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Diffstat (limited to 'libdecnumber/decNumber.c')
| -rw-r--r-- | libdecnumber/decNumber.c | 8122 |
1 files changed, 8122 insertions, 0 deletions
diff --git a/libdecnumber/decNumber.c b/libdecnumber/decNumber.c new file mode 100644 index 0000000..c5e223c --- /dev/null +++ b/libdecnumber/decNumber.c @@ -0,0 +1,8122 @@ +/* Decimal number arithmetic module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal Number arithmetic module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for General Decimal Arithmetic */ +/* as defined in the specification which may be found on the */ +/* http://www2.hursley.ibm.com/decimal web pages. It implements both */ +/* the full ('extended') arithmetic and the simpler ('subset') */ +/* arithmetic. */ +/* */ +/* Usage notes: */ +/* */ +/* 1. This code is ANSI C89 except: */ +/* */ +/* If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ +/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ +/* and DECDPUN<=4 (see documentation). */ +/* */ +/* 2. The decNumber format which this library uses is optimized for */ +/* efficient processing of relatively short numbers; in particular */ +/* it allows the use of fixed sized structures and minimizes copy */ +/* and move operations. It does, however, support arbitrary */ +/* precision (up to 999,999,999 digits) and arbitrary exponent */ +/* range (Emax in the range 0 through 999,999,999 and Emin in the */ +/* range -999,999,999 through 0). Mathematical functions (for */ +/* example decNumberExp) as identified below are restricted more */ +/* tightly: digits, emax, and -emin in the context must be <= */ +/* DEC_MAX_MATH (999999), and their operand(s) must be within */ +/* these bounds. */ +/* */ +/* 3. Logical functions are further restricted; their operands must */ +/* be finite, positive, have an exponent of zero, and all digits */ +/* must be either 0 or 1. The result will only contain digits */ +/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ +/* */ +/* 4. Operands to operator functions are never modified unless they */ +/* are also specified to be the result number (which is always */ +/* permitted). Other than that case, operands must not overlap. */ +/* */ +/* 5. Error handling: the type of the error is ORed into the status */ +/* flags in the current context (decContext structure). The */ +/* SIGFPE signal is then raised if the corresponding trap-enabler */ +/* flag in the decContext is set (is 1). */ +/* */ +/* It is the responsibility of the caller to clear the status */ +/* flags as required. */ +/* */ +/* The result of any routine which returns a number will always */ +/* be a valid number (which may be a special value, such as an */ +/* Infinity or NaN). */ +/* */ +/* 6. The decNumber format is not an exchangeable concrete */ +/* representation as it comprises fields which may be machine- */ +/* dependent (packed or unpacked, or special length, for example). */ +/* Canonical conversions to and from strings are provided; other */ +/* conversions are available in separate modules. */ +/* */ +/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ +/* to 1 for extended operand checking (including NULL operands). */ +/* Results are undefined if a badly-formed structure (or a NULL */ +/* pointer to a structure) is provided, though with DECCHECK */ +/* enabled the operator routines are protected against exceptions. */ +/* (Except if the result pointer is NULL, which is unrecoverable.) */ +/* */ +/* However, the routines will never cause exceptions if they are */ +/* given well-formed operands, even if the value of the operands */ +/* is inappropriate for the operation and DECCHECK is not set. */ +/* (Except for SIGFPE, as and where documented.) */ +/* */ +/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ +/* ------------------------------------------------------------------ */ +/* Implementation notes for maintenance of this module: */ +/* */ +/* 1. Storage leak protection: Routines which use malloc are not */ +/* permitted to use return for fastpath or error exits (i.e., */ +/* they follow strict structured programming conventions). */ +/* Instead they have a do{}while(0); construct surrounding the */ +/* code which is protected -- break may be used to exit this. */ +/* Other routines can safely use the return statement inline. */ +/* */ +/* Storage leak accounting can be enabled using DECALLOC. */ +/* */ +/* 2. All loops use the for(;;) construct. Any do construct does */ +/* not loop; it is for allocation protection as just described. */ +/* */ +/* 3. Setting status in the context must always be the very last */ +/* action in a routine, as non-0 status may raise a trap and hence */ +/* the call to set status may not return (if the handler uses long */ +/* jump). Therefore all cleanup must be done first. In general, */ +/* to achieve this status is accumulated and is only applied just */ +/* before return by calling decContextSetStatus (via decStatus). */ +/* */ +/* Routines which allocate storage cannot, in general, use the */ +/* 'top level' routines which could cause a non-returning */ +/* transfer of control. The decXxxxOp routines are safe (do not */ +/* call decStatus even if traps are set in the context) and should */ +/* be used instead (they are also a little faster). */ +/* */ +/* 4. Exponent checking is minimized by allowing the exponent to */ +/* grow outside its limits during calculations, provided that */ +/* the decFinalize function is called later. Multiplication and */ +/* division, and intermediate calculations in exponentiation, */ +/* require more careful checks because of the risk of 31-bit */ +/* overflow (the most negative valid exponent is -1999999997, for */ +/* a 999999999-digit number with adjusted exponent of -999999999). */ +/* */ +/* 5. Rounding is deferred until finalization of results, with any */ +/* 'off to the right' data being represented as a single digit */ +/* residue (in the range -1 through 9). This avoids any double- */ +/* rounding when more than one shortening takes place (for */ +/* example, when a result is subnormal). */ +/* */ +/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ +/* during many operations, so whole Units are handled and exact */ +/* accounting of digits is not needed. The correct digits value */ +/* is found by decGetDigits, which accounts for leading zeros. */ +/* This must be called before any rounding if the number of digits */ +/* is not known exactly. */ +/* */ +/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ +/* numbers up to four digits, using appropriate constants. This */ +/* is not useful for longer numbers because overflow of 32 bits */ +/* would lead to 4 multiplies, which is almost as expensive as */ +/* a divide (unless a floating-point or 64-bit multiply is */ +/* assumed to be available). */ +/* */ +/* 8. Unusual abbreviations that may be used in the commentary: */ +/* lhs -- left hand side (operand, of an operation) */ +/* lsd -- least significant digit (of coefficient) */ +/* lsu -- least significant Unit (of coefficient) */ +/* msd -- most significant digit (of coefficient) */ +/* msi -- most significant item (in an array) */ +/* msu -- most significant Unit (of coefficient) */ +/* rhs -- right hand side (operand, of an operation) */ +/* +ve -- positive */ +/* -ve -- negative */ +/* ** -- raise to the power */ +/* ------------------------------------------------------------------ */ + +#include <stdlib.h> /* for malloc, free, etc. */ +#include <stdio.h> /* for printf [if needed] */ +#include <string.h> /* for strcpy */ +#include <ctype.h> /* for lower */ +#include "config.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, 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] */ + + if (allocres!=NULL) free(allocres); /* drop any storage used */ + if (status!=0) decStatus(dn, status, set); + return dn; + } /* decNumberFromString */ + +/* ================================================================== */ +/* Operators */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberAbs -- absolute value operator */ +/* */ +/* This computes C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyAbs for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This has the same effect as decNumberPlus unless A is negative, */ +/* in which case it has the same effect as decNumberMinus. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; /* for 0 */ + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); /* set 0 */ + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ + decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberAbs */ + +/* ------------------------------------------------------------------ */ +/* decNumberAdd -- add two Numbers */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This just calls the routine shared with Subtract */ +decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decAddOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberAdd */ + +/* ------------------------------------------------------------------ */ +/* decNumberAnd -- AND two Numbers, digitwise */ +/* */ +/* This computes C = A & B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; /* -> operands */ + const Unit *msua, *msub; /* -> operand msus */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + + /* operands are valid */ + ua=lhs->lsu; /* bottom-up */ + ub=rhs->lsu; /* .. */ + uc=res->lsu; /* .. */ + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ + Unit a, b; /* extract units */ + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; /* can now write back */ + if (a|b) { /* maybe 1 bits to examine */ + Int i, j; + *uc=0; /* can now write back */ + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* both OK */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberAnd */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompare -- compare two Numbers */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPARE, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompare */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareSignal -- compare, signalling on all NaNs */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPSIG, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareSignal */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotal -- compare two Numbers, using total ordering */ +/* */ +/* This computes C = A ? B, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareTotal */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ +/* */ +/* This computes C = |A| ? |B|, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + uInt needbytes; /* for space calculations */ + decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber bufb[D2N(DECBUFFER+1)]; + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ + decNumber *a, *b; /* temporary pointers */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + /* if either is negative, take a copy and absolute */ + if (decNumberIsNegative(lhs)) { /* lhs<0 */ + a=bufa; + needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + decNumberCopy(a, lhs); /* copy content */ + a->bits&=~DECNEG; /* .. and clear the sign */ + lhs=a; /* use copy from here on */ + } + if (decNumberIsNegative(rhs)) { /* rhs<0 */ + b=bufb; + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + decNumberCopy(b, rhs); /* copy content */ + b->bits&=~DECNEG; /* .. and clear the sign */ + rhs=b; /* use copy from here on */ + } + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareTotalMag */ + +/* ------------------------------------------------------------------ */ +/* decNumberDivide -- divide one number by another */ +/* */ +/* This computes C = A / B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, DIVIDE, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberDivide */ + +/* ------------------------------------------------------------------ */ +/* decNumberDivideInteger -- divide and return integer quotient */ +/* */ +/* This computes C = A # B, where # is the integer divide operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberDivideInteger */ + +/* ------------------------------------------------------------------ */ +/* decNumberExp -- exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decExpOp which can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-a) where a can be the tiniest number (Ntiny). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberExp(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; /* accumulator */ + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* Check restrictions; these restrictions ensure that if h=8 (see */ + /* decExpOp) then the result will either overflow or underflow to 0. */ + /* Other math functions restrict the input range, too, for inverses. */ + /* If not violated then carry out the operation. */ + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + decExpOp(res, rhs, set, &status); + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberExp */ + +/* ------------------------------------------------------------------ */ +/* decNumberFMA -- fused multiply add */ +/* */ +/* This computes D = (A * B) + C with only one rounding */ +/* */ +/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ +/* lhs is A */ +/* rhs is B */ +/* fhs is C [far hand side] */ +/* set is the context */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, + const decNumber *rhs, const decNumber *fhs, + decContext *set) { + uInt status=0; /* accumulator */ + decContext dcmul; /* context for the multiplication */ + uInt needbytes; /* for space calculations */ + decNumber bufa[D2N(DECBUFFER*2+1)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *acc; /* accumulator pointer */ + decNumber dzero; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { /* [undefined if subset] */ + status|=DEC_Invalid_operation; + break;} + #endif + /* Check math restrictions [these ensure no overflow or underflow] */ + if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) + || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) + || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; + /* set up context for multiply */ + dcmul=*set; + dcmul.digits=lhs->digits+rhs->digits; /* just enough */ + /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ + dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ + dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ + /* set up decNumber space to receive the result of the multiply */ + acc=bufa; /* may fit */ + needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + acc=allocbufa; /* use the allocated space */ + } + /* multiply with extended range and necessary precision */ + /*printf("emin=%ld\n", dcmul.emin); */ + decMultiplyOp(acc, lhs, rhs, &dcmul, &status); + /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ + /* status; if either is seen than ignore fhs (in case it is */ + /* another sNaN) and set acc to NaN unless we had an sNaN */ + /* [decMultiplyOp leaves that to caller] */ + /* Note sNaN has to go through addOp to shorten payload if */ + /* necessary */ + if ((status&DEC_Invalid_operation)!