| /* Decimal number arithmetic module for the decNumber C Library. |
| Copyright (C) 2005, 2007 Free Software Foundation, Inc. |
| Contributed by IBM Corporation. Author Mike Cowlishaw. |
| |
| This file is part of GCC. |
| |
| GCC is free software; you can redistribute it and/or modify it under |
| the terms of the GNU General Public License as published by the Free |
| Software Foundation; either version 2, or (at your option) any later |
| version. |
| |
| In addition to the permissions in the GNU General Public License, |
| the Free Software Foundation gives you unlimited permission to link |
| the compiled version of this file into combinations with other |
| programs, and to distribute those combinations without any |
| restriction coming from the use of this file. (The General Public |
| License restrictions do apply in other respects; for example, they |
| cover modification of the file, and distribution when not linked |
| into a combine executable.) |
| |
| GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
| WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| for more details. |
| |
| You should have received a copy of the GNU General Public License |
| along with GCC; see the file COPYING. If not, write to the Free |
| Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA |
| 02110-1301, USA. */ |
| |
| /* ------------------------------------------------------------------ */ |
| /* Decimal Number arithmetic module */ |
| /* ------------------------------------------------------------------ */ |
| /* This module comprises the routines for General Decimal Arithmetic */ |
| /* as defined in the specification which may be found on the */ |
| /* http://www2.hursley.ibm.com/decimal web pages. It implements both */ |
| /* the full ('extended') arithmetic and the simpler ('subset') */ |
| /* arithmetic. */ |
| /* */ |
| /* Usage notes: */ |
| /* */ |
| /* 1. This code is ANSI C89 except: */ |
| /* */ |
| /* If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ |
| /* uint64_t types may be used. To avoid these, set DECUSE64=0 */ |
| /* and DECDPUN<=4 (see documentation). */ |
| /* */ |
| /* 2. The decNumber format which this library uses is optimized for */ |
| /* efficient processing of relatively short numbers; in particular */ |
| /* it allows the use of fixed sized structures and minimizes copy */ |
| /* and move operations. It does, however, support arbitrary */ |
| /* precision (up to 999,999,999 digits) and arbitrary exponent */ |
| /* range (Emax in the range 0 through 999,999,999 and Emin in the */ |
| /* range -999,999,999 through 0). Mathematical functions (for */ |
| /* example decNumberExp) as identified below are restricted more */ |
| /* tightly: digits, emax, and -emin in the context must be <= */ |
| /* DEC_MAX_MATH (999999), and their operand(s) must be within */ |
| /* these bounds. */ |
| /* */ |
| /* 3. Logical functions are further restricted; their operands must */ |
| /* be finite, positive, have an exponent of zero, and all digits */ |
| /* must be either 0 or 1. The result will only contain digits */ |
| /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ |
| /* */ |
| /* 4. Operands to operator functions are never modified unless they */ |
| /* are also specified to be the result number (which is always */ |
| /* permitted). Other than that case, operands must not overlap. */ |
| /* */ |
| /* 5. Error handling: the type of the error is ORed into the status */ |
| /* flags in the current context (decContext structure). The */ |
| /* SIGFPE signal is then raised if the corresponding trap-enabler */ |
| /* flag in the decContext is set (is 1). */ |
| /* */ |
| /* It is the responsibility of the caller to clear the status */ |
| /* flags as required. */ |
| /* */ |
| /* The result of any routine which returns a number will always */ |
| /* be a valid number (which may be a special value, such as an */ |
| /* Infinity or NaN). */ |
| /* */ |
| /* 6. The decNumber format is not an exchangeable concrete */ |
| /* representation as it comprises fields which may be machine- */ |
| /* dependent (packed or unpacked, or special length, for example). */ |
