accunits, + rhs->lsu, D2U(rhs->digits), + expunits, accnext, -(Int)powers[exprem]); + accdigits=decGetDigits(accnext, accunits); // count digits exactly + accunits=D2U(accdigits); // and recalculate the units for copy + // [exponent is as for original remainder] + bits^=DECNEG; // flip the sign + } + } // REMNEAR + } // REMAINDER or REMNEAR + } // not DIVIDE + + // Set exponent and bits + res->exponent=exponent; + res->bits=(uByte)(bits&DECNEG); // [cleaned] + + // Now the coefficient. + decSetCoeff(res, set, accnext, accdigits, &residue, status); + + decFinish(res, set, &residue, status); // final cleanup + + #if DECSUBSET + // If a divide then strip trailing zeros if subset [after round] + if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); + #endif + } while(0); // end protected + + if (varalloc!=NULL) free(varalloc); // drop any storage used + if (allocacc!=NULL) free(allocacc); // .. + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decDivideOp + +/* ------------------------------------------------------------------ */ +/* decMultiplyOp -- multiplication operation */ +/* */ +/* This routine performs the multiplication C=A x B. */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* 'Classic' multiplication is used rather than Karatsuba, as the */ +/* latter would give only a minor improvement for the short numbers */ +/* expected to be handled most (and uses much more memory). */ +/* */ +/* There are two major paths here: the general-purpose ('old code') */ +/* path which handles all DECDPUN values, and a fastpath version */ +/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ +/* than two calls to decUnitAddSub would be made. */ +/* */ +/* The fastpath version lumps units together into 8-digit or 9-digit */ +/* chunks, and also uses a lazy carry strategy to minimise expensive */ +/* 64-bit divisions. The chunks are then broken apart again into */ +/* units for continuing processing. Despite this overhead, the */ +/* fastpath can speed up some 16-digit operations by 10x (and much */ +/* more for higher-precision calculations). */ +/* */ +/* A buffer always has to be used for the accumulator; in the */ +/* fastpath, buffers are also always needed for the chunked copies of */ +/* of the operand coefficients. */ +/* Static buffers are larger than needed just for multiply, to allow */ +/* for calls from other operations (notably exp). */ +/* ------------------------------------------------------------------ */ +#define FASTMUL (DECUSE64 && DECDPUN<5) +static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + Int accunits; // Units of accumulator in use + Int exponent; // work + Int residue=0; // rounding residue + uByte bits; // result sign + Unit *acc; // -> accumulator Unit array + Int needbytes; // size calculator + void *allocacc=NULL; // -> allocated accumulator, iff allocated + Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0, + // *4 for calls from other operations) + const Unit *mer, *mermsup; // work + Int madlength; // Units in multiplicand + Int shift; // Units to shift multiplicand by + + #if FASTMUL + // if DECDPUN is 1 or 3 work in base 10**9, otherwise + // (DECDPUN is 2 or 4) then work in base 10**8 + #if DECDPUN & 1 // odd + #define FASTBASE 1000000000 // base + #define FASTDIGS 9 // digits in base + #define FASTLAZY 18 // carry resolution point [1->18] + #else + #define FASTBASE 100000000 + #define FASTDIGS 8 + #define FASTLAZY 1844 // carry resolution point [1->1844] + #endif + // three buffers are used, two for chunked copies of the operands + // (base 10**8 or base 10**9) and one base 2**64 accumulator with + // lazy carry evaluation + uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) + uInt *zlhi=zlhibuff; // -> lhs array + uInt *alloclhi=NULL; // -> allocated buffer, iff allocated + uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) + uInt *zrhi=zrhibuff; // -> rhs array + uInt *allocrhi=NULL; // -> allocated buffer, iff allocated + uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0) + // [allocacc is shared for both paths, as only one will run] + uLong *zacc=zaccbuff; // -> accumulator array for exact result + #if DECDPUN==1 + Int zoff; // accumulator offset + #endif + uInt *lip, *rip; // item pointers + uInt *lmsi, *rmsi; // most significant items + Int ilhs, irhs, iacc; // item counts in the arrays + Int lazy; // lazy carry counter + uLong lcarry; // uLong carry + uInt carry; // carry (NB not uLong) + Int count; // work + const Unit *cup; // .. + Unit *up; // .. + uLong *lp; // .. + Int p; // .. + #endif + + #if DECSUBSET + decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated + decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // precalculate result sign + bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs + decNaNs(res, lhs, rhs, set, status); + return res;} + // one or two infinities; Infinity * 0 is invalid + if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) + ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { + *status|=DEC_Invalid_operation; + return res;} + decNumberZero(res); + res->bits=bits|DECINF; // infinity + return res;} + + // For best speed, as in DMSRCN [the original Rexx numerics + // module], use the shorter number as the multiplier (rhs) and + // the longer as the multiplicand (lhs) to minimise the number of + // adds (partial products) + if (lhs->digits<rhs->digits) { // swap... + const decNumber *hold=lhs; + lhs=rhs; + rhs=hold; + } + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + #if FASTMUL // fastpath can be used + // use the fast path if there are enough digits in the shorter + // operand to make the setup and takedown worthwhile + #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls + if (rhs->digits>NEEDTWO) { // use fastpath... + // calculate the number of elements in each array + ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling] + irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // .. + iacc=ilhs+irhs; + + // allocate buffers if required, as usual + needbytes=ilhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zlhibuff)) { + alloclhi=(uInt *)malloc(needbytes); + zlhi=alloclhi;} + needbytes=irhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zrhibuff)) { + allocrhi=(uInt *)malloc(needbytes); + zrhi=allocrhi;} + + // Allocating the accumulator space needs a special case when + // DECDPUN=1 because when converting the accumulator to Units + // after the multiplication each 8-byte item becomes 9 1-byte + // units. Therefore iacc extra bytes are needed at the front + // (rounded up to a multiple of 8 bytes), and the uLong + // accumulator starts offset the appropriate number of units + // to the right to avoid overwrite during the unchunking. + needbytes=iacc*sizeof(uLong); + #if DECDPUN==1 + zoff=(iacc+7)/8; // items to offset by + needbytes+=zoff*8; + #endif + if (needbytes>(Int)sizeof(zaccbuff)) { + allocacc=(uLong *)malloc(needbytes); + zacc=(uLong *)allocacc;} + if (zlhi==NULL||zrhi==NULL||zacc==NULL) { + *status|=DEC_Insufficient_storage; + break;} + + acc=(Unit *)zacc; // -> target Unit array + #if DECDPUN==1 + zacc+=zoff; // start uLong accumulator to right + #endif + + // assemble the chunked copies of the left and right sides + for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) + for (p=0, *lip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *lip+=*cup*powers[p]; + lmsi=lip-1; // save -> msi + for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) + for (p=0, *rip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *rip+=*cup*powers[p]; + rmsi=rip-1; // save -> msi + + // zero the accumulator + for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; + + /* Start the multiplication */ + // Resolving carries can dominate the cost of accumulating the + // partial products, so this is only done when necessary. + // Each uLong item in the accumulator can hold values up to + // 2**64-1, and each partial product can be as large as + // (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to + // itself 18.4 times in a uLong without overflowing, so during + // the main calculation resolution is carried out every 18th + // add -- every 162 digits. Similarly, when FASTDIGS=8, the + // partial products can be added to themselves 1844.6 times in + // a uLong without overflowing, so intermediate carry + // resolution occurs only every 14752 digits. Hence for common + // short numbers usually only the one final carry resolution + // occurs. + // (The count is set via FASTLAZY to simplify experiments to + // measure the value of this approach: a 35% improvement on a + // [34x34] multiply.) + lazy=FASTLAZY; // carry delay count + for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs + lp=zacc+(rip-zrhi); // where to add the lhs + for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs + *lp+=(uLong)(*lip)*(*rip); // [this should in-line] + } // lip loop + lazy--; + if (lazy>0 && rip!=rmsi) continue; + lazy=FASTLAZY; // reset delay count + // spin up the accumulator resolving overflows + for (lp=zacc; lp<zacc+iacc; lp++) { + if (*lp<FASTBASE) continue; // it fits + lcarry=*lp/FASTBASE; // top part [slow divide] + // lcarry can exceed 2**32-1, so check again; this check + // and occasional extra divide (slow) is well worth it, as + // it allows FASTLAZY to be increased to 18 rather than 4 + // in the FASTDIGS=9 case + if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual] + else { // two-place carry [fairly rare] + uInt carry2=(uInt)(lcarry/FASTBASE); // top top part + *(lp+2)+=carry2; // add to item+2 + *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow] + carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline] + } + *(lp+1)+=carry; // add to item above [inline] + *lp-=((uLong)FASTBASE*carry); // [inline] + } // carry resolution + } // rip loop + + // The multiplication is complete; time to convert back into + // units. This can be done in-place in the accumulator and in + // 32-bit operations, because carries were resolved after the + // final add. This needs N-1 divides and multiplies for + // each item in the accumulator (which will become up to N + // units, where 2<=N<=9). + for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { + uInt item=(uInt)*lp; // decapitate to uInt + for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { + uInt part=item/(DECDPUNMAX+1); + *up=(Unit)(item-(part*(DECDPUNMAX+1))); + item=part; + } // p + *up=(Unit)item; up++; // [final needs no division] + } // lp + accunits=up-acc; // count of units + } + else { // here to use units directly, without chunking ['old code'] + #endif + + // if accumulator will be too long for local storage, then allocate + acc=accbuff; // -> assume buffer for accumulator + needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); + if (needbytes>(Int)sizeof(accbuff)) { + allocacc=(Unit *)malloc(needbytes); + if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} + acc=(Unit *)allocacc; // use the allocated space + } + + /* Now the main long multiplication loop */ + // Unlike the equivalent in the IBM Java implementation, there + // is no advantage in calculating from msu to lsu. So, do it + // by the book, as it were. + // Each iteration calculates ACC=ACC+MULTAND*MULT + accunits=1; // accumulator starts at '0' + *acc=0; // .. (lsu=0) + shift=0; // no multiplicand shift at first + madlength=D2U(lhs->digits); // this won't change + mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier + + for (mer=rhs->lsu; mer<mermsup; mer++) { + // Here, *mer is the next Unit in the multiplier to use + // If non-zero [optimization] add it... + if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, + lhs->lsu, madlength, 0, + &acc[shift], *mer) + + shift; + else { // extend acc with a 0; it will be used shortly + *(acc+accunits)=0; // [this avoids length of <=0 later] + accunits++; + } + // multiply multiplicand by 10**DECDPUN for next Unit to left + shift++; // add this for 'logical length' + } // n + #if FASTMUL + } // unchunked units + #endif + // common end-path + #if DECTRACE + decDumpAr('*', acc, accunits); // Show exact result + #endif + + // acc now contains the exact result of the multiplication, + // possibly with a leading zero unit; build the decNumber from + // it, noting if any residue + res->bits=bits; // set sign + res->digits=decGetDigits(acc, accunits); // count digits exactly + + // There can be a 31-bit wrap in calculating the exponent. + // This can only happen if both input exponents are negative and + // both their magnitudes are large. If there was a wrap, set a + // safe very negative exponent, from which decFinalize() will + // raise a hard underflow shortly. + exponent=lhs->exponent+rhs->exponent; // calculate exponent + if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) + exponent=-2*DECNUMMAXE; // force underflow + res->exponent=exponent; // OK to overwrite now + + + // Set the coefficient. If any rounding, residue records + decSetCoeff(res, set, acc, res->digits, &residue, status); + decFinish(res, set, &residue, status); // final cleanup + } while(0); // end protected + + if (allocacc!=NULL) free(allocacc); // drop any storage used + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + #if FASTMUL + if (allocrhi!=NULL) free(allocrhi); // .. + if (alloclhi!