=0) { + if (!(status&DEC_sNaN)) { /* but be true invalid */ + decNumberZero(res); /* acc not yet set */ + res->bits=DECNAN; + break; + } + decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ + fhs=&dzero; /* use that */ + } + #if DECCHECK + else { /* multiply was OK */ + if (status!=0) printf("Status=%08lx after FMA multiply\n", status); + } + #endif + /* add the third operand and result -> res, and all is done */ + decAddOp(res, acc, fhs, set, 0, &status); + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberFMA */ + +/* ------------------------------------------------------------------ */ +/* decNumberInvert -- invert a Number, digitwise */ +/* */ +/* This computes C = ~A */ +/* */ +/* res is C, the result. C may be A (e.g., X=~X) */ +/* rhs is A */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, + decContext *set) { + const Unit *ua, *msua; /* -> operand and its msu */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + /* operand is valid */ + ua=rhs->lsu; /* bottom-up */ + uc=res->lsu; /* .. */ + msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, uc++) { /* Unit loop */ + Unit a; /* extract unit */ + Int i, j; /* work */ + if (ua>msua) a=0; + else a=*ua; + *uc=0; /* can now write back */ + /* always need to examine all bits in rhs */ + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ + j=a%10; + a=a/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberInvert */ + +/* ------------------------------------------------------------------ */ +/* decNumberLn -- natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decLnOp which can handle the slightly wider */ +/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ +/* to calculate at p+e+2). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLn(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; /* accumulator */ + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* Check restrictions; this is a math function; if not violated */ + /* then carry out the operation. */ + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + /* special check in subset for rhs=0 */ + if (ISZERO(rhs)) { /* +/- zeros -> error */ + status|=DEC_Invalid_operation; + break;} + } /* extended=0 */ + #endif + decLnOp(res, rhs, set, &status); + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberLn */ + +/* ------------------------------------------------------------------ */ +/* decNumberLogB - get adjusted exponent, by 754r 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 754r */ + } + 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, ©stat); /* copy & shorten */ + /* if exact and the digit is 1, rhs is a power of 10 */ + if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { + /* the exponent, conveniently, is the power of 10; making */ + /* this the result needs a little care as it might not fit, */ + /* so first convert it into the working number, and then move */ + /* to res */ + decNumberFromInt32(w, w->exponent); + residue=0; + decCopyFit(res, w, set, &residue, &status); /* copy & round */ + decFinish(res, set, &residue, &status); /* cleanup/set flags */ + break; + } /* not a power of 10 */ + } /* not a candidate for exact */ + + /* simplify the information-content calculation to use 'total */ + /* number of digits in a, including exponent' as compared to the */ + /* requested digits, as increasing this will only rarely cost an */ + /* iteration in ln(a) anyway */ + t=6; /* it can never be >6 */ + + /* allocate space when needed... */ + p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + aset.digits=p; /* as calculated */ + aset.emax=DEC_MAX_MATH; /* usual bounds */ + aset.emin=-DEC_MAX_MATH; /* .. */ + aset.clamp=0; /* and no concrete format */ + decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ + + /* skip the division if the result so far is infinite, NaN, or */ + /* zero, or there was an error; note NaN from sNaN needs copy */ + if (status&DEC_NaNs && !(status&DEC_sNaN)) break; + if (a->bits&DECSPECIAL || ISZERO(a)) { + decNumberCopy(res, a); /* [will fit] */ + break;} + + /* for ln(10) an extra 3 digits of precision are needed */ + p=set->digits+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + decNumberZero(w); /* set up 10... */ + #if DECDPUN==1 + w->lsu[1]=1; w->lsu[0]=0; /* .. */ + #else + w->lsu[0]=10; /* .. */ + #endif + w->digits=2; /* .. */ + + aset.digits=p; + decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ + + aset.digits=set->digits; /* for final divide */ + decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ + } while(0); /* [for break] */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberLog10 */ + +/* ------------------------------------------------------------------ */ +/* decNumberMax -- compare two Numbers and return the maximum */ +/* */ +/* This computes C = A ? B, returning the maximum by 754R 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 754R 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 754R 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 754R 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 754r 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 754r 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 754r nextafter rules */ +/* */ +/* 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 754r 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, &dropped); /* trailing zeros */ + #endif + } while(0); /* end protected */ + + if (allocdac!=NULL) free(allocdac); /* drop any storage used */ + if (allocinv!=NULL) free(allocinv); /* .. */ + #if DECSUBSET + if (alloclhs!=NULL) free(alloclhs); /* .. */ + if (allocrhs!=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberPower */ + +/* ------------------------------------------------------------------ */ +/* decNumberQuantize -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has exponent of B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the number with exponent to match */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to that of B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decQuantizeOp(res, lhs, rhs, set, 1, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberQuantize */ + +/* ------------------------------------------------------------------ */ +/* decNumberReduce -- remove trailing zeros */ +/* */ +/* This computes C = 0 + A, and normalizes the result */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* Previously known as Normalize */ +decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, + decContext *set) { + return decNumberReduce(res, rhs, set); + } /* decNumberNormalize */ + +decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, + decContext *set) { + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + uInt status=0; /* as usual */ + Int residue=0; /* as usual */ + Int dropped; /* work */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* Infinities copy through; NaNs need usual treatment */ + if (decNumberIsNaN(rhs)) { + decNaNs(res, rhs, NULL, set, &status); + break; + } + + /* reduce result to the requested length and copy to result */ + decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ + decFinish(res, set, &residue, &status); /* cleanup/set flags */ + decTrim(res, set, 1, &dropped); /* normalize in place */ + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set);/* then report status */ + return res; + } /* decNumberReduce */ + +/* ------------------------------------------------------------------ */ +/* decNumberRescale -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decQuantizeOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberRescale */ + +/* ------------------------------------------------------------------ */ +/* decNumberRemainder -- divide and return remainder */ +/* */ +/* This computes C = A % B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, REMAINDER, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberRemainder */ + +/* ------------------------------------------------------------------ */ +/* decNumberRemainderNear -- divide and return remainder from nearest */ +/* */ +/* This computes C = A % B, where % is the IEEE remainder operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, REMNEAR, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberRemainderNear */ + +/* ------------------------------------------------------------------ */ +/* decNumberRotate -- rotate the coefficient of a Number left/right */ +/* */ +/* This computes C = A rot B (in base ten and rotating set->digits */ +/* digits). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ +/* lhs is A */ +/* rhs is B, the number of digits to rotate (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are rotated to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. If lhs->digits is less than */ +/* set->digits the coefficient is padded with zeros on the left */ +/* before the rotate. Any leading zeros in the result are removed */ +/* as usual. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + Int rotate; /* rhs as an Int */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* NaNs propagate as normal */ + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + /* rhs must be an integer */ + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { /* both numeric, rhs is an integer */ + rotate=decGetInt(rhs); /* [cannot fail] */ + if (rotate==BADINT /* something bad .. */ + || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ + || abs(rotate)>set->digits) /* .. or out of range */ + status=DEC_Invalid_operation; + else { /* rhs is OK */ + decNumberCopy(res, lhs); + /* convert -ve rotate to equivalent positive rotation */ + if (rotate<0) rotate=set->digits+rotate; + if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ + && !decNumberIsInfinite(res)) { /* lhs was infinite */ + /* left-rotate to do; 0 < rotate < set->digits */ + uInt units, shift; /* work */ + uInt msudigits; /* digits in result msu */ + Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ + Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ + for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ + res->digits=set->digits; /* now full-length */ + msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ + + /* rotation here is done in-place, in three steps */ + /* 1. shift all to least up to one unit to unit-align final */ + /* lsd [any digits shifted out are rotated to the left, */ + /* abutted to the original msd (which may require split)] */ + /* */ + /* [if there are no whole units left to rotate, the */ + /* rotation is now complete] */ + /* */ + /* 2. shift to least, from below the split point only, so that */ + /* the final msd is in the right place in its Unit [any */ + /* digits shifted out will fit exactly in the current msu, */ + /* left aligned, no split required] */ + /* */ + /* 3. rotate all the units by reversing left part, right */ + /* part, and then whole */ + /* */ + /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ + /* */ + /* start: 00a bcd efg hij klm npq */ + /* */ + /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ + /* 1b 00p qab cde fgh|ijk lmn */ + /* */ + /* 2a 00p qab cde fgh|00i jkl [mn saved] */ + /* 2b mnp qab cde fgh|00i jkl */ + /* */ + /* 3a fgh cde qab mnp|00i jkl */ + /* 3b fgh cde qab mnp|jkl 00i */ + /* 3c 00i jkl mnp qab cde fgh */ + + /* Step 1: amount to shift is the partial right-rotate count */ + rotate=set->digits-rotate; /* make it right-rotate */ + units=rotate/DECDPUN; /* whole units to rotate */ + shift=rotate%DECDPUN; /* left-over digits count */ + if (shift>0) { /* not an exact number of units */ + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ + decShiftToLeast(res->lsu, D2U(res->digits), shift); + if (shift>msudigits) { /* msumax-1 needs >0 digits */ + uInt rem=save%powers[shift-msudigits];/* split save */ + *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ + *(msumax-1)=*(msumax-1) + +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ + } + else { /* all fits in msumax */ + *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ + } + } /* digits shift needed */ + + /* If whole units to rotate... */ + if (units>0) { /* some to do */ + /* Step 2: the units to touch are the whole ones in rotate, */ + /* if any, and the shift is DECDPUN-msudigits (which may be */ + /* 0, again) */ + shift=DECDPUN-msudigits; + if (shift>0) { /* not an exact number of units */ + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ + decShiftToLeast(res->lsu, units, shift); + *msumax=*msumax+(Unit)(save*powers[msudigits]); + } /* partial shift needed */ + + /* Step 3: rotate the units array using triple reverse */ + /* (reversing is easy and fast) */ + decReverse(res->lsu+units, msumax); /* left part */ + decReverse(res->lsu, res->lsu+units-1); /* right part */ + decReverse(res->lsu, msumax); /* whole */ + } /* whole units to rotate */ + /* the rotation may have left an undetermined number of zeros */ + /* on the left, so true length needs to be calculated */ + res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); + } /* rotate needed */ + } /* rhs OK */ + } /* numerics */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberRotate */ + +/* ------------------------------------------------------------------ */ +/* decNumberSameQuantum -- test for equal exponents */ +/* */ +/* res is the result number, which will contain either 0 or 1 */ +/* lhs is a number to test */ +/* rhs is the second (usually a pattern) */ +/* */ +/* No errors are possible and no context is needed. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + Unit ret=0; /* return value */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; + #endif + + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; + else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; + /* [anything else with a special gives 0] */ + } + else if (lhs->exponent==rhs->exponent) ret=1; + + decNumberZero(res); /* OK to overwrite an operand now */ + *res->lsu=ret; + return res; + } /* decNumberSameQuantum */ + +/* ------------------------------------------------------------------ */ +/* decNumberScaleB -- multiply by a power of 10 */ +/* */ +/* This computes C = A x 10**B where B is an integer (q=0) with */ +/* maximum magnitude 2*(emax+digits) */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested power of ten to use */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* The result may underflow or overflow. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Int reqexp; /* requested exponent change [B] */ + uInt status=0; /* accumulator */ + Int residue; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* Handle special values except lhs infinite */ + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + /* rhs must be an integer */ + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { + /* lhs is a number; rhs is a finite with q==0 */ + reqexp=decGetInt(rhs); /* [cannot fail] */ + 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)] */ + /* [We would like 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 */ + 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); + + /* [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 (;;) { + /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ + workset.digits=workset.digits*2-2; + if (workset.digits>maxp) workset.digits=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 */ + if (a->digits==maxp) break; /* have required digits */ + } /* 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, &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, */ + /* and it cannot have trailing zeros due to clamping, so these are */ + /* the only (relatively rare) conditions a careful check is needed */ + if (b->digits*2-1 > workp && !set->clamp) { /* 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 */ + if (dropped<todrop) { /* clamp to those available */ + todrop=dropped; + status|=DEC_Clamped; + } + if (todrop>0) { /* have some to drop */ + decShiftToLeast(a->lsu, D2U(a->digits), todrop); + a->exponent+=todrop; /* maintain numerical value */ + a->digits-=todrop; /* new length */ + } + } + } + } + } + + /* double-check Underflow, as perhaps the result could not have */ + /* been subnormal (initial argument too big), or it is now Exact */ + if (status&DEC_Underflow) { + Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ + /* check if truly subnormal */ + #if DECEXTFLAG /* DEC_Subnormal too */ + if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); + #else + if (ae>=set->emin*2) status&=~DEC_Underflow; + #endif + /* check if truly inexact */ + if (!(status&DEC_Inexact)) status&=~DEC_Underflow; + } + + decNumberCopy(res, a); /* a is now the result */ + } while(0); /* end protected */ + + if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ + if (allocbufa!=NULL) free(allocbufa); /* .. */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set);/* then report status */ + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberSquareRoot */ + +/* ------------------------------------------------------------------ */ +/* decNumberSubtract -- subtract two Numbers */ +/* */ +/* This computes C = A - B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + + decAddOp(res, lhs, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberSubtract */ + +/* ------------------------------------------------------------------ */ +/* decNumberToIntegralExact -- round-to-integral-value with InExact */ +/* decNumberToIntegralValue -- round-to-integral-value */ +/* */ +/* res is the result */ +/* rhs is input number */ +/* set is the context */ +/* */ +/* res must have space for any value of rhs. */ +/* */ +/* This implements the IEEE special operators and therefore treats */ +/* special values as valid. For finite numbers it returns */ +/* rescale(rhs, 0) if rhs->exponent is <0. */ +/* Otherwise the result is rhs (so no error is possible, except for */ +/* sNaN). */ +/* */ +/* The context is used for rounding mode and status after sNaN, but */ +/* the digits setting is ignored. The Exact version will signal */ +/* Inexact if the result differs numerically from rhs; the other */ +/* never signals Inexact. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dn; + decContext workset; /* working context */ + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* handle infinities and NaNs */ + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */ + else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ + } + else { /* finite */ + /* have a finite number; no error possible (res must be big enough) */ + if (rhs->exponent>=0) return decNumberCopy(res, rhs); + /* that was easy, but if negative exponent there is work to do... */ + workset=*set; /* clone rounding, etc. */ + workset.digits=rhs->digits; /* no length rounding */ + workset.traps=0; /* no traps */ + decNumberZero(&dn); /* make a number with exponent 0 */ + decNumberQuantize(res, rhs, &dn, &workset); + status|=workset.status; + } + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberToIntegralExact */ + +decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset=*set; /* working context */ + workset.traps=0; /* no traps */ + decNumberToIntegralExact(res, rhs, &workset); + /* this never affects set, except for sNaNs; NaN will have been set */ + /* or propagated already, so no need to call decStatus */ + set->status|=workset.status&DEC_Invalid_operation; + return res; + } /* decNumberToIntegralValue */ + +/* ------------------------------------------------------------------ */ +/* decNumberXor -- XOR two Numbers, digitwise */ +/* */ +/* This computes C = A ^ B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberXor(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; /* -> operands */ + const Unit *msua, *msub; /* -> operand msus */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + /* operands are valid */ + ua=lhs->lsu; /* bottom-up */ + ub=rhs->lsu; /* .. */ + uc=res->lsu; /* .. */ + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ + Unit a, b; /* extract units */ + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; /* can now write back */ + if (a|b) { /* maybe 1 bits to examine */ + Int i, j; + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* non-zero */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberXor */ + + +/* ================================================================== */ +/* Utility routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberClass -- return the decClass of a decNumber */ +/* dn -- the decNumber to test */ +/* set -- the context to use for Emin */ +/* returns the decClass enum */ +/* ------------------------------------------------------------------ */ +enum decClass decNumberClass(const decNumber *dn, decContext *set) { + if (decNumberIsSpecial(dn)) { + if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; + if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; + /* must be an infinity */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; + return DEC_CLASS_POS_INF; + } + /* is finite */ + if (decNumberIsNormal(dn, set)) { /* most common */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; + return DEC_CLASS_POS_NORMAL; + } + /* is subnormal or zero */ + if (decNumberIsZero(dn)) { /* most common */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; + return DEC_CLASS_POS_ZERO; + } + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; + return DEC_CLASS_POS_SUBNORMAL; + } /* decNumberClass */ + +/* ------------------------------------------------------------------ */ +/* decNumberClassToString -- convert decClass to a string */ +/* */ +/* eclass is a valid decClass */ +/* returns a constant string describing the class (max 13+1 chars) */ +/* ------------------------------------------------------------------ */ +const char *decNumberClassToString(enum decClass eclass) { + if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; + if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; + if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; + if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; + if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; + if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; + if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; + if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; + if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; + if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; + return DEC_ClassString_UN; /* Unknown */ + } /* decNumberClassToString */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopy -- copy a number */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* returns dest */ +/* */ +/* (dest==src is allowed and is a no-op) */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { + + #if DECCHECK + if (src==NULL) return decNumberZero(dest); + #endif + + if (dest==src) return dest; /* no copy required */ + + /* Use explicit assignments here as structure assignment could copy */ + /* more than just the lsu (for small DECDPUN). This would not affect */ + /* the value of the results, but could disturb test harness spill */ + /* checking. */ + dest->bits=src->bits; + dest->exponent=src->exponent; + dest->digits=src->digits; + dest->lsu[0]=src->lsu[0]; + if (src->digits>DECDPUN) { /* more Units to come */ + const Unit *smsup, *s; /* work */ + Unit *d; /* .. */ + /* memcpy for the remaining Units would be safe as they cannot */ + /* overlap. However, this explicit loop is faster in short cases. */ + d=dest->lsu+1; /* -> first destination */ + smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ + for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; + } + return dest; + } /* decNumberCopy */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopyAbs -- quiet absolute value operator */ +/* */ +/* This sets C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberAbs for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits&=~DECNEG; /* turn off sign */ + return res; + } /* decNumberCopyAbs */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopyNegate -- quiet negate value operator */ +/* */ +/* This sets C = negate(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberMinus for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits^=DECNEG; /* invert the sign */ + return res; + } /* decNumberCopyNegate */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopySign -- quiet copy and set sign operator */ +/* */ +/* This sets C = A with the sign of B */ +/* */ +/* res is C, the result. C may be A */ +/* lhs is A */ +/* rhs is B */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + uByte sign; /* rhs sign */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + sign=rhs->bits & DECNEG; /* save sign bit */ + decNumberCopy(res, lhs); + res->bits&=~DECNEG; /* clear the sign */ + res->bits|=sign; /* set from rhs */ + return res; + } /* decNumberCopySign */ + +/* ------------------------------------------------------------------ */ +/* decNumberGetBCD -- get the coefficient in BCD8 */ +/* dn is the source decNumber */ +/* bcd is the uInt array that will receive dn->digits BCD bytes, */ +/* most-significant at offset 0 */ +/* returns bcd */ +/* */ +/* bcd must have at least dn->digits bytes. No error is possible; if */ +/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ +/* ------------------------------------------------------------------ */ +uByte * decNumberGetBCD(const decNumber *dn, uint8_t *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. */ +/* ------------------------------------------------------------------ */ +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, &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 854 rules */ + if (adjust<0) res->exponent=lexp; /* set exponent */ + /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ + if (diffsign) { + if (set->round!