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decNumber.c
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/* Decimal number arithmetic module for the decNumber C Library.
Copyright (C) 2005, 2007 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 2, or (at your option) any later
version.
In addition to the permissions in the GNU General Public License,
the Free Software Foundation gives you unlimited permission to link
the compiled version of this file into combinations with other
programs, and to distribute those combinations without any
restriction coming from the use of this file. (The General Public
License restrictions do apply in other respects; for example, they
cover modification of the file, and distribution when not linked
into a combine executable.)
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.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING. If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for General Decimal Arithmetic */
/* as defined in the specification which may be found on the */
/* http://www2.hursley.ibm.com/decimal web pages. It implements both */
/* the full ('extended') arithmetic and the simpler ('subset') */
/* arithmetic. */
/* */
/* Usage notes: */
/* */
/* 1. This code is ANSI C89 except: */
/* */
/* 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). */
/* */
/* 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 "qemu/osdep.h"
#include "qemu/host-utils.h"
#include "libdecnumber/dconfig.h"
#include "libdecnumber/decNumber.h"
#include "libdecnumber/decNumberLocal.h"
/* 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, Int *);
static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
Unit *, Int);
static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
static bool mulUInt128ByPowOf10(uLong *, uLong *, uInt);
#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 */
decNumber *decNumberFromInt64(decNumber *dn, int64_t in)
{
uint64_t unsig = in;
if (in < 0) {
unsig = -unsig;
}
decNumberFromUInt64(dn, unsig);
if (in < 0) {
dn->bits = DECNEG; /* sign needed */
}
return dn;
} /* decNumberFromInt64 */
decNumber *decNumberFromUInt64(decNumber *dn, uint64_t 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;
} /* decNumberFromUInt64 */
decNumber *decNumberFromInt128(decNumber *dn, uint64_t lo, int64_t hi)
{
uint64_t unsig_hi = hi;
if (hi < 0) {
if (lo == 0) {
unsig_hi = -unsig_hi;
} else {
unsig_hi = ~unsig_hi;
lo = -lo;
}
}
decNumberFromUInt128(dn, lo, unsig_hi);
if (hi < 0) {
dn->bits = DECNEG; /* sign needed */
}
return dn;
} /* decNumberFromInt128 */
decNumber *decNumberFromUInt128(decNumber *dn, uint64_t lo, uint64_t hi)
{
uint64_t rem;
Unit *up; /* work pointer */
decNumberZero(dn); /* clean */
if (lo == 0 && hi == 0) {
return dn; /* [or decGetDigits bad call] */
}
for (up = dn->lsu; hi > 0 || lo > 0; up++) {
rem = divu128(&lo, &hi, DECDPUNMAX + 1);
*up = (Unit)rem;
}
dn->digits = decGetDigits(dn->lsu, up - dn->lsu);
return dn;
} /* decNumberFromUInt128 */
/* ------------------------------------------------------------------ */
/* to-int64 -- conversion to int64 */
/* */
/* dn is the decNumber to convert. dn is assumed to have been */
/* rounded to a floating point integer value. */
/* set is the context for reporting errors */
/* returns the converted decNumber, or 0 if Invalid is set */
/* */
/* Invalid is set if the decNumber is a NaN, Infinite or is out of */
/* range for a signed 64 bit integer. */
/* ------------------------------------------------------------------ */
int64_t decNumberIntegralToInt64(const decNumber *dn, decContext *set)
{
if (decNumberIsSpecial(dn) || (dn->exponent < 0) ||
(dn->digits + dn->exponent > 19)) {
goto Invalid;
} else {
int64_t d; /* work */
const Unit *up; /* .. */
uint64_t hi = 0;
up = dn->lsu; /* -> lsu */
for (d = 1; d <= dn->digits; up++, d += DECDPUN) {
uint64_t prev = hi;
hi += *up * powers[d-1];
if ((hi < prev) || (hi > INT64_MAX)) {
goto Invalid;
}
}
uint64_t prev = hi;
hi *= (uint64_t)powers[dn->exponent];
if ((hi < prev) || (hi > INT64_MAX)) {
goto Invalid;
}
return (decNumberIsNegative(dn)) ? -((int64_t)hi) : (int64_t)hi;
}
Invalid:
decContextSetStatus(set, DEC_Invalid_operation);
return 0;
} /* decNumberIntegralToInt64 */
/* ------------------------------------------------------------------ */
/* decNumberIntegralToInt128 -- conversion to int128 */
/* */
/* dn is the decNumber to convert. dn is assumed to have been */
/* rounded to a floating point integer value. */
/* set is the context for reporting errors */
/* returns the converted decNumber via plow and phigh */
/* */
/* Invalid is set if the decNumber is a NaN, Infinite or is out of */
/* range for a signed 128 bit integer. */
/* ------------------------------------------------------------------ */
void decNumberIntegralToInt128(const decNumber *dn, decContext *set,
uint64_t *plow, uint64_t *phigh)
{
int d; /* work */
const Unit *up; /* .. */
uint64_t lo = 0, hi = 0;
if (decNumberIsSpecial(dn) || (dn->exponent < 0) ||
(dn->digits + dn->exponent > 39)) {
goto Invalid;
}
up = dn->lsu; /* -> lsu */
for (d = (dn->digits - 1) / DECDPUN; d >= 0; d--) {
if (mulu128(&lo, &hi, DECDPUNMAX + 1)) {
/* overflow */
goto Invalid;
}
if (uadd64_overflow(lo, up[d], &lo)) {
if (uadd64_overflow(hi, 1, &hi)) {
/* overflow */
goto Invalid;
}
}
}
if (mulUInt128ByPowOf10(&lo, &hi, dn->exponent)) {
/* overflow */
goto Invalid;
}
if (decNumberIsNegative(dn)) {
if (lo == 0) {
*phigh = -hi;
*plow = 0;
} else {
*phigh = ~hi;
*plow = -lo;
}
} else {
*plow = lo;
*phigh = hi;
}
return;
Invalid:
decContextSetStatus(set, DEC_Invalid_operation);
} /* decNumberIntegralToInt128 */
/* ------------------------------------------------------------------ */
/* 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;