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Diffstat (limited to 'gcc-4.2.1-5666.3/libdecnumber/decNumber.c')
| -rw-r--r-- | gcc-4.2.1-5666.3/libdecnumber/decNumber.c | 5963 |
1 files changed, 0 insertions, 5963 deletions
diff --git a/gcc-4.2.1-5666.3/libdecnumber/decNumber.c b/gcc-4.2.1-5666.3/libdecnumber/decNumber.c deleted file mode 100644 index dbc421489..000000000 --- a/gcc-4.2.1-5666.3/libdecnumber/decNumber.c +++ /dev/null @@ -1,5963 +0,0 @@ -/* Decimal Number module for the decNumber C Library - Copyright (C) 2005 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. */ - -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for Standard 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: */ -/* */ -/* a) Line comments (double forward slash) are used. (Most C */ -/* compilers accept these. If yours does not, a simple script */ -/* can be used to convert them to ANSI C comments.) */ -/* */ -/* b) Types from C99 stdint.h are used. If you do not have this */ -/* header file, see the User's Guide section of the decNumber */ -/* documentation; this lists the necessary definitions. */ -/* */ -/* c) If DECDPUN>4, non-ANSI 64-bit 'long long' types are used. */ -/* To avoid these, set 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). */ -/* */ -/* 3. 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 may not overlap. */ -/* */ -/* 4. 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). */ -/* */ -/* 5. The decNumber format is not an exchangeable concrete */ -/* representation as it comprises fields which may be machine- */ -/* dependent (big-endian or little-endian, for example). */ -/* Canonical conversions to and from strings are provided; other */ -/* conversions are available in separate modules. */ -/* */ -/* 6. 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 */ -/* 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. */ -/* */ -/* 7. 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 from this. */ -/* Other routines are allowed to use the return statement inline. */ -/* */ -/* Storage leak accounting can be enabled using DECALLOC. */ -/* */ -/* 2. All loops use the for(;;) construct. Any do construct is for */ -/* 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 we accumulate status and only finally apply it */ -/* by calling decContextSetStatus (via decStatus). */ -/* */ -/* Routines which allocate storage cannot, therefore, 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. We use the multiply-by-reciprocal 'trick' 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 we assumed floating-point multiply available). */ -/* */ -/* 8. Unusual abbreviations possibly 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) */ -/* msu -- most significant Unit (of coefficient) */ -/* rhs -- right hand side (operand, of an operation) */ -/* +ve -- positive */ -/* -ve -- negative */ -/* ------------------------------------------------------------------ */ - -/* Some of glibc's string inlines cause warnings. Plus we'd rather - rely on (and therefore test) GCC's string builtins. */ -#define __NO_STRING_INLINES - -#include <stdlib.h> /* for malloc, free, etc. */ -#include <stdio.h> /* for printf [if needed] */ -#include <string.h> /* for strcpy */ -#include <ctype.h> /* for lower */ -#include "config.h" -#include "decNumber.h" /* base number library */ -#include "decNumberLocal.h" /* decNumber local types, etc. */ - -/* Constants */ -/* Public constant array: powers of ten (powers[n]==10**n) */ -const uInt powers[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, - 10000000, 100000000, 1000000000 -}; - -/* 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 COMPNAN 0x04 /* .. [NaN processing] */ - -#define DEC_sNaN 0x40000000 /* local status: sNaN signal */ -#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ - -static Unit one[] = { 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 we currently use non-ANSI 64-bit types. These could */ - /* be replaced by subroutine calls later. */ -#ifdef long -#undef long -#endif -typedef signed long long Long; -typedef unsigned long long uLong; -#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 void decApplyRound (decNumber *, decContext *, Int, uInt *); -static Int decCompare (const decNumber * lhs, const decNumber * rhs); -static decNumber *decCompareOp (decNumber *, const decNumber *, const decNumber *, - decContext *, Flag, uInt *); -static void decCopyFit (decNumber *, const decNumber *, decContext *, - Int *, uInt *); -static decNumber *decDivideOp (decNumber *, const decNumber *, const decNumber *, - decContext *, Flag, uInt *); -static void decFinalize (decNumber *, decContext *, Int *, uInt *); -static Int decGetDigits (const Unit *, Int); -#if DECSUBSET -static Int decGetInt (const decNumber *, decContext *); -#else -static Int decGetInt (const decNumber *); -#endif -static decNumber *decMultiplyOp (decNumber *, const decNumber *, - const decNumber *, decContext *, uInt *); -static decNumber *decNaNs (decNumber *, const decNumber *, const decNumber *, uInt *); -static decNumber *decQuantizeOp (decNumber *, const decNumber *, - const decNumber *, decContext *, Flag, uInt *); -static void decSetCoeff (decNumber *, decContext *, const Unit *, - Int, Int *, uInt *); -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 Flag decStrEq (const char *, const char *); -static void decToString (const decNumber *, char[], Flag); -static decNumber *decTrim (decNumber *, 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 - -/* 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 should 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 operand 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'. */ -#define DECUNUSED (void *)(0xffffffff) -static Flag decCheckOperands (decNumber *, const decNumber *, - const decNumber *, decContext *); -static Flag decCheckNumber (const decNumber *, decContext *); -#endif - -#if DECTRACE || DECCHECK -/* Optional trace/debugging routines. */ -void decNumberShow (const decNumber *); /* displays the components of a number */ -static void decDumpAr (char, const Unit *, Int); -#endif - -/* ================================================================== */ -/* Conversions */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* 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; -} - -char * -decNumberToEngString (const decNumber * dn, char *string) -{ - decToString (dn, string, 1); - return string; -} - -/* ------------------------------------------------------------------ */ -/* 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[D2U (DECBUFFER + 1)]; /* local buffer in case need temporary */ - Unit *allocres = NULL; /* -> allocated result, iff allocated */ - Int need; /* units needed for result */ - Int d = 0; /* count of digits found in decimal part */ - const char *dotchar = NULL; /* where dot was found */ - const char *cfirst; /* -> first character of decimal part */ - const char *last = NULL; /* -> last digit of decimal part */ - const char *firstexp; /* -> first significant exponent digit */ - const char *c; /* work */ - Unit *up; /* .. */ -#if DECDPUN>1 - Int i; /* .. */ -#endif - Int residue = 0; /* rounding residue */ - uInt status = 0; /* error code */ - -#if DECCHECK - if (decCheckOperands (DECUNUSED, DECUNUSED, DECUNUSED, set)) - return decNumberZero (dn); -#endif - - do - { /* status & malloc protection */ - c = chars; /* -> input character */ - if (*c == '-') - { /* handle leading '-' */ - bits = DECNEG; - c++; - } - else if (*c == '+') - c++; /* step over leading '+' */ - /* We're at the start of the number [we think] */ - cfirst = c; /* save */ - for (;; c++) - { - if (*c >= '0' && *c <= '9') - { /* test for Arabic digit */ - last = c; - d++; /* count of real digits */ - continue; /* still in decimal part */ - } - if (*c != '.') - break; /* done with decimal part */ - /* dot: record, check, and ignore */ - if (dotchar != NULL) - { /* two dots */ - last = NULL; /* indicate bad */ - break; - } /* .. and go report */ - dotchar = c; /* offset into decimal part */ - } /* c */ - - if (last == NULL) - { /* no decimal digits, or >1 . */ -#if DECSUBSET - /* If subset then infinities and NaNs are not allowed */ - if (!set->extended) - { - status = DEC_Conversion_syntax; - break; /* all done */ - } - else - { -#endif - /* Infinities and NaNs are possible, here */ - decNumberZero (dn); /* be optimistic */ - if (decStrEq (c, "Infinity") || decStrEq (c, "Inf")) - { - dn->bits = bits | DECINF; - break; /* all done */ - } - else - { /* a NaN expected */ - /* 2003.09.10 NaNs are now permitted to have a sign */ - status = DEC_Conversion_syntax; /* assume the worst */ - 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 nothing, or nnnn, 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) - break; /* too many digits */ - /* good; drop through and convert the integer */ - status = 0; - bits = dn->bits; /* for copy-back */ - } /* NaN expected */ -#if DECSUBSET - } -#endif - } /* last==NULL */ - - if (*c != '\0') - { /* more there; exponent expected... */ - Flag nege = 0; /* 1=negative exponent */ - if (*c != 'e' && *c != 'E') - { - status = DEC_Conversion_syntax; - break; - } - - /* Found 'e' or 'E' -- now process explicit exponent */ - /* 1998.07.11: sign no longer required */ - c++; /* to (expected) sign */ - if (*c == '-') - { - nege = 1; - c++; - } - else if (*c == '+') - c++; - if (*c == '\0') - { - status = DEC_Conversion_syntax; - 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 we didn't end on '\0' must not be a digit */ - if (*c != '\0') - { - status = DEC_Conversion_syntax; - break; - } - - /* (this next test must be after the syntax check) */ - /* 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 */ - } /* had exponent */ - /* Here when all inspected; syntax is good */ - - /* Handle decimal point... */ - if (dotchar != NULL && dotchar < last) /* embedded . found, so */ - exponent = exponent - (last - dotchar); /* .. adjust exponent */ - /* [we can now ignore the .] */ - - /* strip leading zeros/dot (leave final if all 0's) */ - for (c = cfirst; c < last; c++) - { - if (*c == '0') - d--; /* 0 stripped */ - else if (*c != '.') - break; - cfirst++; /* step past leader */ - } /* c */ - -#if DECSUBSET - /* We can now make a rapid exit for zeros