=DEC_ROUND_FLOOR) res->bits=0; + else res->bits=DECNEG; /* preserve 0 sign */ + } + } + else { /* non-0 res */ + if (adjust<0) { /* 0-padding needed */ + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; /* to fit exactly */ + *status|=DEC_Rounded; /* [but exact] */ + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* set the exponent. */ + } + } /* non-0 res */ + #if DECSUBSET + } /* extended */ + #endif + decFinish(res, set, &residue, status); /* clean and finalize */ + break;} + + if (ISZERO(rhs)) { /* [lhs is non-zero] */ + Int adjust; /* work */ + Int rexp=rhs->exponent; /* save in case RHS==RES */ + bits=rhs->bits; /* be clean */ + residue=0; /* clear accumulator */ + decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ + #if DECSUBSET + if (set->extended) { /* exponents on zeros count */ + #endif + /* exponent will be the lower of the two */ + /* [0-0 case handled above] */ + adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ + if (adjust<0) { /* 0-padding needed */ + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; /* to fit exactly */ + *status|=DEC_Rounded; /* [but exact] */ + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* set the exponent. */ + } + #if DECSUBSET + } /* extended */ + #endif + decFinish(res, set, &residue, status); /* clean and finalize */ + break;} + + /* [NB: both fastpath and mainpath code below assume these cases */ + /* (notably 0-0) have already been handled] */ + + /* calculate the padding needed to align the operands */ + padding=rhs->exponent-lhs->exponent; + + /* Fastpath cases where the numbers are aligned and normal, the RHS */ + /* is all in one unit, no operand rounding is needed, and no carry, */ + /* lengthening, or borrow is needed */ + if (padding==0 + && rhs->digits<=DECDPUN + && rhs->exponent>=set->emin /* [some normals drop through] */ + && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ + && rhs->digits<=reqdigits + && lhs->digits<=reqdigits) { + Int partial=*lhs->lsu; + if (!diffsign) { /* adding */ + partial+=*rhs->lsu; + if ((partial<=DECDPUNMAX) /* result fits in unit */ + && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ + partial<(Int)powers[lhs->digits])) { /* .. */ + if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ + *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ + break; + } + /* else drop out for careful add */ + } + else { /* signs differ */ + partial-=*rhs->lsu; + if (partial>0) { /* no borrow needed, and non-0 result */ + if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ + *res->lsu=(Unit)partial; + /* this could have reduced digits [but result>0] */ + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + break; + } + /* else drop out for careful subtract */ + } + } + + /* Now align (pad) the lhs or rhs so they can be added or */ + /* subtracted, as necessary. If one number is much larger than */ + /* the other (that is, if in plain form there is a least one */ + /* digit between the lowest digit of one and the highest of the */ + /* other) padding with up to DIGITS-1 trailing zeros may be */ + /* needed; then apply rounding (as exotic rounding modes may be */ + /* affected by the residue). */ + rhsshift=0; /* rhs shift to left (padding) in Units */ + bits=lhs->bits; /* assume sign is that of LHS */ + mult=1; /* likely multiplier */ + + /* [if padding==0 the operands are aligned; no padding is needed] */ + if (padding!=0) { + /* some padding needed; always pad the RHS, as any required */ + /* padding can then be effected by a simple combination of */ + /* shifts and a multiply */ + Flag swapped=0; + if (padding<0) { /* LHS needs the padding */ + const decNumber *t; + padding=-padding; /* will be +ve */ + bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ + t=lhs; lhs=rhs; rhs=t; + swapped=1; + } + + /* If, after pad, rhs would be longer than lhs by digits+1 or */ + /* more then lhs cannot affect the answer, except as a residue, */ + /* so only need to pad up to a length of DIGITS+1. */ + if (rhs->digits+padding > lhs->digits+reqdigits+1) { + /* The RHS is sufficient */ + /* for residue use the relative sign indication... */ + Int shift=reqdigits-rhs->digits; /* left shift needed */ + residue=1; /* residue for rounding */ + if (diffsign) residue=-residue; /* signs differ */ + /* copy, shortening if necessary */ + decCopyFit(res, rhs, set, &residue, status); + /* if it was already shorter, then need to pad with zeros */ + if (shift>0) { + res->digits=decShiftToMost(res->lsu, res->digits, shift); + res->exponent-=shift; /* adjust the exponent. */ + } + /* flip the result sign if unswapped and rhs was negated */ + if (!swapped) res->bits^=negate; + decFinish(res, set, &residue, status); /* done */ + break;} + + /* LHS digits may affect result */ + rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ + mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ + } /* padding needed */ + + if (diffsign) mult=-mult; /* signs differ */ + + /* determine the longer operand */ + maxdigits=rhs->digits+padding; /* virtual length of RHS */ + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + + /* Decide on the result buffer to use; if possible place directly */ + /* into result. */ + acc=res->lsu; /* assume add direct to result */ + /* If destructive overlap, or the number is too long, or a carry or */ + /* borrow to DIGITS+1 might be possible, a buffer must be used. */ + /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ + if ((maxdigits>=reqdigits) /* is, or could be, too large */ + || (res==rhs && rhsshift>0)) { /* destructive overlap */ + /* buffer needed, choose it; units for maxdigits digits will be */ + /* needed, +1 Unit for carry or borrow */ + Int need=D2U(maxdigits)+1; + acc=accbuff; /* assume use local buffer */ + if (need*sizeof(Unit)>sizeof(accbuff)) { + /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; + } + } + + res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ + res->exponent=lhs->exponent; /* .. operands (even if aliased) */ + + #if DECTRACE + decDumpAr('A', lhs->lsu, D2U(lhs->digits)); + decDumpAr('B', rhs->lsu, D2U(rhs->digits)); + printf(" :h: %ld %ld\n", rhsshift, mult); + #endif + + /* add [A+B*m] or subtract [A+B*(-m)] */ + res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhsshift, acc, mult) + *DECDPUN; /* [units -> digits] */ + if (res->digits<0) { /* borrowed... */ + res->digits=-res->digits; + res->bits^=DECNEG; /* flip the sign */ + } + #if DECTRACE + decDumpAr('+', acc, D2U(res->digits)); + #endif + + /* If a buffer was used the result must be copied back, possibly */ + /* shortening. (If no buffer was used then the result must have */ + /* fit, so can't need rounding and residue must be 0.) */ + residue=0; /* clear accumulator */ + if (acc!=res->lsu) { + #if DECSUBSET + if (set->extended) { /* round from first significant digit */ + #endif + /* remove leading zeros that were added due to rounding up to */ + /* integral Units -- before the test for rounding. */ + if (res->digits>reqdigits) + res->digits=decGetDigits(acc, D2U(res->digits)); + decSetCoeff(res, set, acc, res->digits, &residue, status); + #if DECSUBSET + } + else { /* subset arithmetic rounds from original significant digit */ + /* May have an underestimate. This only occurs when both */ + /* numbers fit in DECDPUN digits and are padding with a */ + /* negative multiple (-10, -100...) and the top digit(s) become */ + /* 0. (This only matters when using X3.274 rules where the */ + /* leading zero could be included in the rounding.) */ + if (res->digits<maxdigits) { + *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ + res->digits=maxdigits; + } + else { + /* remove leading zeros that added due to rounding up to */ + /* integral Units (but only those in excess of the original */ + /* maxdigits length, unless extended) before test for rounding. */ + if (res->digits>reqdigits) { + res->digits=decGetDigits(acc, D2U(res->digits)); + if (res->digits<maxdigits) res->digits=maxdigits; + } + } + decSetCoeff(res, set, acc, res->digits, &residue, status); + /* Now apply rounding if needed before removing leading zeros. */ + /* This is safe because subnormals are not a possibility */ + if (residue!=0) { + decApplyRound(res, set, residue, status); + residue=0; /* did what needed to be done */ + } + } /* subset */ + #endif + } /* used buffer */ + + /* strip leading zeros [these were left on in case of subset subtract] */ + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + + /* apply checks and rounding */ + decFinish(res, set, &residue, status); + + /* "When the sum of two operands with opposite signs is exactly */ + /* zero, the sign of that sum shall be '+' in all rounding modes */ + /* except round toward -Infinity, in which mode that sign shall be */ + /* '-'." [Subset zeros also never have '-', set by decFinish.] */ + if (ISZERO(res) && diffsign + #if DECSUBSET + && set->extended + #endif + && (*status&DEC_Inexact)==0) { + if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ + else res->bits&=~DECNEG; /* sign + */ + } + } while(0); /* end protected */ + + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decAddOp */ + +/* ------------------------------------------------------------------ */ +/* decDivideOp -- division operation */ +/* */ +/* This routine performs the calculations for all four division */ +/* operators (divide, divideInteger, remainder, remainderNear). */ +/* */ +/* C=A op B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* The underlying algorithm of this routine is the same as in the */ +/* 1981 S/370 implementation, that is, non-restoring long division */ +/* with bi-unit (rather than bi-digit) estimation for each unit */ +/* multiplier. In this pseudocode overview, complications for the */ +/* Remainder operators and division residues for exact rounding are */ +/* omitted for clarity. */ +/* */ +/* Prepare operands and handle special values */ +/* Test for x/0 and then 0/x */ +/* Exp =Exp1 - Exp2 */ +/* Exp =Exp +len(var1) -len(var2) */ +/* Sign=Sign1 * Sign2 */ +/* Pad accumulator (Var1) to double-length with 0's (pad1) */ +/* Pad Var2 to same length as Var1 */ +/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ +/* have=0 */ +/* Do until (have=digits+1 OR residue=0) */ +/* if exp<0 then if integer divide/residue then leave */ +/* this_unit=0 */ +/* Do forever */ +/* compare numbers */ +/* if <0 then leave inner_loop */ +/* if =0 then (* quick exit without subtract *) do */ +/* this_unit=this_unit+1; output this_unit */ +/* leave outer_loop; end */ +/* Compare lengths of numbers (mantissae): */ +/* If same then tops2=msu2pair -- {units 1&2 of var2} */ +/* else tops2=msu2plus -- {0, unit 1 of var2} */ +/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ +/* mult=tops1/tops2 -- Good and safe guess at divisor */ +/* if mult=0 then mult=1 */ +/* this_unit=this_unit+mult */ +/* subtract */ +/* end inner_loop */ +/* if have\=0 | this_unit\=0 then do */ +/* output this_unit */ +/* have=have+1; end */ +/* var2=var2/10 */ +/* exp=exp-1 */ +/* end outer_loop */ +/* exp=exp+1 -- set the proper exponent */ +/* if have=0 then generate answer=0 */ +/* Return (Result is defined by Var1) */ +/* */ +/* ------------------------------------------------------------------ */ +/* Two working buffers are needed during the division; one (digits+ */ +/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ +/* long subtractions. These are acc and var1 respectively. */ +/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ +/* The static buffers may be larger than might be expected to allow */ +/* for calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decDivideOp(decNumber *res, + const decNumber *lhs, const decNumber *rhs, + decContext *set, Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ + Unit *acc=accbuff; /* -> accumulator array for result */ + Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ + Unit *accnext; /* -> where next digit will go */ + Int acclength; /* length of acc needed [Units] */ + Int accunits; /* count of units accumulated */ + Int accdigits; /* count of digits accumulated */ + + Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)*sizeof(Unit)]; /* 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, &dropped); + #endif + } while(0); /* end protected */ + + if (varalloc!=NULL) free(varalloc); /* drop any storage used */ + if (allocacc!