| /* Canonical conversions to and from strings are provided; other */ |
| /* conversions are available in separate modules. */ |
| /* */ |
| /* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ |
| /* to 1 for extended operand checking (including NULL operands). */ |
| /* Results are undefined if a badly-formed structure (or a NULL */ |
| /* pointer to a structure) is provided, though with DECCHECK */ |
| /* enabled the operator routines are protected against exceptions. */ |
| /* (Except if the result pointer is NULL, which is unrecoverable.) */ |
| /* */ |
| /* However, the routines will never cause exceptions if they are */ |
| /* given well-formed operands, even if the value of the operands */ |
| /* is inappropriate for the operation and DECCHECK is not set. */ |
| /* (Except for SIGFPE, as and where documented.) */ |
| /* */ |
| /* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ |
| /* ------------------------------------------------------------------ */ |
| /* Implementation notes for maintenance of this module: */ |
| /* */ |
| /* 1. Storage leak protection: Routines which use malloc are not */ |
| /* permitted to use return for fastpath or error exits (i.e., */ |
| /* they follow strict structured programming conventions). */ |
| /* Instead they have a do{}while(0); construct surrounding the */ |
| /* code which is protected -- break may be used to exit this. */ |
| /* Other routines can safely use the return statement inline. */ |
| /* */ |
| /* Storage leak accounting can be enabled using DECALLOC. */ |
| /* */ |
| /* 2. All loops use the for(;;) construct. Any do construct does */ |
| /* not loop; it is for allocation protection as just described. */ |
| /* */ |
| /* 3. Setting status in the context must always be the very last */ |
| /* action in a routine, as non-0 status may raise a trap and hence */ |
| /* the call to set status may not return (if the handler uses long */ |
| /* jump). Therefore all cleanup must be done first. In general, */ |
| /* to achieve this status is accumulated and is only applied just */ |
| /* before return by calling decContextSetStatus (via decStatus). */ |
| /* */ |
| /* Routines which allocate storage cannot, in general, use the */ |
| /* 'top level' routines which could cause a non-returning */ |
| /* transfer of control. The decXxxxOp routines are safe (do not */ |
| /* call decStatus even if traps are set in the context) and should */ |
| /* be used instead (they are also a little faster). */ |
| /* */ |
| /* 4. Exponent checking is minimized by allowing the exponent to */ |
| /* grow outside its limits during calculations, provided that */ |
| /* the decFinalize function is called later. Multiplication and */ |
| /* division, and intermediate calculations in exponentiation, */ |
| /* require more careful checks because of the risk of 31-bit */ |
| /* overflow (the most negative valid exponent is -1999999997, for */ |
| /* a 999999999-digit number with adjusted exponent of -999999999). */ |
| /* */ |
| /* 5. Rounding is deferred until finalization of results, with any */ |
| /* 'off to the right' data being represented as a single digit */ |
| /* residue (in the range -1 through 9). This avoids any double- */ |
| /* rounding when more than one shortening takes place (for */ |
| /* example, when a result is subnormal). */ |
| /* */ |
| /* 6. The digits count is allowed to rise to a multiple of DECDPUN */ |
| /* during many operations, so whole Units are handled and exact */ |
| /* accounting of digits is not needed. The correct digits value */ |
| /* is found by decGetDigits, which accounts for leading zeros. */ |
| /* This must be called before any rounding if the number of digits */ |
| /* is not known exactly. */ |
| /* */ |
| /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ |
| /* numbers up to four digits, using appropriate constants. This */ |
| /* is not useful for longer numbers because overflow of 32 bits */ |
| /* would lead to 4 multiplies, which is almost as expensive as */ |
| /* a divide (unless a floating-point or 64-bit multiply is */ |
| /* assumed to be available). */ |
| /* */ |