=NULL) free(alloclhi); // .. + #endif + return res; + } // decMultiplyOp + +/* ------------------------------------------------------------------ */ +/* decExpOp -- effect exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. status is updated but */ +/* not set. */ +/* */ +/* Restrictions: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* ------------------------------------------------------------------ */ +/* This approach used here is similar to the algorithm described in */ +/* */ +/* Variable Precision Exponential Function, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ +/* pp79-91, ACM, June 1986. */ +/* */ +/* with the main difference being that the iterations in the series */ +/* evaluation are terminated dynamically (which does not require the */ +/* extra variable-precision variables which are expensive in this */ +/* context). */ +/* */ +/* The error analysis in Hull & Abrham's paper applies except for the */ +/* round-off error accumulation during the series evaluation. This */ +/* code does not precalculate the number of iterations and so cannot */ +/* use Horner's scheme. Instead, the accumulation is done at double- */ +/* precision, which ensures that the additions of the terms are exact */ +/* and do not accumulate round-off (and any round-off errors in the */ +/* terms themselves move 'to the right' faster than they can */ +/* accumulate). This code also extends the calculation by allowing, */ +/* in the spirit of other decNumber operators, the input to be more */ +/* precise than the result (the precision used is based on the more */ +/* precise of the input or requested result). */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decExpOp so it can be called from */ +/* other Mathematical functions (notably Ln) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-x) where x can be the tiniest number (Ntiny). */ +/* */ +/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ +/* iterations by appoximately a third with additional (although */ +/* diminishing) returns as the range is reduced to even smaller */ +/* fractions. However, h (the power of 10 used to correct the */ +/* result at the end, see below) must be kept <=8 as otherwise */ +/* the final result cannot be computed. Hence the leverage is a */ +/* sliding value (8-h), where potentially the range is reduced */ +/* more for smaller values. */ +/* */ +/* The leverage that can be applied in this way is severely */ +/* limited by the cost of the raise-to-the power at the end, */ +/* which dominates when the number of iterations is small (less */ +/* than ten) or when rhs is short. As an example, the adjustment */ +/* x**10,000,000 needs 31 multiplications, all but one full-width. */ +/* */ +/* 3. The restrictions (especially precision) could be raised with */ +/* care, but the full decNumber range seems very hard within the */ +/* 32-bit limits. */ +/* */ +/* 4. The working precisions for the static buffers are twice the */ +/* obvious size to allow for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decExpOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; // working status + Int h; // adjusted exponent for 0.xxxx + Int p; // working precision + Int residue; // rounding residue + uInt needbytes; // for space calculations + const decNumber *x=rhs; // (may point to safe copy later) + decContext aset, tset, dset; // working contexts + Int comp; // work + + // the argument is often copied to normalize it, so (unusually) it + // is treated like other buffers, using DECBUFFER, +1 in case + // DECBUFFER is 0 + decNumber bufr[D2N(DECBUFFER*2+1)]; + decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated + + // the working precision will be no more than set->digits+8+1 + // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER + // is 0 (and twice that for the accumulator) + + // buffer for t, term (working precision plus) + decNumber buft[D2N(DECBUFFER*2+9+1)]; + decNumber *allocbuft=NULL; // -> allocated buft, iff allocated + decNumber *t=buft; // term + // buffer for a, accumulator (working precision * 2), at least 9 + decNumber bufa[D2N(DECBUFFER*4+18+1)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // accumulator + // decNumber for the divisor term; this needs at most 9 digits + // and so can be fixed size [16 so can use standard context] + decNumber bufd[D2N(16)]; + decNumber *d=bufd; // divisor + decNumber numone; // constant 1 + + #if DECCHECK + Int iterations=0; // for later sanity check + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + if (SPECIALARG) { // handle infinities and NaNs + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) // -Infinity -> +0 + decNumberZero(res); + else decNumberCopy(res, rhs); // +Infinity -> self + } + else decNaNs(res, rhs, NULL, set, status); // a NaN + break;} + + if (ISZERO(rhs)) { // zeros -> exact 1 + decNumberZero(res); // make clean 1 + *res->lsu=1; // .. + break;} // [no status to set] + + // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path + // positive and negative tiny cases which will result in inexact + // 1. This also allows the later add-accumulate to always be + // exact (because its length will never be more than twice the + // working precision). + // The comparator (tiny) needs just one digit, so use the + // decNumber d for it (reused as the divisor, etc., below); its + // exponent is such that if x is positive it will have + // set->digits-1 zeros between the decimal point and the digit, + // which is 4, and if x is negative one more zero there as the + // more precise result will be of the form 0.9999999 rather than + // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 + // or 0.00000004 if digits=7 and x<0. If RHS not larger than + // this then the result will be 1.000000 + decNumberZero(d); // clean + *d->lsu=4; // set 4 .. + d->exponent=-set->digits; // * 10**(-d) + if (decNumberIsNegative(rhs)) d->exponent--; // negative case + comp=decCompare(d, rhs, 1); // signless compare + if (comp==BADINT) { + *status|=DEC_Insufficient_storage; + break;} + if (comp>=0) { // rhs < d + Int shift=set->digits-1; + decNumberZero(res); // set 1 + *res->lsu=1; // .. + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; // make 1.0000... + *status|=DEC_Inexact | DEC_Rounded; // .. inexactly + break;} // tiny + + // set up the context to be used for calculating a, as this is + // used on both paths below + decContextDefault(&aset, DEC_INIT_DECIMAL64); + // accumulator bounds are as requested (could underflow) + aset.emax=set->emax; // usual bounds + aset.emin=set->emin; // .. + aset.clamp=0; // and no concrete format + + // calculate the adjusted (Hull & Abrham) exponent (where the + // decimal point is just to the left of the coefficient msd) + h=rhs->exponent+rhs->digits; + // if h>8 then 10**h cannot be calculated safely; however, when + // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at + // least 6.59E+4342944, so (due to the restriction on Emax/Emin) + // overflow (or underflow to 0) is guaranteed -- so this case can + // be handled by simply forcing the appropriate excess + if (h>8) { // overflow/underflow + // set up here so Power call below will over or underflow to + // zero; set accumulator to either 2 or 0.02 + // [stack buffer for a is always big enough for this] + decNumberZero(a); + *a->lsu=2; // not 1 but < exp(1) + if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02 + h=8; // clamp so 10**h computable + p=9; // set a working precision + } + else { // h<=8 + Int maxlever=(rhs->digits>8?1:0); + // [could/should increase this for precisions >40 or so, too] + + // if h is 8, cannot normalize to a lower upper limit because + // the final result will not be computable (see notes above), + // but leverage can be applied whenever h is less than 8. + // Apply as much as possible, up to a MAXLEVER digits, which + // sets the tradeoff against the cost of the later a**(10**h). + // As h is increased, the working precision below also + // increases to compensate for the "constant digits at the + // front" effect. + Int lever=MINI(8-h, maxlever); // leverage attainable + Int use=-rhs->digits-lever; // exponent to use for RHS + h+=lever; // apply leverage selected + if (h<0) { // clamp + use+=h; // [may end up subnormal] + h=0; + } + // Take a copy of RHS if it needs normalization (true whenever x>=1) + if (rhs->exponent!=use) { + decNumber *newrhs=bufr; // assume will fit on stack + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufr)) { // need malloc space + allocrhs=(decNumber *)malloc(needbytes); + if (allocrhs==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + newrhs=allocrhs; // use the allocated space + } + decNumberCopy(newrhs, rhs); // copy to safe space + newrhs->exponent=use; // normalize; now <1 + x=newrhs; // ready for use + // decNumberShow(x); + } + + // Now use the usual power series to evaluate exp(x). The + // series starts as 1 + x + x^2/2 ... so prime ready for the + // third term by setting the term variable t=x, the accumulator + // a=1, and the divisor d=2. + + // First determine the working precision. From Hull & Abrham + // this is set->digits+h+2. However, if x is 'over-precise' we + // need to allow for all its digits to potentially participate + // (consider an x where all the excess digits are 9s) so in + // this case use x->digits+h+2 + p=MAXI(x->digits, set->digits)+h+2; // [h<=8] + + // a and t are variable precision, and depend on p, so space + // must be allocated for them if necessary + + // the accumulator needs to be able to hold 2p digits so that + // the additions on the second and subsequent iterations are + // sufficiently exact. + needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + // the term needs to be able to hold p digits (which is + // guaranteed to be larger than x->digits, so the initial copy + // is safe); it may also be used for the raise-to-power + // calculation below, which needs an extra two digits + needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); + if (needbytes>sizeof(buft)) { // need malloc space + allocbuft=(decNumber *)malloc(needbytes); + if (allocbuft==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + t=allocbuft; // use the allocated space + } + + decNumberCopy(t, x); // term=x + decNumberZero(a); *a->lsu=1; // accumulator=1 + decNumberZero(d); *d->lsu=2; // divisor=2 + decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment + + // set up the contexts for calculating a, t, and d + decContextDefault(&tset, DEC_INIT_DECIMAL64); + dset=tset; + // accumulator bounds are set above, set precision now + aset.digits=p*2; // double + // term bounds avoid any underflow or overflow + tset.digits=p; + tset.emin=DEC_MIN_EMIN; // [emax is plenty] + // [dset.digits=16, etc., are sufficient] + + // finally ready to roll + for (;;) { + #if DECCHECK + iterations++; + #endif + // only the status from the accumulation is interesting + // [but it should remain unchanged after first add] + decAddOp(a, a, t, &aset, 0, status); // a=a+t + decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x + decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d + // the iteration ends when the term cannot affect the result, + // if rounded to p digits, which is when its value is smaller + // than the accumulator by p+1 digits. There must also be + // full precision in a. + if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) + && (a->digits>=p)) break; + decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1 + } // iterate + + #if DECCHECK + // just a sanity check; comment out test to show always + if (iterations>p+3) + printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); + #endif + } // h<=8 + + // apply postconditioning: a=a**(10**h) -- this is calculated + // at a slightly higher precision than Hull & Abrham suggest + if (h>0) { + Int seenbit=0; // set once a 1-bit is seen + Int i; // counter + Int n=powers[h]; // always positive + aset.digits=p+2; // sufficient precision + // avoid the overhead and many extra digits of decNumberPower + // as all that is needed is the short 'multipliers' loop; here + // accumulate the answer into t + decNumberZero(t); *t->lsu=1; // acc=1 + for (i=1;;i++){ // for each bit [top bit ignored] + // abandon if have had overflow or terminal underflow + if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting? + if (*status&DEC_Overflow || ISZERO(t)) break;} + n=n<<1; // move next bit to testable position + if (n<0) { // top bit is set + seenbit=1; // OK, have a significant bit + decMultiplyOp(t, t, a, &aset, status); // acc=acc*x + } + if (i==31) break; // that was the last bit + if (!seenbit) continue; // no need to square 1 + decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square] + } /*i*/ // 32 bits + // decNumberShow(t); + a=t; // and carry on using t instead of a + } + + // Copy and round the result to res + residue=1; // indicate dirt to right .. + if (ISZERO(a)) residue=0; // .. unless underflowed to 0 + aset.digits=set->digits; // [use default rounding] + decCopyFit(res, a, &aset, &residue, status); // copy & shorten + decFinish(res, set, &residue, status); // cleanup/set flags + } while(0); // end protected + + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + if (allocbufa!=NULL) free(allocbufa); // .. + if (allocbuft!