=NULL) free(allocacc); /* .. */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decDivideOp */ + +/* ------------------------------------------------------------------ */ +/* decMultiplyOp -- multiplication operation */ +/* */ +/* This routine performs the multiplication C=A x B. */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* 'Classic' multiplication is used rather than Karatsuba, as the */ +/* latter would give only a minor improvement for the short numbers */ +/* expected to be handled most (and uses much more memory). */ +/* */ +/* There are two major paths here: the general-purpose ('old code') */ +/* path which handles all DECDPUN values, and a fastpath version */ +/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ +/* than two calls to decUnitAddSub would be made. */ +/* */ +/* The fastpath version lumps units together into 8-digit or 9-digit */ +/* chunks, and also uses a lazy carry strategy to minimise expensive */ +/* 64-bit divisions. The chunks are then broken apart again into */ +/* units for continuing processing. Despite this overhead, the */ +/* fastpath can speed up some 16-digit operations by 10x (and much */ +/* more for higher-precision calculations). */ +/* */ +/* A buffer always has to be used for the accumulator; in the */ +/* fastpath, buffers are also always needed for the chunked copies of */ +/* of the operand coefficients. */ +/* Static buffers are larger than needed just for multiply, to allow */ +/* for calls from other operations (notably exp). */ +/* ------------------------------------------------------------------ */ +#define FASTMUL (DECUSE64 && DECDPUN<5) +static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + Int accunits; /* Units of accumulator in use */ + Int exponent; /* work */ + Int residue=0; /* rounding residue */ + uByte bits; /* result sign */ + Unit *acc; /* -> accumulator Unit array */ + Int needbytes; /* size calculator */ + void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ + Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ + /* *4 for calls from other operations) */ + const Unit *mer, *mermsup; /* work */ + Int madlength; /* Units in multiplicand */ + Int shift; /* Units to shift multiplicand by */ + + #if FASTMUL + /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ + /* (DECDPUN is 2 or 4) then work in base 10**8 */ + #if DECDPUN & 1 /* odd */ + #define FASTBASE 1000000000 /* base */ + #define FASTDIGS 9 /* digits in base */ + #define FASTLAZY 18 /* carry resolution point [1->18] */ + #else + #define FASTBASE 100000000 + #define FASTDIGS 8 + #define FASTLAZY 1844 /* carry resolution point [1->1844] */ + #endif + /* three buffers are used, two for chunked copies of the operands */ + /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ + /* lazy carry evaluation */ + uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ + uInt *zlhi=zlhibuff; /* -> lhs array */ + uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ + uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ + uInt *zrhi=zrhibuff; /* -> rhs array */ + uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ + uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ + /* [allocacc is shared for both paths, as only one will run] */ + uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ + #if DECDPUN==1 + Int zoff; /* accumulator offset */ + #endif + uInt *lip, *rip; /* item pointers */ + uInt *lmsi, *rmsi; /* most significant items */ + Int ilhs, irhs, iacc; /* item counts in the arrays */ + Int lazy; /* lazy carry counter */ + uLong lcarry; /* uLong carry */ + uInt carry; /* carry (NB not uLong) */ + Int count; /* work */ + const Unit *cup; /* .. */ + Unit *up; /* .. */ + uLong *lp; /* .. */ + Int p; /* .. */ + #endif + + #if DECSUBSET + decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ + decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* precalculate result sign */ + bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); + + /* handle infinities and NaNs */ + if (SPECIALARGS) { /* a special bit set */ + if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ + decNaNs(res, lhs, rhs, set, status); + return res;} + /* one or two infinities; Infinity * 0 is invalid */ + if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) + ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { + *status|=DEC_Invalid_operation; + return res;} + decNumberZero(res); + res->bits=bits|DECINF; /* infinity */ + return res;} + + /* For best speed, as in DMSRCN [the original Rexx numerics */ + /* module], use the shorter number as the multiplier (rhs) and */ + /* the longer as the multiplicand (lhs) to minimise the number of */ + /* adds (partial products) */ + if (lhs->digits<rhs->digits) { /* swap... */ + const decNumber *hold=lhs; + lhs=rhs; + rhs=hold; + } + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + #if FASTMUL /* fastpath can be used */ + /* use the fast path if there are enough digits in the shorter */ + /* operand to make the setup and takedown worthwhile */ + #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ + if (rhs->digits>NEEDTWO) { /* use fastpath... */ + /* calculate the number of elements in each array */ + ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ + irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ + iacc=ilhs+irhs; + + /* allocate buffers if required, as usual */ + needbytes=ilhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zlhibuff)) { + alloclhi=(uInt *)malloc(needbytes); + zlhi=alloclhi;} + needbytes=irhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zrhibuff)) { + allocrhi=(uInt *)malloc(needbytes); + zrhi=allocrhi;} + + /* Allocating the accumulator space needs a special case when */ + /* DECDPUN=1 because when converting the accumulator to Units */ + /* after the multiplication each 8-byte item becomes 9 1-byte */ + /* units. Therefore iacc extra bytes are needed at the front */ + /* (rounded up to a multiple of 8 bytes), and the uLong */ + /* accumulator starts offset the appropriate number of units */ + /* to the right to avoid overwrite during the unchunking. */ + needbytes=iacc*sizeof(uLong); + #if DECDPUN==1 + zoff=(iacc+7)/8; /* items to offset by */ + needbytes+=zoff*8; + #endif + if (needbytes>(Int)sizeof(zaccbuff)) { + allocacc=(uLong *)malloc(needbytes); + zacc=(uLong *)allocacc;} + if (zlhi==NULL||zrhi==NULL||zacc==NULL) { + *status|=DEC_Insufficient_storage; + break;} + + acc=(Unit *)zacc; /* -> target Unit array */ + #if DECDPUN==1 + zacc+=zoff; /* start uLong accumulator to right */ + #endif + + /* assemble the chunked copies of the left and right sides */ + for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) + for (p=0, *lip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *lip+=*cup*powers[p]; + lmsi=lip-1; /* save -> msi */ + for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) + for (p=0, *rip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *rip+=*cup*powers[p]; + rmsi=rip-1; /* save -> msi */ + + /* zero the accumulator */ + for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; + + /* Start the multiplication */ + /* Resolving carries can dominate the cost of accumulating the */ + /* partial products, so this is only done when necessary. */ + /* Each uLong item in the accumulator can hold values up to */ + /* 2**64-1, and each partial product can be as large as */ + /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ + /* itself 18.4 times in a uLong without overflowing, so during */ + /* the main calculation resolution is carried out every 18th */ + /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ + /* partial products can be added to themselves 1844.6 times in */ + /* a uLong without overflowing, so intermediate carry */ + /* resolution occurs only every 14752 digits. Hence for common */ + /* short numbers usually only the one final carry resolution */ + /* occurs. */ + /* (The count is set via FASTLAZY to simplify experiments to */ + /* measure the value of this approach: a 35% improvement on a */ + /* [34x34] multiply.) */ + lazy=FASTLAZY; /* carry delay count */ + for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ + lp=zacc+(rip-zrhi); /* where to add the lhs */ + for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ + *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ + } /* lip loop */ + lazy--; + if (lazy>0 && rip!=rmsi) continue; + lazy=FASTLAZY; /* reset delay count */ + /* spin up the accumulator resolving overflows */ + for (lp=zacc; lp<zacc+iacc; lp++) { + if (*lp<FASTBASE) continue; /* it fits */ + lcarry=*lp/FASTBASE; /* top part [slow divide] */ + /* lcarry can exceed 2**32-1, so check again; this check */ + /* and occasional extra divide (slow) is well worth it, as */ + /* it allows FASTLAZY to be increased to 18 rather than 4 */ + /* in the FASTDIGS=9 case */ + if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ + else { /* two-place carry [fairly rare] */ + uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ + *(lp+2)+=carry2; /* add to item+2 */ + *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ + carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ + } + *(lp+1)+=carry; /* add to item above [inline] */ + *lp-=((uLong)FASTBASE*carry); /* [inline] */ + } /* carry resolution */ + } /* rip loop */ + + /* The multiplication is complete; time to convert back into */ + /* units. This can be done in-place in the accumulator and in */ + /* 32-bit operations, because carries were resolved after the */ + /* final add. This needs N-1 divides and multiplies for */ + /* each item in the accumulator (which will become up to N */ + /* units, where 2<=N<=9). */ + for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { + uInt item=(uInt)*lp; /* decapitate to uInt */ + for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { + uInt part=item/(DECDPUNMAX+1); + *up=(Unit)(item-(part*(DECDPUNMAX+1))); + item=part; + } /* p */ + *up=(Unit)item; up++; /* [final needs no division] */ + } /* lp */ + accunits=up-acc; /* count of units */ + } + else { /* here to use units directly, without chunking ['old code'] */ + #endif + + /* if accumulator will be too long for local storage, then allocate */ + acc=accbuff; /* -> assume buffer for accumulator */ + needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); + if (needbytes>(Int)sizeof(accbuff)) { + allocacc=(Unit *)malloc(needbytes); + if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} + acc=(Unit *)allocacc; /* use the allocated space */ + } + + /* Now the main long multiplication loop */ + /* Unlike the equivalent in the IBM Java implementation, there */ + /* is no advantage in calculating from msu to lsu. So, do it */ + /* by the book, as it were. */ + /* Each iteration calculates ACC=ACC+MULTAND*MULT */ + accunits=1; /* accumulator starts at '0' */ + *acc=0; /* .. (lsu=0) */ + shift=0; /* no multiplicand shift at first */ + madlength=D2U(lhs->digits); /* this won't change */ + mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ + + for (mer=rhs->lsu; mer<mermsup; mer++) { + /* Here, *mer is the next Unit in the multiplier to use */ + /* If non-zero [optimization] add it... */ + if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, + lhs->lsu, madlength, 0, + &acc[shift], *mer) + + shift; + else { /* extend acc with a 0; it will be used shortly */ + *(acc+accunits)=0; /* [this avoids length of <=0 later] */ + accunits++; + } + /* multiply multiplicand by 10**DECDPUN for next Unit to left */ + shift++; /* add this for 'logical length' */ + } /* n */ + #if FASTMUL + } /* unchunked units */ + #endif + /* common end-path */ + #if DECTRACE + decDumpAr('*', acc, accunits); /* Show exact result */ + #endif + + /* acc now contains the exact result of the multiplication, */ + /* possibly with a leading zero unit; build the decNumber from */ + /* it, noting if any residue */ + res->bits=bits; /* set sign */ + res->digits=decGetDigits(acc, accunits); /* count digits exactly */ + + /* There can be a 31-bit wrap in calculating the exponent. */ + /* This can only happen if both input exponents are negative and */ + /* both their magnitudes are large. If there was a wrap, set a */ + /* safe very negative exponent, from which decFinalize() will */ + /* raise a hard underflow shortly. */ + exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ + if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) + exponent=-2*DECNUMMAXE; /* force underflow */ + res->exponent=exponent; /* OK to overwrite now */ + + + /* Set the coefficient. If any rounding, residue records */ + decSetCoeff(res, set, acc, res->digits, &residue, status); + decFinish(res, set, &residue, status); /* final cleanup */ + } while(0); /* end protected */ + + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + #if FASTMUL + if (allocrhi!=NULL) free(allocrhi); /* .. */ + if (alloclhi!=NULL) free(alloclhi); /* .. */ + #endif + return res; + } /* decMultiplyOp */ + +/* ------------------------------------------------------------------ */ +/* decExpOp -- effect exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. status is updated but */ +/* not set. */ +/* */ +/* Restrictions: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* ------------------------------------------------------------------ */ +/* This approach used here is similar to the algorithm described in */ +/* */ +/* Variable Precision Exponential Function, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ +/* pp79-91, ACM, June 1986. */ +/* */ +/* with the main difference being that the iterations in the series */ +/* evaluation are terminated dynamically (which does not require the */ +/* extra variable-precision variables which are expensive in this */ +/* context). */ +/* */ +/* The error analysis in Hull & Abrham's paper applies except for the */ +/* round-off error accumulation during the series evaluation. This */ +/* code does not precalculate the number of iterations and so cannot */ +/* use Horner's scheme. Instead, the accumulation is done at double- */ +/* precision, which ensures that the additions of the terms are exact */ +/* and do not accumulate round-off (and any round-off errors in the */ +/* terms themselves move 'to the right' faster than they can */ +/* accumulate). This code also extends the calculation by allowing, */ +/* in the spirit of other decNumber operators, the input to be more */ +/* precise than the result (the precision used is based on the more */ +/* precise of the input or requested result). */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decExpOp so it can be called from */ +/* other Mathematical functions (notably Ln) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-x) where x can be the tiniest number (Ntiny). */ +/* */ +/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ +/* iterations by appoximately a third with additional (although */ +/* diminishing) returns as the range is reduced to even smaller */ +/* fractions. However, h (the power of 10 used to correct the */ +/* result at the end, see below) must be kept <=8 as otherwise */ +/* the final result cannot be computed. Hence the leverage is a */ +/* sliding value (8-h), where potentially the range is reduced */ +/* more for smaller values. */ +/* */ +/* The leverage that can be applied in this way is severely */ +/* limited by the cost of the raise-to-the power at the end, */ +/* which dominates when the number of iterations is small (less */ +/* than ten) or when rhs is short. As an example, the adjustment */ +/* x**10,000,000 needs 31 multiplications, all but one