| /* 8. Unusual abbreviations that may be used in the commentary: */ |
| /* lhs -- left hand side (operand, of an operation) */ |
| /* lsd -- least significant digit (of coefficient) */ |
| /* lsu -- least significant Unit (of coefficient) */ |
| /* msd -- most significant digit (of coefficient) */ |
| /* msi -- most significant item (in an array) */ |
| /* msu -- most significant Unit (of coefficient) */ |
| /* rhs -- right hand side (operand, of an operation) */ |
| /* +ve -- positive */ |
| /* -ve -- negative */ |
| /* ** -- raise to the power */ |
| /* ------------------------------------------------------------------ */ |
| |
| #include "qemu/osdep.h" |
| #include "libdecnumber/dconfig.h" |
| #include "libdecnumber/decNumber.h" |
| #include "libdecnumber/decNumberLocal.h" |
| |
| /* Constants */ |
| /* Public lookup table used by the D2U macro */ |
| const uByte d2utable[DECMAXD2U+1]=D2UTABLE; |
| |
| #define DECVERB 1 /* set to 1 for verbose DECCHECK */ |
| #define powers DECPOWERS /* old internal name */ |
| |
| /* Local constants */ |
| #define DIVIDE 0x80 /* Divide operators */ |
| #define REMAINDER 0x40 /* .. */ |
| #define DIVIDEINT 0x20 /* .. */ |
| #define REMNEAR 0x10 /* .. */ |
| #define COMPARE 0x01 /* Compare operators */ |
| #define COMPMAX 0x02 /* .. */ |
| #define COMPMIN 0x03 /* .. */ |
| #define COMPTOTAL 0x04 /* .. */ |
| #define COMPNAN 0x05 /* .. [NaN processing] */ |
| #define COMPSIG 0x06 /* .. [signaling COMPARE] */ |
| #define COMPMAXMAG 0x07 /* .. */ |
| #define COMPMINMAG 0x08 /* .. */ |
| |
| #define DEC_sNaN 0x40000000 /* local status: sNaN signal */ |
| #define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ |
| /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ |
| #define BIGEVEN (Int)0x80000002 |
| #define BIGODD (Int)0x80000003 |
| |
| static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ |
| |
| /* Granularity-dependent code */ |
| #if DECDPUN<=4 |
| #define eInt Int /* extended integer */ |
| #define ueInt uInt /* unsigned extended integer */ |
| /* Constant multipliers for divide-by-power-of five using reciprocal */ |
| /* multiply, after removing powers of 2 by shifting, and final shift */ |
| /* of 17 [we only need up to **4] */ |
| static const uInt multies[]={131073, 26215, 5243, 1049, 210}; |
| /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ |
| #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) |
| #else |
| /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ |
| #if !DECUSE64 |
| #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 |
| #endif |
| #define eInt Long /* extended integer */ |
| #define ueInt uLong /* unsigned extended integer */ |
| #endif |
| |
| /* Local routines */ |
| static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, |
| decContext *, uByte, uInt *); |
| static Flag decBiStr(const char *, const char *, const char *); |
| static uInt decCheckMath(const decNumber *, decContext *, uInt *); |
| static void decApplyRound(decNumber *, decContext *, Int, uInt *); |
| static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); |
| static decNumber * decCompareOp(decNumber *, const decNumber *, |
| const decNumber *, decContext *, |
| Flag, uInt *); |
| static void decCopyFit(decNumber *, const decNumber *, decContext *, |
| Int *, uInt *); |
| static decNumber * decDecap(decNumber *, Int); |
| static decNumber * decDivideOp(decNumber *, const decNumber *, |
| const decNumber *, decContext *, Flag, uInt *); |
| static decNumber * decExpOp(decNumber *, const decNumber *, |
| decContext *, uInt *); |
| static void decFinalize(decNumber *, decContext *, Int *, uInt *); |
| static Int decGetDigits(Unit *, Int); |
| static Int decGetInt(const decNumber *); |
| static decNumber * decLnOp(decNumber *, const decNumber *, |
| decContext *, uInt *); |
| static decNumber * decMultiplyOp(decNumber *, const decNumber *, |
| const decNumber *, decContext *, |
| uInt *); |
| static decNumber * decNaNs(decNumber *, const decNumber *, |
| const decNumber *, decContext *, uInt *); |
| static decNumber * decQuantizeOp(decNumber *, const decNumber *, |
| const decNumber *, decContext *, Flag, |
| uInt *); |