=NULL) free(allocbuft); // .. + // [status is handled by caller] + return res; + } // decExpOp + +/* ------------------------------------------------------------------ */ +/* Initial-estimate natural logarithm table */ +/* */ +/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ +/* The result is a 4-digit encode of the coefficient (c=the */ +/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ +/* exponent (e=the bottom 2 bits encoding 0-3) */ +/* */ +/* The resulting value is given by: */ +/* */ +/* v = -c * 10**(-e-3) */ +/* */ +/* where e and c are extracted from entry k = LNnn[x-10] */ +/* where x is truncated (NB) into the range 10 through 99, */ +/* and then c = k>>2 and e = k&3. */ +/* ------------------------------------------------------------------ */ +const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, + 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, + 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, + 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, + 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, + 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, + 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, + 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, + 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, + 10130, 6046, 20055}; + +/* ------------------------------------------------------------------ */ +/* decLnOp -- effect natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Restrictions (as for Exp): */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* The result is calculated using Newton's method, with each */ +/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ +/* Epperson 1989. */ +/* */ +/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ +/* This has to be calculated at the sum of the precision of x and the */ +/* working precision. */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decLnOp so it can be called from */ +/* other Mathematical functions (e.g., Log 10) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (+9+2) range needed by a power function. */ +/* */ +/* 2. The speed of this function is about 10x slower than exp, as */ +/* it typically needs 4-6 iterations for short numbers, and the */ +/* extra precision needed adds a squaring effect, twice. */ +/* */ +/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ +/* as these are common requests. ln(10) is used by log10(x). */ +/* */ +/* 4. An iteration might be saved by widening the LNnn table, and */ +/* would certainly save at least one if it were made ten times */ +/* bigger, too (for truncated fractions 0.100 through 0.999). */ +/* However, for most practical evaluations, at least four or five */ +/* iterations will be neede -- so this would only speed up by */ +/* 20-25% and that probably does not justify increasing the table */ +/* size. */ +/* */ +/* 5. The static buffers are larger than might be expected to allow */ +/* for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decLnOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; // working status accumulator + uInt needbytes; // for space calculations + Int residue; // rounding residue + Int r; // rhs=f*10**r [see below] + Int p; // working precision + Int pp; // precision for iteration + Int t; // work + + // buffers for a (accumulator, typically precision+2) and b + // (adjustment calculator, same size) + decNumber bufa[D2N(DECBUFFER+12)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // accumulator/work + decNumber bufb[D2N(DECBUFFER*2+2)]; + decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated + decNumber *b=bufb; // adjustment/work + + decNumber numone; // constant 1 + decNumber cmp; // work + decContext aset, bset; // working contexts + + #if DECCHECK + Int iterations=0; // for later sanity check + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + if (SPECIALARG) { // handle infinities and NaNs + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) // -Infinity -> error + *status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); // +Infinity -> self + } + else decNaNs(res, rhs, NULL, set, status); // a NaN + break;} + + if (ISZERO(rhs)) { // +/- zeros -> -Infinity + decNumberZero(res); // make clean + res->bits=DECINF|DECNEG; // set - infinity + break;} // [no status to set] + + // Non-zero negatives are bad... + if (decNumberIsNegative(rhs)) { // -x -> error + *status|=DEC_Invalid_operation; + break;} + + // Here, rhs is positive, finite, and in range + + // lookaside fastpath code for ln(2) and ln(10) at common lengths + if (rhs->exponent==0 && set->digits<=40) { + #if DECDPUN==1 + if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10) + #else + if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10) + #endif + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN10 "2.302585092994045684017991454684364207601" + decNumberFromString(res, LN10, &aset); + *status|=(DEC_Inexact | DEC_Rounded); // is inexact + break;} + if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2) + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN2 "0.6931471805599453094172321214581765680755" + decNumberFromString(res, LN2, &aset); + *status|=(DEC_Inexact | DEC_Rounded); + break;} + } // integer and short + + // Determine the working precision. This is normally the + // requested precision + 2, with a minimum of 9. However, if + // the rhs is 'over-precise' then allow for all its digits to + // potentially participate (consider an rhs where all the excess + // digits are 9s) so in this case use rhs->digits+2. + p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; + + // Allocate space for the accumulator and the high-precision + // adjustment calculator, if necessary. The accumulator must + // be able to hold p digits, and the adjustment up to + // rhs->digits+p digits. They are also made big enough for 16 + // digits so that they can be used for calculating the initial + // estimate. + needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + pp=p+rhs->digits; + needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + + // Prepare an initial estimate in acc. Calculate this by + // considering the coefficient of x to be a normalized fraction, + // f, with the decimal point at far left and multiplied by + // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and + // ln(x) = ln(f) + ln(10)*r + // Get the initial estimate for ln(f) from a small lookup + // table (see above) indexed by the first two digits of f, + // truncated. + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended + r=rhs->exponent+rhs->digits; // 'normalised' exponent + decNumberFromInt32(a, r); // a=r + decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585) + b->exponent=-6; // .. + decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b + // now get top two digits of rhs into b by simple truncate and + // force to integer + residue=0; // (no residue) + aset.digits=2; aset.round=DEC_ROUND_DOWN; + decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten + b->exponent=0; // make integer + t=decGetInt(b); // [cannot fail] + if (t<10) t=X10(t); // adjust single-digit b + t=LNnn[t-10]; // look up ln(b) + decNumberFromInt32(b, t>>2); // b=ln(b) coefficient + b->exponent=-(t&3)-3; // set exponent + b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve + aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore + decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b + // the initial estimate is now in a, with up to 4 digits correct. + // When rhs is at or near Nmax the estimate will be low, so we + // will approach it from below, avoiding overflow when calling exp. + + decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment + + // accumulator bounds are as requested (could underflow, but + // cannot overflow) + aset.emax=set->emax; + aset.emin=set->emin; + aset.clamp=0; // no concrete format + // set up a context to be used for the multiply and subtract + bset=aset; + bset.emax=DEC_MAX_MATH*2; // use double bounds for the + bset.emin=-DEC_MAX_MATH*2; // adjustment calculation + // [see decExpOp call below] + // for each iteration double the number of digits to calculate, + // up to a maximum of p + pp=9; // initial precision + // [initially 9 as then the sequence starts 7+2, 16+2, and + // 34+2, which is ideal for standard-sized numbers] + aset.digits=pp; // working context + bset.digits=pp+rhs->digits; // wider context + for (;;) { // iterate + #if DECCHECK + iterations++; + if (iterations>24) break; // consider 9 * 2**24 + #endif + // calculate the adjustment (exp(-a)*x-1) into b. This is a + // catastrophic subtraction but it really is the difference + // from 1 that is of interest. + // Use the internal entry point to Exp as it allows the double + // range for calculating exp(-a) when a is the tiniest subnormal. + a->bits^=DECNEG; // make -a + decExpOp(b, a, &bset, &ignore); // b=exp(-a) + a->bits^=DECNEG; // restore sign of a + // now multiply by rhs and subtract 1, at the wider precision + decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs + decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1 + + // the iteration ends when the adjustment cannot affect the + // result by >=0.5 ulp (at the requested digits), which + // is when its value is smaller than the accumulator by + // set->digits+1 digits (or it is zero) -- this is a looser + // requirement than for Exp because all that happens to the + // accumulator after this is the final rounding (but note that + // there must also be full precision in a, or a=0). + + if (decNumberIsZero(b) || + (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { + if (a->digits==p) break; + if (decNumberIsZero(a)) { + decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ? + if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0 + else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact + break; + } + // force padding if adjustment has gone to 0 before full length + if (decNumberIsZero(b)) b->exponent=a->exponent-p; + } + + // not done yet ... + decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate + if (pp==p) continue; // precision is at maximum + // lengthen the next calculation + pp=pp*2; // double precision + if (pp>p) pp=p; // clamp to maximum + aset.digits=pp; // working context + bset.digits=pp+rhs->digits; // wider context + } // Newton's iteration + + #if DECCHECK + // just a sanity check; remove the test to show always + if (iterations>24) + printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); + #endif + + // Copy and round the result to res + residue=1; // indicate dirt to right + if (ISZERO(a)) residue=0; // .. unless underflowed to 0 + aset.digits=set->digits; // [use default rounding] + decCopyFit(res, a, &aset, &residue, status); // copy & shorten + decFinish(res, set, &residue, status); // cleanup/set flags + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + // [status is handled by caller] + return res; + } // decLnOp + +/* ------------------------------------------------------------------ */ +/* decQuantizeOp -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B or matches the exponent of B. */ +/* The numerical value of C will equal A, except for the effects of */ +/* any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* quant is 1 for quantize or 0 for rescale */ +/* status is the status accumulator (this can be called without */ +/* risk of control loss) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be that requested. */ +/* ------------------------------------------------------------------ */ +static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag quant, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + const decNumber *inrhs=rhs; // save original rhs + Int reqdigits=set->digits; // requested DIGITS + Int reqexp; // requested exponent [-scale] + Int residue=0; // rounding residue + Int etiny=set->emin-(reqdigits-1); + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { // [this only checks lostDigits] + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // Handle special values + if (SPECIALARGS) { + // NaNs get usual processing + if (SPECIALARGS & (DECSNAN | DECNAN)) + decNaNs(res, lhs, rhs, set, status); + // one infinity but not both is bad + else if ((lhs->bits ^ rhs->bits) & DECINF) + *status|=DEC_Invalid_operation; + // both infinity: return lhs + else decNumberCopy(res, lhs); // [nop if in place] + break; + } + + // set requested exponent + if (quant) reqexp=inrhs->exponent; // quantize -- match exponents + else { // rescale -- use value of rhs + // Original rhs must be an integer that fits and is in range, + // which could be from -1999999997 to +999999999, thanks to + // subnormals + reqexp=decGetInt(inrhs); // [cannot fail] + } + + #if DECSUBSET + if (!set->extended) etiny=set->emin; // no subnormals + #endif + + if (reqexp==BADINT // bad (rescale only) or .. + || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or .. + || (reqexp<etiny) // < lowest + || (reqexp>set->emax)) { // > emax + *status|=DEC_Invalid_operation; + break;} + + // the RHS has been processed, so it can be overwritten now if necessary + if (ISZERO(lhs)) { // zero coefficient unchanged + decNumberCopy(res, lhs); // [nop if in place] + res->exponent=reqexp; // .. just set exponent + #if DECSUBSET + if (!set->extended) res->bits=0; // subset specification; no -0 + #endif + } + else { // non-zero lhs + Int adjust=reqexp-lhs->exponent; // digit adjustment needed + // if adjusted coefficient will definitely not fit, give up now + if ((lhs->digits-adjust)>reqdigits) { + *status|=DEC_Invalid_operation; + break; + } + + if (adjust>0) { // increasing exponent + // this will decrease the length of the coefficient by adjust + // digits, and must round as it does so + decContext workset; // work + workset=*set; // clone rounding, etc. + workset.digits=lhs->digits-adjust; // set requested length + // [note that the latter can be <1, here] + decCopyFit(res, lhs, &workset, &residue, status); // fit to result + decApplyRound(res, &workset, residue, status); // .. and round + residue=0; // [used] + // If just rounded a 999s case, exponent will be off by one; + // adjust back (after checking space), if so. + if (res->exponent>reqexp) { + // re-check needed, e.g., for quantize(0.9999, 0.001) under + // set->digits==3 + if (res->digits==reqdigits) { // cannot shift by 1 + *status&=~(DEC_Inexact | DEC_Rounded); // [clean these] + *status|=DEC_Invalid_operation; + break; + } + res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift + res->exponent--; // (re)adjust the exponent. + } + #if DECSUBSET + if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0 + #endif + } // increase + else /* adjust<=0 */ { // decreasing or = exponent + // this will increase the length of the coefficient by -adjust + // digits, by adding zero or more trailing zeros; this is + // already checked for fit, above + decNumberCopy(res, lhs); // [it will fit] + // if padding needed (adjust<0), add it now... + if (adjust<0) { + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // adjust the exponent + } + } // decrease + } // non-zero + + // Check for overflow [do not use Finalize in this case, as an + // overflow here is a "don't fit" situation] + if (res->exponent>set->emax-res->digits+1) { // too big + *status|=DEC_Invalid_operation; + break; + } + else { + decFinalize(res, set, &residue, status); // set subnormal flags + *status&=~DEC_Underflow; // suppress Underflow [as per 754] + } + } while(0); // end protected + + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // drop any storage used + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decQuantizeOp + +/* ------------------------------------------------------------------ */ +/* decCompareOp -- compare, min, or max two Numbers */ +/* */ +/* This computes C = A ? B and carries out one of four operations: */ +/* COMPARE -- returns the signum (as a number) giving the */ +/* result of a comparison unless one or both */ +/* operands is a NaN (in which case a NaN results) */ +/* COMPSIG -- as COMPARE except that a quiet NaN raises */ +/* Invalid operation. */ +/* COMPMAX -- returns the larger of the operands, using the */ +/* 754 maxnum operation */ +/* COMPMAXMAG -- ditto, comparing absolute values */ +/* COMPMIN -- the 754 minnum operation */ +/* COMPMINMAG -- ditto, comparing absolute values */ +/* COMTOTAL -- returns the signum (as a number) giving the */ +/* result of a comparison using 754 total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is the operation flag */ +/* status is the usual accumulator */ +/* */ +/* C must have space for one digit for COMPARE or set->digits for */ +/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ +/* ------------------------------------------------------------------ */ +/* The emphasis here is on speed for common cases, and avoiding */ +/* coefficient comparison if possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decCompareOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Int result=0; // default result value + uByte merged; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) {result=BADINT; break;} + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) {result=BADINT; break;} + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // If total ordering then handle differing signs 'up front' + if (op==COMPTOTAL) { // total ordering + if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { + result=-1; + break; + } + if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { + result=+1; + break; + } + } + + // handle NaNs specially; let infinities drop through + // This assumes sNaN (even just one) leads to NaN. + merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); + if (merged) { // a NaN bit set + if (op==COMPARE); // result will be NaN + else if (op==COMPSIG) // treat qNaN as sNaN + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (op==COMPTOTAL) { // total ordering, always finite + // signs are known to be the same; compute the ordering here + // as if the signs are both positive, then invert for negatives + if (!decNumberIsNaN(lhs)) result=-1; + else if (!decNumberIsNaN(rhs)) result=+1; + // here if both NaNs + else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; + else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; + else { // both NaN or both sNaN + // now it just depends on the payload + result=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), 0); + // [Error not possible, as these are 'aligned'] + } // both same NaNs + if (decNumberIsNegative(lhs)) result=-result; + break; + } // total order + + else if (merged & DECSNAN); // sNaN -> qNaN + else { // here if MIN or MAX and one or two quiet NaNs + // min or max -- 754 rules ignore single NaN + if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { + // just one NaN; force choice to be the non-NaN operand + op=COMPMAX; + if (lhs->bits & DECNAN) result=-1; // pick rhs + else result=+1; // pick lhs + break; + } + } // max or min + op=COMPNAN; // use special path + decNaNs(res, lhs, rhs, set, status); // propagate NaN + break; + } + // have numbers + if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); + else result=decCompare(lhs, rhs, 0); // sign matters + } while(0); // end protected + + if (result==BADINT) *status|=DEC_Insufficient_storage; // rare + else { + if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum + if (op==COMPTOTAL && result==0) { + // operands are numerically equal or same NaN (and same sign, + // tested first); if identical, leave result 0 + if (lhs->exponent!=rhs->exponent) { + if (lhs->exponent<rhs->exponent) result=-1; + else result=+1; + if (decNumberIsNegative(lhs)) result=-result; + } // lexp!=rexp + } // total-order by exponent + decNumberZero(res); // [always a valid result] + if (result!=0) { // must be -1 or +1 + *res->lsu=1; + if (result<0) res->bits=DECNEG; + } + } + else if (op==COMPNAN); // special, drop through + else { // MAX or MIN, non-NaN result + Int residue=0; // rounding accumulator + // choose the operand for the result + const decNumber *choice; + if (result==0) { // operands are numerically equal + // choose according to sign then exponent (see 754) + uByte slhs=(lhs->bits & DECNEG); + uByte srhs=(rhs->bits & DECNEG); + #if DECSUBSET + if (!set->extended) { // subset: force left-hand + op=COMPMAX; + result=+1; + } + else + #endif + if (slhs!=srhs) { // signs differ + if (slhs) result=-1; // rhs is max + else result=+1; // lhs is max + } + else if (slhs && srhs) { // both negative + if (lhs->exponent<rhs->exponent) result=+1; + else result=-1; + // [if equal, use lhs, technically identical] + } + else { // both positive + if (lhs->exponent>rhs->exponent) result=+1; + else result=-1; + // [ditto] + } + } // numerically equal + // here result will be non-0; reverse if looking for MIN + if (op==COMPMIN || op==COMPMINMAG) result=-result; + choice=(result>0 ? lhs : rhs); // choose + // copy chosen to result, rounding if need be + decCopyFit(res, choice, set, &residue, status); + decFinish(res, set, &residue, status); + } + } + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // free any storage used + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decCompareOp + +/* ------------------------------------------------------------------ */ +/* decCompare -- compare two decNumbers by numerical value */ +/* */ +/* This routine compares A ? B without altering them. */ +/* */ +/* Arg1 is A, a decNumber which is not a NaN */ +/* Arg2 is B, a decNumber which is not a NaN */ +/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error) */ +/* ------------------------------------------------------------------ */ +static Int decCompare(const decNumber *lhs, const decNumber *rhs, + Flag abs) { + Int result; // result value + Int sigr; // rhs signum + Int compare; // work + + result=1; // assume signum(lhs) + if (ISZERO(lhs)) result=0; + if (abs) { + if (ISZERO(rhs)) return result; // LHS wins or both 0 + // RHS is non-zero + if (result==0) return -1; // LHS is 0; RHS wins + // [here, both non-zero, result=1] + } + else { // signs matter + if (result && decNumberIsNegative(lhs)) result=-1; + sigr=1; // compute signum(rhs) + if (ISZERO(rhs)) sigr=0; + else if (decNumberIsNegative(rhs)) sigr=-1; + if (result > sigr) return +1; // L > R, return 1 + if (result < sigr) return -1; // L < R, return -1 + if (result==0) return 0; // both 0 + } + + // signums are the same; both are non-zero + if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities + if (decNumberIsInfinite(rhs)) { + if (decNumberIsInfinite(lhs)) result=0;// both infinite + else result=-result; // only rhs infinite + } + return result; + } + // must compare the coefficients, allowing for exponents + if (lhs->exponent>rhs->exponent) { // LHS exponent larger + // swap sides, and sign + const decNumber *temp=lhs; + lhs=rhs; + rhs=temp; + result=-result; + } + compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhs->exponent-lhs->exponent); + if (compare!=BADINT) compare*=result; // comparison succeeded + return compare; + } // decCompare + +/* ------------------------------------------------------------------ */ +/* decUnitCompare -- compare two >=0 integers in Unit arrays */ +/* */ +/* This routine compares A ? B*10**E where A and B are unit arrays */ +/* A is a plain integer */ +/* B has an exponent of E (which must be non-negative) */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is E (0 if the units are aligned) */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error, which can */ +/* only occur if E!=0) */ +/* ------------------------------------------------------------------ */ +static Int decUnitCompare(const Unit *a, Int alength, + const Unit *b, Int blength, Int exp) { + Unit *acc; // accumulator for result + Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer + Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated + Int accunits, need; // units in use or needed for acc + const Unit *l, *r, *u; // work + Int expunits, exprem, result; // .. + + if (exp==0) { // aligned; fastpath + if (alength>blength) return 1; + if (alength<blength) return -1; + // same number of units in both -- need unit-by-unit compare + l=a+alength-1; + r=b+alength-1; + for (;l>=a; l--, r--) { + if (*l>*r) return 1; + if (*l<*r) return -1; + } + return 0; // all units match + } // aligned + + // Unaligned. If one is >1 unit longer than the other, padded + // approximately, then can return easily + if (alength>blength+(Int)D2U(exp)) return 1; + if (alength+1<blength+(Int)D2U(exp)) return -1; + + // Need to do a real subtract. For this, a result buffer is needed + // even though only the sign is of interest. Its length needs + // to be the larger of alength and padded blength, +2 + need=blength+D2U(exp); // maximum real length of B + if (need<alength) need=alength; + need+=2; + acc=accbuff; // assume use local buffer + if (need*sizeof(Unit)>sizeof(accbuff)) { + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) return BADINT; // hopeless -- abandon + acc=allocacc; + } + // Calculate units and remainder from exponent. + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + // subtract [A+B*(-m)] + accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, + -(Int)powers[exprem]); + // [UnitAddSub result may have leading zeros, even on zero] + if (accunits<0) result=-1; // negative result + else { // non-negative result + // check units of the result before freeing any storage + for (u=acc; u<acc+accunits-1 && *u==0;) u++; + result=(*u==0 ? 0 : +1); + } + // clean up and return the result + if (allocacc!=NULL) free(allocacc); // drop any storage used + return result; + } // decUnitCompare + +/* ------------------------------------------------------------------ */ +/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ +/* */ +/* This routine performs the calculation: */ +/* */ +/* C=A+(B*M) */ +/* */ +/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ +/* */ +/* A may be shorter or longer than B. */ +/* */ +/* Leading zeros are not removed after a calculation. The result is */ +/* either the same length as the longer of A and B (adding any */ +/* shift), or one Unit longer than that (if a Unit carry occurred). */ +/* */ +/* A and B content are not altered unless C is also A or B. */ +/* C may be the same array as A or B, but only if no zero padding is */ +/* requested (that is, C may be B only if bshift==0). */ +/* C is filled from the lsu; only those units necessary to complete */ +/* the calculation are referenced. */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ +/* Arg6 is C first Unit (lsu) */ +/* Arg7 is M, the multiplier */ +/* */ +/* returns the count of Units written to C, which will be non-zero */ +/* and negated if the result is negative. That is, the sign of the */ +/* returned Int is the sign of the result (positive for zero) and */ +/* the absolute value of the Int is the count of Units. */ +/* */ +/* It is the caller's responsibility to make sure that C size is */ +/* safe, allowing space if necessary for a one-Unit carry. */ +/* */ +/* This routine is severely performance-critical; *any* change here */ +/* must be measured (timed) to assure no performance degradation. */ +/* In particular, trickery here tends to be counter-productive, as */ +/* increased complexity of code hurts register optimizations on */ +/* register-poor architectures. Avoiding divisions is nearly */ +/* always a Good Idea, however. */ +/* */ +/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ +/* (IBM Warwick, UK) for some of the ideas used in this routine. */ +/* ------------------------------------------------------------------ */ +static Int decUnitAddSub(const Unit *a, Int alength, + const Unit *b, Int blength, Int bshift, + Unit *c, Int m) { + const Unit *alsu=a; // A lsu [need to remember it] + Unit *clsu=c; // C ditto + Unit *minC; // low water mark for C + Unit *maxC; // high water mark for C + eInt carry=0; // carry integer (could be Long) + Int add; // work + #if DECDPUN<=4 // myriadal, millenary, etc. + Int est; // estimated quotient + #endif + + #if DECTRACE + if (alength<1 || blength<1) + printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); + #endif + + maxC=c+alength; // A is usually the longer + minC=c+blength; // .. and B the shorter + if (bshift!