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decNumber.c
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decNumber.c
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/* Decimal number arithmetic module for the decNumber C Library.
Copyright (C) 2005, 2007, 2009 Free Software Foundation, Inc.
Contributed by IBM Corporation. Author Mike Cowlishaw.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module */
/* ------------------------------------------------------------------ */
/* 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 "dconfig.h" /* for GCC definitions */
#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
#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] */
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 */
free(allocbufa); /* drop any storage used */
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 */