| static void decReverse(Unit *, Unit *); |
| static void decSetCoeff(decNumber *, decContext *, const Unit *, |
| Int, Int *, uInt *); |
| static void decSetMaxValue(decNumber *, decContext *); |
| static void decSetOverflow(decNumber *, decContext *, uInt *); |
| static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); |
| static Int decShiftToLeast(Unit *, Int, Int); |
| static Int decShiftToMost(Unit *, Int, Int); |
| static void decStatus(decNumber *, uInt, decContext *); |
| static void decToString(const decNumber *, char[], Flag); |
| static decNumber * decTrim(decNumber *, decContext *, Flag, Int *); |
| static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, |
| Unit *, Int); |
| static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); |
| |
| #if !DECSUBSET |
| /* decFinish == decFinalize when no subset arithmetic needed */ |
| #define decFinish(a,b,c,d) decFinalize(a,b,c,d) |
| #else |
| static void decFinish(decNumber *, decContext *, Int *, uInt *); |
| static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); |
| #endif |
| |
| /* Local macros */ |
| /* masked special-values bits */ |
| #define SPECIALARG (rhs->bits & DECSPECIAL) |
| #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) |
| |
| /* Diagnostic macros, etc. */ |
| #if DECALLOC |
| /* Handle malloc/free accounting. If enabled, our accountable routines */ |
| /* are used; otherwise the code just goes straight to the system malloc */ |
| /* and free routines. */ |
| #define malloc(a) decMalloc(a) |
| #define free(a) decFree(a) |
| #define DECFENCE 0x5a /* corruption detector */ |
| /* 'Our' malloc and free: */ |
| static void *decMalloc(size_t); |
| static void decFree(void *); |
| uInt decAllocBytes=0; /* count of bytes allocated */ |
| /* Note that DECALLOC code only checks for storage buffer overflow. */ |
| /* To check for memory leaks, the decAllocBytes variable must be */ |
| /* checked to be 0 at appropriate times (e.g., after the test */ |
| /* harness completes a set of tests). This checking may be unreliable */ |
| /* if the testing is done in a multi-thread environment. */ |
| #endif |
| |
| #if DECCHECK |
| /* Optional checking routines. Enabling these means that decNumber */ |
| /* and decContext operands to operator routines are checked for */ |
| /* correctness. This roughly doubles the execution time of the */ |
| /* fastest routines (and adds 600+ bytes), so should not normally be */ |
| /* used in 'production'. */ |
| /* decCheckInexact is used to check that inexact results have a full */ |
| /* complement of digits (where appropriate -- this is not the case */ |
| /* for Quantize, for example) */ |
| #define DECUNRESU ((decNumber *)(void *)0xffffffff) |
| #define DECUNUSED ((const decNumber *)(void *)0xffffffff) |
| #define DECUNCONT ((decContext *)(void *)(0xffffffff)) |
| static Flag decCheckOperands(decNumber *, const decNumber *, |
| const decNumber *, decContext *); |
| static Flag decCheckNumber(const decNumber *); |
| static void decCheckInexact(const decNumber *, decContext *); |
| #endif |
| |
| #if DECTRACE || DECCHECK |
| /* Optional trace/debugging routines (may or may not be used) */ |
| void decNumberShow(const decNumber *); /* displays the components of a number */ |
| static void decDumpAr(char, const Unit *, Int); |
| #endif |
| |
| /* ================================================================== */ |
| /* Conversions */ |
| /* ================================================================== */ |
| |
| /* ------------------------------------------------------------------ */ |
| /* from-int32 -- conversion from Int or uInt */ |
| /* */ |
| /* dn is the decNumber to receive the integer */ |
| /* in or uin is the integer to be converted */ |
| /* returns dn */ |
| /* */ |
| /* No error is possible. */ |
| /* ------------------------------------------------------------------ */ |
| decNumber * decNumberFromInt32(decNumber *dn, Int in) { |
| uInt unsig; |
| if (in>=0) unsig=in; |
| else { /* negative (possibly BADINT) */ |
| if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ |
| else unsig=-in; /* invert */ |
| } |
| /* in is now positive */ |
| decNumberFromUInt32(dn, unsig); |