=0) { // B is shifted; low As copy across + minC+=bshift; + // if in place [common], skip copy unless there's a gap [rare] + if (a==c && bshift<=alength) { + c+=bshift; + a+=bshift; + } + else for (; c<clsu+bshift; a++, c++) { // copy needed + if (a<alsu+alength) *c=*a; + else *c=0; + } + } + if (minC>maxC) { // swap + Unit *hold=minC; + minC=maxC; + maxC=hold; + } + + // For speed, do the addition as two loops; the first where both A + // and B contribute, and the second (if necessary) where only one or + // other of the numbers contribute. + // Carry handling is the same (i.e., duplicated) in each case. + for (; c<minC; c++) { + carry+=*a; + a++; + carry+=((eInt)*b)*m; // [special-casing m=1/-1 + b++; // here is not a win] + // here carry is new Unit of digits; it could be +ve or -ve + if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX + *c=(Unit)carry; + carry=0; + continue; + } + #if DECDPUN==4 // use divide-by-multiply + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [89%] + if (*c<DECDPUNMAX+1) continue; // estimate was correct + carry++; + *c-=DECDPUNMAX+1; + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c<DECDPUNMAX+1) continue; // was OK + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [99%] + if (*c<DECDPUNMAX+1) continue; // estimate was correct + carry++; + *c-=DECDPUNMAX+1; + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c<DECDPUNMAX+1) continue; // was OK + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + // Can use QUOT10 as carry <= 4 digits + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // quotient + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + #else + // remainder operator is undefined if negative, so must test + if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1 + *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions] + carry=1; + continue; + } + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } // c + + // now may have one or other to complete + // [pretest to avoid loop setup/shutdown] + if (c<maxC) for (; c<maxC; c++) { + if (a<alsu+alength) { // still in A + carry+=*a; + a++; + } + else { // inside B + carry+=((eInt)*b)*m; + b++; + } + // here carry is new Unit of digits; it could be +ve or -ve and + // magnitude up to DECDPUNMAX squared + if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX + *c=(Unit)carry; + carry=0; + continue; + } + // result for this unit is negative or >DECDPUNMAX + #if DECDPUN==4 // use divide-by-multiply + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [79.7%] + if (*c<DECDPUNMAX+1) continue; // estimate was correct + carry++; + *c-=DECDPUNMAX+1; + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c<DECDPUNMAX+1) continue; // was OK + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [99%] + if (*c<DECDPUNMAX+1) continue; // estimate was correct + carry++; + *c-=DECDPUNMAX+1; + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c<DECDPUNMAX+1) continue; // was OK + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // quotient + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + #else + if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1 + *c=(Unit)(carry-(DECDPUNMAX+1)); + carry=1; + continue; + } + // remainder operator is undefined if negative, so must test + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } // c + + // OK, all A and B processed; might still have carry or borrow + // return number of Units in the result, negated if a borrow + if (carry==0) return c-clsu; // no carry, so no more to do + if (carry>0) { // positive carry + *c=(Unit)carry; // place as new unit + c++; // .. + return c-clsu; + } + // -ve carry: it's a borrow; complement needed + add=1; // temporary carry... + for (c=clsu; c<maxC; c++) { + add=DECDPUNMAX+add-*c; + if (add<=DECDPUNMAX) { + *c=(Unit)add; + add=0; + } + else { + *c=0; + add=1; + } + } + // add an extra unit iff it would be non-zero + #if DECTRACE + printf("UAS borrow: add %ld, carry %ld\n", add, carry); + #endif + if ((add-carry-1)!=0) { + *c=(Unit)(add-carry-1); + c++; // interesting, include it + } + return clsu-c; // -ve result indicates borrowed + } // decUnitAddSub + +/* ------------------------------------------------------------------ */ +/* decTrim -- trim trailing zeros or normalize */ +/* */ +/* dn is the number to trim or normalize */ +/* set is the context to use to check for clamp */ +/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ +/* noclamp is 1 to unconditional (unclamped) trim */ +/* dropped returns the number of discarded trailing zeros */ +/* returns dn */ +/* */ +/* If clamp is set in the context then the number of zeros trimmed */ +/* may be limited if the exponent is high. */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, + Flag noclamp, Int *dropped) { + Int d, exp; // work + uInt cut; // .. + Unit *up; // -> current Unit + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + *dropped=0; // assume no zeros dropped + if ((dn->bits & DECSPECIAL) // fast exit if special .. + || (*dn->lsu & 0x01)) return dn; // .. or odd + if (ISZERO(dn)) { // .. or 0 + dn->exponent=0; // (sign is preserved) + return dn; + } + + // have a finite number which is even + exp=dn->exponent; + cut=1; // digit (1-DECDPUN) in Unit + up=dn->lsu; // -> current Unit + for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit] + // slice by powers + #if DECDPUN<=4 + uInt quot=QUOT10(*up, cut); + if ((*up-quot*powers[cut])!=0) break; // found non-0 digit + #else + if (*up%powers[cut]!=0) break; // found non-0 digit + #endif + // have a trailing 0 + if (!all) { // trimming + // [if exp>0 then all trailing 0s are significant for trim] + if (exp<=0) { // if digit might be significant + if (exp==0) break; // then quit + exp++; // next digit might be significant + } + } + cut++; // next power + if (cut>DECDPUN) { // need new Unit + up++; + cut=1; + } + } // d + if (d==0) return dn; // none to drop + + // may need to limit drop if clamping + if (set->clamp && !noclamp) { + Int maxd=set->emax-set->digits+1-dn->exponent; + if (maxd<=0) return dn; // nothing possible + if (d>maxd) d=maxd; + } + + // effect the drop + decShiftToLeast(dn->lsu, D2U(dn->digits), d); + dn->exponent+=d; // maintain numerical value + dn->digits-=d; // new length + *dropped=d; // report the count + return dn; + } // decTrim + +/* ------------------------------------------------------------------ */ +/* decReverse -- reverse a Unit array in place */ +/* */ +/* ulo is the start of the array */ +/* uhi is the end of the array (highest Unit to include) */ +/* */ +/* The units ulo through uhi are reversed in place (if the number */ +/* of units is odd, the middle one is untouched). Note that the */ +/* digit(s) in each unit are unaffected. */ +/* ------------------------------------------------------------------ */ +static void decReverse(Unit *ulo, Unit *uhi) { + Unit temp; + for (; ulo<uhi; ulo++, uhi--) { + temp=*ulo; + *ulo=*uhi; + *uhi=temp; + } + return; + } // decReverse + +/* ------------------------------------------------------------------ */ +/* decShiftToMost -- shift digits in array towards most significant */ +/* */ +/* uar is the array */ +/* digits is the count of digits in use in the array */ +/* shift is the number of zeros to pad with (least significant); */ +/* it must be zero or positive */ +/* */ +/* returns the new length of the integer in the array, in digits */ +/* */ +/* No overflow is permitted (that is, the uar array must be known to */ +/* be large enough to hold the result, after shifting). */ +/* ------------------------------------------------------------------ */ +static Int decShiftToMost(Unit *uar, Int digits, Int shift) { + Unit *target, *source, *first; // work + Int cut; // odd 0's to add + uInt next; // work + + if (shift==0) return digits; // [fastpath] nothing to do + if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case + *uar=(Unit)(*uar*powers[shift]); + return digits+shift; + } + + next=0; // all paths + source=uar+D2U(digits)-1; // where msu comes from + target=source+D2U(shift); // where upper part of first cut goes + cut=DECDPUN-MSUDIGITS(shift); // where to slice + if (cut==0) { // unit-boundary case + for (; source>=uar; source--, target--) *target=*source; + } + else { + first=uar+D2U(digits+shift)-1; // where msu of source will end up + for (; source>=uar; source--, target--) { + // split the source Unit and accumulate remainder for next + #if DECDPUN<=4 + uInt quot=QUOT10(*source, cut); + uInt rem=*source-quot*powers[cut]; + next+=quot; + #else + uInt rem=*source%powers[cut]; + next+=*source/powers[cut]; + #endif + if (target<=first) *target=(Unit)next; // write to target iff valid + next=rem*powers[DECDPUN-cut]; // save remainder for next Unit + } + } // shift-move + + // propagate any partial unit to one below and clear the rest + for (; target>=uar; target--) { + *target=(Unit)next; + next=0; + } + return digits+shift; + } // decShiftToMost + +/* ------------------------------------------------------------------ */ +/* decShiftToLeast -- shift digits in array towards least significant */ +/* */ +/* uar is the array */ +/* units is length of the array, in units */ +/* shift is the number of digits to remove from the lsu end; it */ +/* must be zero or positive and <= than units*DECDPUN. */ +/* */ +/* returns the new length of the integer in the array, in units */ +/* */ +/* Removed digits are discarded (lost). Units not required to hold */ +/* the final result are unchanged. */ +/* ------------------------------------------------------------------ */ +static Int decShiftToLeast(Unit *uar, Int units, Int shift) { + Unit *target, *up; // work + Int cut, count; // work + Int quot, rem; // for division + + if (shift==0) return units; // [fastpath] nothing to do + if (shift==units*DECDPUN) { // [fastpath] little to do + *uar=0; // all digits cleared gives zero + return 1; // leaves just the one + } + + target=uar; // both paths + cut=MSUDIGITS(shift); + if (cut==DECDPUN) { // unit-boundary case; easy + up=uar+D2U(shift); + for (; up<uar+units; target++, up++) *target=*up; + return target-uar; + } + + // messier + up=uar+D2U(shift-cut); // source; correct to whole Units + count=units*DECDPUN-shift; // the maximum new length + #if DECDPUN<=4 + quot=QUOT10(*up, cut); + #else + quot=*up/powers[cut]; + #endif + for (; ; target++) { + *target=(Unit)quot; + count-=(DECDPUN-cut); + if (count<=0) break; + up++; + quot=*up; + #if DECDPUN<=4 + quot=QUOT10(quot, cut); + rem=*up-quot*powers[cut]; + #else + rem=quot%powers[cut]; + quot=quot/powers[cut]; + #endif + *target=(Unit)(*target+rem*powers[DECDPUN-cut]); + count-=cut; + if (count<=0) break; + } + return target-uar+1; + } // decShiftToLeast + +#if DECSUBSET +/* ------------------------------------------------------------------ */ +/* decRoundOperand -- round an operand [used for subset only] */ +/* */ +/* dn is the number to round (dn->digits is > set->digits) */ +/* set is the relevant context */ +/* status is the status accumulator */ +/* */ +/* returns an allocated decNumber with the rounded result. */ +/* */ +/* lostDigits and other status may be set by this. */ +/* */ +/* Since the input is an operand, it must not be modified. */ +/* Instead, return an allocated decNumber, rounded as required. */ +/* It is the caller's responsibility to free the allocated storage. */ +/* */ +/* If no storage is available then the result cannot be used, so NULL */ +/* is returned. */ +/* ------------------------------------------------------------------ */ +static decNumber *decRoundOperand(const decNumber *dn, decContext *set, + uInt *status) { + decNumber *res; // result structure + uInt newstatus=0; // status from round + Int residue=0; // rounding accumulator + + // Allocate storage for the returned decNumber, big enough for the + // length specified by the context + res=(decNumber *)malloc(sizeof(decNumber) + +(D2U(set->digits)-1)*sizeof(Unit)); + if (res==NULL) { + *status|=DEC_Insufficient_storage; + return NULL; + } + decCopyFit(res, dn, set, &residue, &newstatus); + decApplyRound(res, set, residue, &newstatus); + + // If that set Inexact then "lost digits" is raised... + if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; + *status|=newstatus; + return res; + } // decRoundOperand +#endif + +/* ------------------------------------------------------------------ */ +/* decCopyFit -- copy a number, truncating the coefficient if needed */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* set is the context [used for length (digits) and rounding mode] */ +/* residue is the residue accumulator */ +/* status contains the current status to be updated */ +/* */ +/* (dest==src is allowed and will be a no-op if fits) */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decCopyFit(decNumber *dest, const decNumber *src, + decContext *set, Int *residue, uInt *status) { + dest->bits=src->bits; + dest->exponent=src->exponent; + decSetCoeff(dest, set, src->lsu, src->digits, residue, status); + } // decCopyFit + +/* ------------------------------------------------------------------ */ +/* decSetCoeff -- set the coefficient of a number */ +/* */ +/* dn is the number whose coefficient array is to be set. */ +/* It must have space for set->digits digits */ +/* set is the context [for size] */ +/* lsu -> lsu of the source coefficient [may be dn->lsu] */ +/* len is digits in the source coefficient [may be dn->digits] */ +/* residue is the residue accumulator. This has values as in */ +/* decApplyRound, and will be unchanged unless the */ +/* target size is less than len. In this case, the */ +/* coefficient is truncated and the residue is updated to */ +/* reflect the previous residue and the dropped digits. */ +/* status is the status accumulator, as usual */ +/* */ +/* The coefficient may already be in the number, or it can be an */ +/* external intermediate array. If it is in the number, lsu must == */ +/* dn->lsu and len must == dn->digits. */ +/* */ +/* Note that the coefficient length (len) may be < set->digits, and */ +/* in this case this merely copies the coefficient (or is a no-op */ +/* if dn->lsu==lsu). */ +/* */ +/* Note also that (only internally, from decQuantizeOp and */ +/* decSetSubnormal) the value of set->digits may be less than one, */ +/* indicating a round to left. This routine handles that case */ +/* correctly; caller ensures space. */ +/* */ +/* dn->digits, dn->lsu (and as required), and dn->exponent are */ +/* updated as necessary. dn->bits (sign) is unchanged. */ +/* */ +/* DEC_Rounded status is set if any digits are discarded. */ +/* DEC_Inexact status is set if any non-zero digits are discarded, or */ +/* incoming residue was non-0 (implies rounded) */ +/* ------------------------------------------------------------------ */ +// mapping array: maps 0-9 to canonical residues, so that a residue +// can be adjusted in the range [-1, +1] and achieve correct rounding +// 0 1 2 3 4 5 6 7 8 9 +static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; +static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, + Int len, Int *residue, uInt *status) { + Int discard; // number of digits to discard + uInt cut; // cut point in Unit + const Unit *up; // work + Unit *target; // .. + Int count; // .. + #if DECDPUN<=4 + uInt temp; // .. + #endif + + discard=len-set->digits; // digits to discard + if (discard<=0) { // no digits are being discarded + if (dn->lsu!