full-width. */ +/* */ +/* 3. The restrictions (especially precision) could be raised with */ +/* care, but the full decNumber range seems very hard within the */ +/* 32-bit limits. */ +/* */ +/* 4. The working precisions for the static buffers are twice the */ +/* obvious size to allow for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decExpOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; /* working status */ + Int h; /* adjusted exponent for 0.xxxx */ + Int p; /* working precision */ + Int residue; /* rounding residue */ + uInt needbytes; /* for space calculations */ + const decNumber *x=rhs; /* (may point to safe copy later) */ + decContext aset, tset, dset; /* working contexts */ + Int comp; /* work */ + + /* the argument is often copied to normalize it, so (unusually) it */ + /* is treated like other buffers, using DECBUFFER, +1 in case */ + /* DECBUFFER is 0 */ + decNumber bufr[D2N(DECBUFFER*2+1)]; + decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ + + /* the working precision will be no more than set->digits+8+1 */ + /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ + /* is 0 (and twice that for the accumulator) */ + + /* buffer for t, term (working precision plus) */ + decNumber buft[D2N(DECBUFFER*2+9+1)]; + decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ + decNumber *t=buft; /* term */ + /* buffer for a, accumulator (working precision * 2), at least 9 */ + decNumber bufa[D2N(DECBUFFER*4+18+1)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *a=bufa; /* accumulator */ + /* decNumber for the divisor term; this needs at most 9 digits */ + /* and so can be fixed size [16 so can use standard context] */ + decNumber bufd[D2N(16)]; + decNumber *d=bufd; /* divisor */ + decNumber numone; /* constant 1 */ + + #if DECCHECK + Int iterations=0; /* for later sanity check */ + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + if (SPECIALARG) { /* handle infinities and NaNs */ + if (decNumberIsInfinite(rhs)) { /* an infinity */ + if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ + decNumberZero(res); + else decNumberCopy(res, rhs); /* +Infinity -> self */ + } + else decNaNs(res, rhs, NULL, set, status); /* a NaN */ + break;} + + if (ISZERO(rhs)) { /* zeros -> exact 1 */ + decNumberZero(res); /* make clean 1 */ + *res->lsu=1; /* .. */ + break;} /* [no status to set] */ + + /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ + /* positive and negative tiny cases which will result in inexact */ + /* 1. This also allows the later add-accumulate to always be */ + /* exact (because its length will never be more than twice the */ + /* working precision). */ + /* The comparator (tiny) needs just one digit, so use the */ + /* decNumber d for it (reused as the divisor, etc., below); its */ + /* exponent is such that if x is positive it will have */ + /* set->digits-1 zeros between the decimal point and the digit, */ + /* which is 4, and if x is negative one more zero there as the */ + /* more precise result will be of the form 0.9999999 rather than */ + /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ + /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ + /* this then the result will be 1.000000 */ + decNumberZero(d); /* clean */ + *d->lsu=4; /* set 4 .. */ + d->exponent=-set->digits; /* * 10**(-d) */ + if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ + comp=decCompare(d, rhs, 1); /* signless compare */ + if (comp==BADINT) { + *status|=DEC_Insufficient_storage; + break;} + if (comp>=0) { /* rhs < d */ + Int shift=set->digits-1; + decNumberZero(res); /* set 1 */ + *res->lsu=1; /* .. */ + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; /* make 1.0000... */ + *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ + break;} /* tiny */ + + /* set up the context to be used for calculating a, as this is */ + /* used on both paths below */ + decContextDefault(&aset, DEC_INIT_DECIMAL64); + /* accumulator bounds are as requested (could underflow) */ + aset.emax=set->emax; /* usual bounds */ + aset.emin=set->emin; /* .. */ + aset.clamp=0; /* and no concrete format */ + + /* calculate the adjusted (Hull & Abrham) exponent (where the */ + /* decimal point is just to the left of the coefficient msd) */ + h=rhs->exponent+rhs->digits; + /* if h>8 then 10**h cannot be calculated safely; however, when */ + /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ + /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ + /* overflow (or underflow to 0) is guaranteed -- so this case can */ + /* be handled by simply forcing the appropriate excess */ + if (h>8) { /* overflow/underflow */ + /* set up here so Power call below will over or underflow to */ + /* zero; set accumulator to either 2 or 0.02 */ + /* [stack buffer for a is always big enough for this] */ + decNumberZero(a); + *a->lsu=2; /* not 1 but < exp(1) */ + if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ + h=8; /* clamp so 10**h computable */ + p=9; /* set a working precision */ + } + else { /* h<=8 */ + Int maxlever=(rhs->digits>8?1:0); + /* [could/should increase this for precisions >40 or so, too] */ + + /* if h is 8, cannot normalize to a lower upper limit because */ + /* the final result will not be computable (see notes above), */ + /* but leverage can be applied whenever h is less than 8. */ + /* Apply as much as possible, up to a MAXLEVER digits, which */ + /* sets the tradeoff against the cost of the later a**(10**h). */ + /* As h is increased, the working precision below also */ + /* increases to compensate for the "constant digits at the */ + /* front" effect. */ + Int lever=MINI(8-h, maxlever); /* leverage attainable */ + Int use=-rhs->digits-lever; /* exponent to use for RHS */ + h+=lever; /* apply leverage selected */ + if (h<0) { /* clamp */ + use+=h; /* [may end up subnormal] */ + h=0; + } + /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ + if (rhs->exponent!=use) { + decNumber *newrhs=bufr; /* assume will fit on stack */ + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufr)) { /* need malloc space */ + allocrhs=(decNumber *)malloc(needbytes); + if (allocrhs==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + newrhs=allocrhs; /* use the allocated space */ + } + decNumberCopy(newrhs, rhs); /* copy to safe space */ + newrhs->exponent=use; /* normalize; now <1 */ + x=newrhs; /* ready for use */ + /* decNumberShow(x); */ + } + + /* Now use the usual power series to evaluate exp(x). The */ + /* series starts as 1 + x + x^2/2 ... so prime ready for the */ + /* third term by setting the term variable t=x, the accumulator */ + /* a=1, and the divisor d=2. */ + + /* First determine the working precision. From Hull & Abrham */ + /* this is set->digits+h+2. However, if x is 'over-precise' we */ + /* need to allow for all its digits to potentially participate */ + /* (consider an x where all the excess digits are 9s) so in */ + /* this case use x->digits+h+2 */ + p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ + + /* a and t are variable precision, and depend on p, so space */ + /* must be allocated for them if necessary */ + + /* the accumulator needs to be able to hold 2p digits so that */ + /* the additions on the second and subsequent iterations are */ + /* sufficiently exact. */ + needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + /* the term needs to be able to hold p digits (which is */ + /* guaranteed to be larger than x->digits, so the initial copy */ + /* is safe); it may also be used for the raise-to-power */ + /* calculation below, which needs an extra two digits */ + needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); + if (needbytes>sizeof(buft)) { /* need malloc space */ + allocbuft=(decNumber *)malloc(needbytes); + if (allocbuft==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + t=allocbuft; /* use the allocated space */ + } + + decNumberCopy(t, x); /* term=x */ + decNumberZero(a); *a->lsu=1; /* accumulator=1 */ + decNumberZero(d); *d->lsu=2; /* divisor=2 */ + decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ + + /* set up the contexts for calculating a, t, and d */ + decContextDefault(&tset, DEC_INIT_DECIMAL64); + dset=tset; + /* accumulator bounds are set above, set precision now */ + aset.digits=p*2; /* double */ + /* term bounds avoid any underflow or overflow */ + tset.digits=p; + tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ + /* [dset.digits=16, etc., are sufficient] */ + + /* finally ready to roll */ + for (;;) { + #if DECCHECK + iterations++; + #endif + /* only the status from the accumulation is interesting */ + /* [but it should remain unchanged after first add] */ + decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ + decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ + decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ + /* the iteration ends when the term cannot affect the result, */ + /* if rounded to p digits, which is when its value is smaller */ + /* than the accumulator by p+1 digits. There must also be */ + /* full precision in a. */ + if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) + && (a->digits>=p)) break; + decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ + } /* iterate */ + + #if DECCHECK + /* just a sanity check; comment out test to show always */ + if (iterations>p+3) + printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + iterations, *status, p, x->digits); + #endif + } /* h<=8 */ + + /* apply postconditioning: a=a**(10**h) -- this is calculated */ + /* at a slightly higher precision than Hull & Abrham suggest */ + if (h>0) { + Int seenbit=0; /* set once a 1-bit is seen */ + Int i; /* counter */ + Int n=powers[h]; /* always positive */ + aset.digits=p+2; /* sufficient precision */ + /* avoid the overhead and many extra digits of decNumberPower */ + /* as all that is needed is the short 'multipliers' loop; here */ + /* accumulate the answer into t */ + decNumberZero(t); *t->lsu=1; /* acc=1 */ + for (i=1;;i++){ /* for each bit [top bit ignored] */ + /* abandon if have had overflow or terminal underflow */ + if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ + if (*status&DEC_Overflow || ISZERO(t)) break;} + n=n<<1; /* move next bit to testable position */ + if (n<0) { /* top bit is set */ + seenbit=1; /* OK, have a significant bit */ + decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ + } + if (i==31) break; /* that was the last bit */ + if (!seenbit) continue; /* no need to square 1 */ + decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ + } /*i*/ /* 32 bits */ + /* decNumberShow(t); */ + a=t; /* and carry on using t instead of a */ + } + + /* Copy and round the result to res */ + residue=1; /* indicate dirt to right .. */ + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ + aset.digits=set->digits; /* [use default rounding] */ + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ + decFinish(res, set, &residue, status); /* cleanup/set flags */ + } while(0); /* end protected */ + + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + if (allocbufa!=NULL) free(allocbufa); /* .. */ + if (allocbuft!=NULL) free(allocbuft); /* .. */ + /* [status is handled by caller] */ + return res; + } /* decExpOp */ + +/* ------------------------------------------------------------------ */ +/* Initial-estimate natural logarithm table */ +/* */ +/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ +/* The result is a 4-digit encode of the coefficient (c=the */ +/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ +/* exponent (e=the bottom 2 bits encoding 0-3) */ +/* */ +/* The resulting value is given by: */ +/* */ +/* v = -c * 10**(-e-3) */ +/* */ +/* where e and c are extracted from entry k = LNnn[x-10] */ +/* where x is truncated (NB) into the range 10 through 99, */ +/* and then c = k>>2 and e = k&3. */ +/* ------------------------------------------------------------------ */ +const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, + 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, + 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, + 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, + 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, + 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, + 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, + 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, + 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, + 10130, 6046, 20055}; + +/* ------------------------------------------------------------------ */ +/* decLnOp -- effect natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Restrictions (as for Exp): */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* The result is calculated using Newton's method, with each */ +/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ +/* Epperson 1989. */ +/* */ +/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ +/* This has to be calculated at the sum of the precision of x and the */ +/* working precision. */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decLnOp so it can be called from */ +/* other Mathematical functions (e.g., Log 10) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (+9+2) range needed by a power function. */ +/* */ +/* 2. The speed of this function is about 10x slower than exp, as */ +/* it typically needs 4-6 iterations for short numbers, and the */ +/* extra precision needed adds a squaring effect, twice. */ +/* */ +/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ +/* as these are common requests. ln(10) is used by log10(x). */ +/* */ +/* 4. An iteration might be saved by widening the LNnn table, and */ +/* would certainly save at least one if it were made ten times */ +/* bigger, too (for truncated fractions 0.100 through 0.999). */ +/* However, for