| if (in<0) dn->bits=DECNEG; /* sign needed */ |
| return dn; |
| } /* decNumberFromInt32 */ |
| |
| decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { |
| Unit *up; /* work pointer */ |
| decNumberZero(dn); /* clean */ |
| if (uin==0) return dn; /* [or decGetDigits bad call] */ |
| for (up=dn->lsu; uin>0; up++) { |
| *up=(Unit)(uin%(DECDPUNMAX+1)); |
| uin=uin/(DECDPUNMAX+1); |
| } |
| dn->digits=decGetDigits(dn->lsu, up-dn->lsu); |
| return dn; |
| } /* decNumberFromUInt32 */ |
| |
| /* ------------------------------------------------------------------ */ |
| /* to-int32 -- conversion to Int or uInt */ |
| /* */ |
| /* dn is the decNumber to convert */ |
| /* set is the context for reporting errors */ |
| /* returns the converted decNumber, or 0 if Invalid is set */ |
| /* */ |
| /* Invalid is set if the decNumber does not have exponent==0 or if */ |
| /* it is a NaN, Infinite, or out-of-range. */ |
| /* ------------------------------------------------------------------ */ |
| Int decNumberToInt32(const decNumber *dn, decContext *set) { |
| #if DECCHECK |
| if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| #endif |
| |
| /* special or too many digits, or bad exponent */ |
| if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ |
| else { /* is a finite integer with 10 or fewer digits */ |
| Int d; /* work */ |
| const Unit *up; /* .. */ |
| uInt hi=0, lo; /* .. */ |
| up=dn->lsu; /* -> lsu */ |
| lo=*up; /* get 1 to 9 digits */ |
| #if DECDPUN>1 /* split to higher */ |
| hi=lo/10; |
| lo=lo%10; |
| #endif |
| up++; |
| /* collect remaining Units, if any, into hi */ |
| for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
| /* now low has the lsd, hi the remainder */ |
| if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ |
| /* most-negative is a reprieve */ |
| if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; |
| /* bad -- drop through */ |
| } |
| else { /* in-range always */ |
| Int i=X10(hi)+lo; |
| if (dn->bits&DECNEG) return -i; |
| return i; |
| } |
| } /* integer */ |
| decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
| return 0; |
| } /* decNumberToInt32 */ |
| |
| uInt decNumberToUInt32(const decNumber *dn, decContext *set) { |
| #if DECCHECK |
| if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| #endif |
| /* special or too many digits, or bad exponent, or negative (<0) */ |
| if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 |
| || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ |
| else { /* is a finite integer with 10 or fewer digits */ |
| Int d; /* work */ |
| const Unit *up; /* .. */ |
| uInt hi=0, lo; /* .. */ |
| up=dn->lsu; /* -> lsu */ |
| lo=*up; /* get 1 to 9 digits */ |
| #if DECDPUN>1 /* split to higher */ |
| hi=lo/10; |
| lo=lo%10; |
| #endif |
| up++; |
| /* collect remaining Units, if any, into hi */ |
| for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
| |
| /* now low has the lsd, hi the remainder */ |
| if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ |
| else return X10(hi)+lo; |
| } /* integer */ |
| decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
| return 0; |
| } /* decNumberToUInt32 */ |
| |
| decNumber *decNumberFromInt64(decNumber *dn, int64_t in) |
| { |
| uint64_t unsig = in; |
| if (in < 0) { |
| unsig = -unsig; |
| } |
| |
| decNumberFromUInt64(dn, unsig); |
| if (in < 0) { |
| dn->bits = DECNEG; /* sign needed */ |
| } |
| return dn; |
| } /* decNumberFromInt64 */ |
| |
| decNumber *decNumberFromUInt64(decNumber *dn, uint64_t uin) |
| { |
| Unit *up; /* work pointer */ |
| decNumberZero(dn); /* clean */ |
| if (uin == 0) { |
| return dn; /* [or decGetDigits bad call] */ |
| } |
| for (up = dn->lsu; uin > 0; up++) { |
| *up = (Unit)(uin % (DECDPUNMAX + 1)); |
| uin = uin / (DECDPUNMAX + 1); |
| } |
| dn->digits = decGetDigits(dn->lsu, up-dn->lsu); |
| return dn; |
| } /* decNumberFromUInt64 */ |
| |
| /* ------------------------------------------------------------------ */ |
| /* to-int64 -- conversion to int64 */ |
| /* */ |
| /* dn is the decNumber to convert. dn is assumed to have been */ |
| /* rounded to a floating point integer value. */ |