=lsu) { // copy needed + // copy the coefficient array to the result number; no shift needed + count=len; // avoids D2U + up=lsu; + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + dn->digits=len; // set the new length + } + // dn->exponent and residue are unchanged, record any inexactitude + if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); + return; + } + + // some digits must be discarded ... + dn->exponent+=discard; // maintain numerical value + *status|=DEC_Rounded; // accumulate Rounded status + if (*residue>1) *residue=1; // previous residue now to right, so reduce + + if (discard>len) { // everything, +1, is being discarded + // guard digit is 0 + // residue is all the number [NB could be all 0s] + if (*residue<=0) { // not already positive + count=len; // avoids D2U + for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0 + *residue=1; + break; // no need to check any others + } + } + if (*residue!=0) *status|=DEC_Inexact; // record inexactitude + *dn->lsu=0; // coefficient will now be 0 + dn->digits=1; // .. + return; + } // total discard + + // partial discard [most common case] + // here, at least the first (most significant) discarded digit exists + + // spin up the number, noting residue during the spin, until get to + // the Unit with the first discarded digit. When reach it, extract + // it and remember its position + count=0; + for (up=lsu;; up++) { + count+=DECDPUN; + if (count>=discard) break; // full ones all checked + if (*up!=0) *residue=1; + } // up + + // here up -> Unit with first discarded digit + cut=discard-(count-DECDPUN)-1; + if (cut==DECDPUN-1) { // unit-boundary case (fast) + Unit half=(Unit)powers[DECDPUN]>>1; + // set residue directly + if (*up>=half) { + if (*up>half) *residue=7; + else *residue+=5; // add sticky bit + } + else { // <half + if (*up!=0) *residue=3; // [else is 0, leave as sticky bit] + } + if (set->digits<=0) { // special for Quantize/Subnormal :-( + *dn->lsu=0; // .. result is 0 + dn->digits=1; // .. + } + else { // shift to least + count=set->digits; // now digits to end up with + dn->digits=count; // set the new length + up++; // move to next + // on unit boundary, so shift-down copy loop is simple + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + } + } // unit-boundary case + + else { // discard digit is in low digit(s), and not top digit + uInt discard1; // first discarded digit + uInt quot, rem; // for divisions + if (cut==0) quot=*up; // is at bottom of unit + else /* cut>0 */ { // it's not at bottom of unit + #if DECDPUN<=4 + quot=QUOT10(*up, cut); + rem=*up-quot*powers[cut]; + #else + rem=*up%powers[cut]; + quot=*up/powers[cut]; + #endif + if (rem!=0) *residue=1; + } + // discard digit is now at bottom of quot + #if DECDPUN<=4 + temp=(quot*6554)>>16; // fast /10 + // Vowels algorithm here not a win (9 instructions) + discard1=quot-X10(temp); + quot=temp; + #else + discard1=quot%10; + quot=quot/10; + #endif + // here, discard1 is the guard digit, and residue is everything + // else [use mapping array to accumulate residue safely] + *residue+=resmap[discard1]; + cut++; // update cut + // here: up -> Unit of the array with bottom digit + // cut is the division point for each Unit + // quot holds the uncut high-order digits for the current unit + if (set->digits<=0) { // special for Quantize/Subnormal :-( + *dn->lsu=0; // .. result is 0 + dn->digits=1; // .. + } + else { // shift to least needed + count=set->digits; // now digits to end up with + dn->digits=count; // set the new length + // shift-copy the coefficient array to the result number + for (target=dn->lsu; ; target++) { + *target=(Unit)quot; + count-=(DECDPUN-cut); + if (count<=0) break; + up++; + quot=*up; + #if DECDPUN<=4 + quot=QUOT10(quot, cut); + rem=*up-quot*powers[cut]; + #else + rem=quot%powers[cut]; + quot=quot/powers[cut]; + #endif + *target=(Unit)(*target+rem*powers[DECDPUN-cut]); + count-=cut; + if (count<=0) break; + } // shift-copy loop + } // shift to least + } // not unit boundary + + if (*residue!=0) *status|=DEC_Inexact; // record inexactitude + return; + } // decSetCoeff + +/* ------------------------------------------------------------------ */ +/* decApplyRound -- apply pending rounding to a number */ +/* */ +/* dn is the number, with space for set->digits digits */ +/* set is the context [for size and rounding mode] */ +/* residue indicates pending rounding, being any accumulated */ +/* guard and sticky information. It may be: */ +/* 6-9: rounding digit is >5 */ +/* 5: rounding digit is exactly half-way */ +/* 1-4: rounding digit is <5 and >0 */ +/* 0: the coefficient is exact */ +/* -1: as 1, but the hidden digits are subtractive, that */ +/* is, of the opposite sign to dn. In this case the */ +/* coefficient must be non-0. This case occurs when */ +/* subtracting a small number (which can be reduced to */ +/* a sticky bit); see decAddOp. */ +/* status is the status accumulator, as usual */ +/* */ +/* This routine applies rounding while keeping the length of the */ +/* coefficient constant. The exponent and status are unchanged */ +/* except if: */ +/* */ +/* -- the coefficient was increased and is all nines (in which */ +/* case Overflow could occur, and is handled directly here so */ +/* the caller does not need to re-test for overflow) */ +/* */ +/* -- the coefficient was decreased and becomes all nines (in which */ +/* case Underflow could occur, and is also handled directly). */ +/* */ +/* All fields in dn are updated as required. */ +/* */ +/* ------------------------------------------------------------------ */ +static void decApplyRound(decNumber *dn, decContext *set, Int residue, + uInt *status) { + Int bump; // 1 if coefficient needs to be incremented + // -1 if coefficient needs to be decremented + + if (residue==0) return; // nothing to apply + + bump=0; // assume a smooth ride + + // now decide whether, and how, to round, depending on mode + switch (set->round) { + case DEC_ROUND_05UP: { // round zero or five up (for reround) + // This is the same as DEC_ROUND_DOWN unless there is a + // positive residue and the lsd of dn is 0 or 5, in which case + // it is bumped; when residue is <0, the number is therefore + // bumped down unless the final digit was 1 or 6 (in which + // case it is bumped down and then up -- a no-op) + Int lsd5=*dn->lsu%5; // get lsd and quintate + if (residue<0 && lsd5!=1) bump=-1; + else if (residue>0 && lsd5==0) bump=1; + // [bump==1 could be applied directly; use common path for clarity] + break;} // r-05 + + case DEC_ROUND_DOWN: { + // no change, except if negative residue + if (residue<0) bump=-1; + break;} // r-d + + case DEC_ROUND_HALF_DOWN: { + if (residue>5) bump=1; + break;} // r-h-d + + case DEC_ROUND_HALF_EVEN: { + if (residue>5) bump=1; // >0.5 goes up + else if (residue==5) { // exactly 0.5000... + // 0.5 goes up iff [new] lsd is odd + if (*dn->lsu & 0x01) bump=1; + } + break;} // r-h-e + + case DEC_ROUND_HALF_UP: { + if (residue>=5) bump=1; + break;} // r-h-u + + case DEC_ROUND_UP: { + if (residue>0) bump=1; + break;} // r-u + + case DEC_ROUND_CEILING: { + // same as _UP for positive numbers, and as _DOWN for negatives + // [negative residue cannot occur on 0] + if (decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} // r-c + + case DEC_ROUND_FLOOR: { + // same as _UP for negative numbers, and as _DOWN for positive + // [negative residue cannot occur on 0] + if (!decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} // r-f + + default: { // e.g., DEC_ROUND_MAX + *status|=DEC_Invalid_context; + #if DECTRACE || (DECCHECK && DECVERB) + printf("Unknown rounding mode: %d\n", set->round); + #endif + break;} + } // switch + + // now bump the number, up or down, if need be + if (bump==0) return; // no action required + + // Simply use decUnitAddSub unless bumping up and the number is + // all nines. In this special case set to 100... explicitly + // and adjust the exponent by one (as otherwise could overflow + // the array) + // Similarly handle all-nines result if bumping down. + if (bump>0) { + Unit *up; // work + uInt count=dn->digits; // digits to be checked + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + // this is the last Unit (the msu) + if (*up!=powers[count]-1) break; // not still 9s + // here if it, too, is all nines + *up=(Unit)powers[count-1]; // here 999 -> 100 etc. + for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0 + dn->exponent++; // and bump exponent + // [which, very rarely, could cause Overflow...] + if ((dn->exponent+dn->digits)>set->emax+1) { + decSetOverflow(dn, set, status); + } + return; // done + } + // a full unit to check, with more to come + if (*up!=DECDPUNMAX) break; // not still 9s + count-=DECDPUN; + } // up + } // bump>0 + else { // -1 + // here checking for a pre-bump of 1000... (leading 1, all + // other digits zero) + Unit *up, *sup; // work + uInt count=dn->digits; // digits to be checked + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + // this is the last Unit (the msu) + if (*up!=powers[count-1]) break; // not 100.. + // here if have the 1000... case + sup=up; // save msu pointer + *up=(Unit)powers[count]-1; // here 100 in msu -> 999 + // others all to all-nines, too + for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; + dn->exponent--; // and bump exponent + + // iff the number was at the subnormal boundary (exponent=etiny) + // then the exponent is now out of range, so it will in fact get + // clamped to etiny and the final 9 dropped. + // printf(">> emin=%d exp=%d sdig=%d\n", set->emin, + // dn->exponent, set->digits); + if (dn->exponent+1==set->emin-set->digits+1) { + if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9] + else { + *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99.. + dn->digits--; + } + dn->exponent++; + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + } + return; // done + } + + // a full unit to check, with more to come + if (*up!=0) break; // not still 0s + count-=DECDPUN; + } // up + + } // bump<0 + + // Actual bump needed. Do it. + decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); + } // decApplyRound + +#if DECSUBSET +/* ------------------------------------------------------------------ */ +/* decFinish -- finish processing a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the accumulator */ +/* */ +/* This finishes off the current number by: */ +/* 1. If not extended: */ +/* a. Converting a zero result to clean '0' */ +/* b. Reducing positive exponents to 0, if would fit in digits */ +/* 2. Checking for overflow and subnormals (always) */ +/* Note this is just Finalize when no subset arithmetic. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinish(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + if (!set->extended) { + if ISZERO(dn) { // value is zero + dn->exponent=0; // clean exponent .. + dn->bits=0; // .. and sign + return; // no error possible + } + if (dn->exponent>=0) { // non-negative exponent + // >0; reduce to integer if possible + if (set->digits >= (dn->exponent+dn->digits)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); + dn->exponent=0; + } + } + } // !extended + + decFinalize(dn, set, residue, status); + } // decFinish +#endif + +/* ------------------------------------------------------------------ */ +/* decFinalize -- final check, clamp, and round of a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the status accumulator */ +/* */ +/* This finishes off the current number by checking for subnormal */ +/* results, applying any pending rounding, checking for overflow, */ +/* and applying any clamping. */ +/* Underflow and overflow conditions are raised as appropriate. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinalize(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + Int shift; // shift needed if clamping + Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary + + // Must be careful, here, when checking the exponent as the + // adjusted exponent could overflow 31 bits [because it may already + // be up to twice the expected]. + + // First test for subnormal. This must be done before any final + // round as the result could be rounded to Nmin or 0. + if (dn->exponent<=tinyexp) { // prefilter + Int comp; + decNumber nmin; + // A very nasty case here is dn == Nmin and residue<0 + if (dn->exponent<tinyexp) { + // Go handle subnormals; this will apply round if needed. + decSetSubnormal(dn, set, residue, status); + return; + } + // Equals case: only subnormal if dn=Nmin and negative residue + decNumberZero(&nmin); + nmin.lsu[0]=1; + nmin.exponent=set->emin; + comp=decCompare(dn, &nmin, 1); // (signless compare) + if (comp==BADINT) { // oops + *status|=DEC_Insufficient_storage; // abandon... + return; + } + if (*residue<0 && comp==0) { // neg residue and dn==Nmin + decApplyRound(dn, set, *residue, status); // might force down + decSetSubnormal(dn, set, residue, status); + return; + } + } + + // now apply any pending round (this could raise overflow). + if (*residue!