most practical evaluations, at least four or five */ +/* iterations will be neede -- so this would only speed up by */ +/* 20-25% and that probably does not justify increasing the table */ +/* size. */ +/* */ +/* 5. The static buffers are larger than might be expected to allow */ +/* for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decLnOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; /* working status accumulator */ + uInt needbytes; /* for space calculations */ + Int residue; /* rounding residue */ + Int r; /* rhs=f*10**r [see below] */ + Int p; /* working precision */ + Int pp; /* precision for iteration */ + Int t; /* work */ + + /* buffers for a (accumulator, typically precision+2) and b */ + /* (adjustment calculator, same size) */ + decNumber bufa[D2N(DECBUFFER+12)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *a=bufa; /* accumulator/work */ + decNumber bufb[D2N(DECBUFFER*2+2)]; + decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ + decNumber *b=bufb; /* adjustment/work */ + + decNumber numone; /* constant 1 */ + decNumber cmp; /* work */ + decContext aset, bset; /* working contexts */ + + #if DECCHECK + Int iterations=0; /* for later sanity check */ + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + if (SPECIALARG) { /* handle infinities and NaNs */ + if (decNumberIsInfinite(rhs)) { /* an infinity */ + if (decNumberIsNegative(rhs)) /* -Infinity -> error */ + *status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); /* +Infinity -> self */ + } + else decNaNs(res, rhs, NULL, set, status); /* a NaN */ + break;} + + if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ + decNumberZero(res); /* make clean */ + res->bits=DECINF|DECNEG; /* set - infinity */ + break;} /* [no status to set] */ + + /* Non-zero negatives are bad... */ + if (decNumberIsNegative(rhs)) { /* -x -> error */ + *status|=DEC_Invalid_operation; + break;} + + /* Here, rhs is positive, finite, and in range */ + + /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ + if (rhs->exponent==0 && set->digits<=40) { + #if DECDPUN==1 + if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ + #else + if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ + #endif + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN10 "2.302585092994045684017991454684364207601" + decNumberFromString(res, LN10, &aset); + *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ + break;} + if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN2 "0.6931471805599453094172321214581765680755" + decNumberFromString(res, LN2, &aset); + *status|=(DEC_Inexact | DEC_Rounded); + break;} + } /* integer and short */ + + /* Determine the working precision. This is normally the */ + /* requested precision + 2, with a minimum of 9. However, if */ + /* the rhs is 'over-precise' then allow for all its digits to */ + /* potentially participate (consider an rhs where all the excess */ + /* digits are 9s) so in this case use rhs->digits+2. */ + p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; + + /* Allocate space for the accumulator and the high-precision */ + /* adjustment calculator, if necessary. The accumulator must */ + /* be able to hold p digits, and the adjustment up to */ + /* rhs->digits+p digits. They are also made big enough for 16 */ + /* digits so that they can be used for calculating the initial */ + /* estimate. */ + needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + pp=p+rhs->digits; + needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + + /* Prepare an initial estimate in acc. Calculate this by */ + /* considering the coefficient of x to be a normalized fraction, */ + /* f, with the decimal point at far left and multiplied by */ + /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ + /* ln(x) = ln(f) + ln(10)*r */ + /* Get the initial estimate for ln(f) from a small lookup */ + /* table (see above) indexed by the first two digits of f, */ + /* truncated. */ + + decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ + r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ + decNumberFromInt32(a, r); /* a=r */ + decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ + b->exponent=-6; /* .. */ + decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ + /* now get top two digits of rhs into b by simple truncate and */ + /* force to integer */ + residue=0; /* (no residue) */ + aset.digits=2; aset.round=DEC_ROUND_DOWN; + decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ + b->exponent=0; /* make integer */ + t=decGetInt(b); /* [cannot fail] */ + if (t<10) t=X10(t); /* adjust single-digit b */ + t=LNnn[t-10]; /* look up ln(b) */ + decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ + b->exponent=-(t&3)-3; /* set exponent */ + b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ + aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ + decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ + /* the initial estimate is now in a, with up to 4 digits correct. */ + /* When rhs is at or near Nmax the estimate will be low, so we */ + /* will approach it from below, avoiding overflow when calling exp. */ + + decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ + + /* accumulator bounds are as requested (could underflow, but */ + /* cannot overflow) */ + aset.emax=set->emax; + aset.emin=set->emin; + aset.clamp=0; /* no concrete format */ + /* set up a context to be used for the multiply and subtract */ + bset=aset; + bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ + bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ + /* [see decExpOp call below] */ + /* for each iteration double the number of digits to calculate, */ + /* up to a maximum of p */ + pp=9; /* initial precision */ + /* [initially 9 as then the sequence starts 7+2, 16+2, and */ + /* 34+2, which is ideal for standard-sized numbers] */ + aset.digits=pp; /* working context */ + bset.digits=pp+rhs->digits; /* wider context */ + for (;;) { /* iterate */ + #if DECCHECK + iterations++; + if (iterations>24) break; /* consider 9 * 2**24 */ + #endif + /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ + /* catastrophic subtraction but it really is the difference */ + /* from 1 that is of interest. */ + /* Use the internal entry point to Exp as it allows the double */ + /* range for calculating exp(-a) when a is the tiniest subnormal. */ + a->bits^=DECNEG; /* make -a */ + decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ + a->bits^=DECNEG; /* restore sign of a */ + /* now multiply by rhs and subtract 1, at the wider precision */ + decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ + decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ + + /* the iteration ends when the adjustment cannot affect the */ + /* result by >=0.5 ulp (at the requested digits), which */ + /* is when its value is smaller than the accumulator by */ + /* set->digits+1 digits (or it is zero) -- this is a looser */ + /* requirement than for Exp because all that happens to the */ + /* accumulator after this is the final rounding (but note that */ + /* there must also be full precision in a, or a=0). */ + + if (decNumberIsZero(b) || + (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { + if (a->digits==p) break; + if (decNumberIsZero(a)) { + decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ + if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ + else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ + break; + } + /* force padding if adjustment has gone to 0 before full length */ + if (decNumberIsZero(b)) b->exponent=a->exponent-p; + } + + /* not done yet ... */ + decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ + if (pp==p) continue; /* precision is at maximum */ + /* lengthen the next calculation */ + pp=pp*2; /* double precision */ + if (pp>p) pp=p; /* clamp to maximum */ + aset.digits=pp; /* working context */ + bset.digits=pp+rhs->digits; /* wider context */ + } /* Newton's iteration */ + + #if DECCHECK + /* just a sanity check; remove the test to show always */ + if (iterations>24) + printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + iterations, *status, p, rhs->digits); + #endif + + /* Copy and round the result to res */ + residue=1; /* indicate dirt to right */ + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ + aset.digits=set->digits; /* [use default rounding] */ + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ + decFinish(res, set, &residue, status); /* cleanup/set flags */ + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + /* [status is handled by caller] */ + return res; + } /* decLnOp */ + +/* ------------------------------------------------------------------ */ +/* decQuantizeOp -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B or matches the exponent of B. */ +/* The numerical value of C will equal A, except for the effects of */ +/* any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* quant is 1 for quantize or 0 for rescale */ +/* status is the status accumulator (this can be called without */ +/* risk of control loss) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be that requested. */ +/* ------------------------------------------------------------------ */ +static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag quant, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + const decNumber *inrhs=rhs; /* save original rhs */ + Int reqdigits=set->digits; /* requested DIGITS */ + Int reqexp; /* requested exponent [-scale] */ + Int residue=0; /* rounding residue */ + Int etiny=set->emin-(reqdigits-1); + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* Handle special values */ + if (SPECIALARGS) { + /* NaNs get usual processing */ + if (SPECIALARGS & (DECSNAN | DECNAN)) + decNaNs(res, lhs, rhs, set, status); + /* one infinity but not both is bad */ + else if ((lhs->bits ^ rhs->bits) & DECINF) + *status|=DEC_Invalid_operation; + /* both infinity: return lhs */ + else decNumberCopy(res, lhs); /* [nop if in place] */ + break; + } + + /* set requested exponent */ + if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ + else { /* rescale -- use value of rhs */ + /* Original rhs must be an integer that fits and is in range, */ + /* which could be from -1999999997 to +999999999, thanks to */ + /* subnormals */ + reqexp=decGetInt(inrhs); /* [cannot fail] */ + } + + #if DECSUBSET + if (!set->extended) etiny=set->emin; /* no subnormals */ + #endif + + if (reqexp==BADINT /* bad (rescale only) or .. */ + || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ + || (reqexp<etiny) /* < lowest */ + || (reqexp>set->emax)) { /* > emax */ + *status|=DEC_Invalid_operation; + break;} + + /* the RHS has been processed, so it can be overwritten now if necessary */ + if (ISZERO(lhs)) { /* zero coefficient unchanged */ + decNumberCopy(res, lhs); /* [nop if in place] */ + res->exponent=reqexp; /* .. just set exponent */ + #if DECSUBSET + if (!set->extended) res->bits=0; /* subset specification; no -0 */ + #endif + } + else { /* non-zero lhs */ + Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ + /* if adjusted coefficient will definitely not fit, give up now */ + if ((lhs->digits-adjust)>reqdigits) { + *status|=DEC_Invalid_operation; + break; + } + + if (adjust>0) { /* increasing exponent */ + /* this will decrease the length of the coefficient by adjust */ + /* digits, and must round as it does so */ + decContext workset; /* work */ + workset=*set; /* clone rounding, etc. */ + workset.digits=lhs->digits-adjust; /* set requested length */ + /* [note that the latter can be <1, here] */ + decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ + decApplyRound(res, &workset, residue, status); /* .. and round */ + residue=0; /* [used] */ + /* If just rounded a 999s case, exponent will be off by one; */ + /* adjust back (after checking space), if so. */ + if (res->exponent>reqexp) { + /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ + /* set->digits==3 */ + if (res->digits==reqdigits) { /* cannot shift by 1 */ + *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ + *status|=DEC_Invalid_operation; + break; + } + res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ + res->exponent--; /* (re)adjust the exponent. */ + } + #if DECSUBSET + if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ + #endif + } /* increase */ + else /* adjust<=0 */ { /* decreasing or = exponent */ + /* this will increase the length of the coefficient by -adjust */ + /* digits, by adding zero or more trailing zeros; this is */ + /* already checked for fit, above */ + decNumberCopy(res, lhs); /* [it will fit] */ + /* if padding needed (adjust<0), add it now... */ + if (adjust<0) { + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* adjust the exponent */ + } + } /* decrease */ + } /* non-zero */ + + /* Check for overflow [do not use Finalize in this case, as an */ + /* overflow here is a "don't fit" situation] */ + if (res->exponent>set->emax-res->digits+1) { /* too big */ + *status|=DEC_Invalid_operation; + break; + } + else { + decFinalize(res, set, &residue, status); /* set subnormal flags */ + *status&=~DEC_Underflow; /* suppress Underflow [754r] */ + } + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decQuantizeOp */ + +/* ------------------------------------------------------------------ */ +/* decCompareOp -- compare, min, or max two Numbers */ +/* */ +/* This computes C = A ? B and carries out one of four operations: */ +/* COMPARE -- returns the signum (as a number) giving the */ +/* result of a comparison unless one or both */ +/* operands is a NaN (in which case a NaN results) */ +/* COMPSIG -- as COMPARE except that a quiet NaN raises */ +/* Invalid operation. */ +/* COMPMAX -- returns the larger of the operands, using the */ +/* 754r maxnum operation */ +/* COMPMAXMAG -- ditto, comparing absolute values */ +/* COMPMIN -- the 754r minnum operation */ +/* COMPMINMAG -- ditto, comparing absolute values */ +/* COMTOTAL -- returns the signum (as a number) giving the */ +/* result of a comparison using 754r 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 -- 754r 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 754r) */ + uByte slhs=(lhs->bits & DECNEG); + uByte srhs=(rhs->bits & DECNEG); + #if DECSUBSET + if (!set->extended) { /* subset: force left-hand */ + op=COMPMAX; + result=+1; + } + else + #endif + if (slhs!