| /* set is the context for reporting errors */ |
| /* returns the converted decNumber, or 0 if Invalid is set */ |
| /* */ |
| /* Invalid is set if the decNumber is a NaN, Infinite or is out of */ |
| /* range for a signed 64 bit integer. */ |
| /* ------------------------------------------------------------------ */ |
| |
| int64_t decNumberIntegralToInt64(const decNumber *dn, decContext *set) |
| { |
| if (decNumberIsSpecial(dn) || (dn->exponent < 0) || |
| (dn->digits + dn->exponent > 19)) { |
| goto Invalid; |
| } else { |
| int64_t d; /* work */ |
| const Unit *up; /* .. */ |
| uint64_t hi = 0; |
| up = dn->lsu; /* -> lsu */ |
| |
| for (d = 1; d <= dn->digits; up++, d += DECDPUN) { |
| uint64_t prev = hi; |
| hi += *up * powers[d-1]; |
| if ((hi < prev) || (hi > INT64_MAX)) { |
| goto Invalid; |
| } |
| } |
| |
| uint64_t prev = hi; |
| hi *= (uint64_t)powers[dn->exponent]; |
| if ((hi < prev) || (hi > INT64_MAX)) { |
| goto Invalid; |
| } |
| return (decNumberIsNegative(dn)) ? -((int64_t)hi) : (int64_t)hi; |
| } |
| |
| Invalid: |
| decContextSetStatus(set, DEC_Invalid_operation); |
| return 0; |
| } /* decNumberIntegralToInt64 */ |
| |
| |
| /* ------------------------------------------------------------------ */ |
| /* 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; /* assume 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(n) - 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 functions (notably 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 functions (notably 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; /* .. */ |
| uLong 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 approximately 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. */ |
| /* ------------------------------------------------------------------ */ |
| static 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. */ |
| /* ------------------------------------------------------------------ */ |
| static 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. */ |
| /* ------------------------------------------------------------------ */ |
| static 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. */ |
| /* ------------------------------------------------------------------ */ |
| static 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) { |
| decContext workset; /* work */ |
| Int etiny, adjust; /* .. */ |
| |
| #if DECSUBSET |
| /* simple set to zero and 'hard underflow' for subset */ |
| if (!set->extended) { |
| decNumberZero(dn); |
| /* always full overflow */ |
| *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; |
| return; |
| } |
| #endif |
| |
| /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ |
| /* (Etiny) if needed */ |
| etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ |
| |
| if ISZERO(dn) { /* value is zero */ |
| /* residue can never be non-zero here */ |
| #if DECCHECK |
| if (*residue!=0) { |
| printf("++ Subnormal 0 residue %ld\n", (LI)*residue); |
| *status|=DEC_Invalid_operation; |
| } |
| #endif |
| if (dn->exponent<etiny) { /* clamp required */ |
| dn->exponent=etiny; |
| *status|=DEC_Clamped; |
| } |
| return; |
| } |
| |
| *status|=DEC_Subnormal; /* have a non-zero subnormal */ |
| adjust=etiny-dn->exponent; /* calculate digits to remove */ |
| if (adjust<=0) { /* not out of range; unrounded */ |
| /* residue can never be non-zero here, except in the Nmin-residue */ |
| /* case (which is a subnormal result), so can take fast-path here */ |
| /* it may already be inexact (from setting the coefficient) */ |
| if (*status&DEC_Inexact) *status|=DEC_Underflow; |
| return; |
| } |
| |
| /* adjust>0, so need to rescale the result so exponent becomes Etiny */ |
| /* [this code is similar to that in rescale] */ |
| workset=*set; /* clone rounding, etc. */ |
| workset.digits=dn->digits-adjust; /* set requested length */ |
| workset.emin-=adjust; /* and adjust emin to match */ |
| /* [note that the latter can be <1, here, similar to Rescale case] */ |
| decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); |
| decApplyRound(dn, &workset, *residue, status); |
| |
| /* Use 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 |