=0) decApplyRound(dn, set, *residue, status); + + // Check for overflow [redundant in the 'rare' case] or clamp + if (dn->exponent<=set->emax-set->digits+1) return; // neither needed + + + // here when might have an overflow or clamp to do + if (dn->exponent>set->emax-dn->digits+1) { // too big + decSetOverflow(dn, set, status); + return; + } + // here when the result is normal but in clamp range + if (!set->clamp) return; + + // here when need to apply the IEEE exponent clamp (fold-down) + shift=dn->exponent-(set->emax-set->digits+1); + + // shift coefficient (if non-zero) + if (!ISZERO(dn)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); + } + dn->exponent-=shift; // adjust the exponent to match + *status|=DEC_Clamped; // and record the dirty deed + return; + } // decFinalize + +/* ------------------------------------------------------------------ */ +/* decSetOverflow -- set number to proper overflow value */ +/* */ +/* dn is the number (used for sign [only] and result) */ +/* set is the context [used for the rounding mode, etc.] */ +/* status contains the current status to be updated */ +/* */ +/* This sets the sign of a number and sets its value to either */ +/* Infinity or the maximum finite value, depending on the sign of */ +/* dn and the rounding mode, following IEEE 754 rules. */ +/* ------------------------------------------------------------------ */ +static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { + Flag needmax=0; // result is maximum finite value + uByte sign=dn->bits&DECNEG; // clean and save sign bit + + if (ISZERO(dn)) { // zero does not overflow magnitude + Int emax=set->emax; // limit value + if (set->clamp) emax-=set->digits-1; // lower if clamping + if (dn->exponent>emax) { // clamp required + dn->exponent=emax; + *status|=DEC_Clamped; + } + return; + } + + decNumberZero(dn); + switch (set->round) { + case DEC_ROUND_DOWN: { + needmax=1; // never Infinity + break;} // r-d + case DEC_ROUND_05UP: { + needmax=1; // never Infinity + break;} // r-05 + case DEC_ROUND_CEILING: { + if (sign) needmax=1; // Infinity if non-negative + break;} // r-c + case DEC_ROUND_FLOOR: { + if (!sign) needmax=1; // Infinity if negative + break;} // r-f + default: break; // Infinity in all other cases + } + if (needmax) { + decSetMaxValue(dn, set); + dn->bits=sign; // set sign + } + else dn->bits=sign|DECINF; // Value is +/-Infinity + *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; + } // decSetOverflow + +/* ------------------------------------------------------------------ */ +/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ +/* */ +/* dn is the number to set */ +/* set is the context [used for digits and emax] */ +/* */ +/* This sets the number to the maximum positive value. */ +/* ------------------------------------------------------------------ */ +static void decSetMaxValue(decNumber *dn, decContext *set) { + Unit *up; // work + Int count=set->digits; // nines to add + dn->digits=count; + // fill in all nines to set maximum value + for (up=dn->lsu; ; up++) { + if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines + else { // this is the msu + *up=(Unit)(powers[count]-1); + break; + } + count-=DECDPUN; // filled those digits + } // up + dn->bits=0; // + sign + dn->exponent=set->emax-set->digits+1; + } // decSetMaxValue + +/* ------------------------------------------------------------------ */ +/* decSetSubnormal -- process value whose exponent is <Emin */ +/* */ +/* dn is the number (used as input as well as output; it may have */ +/* an allowed subnormal value, which may need to be rounded) */ +/* set is the context [used for the rounding mode] */ +/* residue is any pending residue */ +/* status contains the current status to be updated */ +/* */ +/* If subset mode, set result to zero and set Underflow flags. */ +/* */ +/* Value may be zero with a low exponent; this does not set Subnormal */ +/* but the exponent will be clamped to Etiny. */ +/* */ +/* Otherwise ensure exponent is not out of range, and round as */ +/* necessary. Underflow is set if the result is Inexact. */ +/* ------------------------------------------------------------------ */ +static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + decContext workset; // work + Int etiny, adjust; // .. + + #if DECSUBSET + // simple set to zero and 'hard underflow' for subset + if (!set->extended) { + decNumberZero(dn); + // always full overflow + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + return; + } + #endif + + // Full arithmetic -- allow subnormals, rounded to minimum exponent + // (Etiny) if needed + etiny=set->emin-(set->digits-1); // smallest allowed exponent + + if ISZERO(dn) { // value is zero + // residue can never be non-zero here + #if DECCHECK + if (*residue!=0) { + printf("++ Subnormal 0 residue %ld\n", (LI)*residue); + *status|=DEC_Invalid_operation; + } + #endif + if (dn->exponent<etiny) { // clamp required + dn->exponent=etiny; + *status|=DEC_Clamped; + } + return; + } + + *status|=DEC_Subnormal; // have a non-zero subnormal + adjust=etiny-dn->exponent; // calculate digits to remove + if (adjust<=0) { // not out of range; unrounded + // residue can never be non-zero here, except in the Nmin-residue + // case (which is a subnormal result), so can take fast-path here + // it may already be inexact (from setting the coefficient) + if (*status&DEC_Inexact) *status|=DEC_Underflow; + return; + } + + // adjust>0, so need to rescale the result so exponent becomes Etiny + // [this code is similar to that in rescale] + workset=*set; // clone rounding, etc. + workset.digits=dn->digits-adjust; // set requested length + workset.emin-=adjust; // and adjust emin to match + // [note that the latter can be <1, here, similar to Rescale case] + decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); + decApplyRound(dn, &workset, *residue, status); + + // Use 754 default rule: Underflow is set iff Inexact + // [independent of whether trapped] + if (*status&DEC_Inexact) *status|=DEC_Underflow; + + // if rounded up a 999s case, exponent will be off by one; adjust + // back if so [it will fit, because it was shortened earlier] + if (dn->exponent>etiny) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); + dn->exponent--; // (re)adjust the exponent. + } + + // if rounded to zero, it is by definition clamped... + if (ISZERO(dn)) *status|=DEC_Clamped; + } // decSetSubnormal + +/* ------------------------------------------------------------------ */ +/* decCheckMath - check entry conditions for a math function */ +/* */ +/* This checks the context and the operand */ +/* */ +/* rhs is the operand to check */ +/* set is the context to check */ +/* status is unchanged if both are good */ +/* */ +/* returns non-zero if status is changed, 0 otherwise */ +/* */ +/* Restrictions enforced: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH (999999), and A must be within these bounds if */ +/* non-zero. Invalid_operation is set in the status if a */ +/* restriction is violated. */ +/* ------------------------------------------------------------------ */ +static uInt decCheckMath(const decNumber *rhs, decContext *set, + uInt *status) { + uInt save=*status; // record + if (set->digits>DEC_MAX_MATH + || set->emax>DEC_MAX_MATH + || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; + else if ((rhs->digits>DEC_MAX_MATH + || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 + || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) + && !ISZERO(rhs)) *status|=DEC_Invalid_operation; + return (*status!=save); + } // decCheckMath + +/* ------------------------------------------------------------------ */ +/* decGetInt -- get integer from a number */ +/* */ +/* dn is the number [which will not be altered] */ +/* */ +/* returns one of: */ +/* BADINT if there is a non-zero fraction */ +/* the converted integer */ +/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ +/* BIGODD if the integer is odd and magnitude > 2*10**9 */ +/* */ +/* This checks and gets a whole number from the input decNumber. */ +/* The sign can be determined from dn by the caller when BIGEVEN or */ +/* BIGODD is returned. */ +/* ------------------------------------------------------------------ */ +static Int decGetInt(const decNumber *dn) { + Int theInt; // result accumulator + const Unit *up; // work + Int got; // digits (real or not) processed + Int ilength=dn->digits+dn->exponent; // integral length + Flag neg=decNumberIsNegative(dn); // 1 if -ve + + // The number must be an integer that fits in 10 digits + // Assert, here, that 10 is enough for any rescale Etiny + #if DEC_MAX_EMAX > 999999999 + #error GetInt may need updating [for Emax] + #endif + #if DEC_MIN_EMIN < -999999999 + #error GetInt may need updating [for Emin] + #endif + if (ISZERO(dn)) return 0; // zeros are OK, with any exponent + + up=dn->lsu; // ready for lsu + theInt=0; // ready to accumulate + if (dn->exponent>=0) { // relatively easy + // no fractional part [usual]; allow for positive exponent + got=dn->exponent; + } + else { // -ve exponent; some fractional part to check and discard + Int count=-dn->exponent; // digits to discard + // spin up whole units until reach the Unit with the unit digit + for (; count>=DECDPUN; up++) { + if (*up!=0) return BADINT; // non-zero Unit to discard + count-=DECDPUN; + } + if (count==0) got=0; // [a multiple of DECDPUN] + else { // [not multiple of DECDPUN] + Int rem; // work + // slice off fraction digits and check for non-zero + #if DECDPUN<=4 + theInt=QUOT10(*up, count); + rem=*up-theInt*powers[count]; + #else + rem=*up%powers[count]; // slice off discards + theInt=*up/powers[count]; + #endif + if (rem!=0) return BADINT; // non-zero fraction + // it looks good + got=DECDPUN-count; // number of digits so far + up++; // ready for next + } + } + // now it's known there's no fractional part + + // tricky code now, to accumulate up to 9.3 digits + if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there + + if (ilength<11) { + Int save=theInt; + // collect any remaining unit(s) + for (; got<ilength; up++) { + theInt+=*up*powers[got]; + got+=DECDPUN; + } + if (ilength==10) { // need to check for wrap + if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; + // [that test also disallows the BADINT result case] + else if (neg && theInt>1999999997) ilength=11; + else if (!neg && theInt>999999999) ilength=11; + if (ilength==11) theInt=save; // restore correct low bit + } + } + + if (ilength>10) { // too big + if (theInt&1) return BIGODD; // bottom bit 1 + return BIGEVEN; // bottom bit 0 + } + + if (neg) theInt=-theInt; // apply sign + return theInt; + } // decGetInt + +/* ------------------------------------------------------------------ */ +/* decDecap -- decapitate the coefficient of a number */ +/* */ +/* dn is the number to be decapitated */ +/* drop is the number of digits to be removed from the left of dn; */ +/* this must be <= dn->digits (if equal, the coefficient is */ +/* set to 0) */ +/* */ +/* Returns dn; dn->digits will be <= the initial digits less drop */ +/* (after removing drop digits there may be leading zero digits */ +/* which will also be removed). Only dn->lsu and dn->digits change. */ +/* ------------------------------------------------------------------ */ +static decNumber *decDecap(decNumber *dn, Int drop) { + Unit *msu; // -> target cut point + Int cut; // work + if (drop>=dn->digits) { // losing the whole thing + #if DECCHECK + if (drop>dn->digits) + printf("decDecap called with drop>digits [%ld>%ld]\n", + (LI)drop, (LI)dn->digits); + #endif + dn->lsu[0]=0; + dn->digits=1; + return dn; + } + msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu + cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu + if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits + // that may have left leading zero digits, so do a proper count... + dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); + return dn; + } // decDecap + +/* ------------------------------------------------------------------ */ +/* decBiStr -- compare string with pairwise options */ +/* */ +/* targ is the string to compare */ +/* str1 is one of the strings to compare against (length may be 0) */ +/* str2 is the other; it must be the same length as str1 */ +/* */ +/* returns 1 if strings compare equal, (that is, it is the same */ +/* length as str1 and str2, and each character of targ is in either */ +/* str1 or str2 in the corresponding position), or 0 otherwise */ +/* */ +/* This is used for generic caseless compare, including the awkward */ +/* case of the Turkish dotted and dotless Is. Use as (for example): */ +/* if (decBiStr(test, "mike", "MIKE")) ... */ +/* ------------------------------------------------------------------ */ +static Flag decBiStr(const char *targ, const char *str1, const char *str2) { + for (;;targ++, str1++, str2++) { + if (*targ!=*str1 && *targ!