=srhs) { /* signs differ */ + if (slhs) result=-1; /* rhs is max */ + else result=+1; /* lhs is max */ + } + else if (slhs && srhs) { /* both negative */ + if (lhs->exponent<rhs->exponent) result=+1; + else result=-1; + /* [if equal, use lhs, technically identical] */ + } + else { /* both positive */ + if (lhs->exponent>rhs->exponent) result=+1; + else result=-1; + /* [ditto] */ + } + } /* numerically equal */ + /* here result will be non-0; reverse if looking for MIN */ + if (op==COMPMIN || op==COMPMINMAG) result=-result; + choice=(result>0 ? lhs : rhs); /* choose */ + /* copy chosen to result, rounding if need be */ + decCopyFit(res, choice, set, &residue, status); + decFinish(res, set, &residue, status); + } + } + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decCompareOp */ + +/* ------------------------------------------------------------------ */ +/* decCompare -- compare two decNumbers by numerical value */ +/* */ +/* This routine compares A ? B without altering them. */ +/* */ +/* Arg1 is A, a decNumber which is not a NaN */ +/* Arg2 is B, a decNumber which is not a NaN */ +/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error) */ +/* ------------------------------------------------------------------ */ +static Int decCompare(const decNumber *lhs, const decNumber *rhs, + Flag abs) { + Int result; /* result value */ + Int sigr; /* rhs signum */ + Int compare; /* work */ + + result=1; /* assume signum(lhs) */ + if (ISZERO(lhs)) result=0; + if (abs) { + if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ + /* RHS is non-zero */ + if (result==0) return -1; /* LHS is 0; RHS wins */ + /* [here, both non-zero, result=1] */ + } + else { /* signs matter */ + if (result && decNumberIsNegative(lhs)) result=-1; + sigr=1; /* compute signum(rhs) */ + if (ISZERO(rhs)) sigr=0; + else if (decNumberIsNegative(rhs)) sigr=-1; + if (result > sigr) return +1; /* L > R, return 1 */ + if (result < sigr) return -1; /* L < R, return -1 */ + if (result==0) return 0; /* both 0 */ + } + + /* signums are the same; both are non-zero */ + if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ + if (decNumberIsInfinite(rhs)) { + if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ + else result=-result; /* only rhs infinite */ + } + return result; + } + /* must compare the coefficients, allowing for exponents */ + if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ + /* swap sides, and sign */ + const decNumber *temp=lhs; + lhs=rhs; + rhs=temp; + result=-result; + } + compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhs->exponent-lhs->exponent); + if (compare!=BADINT) compare*=result; /* comparison succeeded */ + return compare; + } /* decCompare */ + +/* ------------------------------------------------------------------ */ +/* decUnitCompare -- compare two >=0 integers in Unit arrays */ +/* */ +/* This routine compares A ? B*10**E where A and B are unit arrays */ +/* A is a plain integer */ +/* B has an exponent of E (which must be non-negative) */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is E (0 if the units are aligned) */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error, which can */ +/* only occur if E!=0) */ +/* ------------------------------------------------------------------ */ +static Int decUnitCompare(const Unit *a, Int alength, + const Unit *b, Int blength, Int exp) { + Unit *acc; /* accumulator for result */ + Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ + Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ + Int accunits, need; /* units in use or needed for acc */ + const Unit *l, *r, *u; /* work */ + Int expunits, exprem, result; /* .. */ + + if (exp==0) { /* aligned; fastpath */ + if (alength>blength) return 1; + if (alength<blength) return -1; + /* same number of units in both -- need unit-by-unit compare */ + l=a+alength-1; + r=b+alength-1; + for (;l>=a; l--, r--) { + if (*l>*r) return 1; + if (*l<*r) return -1; + } + return 0; /* all units match */ + } /* aligned */ + + /* Unaligned. If one is >1 unit longer than the other, padded */ + /* approximately, then can return easily */ + if (alength>blength+(Int)D2U(exp)) return 1; + if (alength+1<blength+(Int)D2U(exp)) return -1; + + /* Need to do a real subtract. For this, a result buffer is needed */ + /* even though only the sign is of interest. Its length needs */ + /* to be the larger of alength and padded blength, +2 */ + need=blength+D2U(exp); /* maximum real length of B */ + if (need<alength) need=alength; + need+=2; + acc=accbuff; /* assume use local buffer */ + if (need*sizeof(Unit)>sizeof(accbuff)) { + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ + acc=allocacc; + } + /* Calculate units and remainder from exponent. */ + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + /* subtract [A+B*(-m)] */ + accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, + -(Int)powers[exprem]); + /* [UnitAddSub result may have leading zeros, even on zero] */ + if (accunits<0) result=-1; /* negative result */ + else { /* non-negative result */ + /* check units of the result before freeing any storage */ + for (u=acc; u<acc+accunits-1 && *u==0;) u++; + result=(*u==0 ? 0 : +1); + } + /* clean up and return the result */ + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + return result; + } /* decUnitCompare */ + +/* ------------------------------------------------------------------ */ +/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ +/* */ +/* This routine performs the calculation: */ +/* */ +/* C=A+(B*M) */ +/* */ +/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ +/* */ +/* A may be shorter or longer than B. */ +/* */ +/* Leading zeros are not removed after a calculation. The result is */ +/* either the same length as the longer of A and B (adding any */ +/* shift), or one Unit longer than that (if a Unit carry occurred). */ +/* */ +/* A and B content are not altered unless C is also A or B. */ +/* C may be the same array as A or B, but only if no zero padding is */ +/* requested (that is, C may be B only if bshift==0). */ +/* C is filled from the lsu; only those units necessary to complete */ +/* the calculation are referenced. */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ +/* Arg6 is C first Unit (lsu) */ +/* Arg7 is M, the multiplier */ +/* */ +/* returns the count of Units written to C, which will be non-zero */ +/* and negated if the result is negative. That is, the sign of the */ +/* returned Int is the sign of the result (positive for zero) and */ +/* the absolute value of the Int is the count of Units. */ +/* */ +/* It is the caller's responsibility to make sure that C size is */ +/* safe, allowing space if necessary for a one-Unit carry. */ +/* */ +/* This routine is severely performance-critical; *any* change here */ +/* must be measured (timed) to assure no performance degradation. */ +/* In particular, trickery here tends to be counter-productive, as */ +/* increased complexity of code hurts register optimizations on */ +/* register-poor architectures. Avoiding divisions is nearly */ +/* always a Good Idea, however. */ +/* */ +/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ +/* (IBM Warwick, UK) for some of the ideas used in this routine. */ +/* ------------------------------------------------------------------ */ +static Int decUnitAddSub(const Unit *a, Int alength, + const Unit *b, Int blength, Int bshift, + Unit *c, Int m) { + const Unit *alsu=a; /* A lsu [need to remember it] */ + Unit *clsu=c; /* C ditto */ + Unit *minC; /* low water mark for C */ + Unit *maxC; /* high water mark for C */ + eInt carry=0; /* carry integer (could be Long) */ + Int add; /* work */ + #if DECDPUN<=4 /* myriadal, millenary, etc. */ + Int est; /* estimated quotient */ + #endif + + #if DECTRACE + if (alength<1 || blength<1) + printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); + #endif + + maxC=c+alength; /* A is usually the longer */ + minC=c+blength; /* .. and B the shorter */ + if (bshift!=0) { /* B is shifted; low As copy across */ + minC+=bshift; + /* if in place [common], skip copy unless there's a gap [rare] */ + if (a==c && bshift<=alength) { + c+=bshift; + a+=bshift; + } + else for (; c<clsu+bshift; a++, c++) { /* copy needed */ + if (a<alsu+alength) *c=*a; + else *c=0; + } + } + if (minC>maxC) { /* swap */ + Unit *hold=minC; + minC=maxC; + maxC=hold; + } + + /* For speed, do the addition as two loops; the first where both A */ + /* and B contribute, and the second (if necessary) where only one or */ + /* other of the numbers contribute. */ + /* Carry handling is the same (i.e., duplicated) in each case. */ + for (; c<minC; c++) { + carry+=*a; + a++; + carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ + b++; /* here is not a win] */ + /* here carry is new Unit of digits; it could be +ve or -ve */ + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ + *c=(Unit)carry; + carry=0; + continue; + } + #if DECDPUN==4 /* use divide-by-multiply */ + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [89%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [99%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + /* Can use QUOT10 as carry <= 4 digits */ + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* quotient */ + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + #else + /* remainder operator is undefined if negative, so must test */ + if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ + *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ + carry=1; + continue; + } + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } /* c */ + + /* now may have one or other to complete */ + /* [pretest to avoid loop setup/shutdown] */ + if (c<maxC) for (; c<maxC; c++) { + if (a<alsu+alength) { /* still in A */ + carry+=*a; + a++; + } + else { /* inside B */ + carry+=((eInt)*b)*m; + b++; + } + /* here carry is new Unit of digits; it could be +ve or -ve and */ + /* magnitude up to DECDPUNMAX squared */ + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ + *c=(Unit)carry; + carry=0; + continue; + } + /* result for this unit is negative or >DECDPUNMAX */ + #if DECDPUN==4 /* use divide-by-multiply */ + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [79.7%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [99%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* quotient */ + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + #else + if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ + *c=(Unit)(carry-(DECDPUNMAX+1)); + carry=1; + continue; + } + /* remainder operator is undefined if negative, so must test */ + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } /* c */ + + /* OK, all A and B processed; might still have carry or borrow */ + /* return number of Units in the result, negated if a borrow */ + if (carry==0) return c-clsu; /* no carry, so no more to do */ + if (carry>0) { /* positive carry */ + *c=(Unit)carry; /* place as new unit */ + c++; /* .. */ + return c-clsu; + } + /* -ve carry: it's a borrow; complement needed */ + add=1; /* temporary carry... */ + for (c=clsu; c<maxC; c++) { + add=DECDPUNMAX+add-*c; + if (add<=DECDPUNMAX) { + *c=(Unit)add; + add=0; + } + else { + *c=0; + add=1; + } + } + /* add an extra unit iff it would be non-zero */ + #if DECTRACE + printf("UAS borrow: add %ld, carry %ld\n", add, carry); + #endif + if ((add-carry-1)!=0) { + *c=(Unit)(add-carry-1); + c++; /* interesting, include it */ + } + return clsu-c; /* -ve result indicates borrowed */ + } /* decUnitAddSub */ + +/* ------------------------------------------------------------------ */ +/* decTrim -- trim trailing zeros or normalize */ +/* */ +/* dn is the number to trim or normalize */ +/* set is the context to use to check for clamp */ +/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ +/* 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, + 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) { + 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 854 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) { + Int dnexp; /* saves original exponent */ + 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] */ + dnexp=dn->exponent; /* save exponent */ + 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 754R/854 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 */ + uInt *j; /* work */ + uByte *b, *b0; /* .. */ + + alloc=malloc(size); /* -> allocated storage */ + if (alloc==NULL) return NULL; /* out of strorage */ + b0=(uByte *)alloc; /* as bytes */ + decAllocBytes+=n; /* account for storage */ + j=(uInt *)alloc; /* -> first four bytes */ + *j=n; /* save n */ + /* printf(" alloc ++ dAB: %ld (%d)\n", decAllocBytes, 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 *j, n; /* pointer, original length */ + uByte *b, *b0; /* work */ + + if (alloc==NULL) return; /* allowed; it's a nop */ + b0=(uByte *)alloc; /* as bytes */ + b0-=8; /* -> true start of storage */ + j=(uInt *)b0; /* -> first four bytes */ + n=*j; /* lift */ + 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, (Int)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, (Int)b0, 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 |