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Retro68/gcc/libdecnumber/decNumber.c
Wolfgang Thaller 0a883ac4aa upgrade gcc to 6.3.0, binutils to 2.28
2017-04-10 13:32:00 +02:00

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/* Decimal number arithmetic module for the decNumber C Library.
Copyright (C) 2005-2016 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 */
/* ------------------------------------------------------------------ */
/* 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
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 */
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
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 */
/* */
/* C must have space for 10 digits (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 */
decNumberFromInt32(res, ae); /* lay it out */
}
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, &copystat); /* 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] */
free(allocbufa); /* drop any storage used */
free(allocbufb); /* .. */
#if DECSUBSET
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 */
free(allocdac); /* drop any storage used */
free(allocinv); /* .. */
#if DECSUBSET
free(alloclhs); /* .. */
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
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] */
if (reqexp==BADINT /* something bad .. */
|| reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */
|| abs(reqexp)>(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 */
res->exponent+=reqexp; /* adjust the exponent */
residue=0;
decFinalize(res, set, &residue, &status); /* .. and 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 */
free(allocbuff); /* drop any storage used */
free(allocbufa); /* .. */
free(allocbufb); /* .. */
#if DECSUBSET
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 */
free(allocacc); /* drop any storage used */
#if DECSUBSET
free(allocrhs); /* .. */
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 */
free(varalloc); /* drop any storage used */
free(allocacc); /* .. */
#if DECSUBSET
free(allocrhs); /* .. */
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 */
free(allocacc); /* drop any storage used */
#if DECSUBSET
free(allocrhs); /* .. */
free(alloclhs); /* .. */
#endif
#if FASTMUL
free(allocrhi); /* .. */
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 */
free(allocrhs); /* drop any storage used */
free(allocbufa); /* .. */
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 */
free(allocbufa); /* drop any storage used */
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
free(allocrhs); /* drop any storage used */
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
free(allocrhs); /* free any storage used */
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 */
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
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