=*str2) return 0; + // *targ has a match in one (or both, if terminator) + if (*targ=='\0') break; + } // forever + return 1; + } // decBiStr + +/* ------------------------------------------------------------------ */ +/* decNaNs -- handle NaN operand or operands */ +/* */ +/* res is the result number */ +/* lhs is the first operand */ +/* rhs is the second operand, or NULL if none */ +/* context is used to limit payload length */ +/* status contains the current status */ +/* returns res in case convenient */ +/* */ +/* Called when one or both operands is a NaN, and propagates the */ +/* appropriate result to res. When an sNaN is found, it is changed */ +/* to a qNaN and Invalid operation is set. */ +/* ------------------------------------------------------------------ */ +static decNumber * decNaNs(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + // This decision tree ends up with LHS being the source pointer, + // and status updated if need be + if (lhs->bits & DECSNAN) + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (rhs==NULL); + else if (rhs->bits & DECSNAN) { + lhs=rhs; + *status|=DEC_Invalid_operation | DEC_sNaN; + } + else if (lhs->bits & DECNAN); + else lhs=rhs; + + // propagate the payload + if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy + else { // too long + const Unit *ul; + Unit *ur, *uresp1; + // copy safe number of units, then decapitate + res->bits=lhs->bits; // need sign etc. + uresp1=res->lsu+D2U(set->digits); + for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; + res->digits=D2U(set->digits)*DECDPUN; + // maybe still too long + if (res->digits>set->digits) decDecap(res, res->digits-set->digits); + } + + res->bits&=~DECSNAN; // convert any sNaN to NaN, while + res->bits|=DECNAN; // .. preserving sign + res->exponent=0; // clean exponent + // [coefficient was copied/decapitated] + return res; + } // decNaNs + +/* ------------------------------------------------------------------ */ +/* decStatus -- apply non-zero status */ +/* */ +/* dn is the number to set if error */ +/* status contains the current status (not yet in context) */ +/* set is the context */ +/* */ +/* If the status is an error status, the number is set to a NaN, */ +/* unless the error was an overflow, divide-by-zero, or underflow, */ +/* in which case the number will have already been set. */ +/* */ +/* The context status is then updated with the new status. Note that */ +/* this may raise a signal, so control may never return from this */ +/* routine (hence resources must be recovered before it is called). */ +/* ------------------------------------------------------------------ */ +static void decStatus(decNumber *dn, uInt status, decContext *set) { + if (status & DEC_NaNs) { // error status -> NaN + // if cause was an sNaN, clear and propagate [NaN is already set up] + if (status & DEC_sNaN) status&=~DEC_sNaN; + else { + decNumberZero(dn); // other error: clean throughout + dn->bits=DECNAN; // and make a quiet NaN + } + } + decContextSetStatus(set, status); // [may not return] + return; + } // decStatus + +/* ------------------------------------------------------------------ */ +/* decGetDigits -- count digits in a Units array */ +/* */ +/* uar is the Unit array holding the number (this is often an */ +/* accumulator of some sort) */ +/* len is the length of the array in units [>=1] */ +/* */ +/* returns the number of (significant) digits in the array */ +/* */ +/* All leading zeros are excluded, except the last if the array has */ +/* only zero Units. */ +/* ------------------------------------------------------------------ */ +// This may be called twice during some operations. +static Int decGetDigits(Unit *uar, Int len) { + Unit *up=uar+(len-1); // -> msu + Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu + #if DECDPUN>4 + uInt const *pow; // work + #endif + // (at least 1 in final msu) + #if DECCHECK + if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); + #endif + + for (; up>=uar; up--) { + if (*up==0) { // unit is all 0s + if (digits==1) break; // a zero has one digit + digits-=DECDPUN; // adjust for 0 unit + continue;} + // found the first (most significant) non-zero Unit + #if DECDPUN>1 // not done yet + if (*up<10) break; // is 1-9 + digits++; + #if DECDPUN>2 // not done yet + if (*up<100) break; // is 10-99 + digits++; + #if DECDPUN>3 // not done yet + if (*up<1000) break; // is 100-999 + digits++; + #if DECDPUN>4 // count the rest ... + for (pow=&powers[4]; *up>=*pow; pow++) digits++; + #endif + #endif + #endif + #endif + break; + } // up + return digits; + } // decGetDigits + +#if DECTRACE | DECCHECK +/* ------------------------------------------------------------------ */ +/* decNumberShow -- display a number [debug aid] */ +/* dn is the number to show */ +/* */ +/* Shows: sign, exponent, coefficient (msu first), digits */ +/* or: sign, special-value */ +/* ------------------------------------------------------------------ */ +// this is public so other modules can use it +void decNumberShow(const decNumber *dn) { + const Unit *up; // work + uInt u, d; // .. + Int cut; // .. + char isign='+'; // main sign + if (dn==NULL) { + printf("NULL\n"); + return;} + if (decNumberIsNegative(dn)) isign='-'; + printf(" >> %c ", isign); + if (dn->bits&DECSPECIAL) { // Is a special value + if (decNumberIsInfinite(dn)) printf("Infinity"); + else { // a NaN + if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN + else printf("NaN"); + } + // if coefficient and exponent are 0, no more to do + if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { + printf("\n"); + return;} + // drop through to report other information + printf(" "); + } + + // now carefully display the coefficient + up=dn->lsu+D2U(dn->digits)-1; // msu + printf("%ld", (LI)*up); + for (up=up-1; up>=dn->lsu; up--) { + u=*up; + printf(":"); + for (cut=DECDPUN-1; cut>=0; cut--) { + d=u/powers[cut]; + u-=d*powers[cut]; + printf("%ld", (LI)d); + } // cut + } // up + if (dn->exponent!=0) { + char esign='+'; + if (dn->exponent<0) esign='-'; + printf(" E%c%ld", esign, (LI)abs(dn->exponent)); + } + printf(" [%ld]\n", (LI)dn->digits); + } // decNumberShow +#endif + +#if DECTRACE || DECCHECK +/* ------------------------------------------------------------------ */ +/* decDumpAr -- display a unit array [debug/check aid] */ +/* name is a single-character tag name */ +/* ar is the array to display */ +/* len is the length of the array in Units */ +/* ------------------------------------------------------------------ */ +static void decDumpAr(char name, const Unit *ar, Int len) { + Int i; + const char *spec; + #if DECDPUN==9 + spec="%09d "; + #elif DECDPUN==8 + spec="%08d "; + #elif DECDPUN==7 + spec="%07d "; + #elif DECDPUN==6 + spec="%06d "; + #elif DECDPUN==5 + spec="%05d "; + #elif DECDPUN==4 + spec="%04d "; + #elif DECDPUN==3 + spec="%03d "; + #elif DECDPUN==2 + spec="%02d "; + #else + spec="%d "; + #endif + printf(" :%c: ", name); + for (i=len-1; i>=0; i--) { + if (i==len-1) printf("%ld ", (LI)ar[i]); + else printf(spec, ar[i]); + } + printf("\n"); + return;} +#endif + +#if DECCHECK +/* ------------------------------------------------------------------ */ +/* decCheckOperands -- check operand(s) to a routine */ +/* res is the result structure (not checked; it will be set to */ +/* quiet NaN if error found (and it is not NULL)) */ +/* lhs is the first operand (may be DECUNRESU) */ +/* rhs is the second (may be DECUNUSED) */ +/* set is the context (may be DECUNCONT) */ +/* returns 0 if both operands, and the context are clean, or 1 */ +/* otherwise (in which case the context will show an error, */ +/* unless NULL). Note that res is not cleaned; caller should */ +/* handle this so res=NULL case is safe. */ +/* The caller is expected to abandon immediately if 1 is returned. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckOperands(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Flag bad=0; + if (set==NULL) { // oops; hopeless + #if DECTRACE || DECVERB + printf("Reference to context is NULL.\n"); + #endif + bad=1; + return 1;} + else if (set!=DECUNCONT + && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { + bad=1; + #if DECTRACE || DECVERB + printf("Bad context [digits=%ld round=%ld].\n", + (LI)set->digits, (LI)set->round); + #endif + } + else { + if (res==NULL) { + bad=1; + #if DECTRACE + // this one not DECVERB as standard tests include NULL + printf("Reference to result is NULL.\n"); + #endif + } + if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); + if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); + } + if (bad) { + if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); + if (res!=DECUNRESU && res!=NULL) { + decNumberZero(res); + res->bits=DECNAN; // qNaN + } + } + return bad; + } // decCheckOperands + +/* ------------------------------------------------------------------ */ +/* decCheckNumber -- check a number */ +/* dn is the number to check */ +/* returns 0 if the number is clean, or 1 otherwise */ +/* */ +/* The number is considered valid if it could be a result from some */ +/* operation in some valid context. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckNumber(const decNumber *dn) { + const Unit *up; // work + uInt maxuint; // .. + Int ae, d, digits; // .. + Int emin, emax; // .. + + if (dn==NULL) { // hopeless + #if DECTRACE + // this one not DECVERB as standard tests include NULL + printf("Reference to decNumber is NULL.\n"); + #endif + return 1;} + + // check special values + if (dn->bits & DECSPECIAL) { + if (dn->exponent!=0) { + #if DECTRACE || DECVERB + printf("Exponent %ld (not 0) for a special value [%02x].\n", + (LI)dn->exponent, dn->bits); + #endif + return 1;} + + // 2003.09.08: NaNs may now have coefficients, so next tests Inf only + if (decNumberIsInfinite(dn)) { + if (dn->digits!=1) { + #if DECTRACE || DECVERB + printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); + #endif + return 1;} + if (*dn->lsu!=0) { + #if DECTRACE || DECVERB + printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); + #endif + decDumpAr('I', dn->lsu, D2U(dn->digits)); + return 1;} + } // Inf + // 2002.12.26: negative NaNs can now appear through proposed IEEE + // concrete formats (decimal64, etc.). + return 0; + } + + // check the coefficient + if (dn->digits<1 || dn->digits>DECNUMMAXP) { + #if DECTRACE || DECVERB + printf("Digits %ld in number.\n", (LI)dn->digits); + #endif + return 1;} + + d=dn->digits; + + for (up=dn->lsu; d>0; up++) { + if (d>DECDPUN) maxuint=DECDPUNMAX; + else { // reached the msu + maxuint=powers[d]-1; + if (dn->digits>1 && *up<powers[d-1]) { + #if DECTRACE || DECVERB + printf("Leading 0 in number.\n"); + decNumberShow(dn); + #endif + return 1;} + } + if (*up>maxuint) { + #if DECTRACE || DECVERB + printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", + (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); + #endif + return 1;} + d-=DECDPUN; + } + + // check the exponent. Note that input operands can have exponents + // which are out of the set->emin/set->emax and set->digits range + // (just as they can have more digits than set->digits). + ae=dn->exponent+dn->digits-1; // adjusted exponent + emax=DECNUMMAXE; + emin=DECNUMMINE; + digits=DECNUMMAXP; + if (ae<emin-(digits-1)) { + #if DECTRACE || DECVERB + printf("Adjusted exponent underflow [%ld].\n", (LI)ae); + decNumberShow(dn); + #endif + return 1;} + if (ae>+emax) { + #if DECTRACE || DECVERB + printf("Adjusted exponent overflow [%ld].\n", (LI)ae); + decNumberShow(dn); + #endif + return 1;} + + return 0; // it's OK + } // decCheckNumber + +/* ------------------------------------------------------------------ */ +/* decCheckInexact -- check a normal finite inexact result has digits */ +/* dn is the number to check */ +/* set is the context (for status and precision) */ +/* sets Invalid operation, etc., if some digits are missing */ +/* [this check is not made for DECSUBSET compilation or when */ +/* subnormal is not set] */ +/* ------------------------------------------------------------------ */ +static void decCheckInexact(const decNumber *dn, decContext *set) { + #if !DECSUBSET && DECEXTFLAG + if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact + && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { + #if DECTRACE || DECVERB + printf("Insufficient digits [%ld] on normal Inexact result.\n", + (LI)dn->digits); + decNumberShow(dn); + #endif + decContextSetStatus(set, DEC_Invalid_operation); + } + #else + // next is a noop for quiet compiler + if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; + #endif + return; + } // decCheckInexact +#endif + +#if DECALLOC +#undef malloc +#undef free +/* ------------------------------------------------------------------ */ +/* decMalloc -- accountable allocation routine */ +/* n is the number of bytes to allocate */ +/* */ +/* Semantics is the same as the stdlib malloc routine, but bytes */ +/* allocated are accounted for globally, and corruption fences are */ +/* added before and after the 'actual' storage. */ +/* ------------------------------------------------------------------ */ +/* This routine allocates storage with an extra twelve bytes; 8 are */ +/* at the start and hold: */ +/* 0-3 the original length requested */ +/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ +/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ +/* ------------------------------------------------------------------ */ +static void *decMalloc(size_t n) { + uInt size=n+12; // true size + void *alloc; // -> allocated storage + uByte *b, *b0; // work + uInt uiwork; // for macros + + alloc=malloc(size); // -> allocated storage + if (alloc==NULL) return NULL; // out of strorage + b0=(uByte *)alloc; // as bytes + decAllocBytes+=n; // account for storage + UBFROMUI(alloc, n); // save n + // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); + for (b=b0+4; b<b0+8; b++) *b=DECFENCE; + for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; + return b0+8; // -> play area + } // decMalloc + +/* ------------------------------------------------------------------ */ +/* decFree -- accountable free routine */ +/* alloc is the storage to free */ +/* */ +/* Semantics is the same as the stdlib malloc routine, except that */ +/* the global storage accounting is updated and the fences are */ +/* checked to ensure that no routine has written 'out of bounds'. */ +/* ------------------------------------------------------------------ */ +/* This routine first checks that the fences have not been corrupted. */ +/* It then frees the storage using the 'truw' storage address (that */ +/* is, offset by 8). */ +/* ------------------------------------------------------------------ */ +static void decFree(void *alloc) { + uInt n; // original length + uByte *b, *b0; // work + uInt uiwork; // for macros + + if (alloc==NULL) return; // allowed; it's a nop + b0=(uByte *)alloc; // as bytes + b0-=8; // -> true start of storage + n=UBTOUI(b0); // lift length + for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) + printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, + b-b0-8, (LI)b0); + for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) + printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, + b-b0-8, (LI)b0, (LI)n); + free(b0); // drop the storage + decAllocBytes-=n; // account for storage + // printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); + } // decFree +#define malloc(a) decMalloc(a) +#define free(a) decFree(a) +#endif |