if !extended */ - if (*cfirst == '0' && !set->extended) - { - decNumberZero (dn); /* clean result */ - break; /* [could be return] */ - } -#endif - - /* OK, the digits string is good. Copy to the decNumber, or to - a temporary decNumber if rounding is needed */ - if (d <= set->digits) - res = dn->lsu; /* fits into given decNumber */ - else - { /* rounding needed */ - need = D2U (d); /* units needed */ - res = resbuff; /* assume use local buffer */ - if (need * sizeof (Unit) > sizeof (resbuff)) - { /* too big for local */ - allocres = (Unit *) malloc (need * sizeof (Unit)); - 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 */ -#if DECDPUN>1 - i = d % DECDPUN; /* digits in top unit */ - if (i == 0) - i = DECDPUN; - up = res + D2U (d) - 1; /* -> msu */ - *up = 0; - for (c = cfirst;; c++) - { /* along the digits */ - if (*c == '.') - { /* ignore . [don't decrement i] */ - if (c != last) - continue; - break; - } - *up = (Unit) (X10 (*up) + (Int) * c - (Int) '0'); - i--; - if (i > 0) - continue; /* more for this unit */ - if (up == res) - break; /* just filled the last unit */ - i = DECDPUN; - up--; - *up = 0; - } /* c */ -#else - /* DECDPUN==1 */ - up = res; /* -> lsu */ - for (c = last; c >= cfirst; c--) - { /* over each character, from least */ - if (*c == '.') - continue; /* ignore . [don't step b] */ - *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) - decSetCoeff (dn, set, res, d, &residue, &status); - - /* Finally check for overflow or subnormal and round as needed */ - decFinalize (dn, set, &residue, &status); - /* decNumberShow(dn); */ - } - while (0); /* [for break] */ - - if (allocres != NULL) - free (allocres); /* drop any storage we used */ - if (status != 0) - decStatus (dn, status, set); - return dn; -} - -/* ================================================================== */ -/* 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 */ -/* */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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. */ -/* ------------------------------------------------------------------ */ -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; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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; -} - -/* ------------------------------------------------------------------ */ -/* decNumberMax -- compare two Numbers and return the maximum */ -/* */ -/* This computes C = A ? B, returning the maximum or A if equal */ -/* */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* decNumberMin -- compare two Numbers and return the minimum */ -/* */ -/* This computes C = A ? B, returning the minimum or A if equal */ -/* */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* We 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* We simply use 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* decNumberNormalize -- 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. */ -/* ------------------------------------------------------------------ */ -decNumber * -decNumberNormalize (decNumber * res, const decNumber * rhs, decContext * set) -{ - decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */ - 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] */ - - /* specials copy through, except NaNs need care */ - if (decNumberIsNaN (rhs)) - { - decNaNs (res, rhs, NULL, &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, 1, &dropped); /* normalize in place */ - } - while (0); /* end protected */ - - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (status != 0) - decStatus (res, status, set); /* then report status */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* decNumberPower -- raise a number to an integer 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. */ -/* */ -/* Specification restriction: abs(n) must be <=999999999 */ -/* ------------------------------------------------------------------ */ -decNumber * -decNumberPower (decNumber * res, const decNumber * lhs, - const decNumber * rhs, decContext * set) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - decNumber *allocdac = NULL; /* -> allocated acc buffer, iff used */ - const decNumber *inrhs = rhs; /* save original rhs */ - Int reqdigits = set->digits; /* requested DIGITS */ - Int n; /* RHS in binary */ - 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; /* accumulator */ - uByte bits = 0; /* result sign if errors */ - decContext workset; /* working context */ - decNumber dnOne; /* work value 1... */ - /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ - uByte dacbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)]; - /* same again for possible 1/lhs calculation */ - uByte lhsbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)]; - decNumber *dac = (decNumber *) dacbuff; /* -> result accumulator */ - -#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; - } - /* rounding won't affect the result, but we might signal lostDigits */ - /* as well as the error for non-integer [x**y would need this too] */ - if (rhs->digits > reqdigits) - { - allocrhs = decRoundOperand (rhs, set, &status); - if (allocrhs == NULL) - break; - rhs = allocrhs; - } - } -#endif - /* [following code does not require input rounding] */ - - /* handle rhs Infinity */ - if (decNumberIsInfinite (rhs)) - { - status |= DEC_Invalid_operation; /* bad */ - break; - } - /* handle NaNs */ - if ((lhs->bits | rhs->bits) & (DECNAN | DECSNAN)) - { - decNaNs (res, lhs, rhs, &status); - break; - } - - /* Original rhs must be an integer that fits and is in range */ -#if DECSUBSET - n = decGetInt (inrhs, set); -#else - n = decGetInt (inrhs); -#endif - if (n == BADINT || n > 999999999 || n < -999999999) - { - status |= DEC_Invalid_operation; - break; - } - if (n < 0) - { /* negative */ - n = -n; /* use the absolute value */ - } - if (decNumberIsNegative (lhs) /* -x .. */ - && (n & 0x00000001)) - bits = DECNEG; /* .. to an odd power */ - - /* handle LHS infinity */ - if (decNumberIsInfinite (lhs)) - { /* [NaNs already handled] */ - uByte rbits = rhs->bits; /* save */ - decNumberZero (res); - if (n == 0) - *res->lsu = 1; /* [-]Inf**0 => 1 */ - else - { - if (!(rbits & DECNEG)) - bits |= DECINF; /* was not a **-n */ - /* [otherwise will be 0 or -0] */ - res->bits = bits; - } - break; - } - - /* clone the context */ - workset = *set; /* copy all fields */ - /* calculate the working DIGITS */ - workset.digits = reqdigits + (inrhs->digits + inrhs->exponent) + 1; - /* it's an error if this is more than we can handle */ - if (workset.digits > DECNUMMAXP) - { - status |= DEC_Invalid_operation; - break; - } - - /* workset.digits is the count of digits for the accumulator we need */ - /* if accumulator is too long for local storage, then allocate */ - needbytes = - sizeof (decNumber) + (D2U (workset.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 */ - } - decNumberZero (dac); /* acc=1 */ - *dac->lsu = 1; /* .. */ - - if (n == 0) - { /* x**0 is usually 1 */ - /* 0**0 is bad unless subset, when it becomes 1 */ - if (ISZERO (lhs) -#if DECSUBSET - && set->extended -#endif - ) - status |= DEC_Invalid_operation; - else - decNumberCopy (res, dac); /* copy the 1 */ - break; - } - - /* if a negative power we'll need the constant 1, and if not subset */ - /* we'll invert the lhs now rather than inverting the result later */ - if (decNumberIsNegative (rhs)) - { /* was a **-n [hence digits>0] */ - decNumber * newlhs; - 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, &workset, DIVIDE, &status); - if (alloclhs != NULL) - { - free (alloclhs); /* done with intermediate */ - alloclhs = NULL; /* indicate freed */ - } - /* now locate or allocate space for the inverted lhs */ - if (needbytes > sizeof (lhsbuff)) - { - alloclhs = (decNumber *) malloc (needbytes); - if (alloclhs == NULL) - { /* hopeless -- abandon */ - status |= DEC_Insufficient_storage; - break; - } - newlhs = alloclhs; /* use the allocated space */ - } - else - newlhs = (decNumber *) lhsbuff; /* use stack storage */ - /* [lhs now points to buffer or allocated storage] */ - decNumberCopy (newlhs, dac); /* copy the 1/lhs */ - decNumberCopy (dac, &dnOne); /* restore acc=1 */ - lhs = newlhs; -#if DECSUBSET - } -#endif - } - - /* Raise-to-the-power loop... */ - seenbit = 0; /* set once we've seen a 1-bit */ - for (i = 1;; i++) - { /* for each bit [top bit ignored] */ - /* abandon if we have 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, we're off */ - decMultiplyOp (dac, dac, lhs, &workset, &status); /* dac=dac*x */ - } - if (i == 31) - break; /* that was the last bit */ - if (!seenbit) - continue; /* we don't have to square 1 */ - decMultiplyOp (dac, dac, dac, &workset, &status); /* dac=dac*dac [square] */ - } /*i *//* 32 bits */ - - /* complete internal overflow or underflow processing */ - if (status & (DEC_Overflow | DEC_Subnormal)) - { -#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 workset.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, &workset, DIVIDE, &status); - } -#endif - - /* 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, 0, &dropped); /* trailing zeros */ -#endif - } - while (0); /* end protected */ - - if (allocdac != NULL) - free (allocdac); /* drop any storage we used */ - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - if (status != 0) - decStatus (res, status, set); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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; -} - -/* ------------------------------------------------------------------ */ -/* 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; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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) -{ - uByte merged; /* merged flags */ - Unit ret = 0; /* return value */ - -#if DECCHECK - if (decCheckOperands (res, lhs, rhs, DECUNUSED)) - return res; -#endif - - merged = (lhs->bits | rhs->bits) & DECSPECIAL; - if (merged) - { - 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 */ - *res->lsu = ret; - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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. */ -/* */ -/* % [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 = set->digits + 2; /* largest working precision */ - Int residue = 0; /* rounding residue */ - uInt status = 0, ignore = 0; /* status accumulators */ - Int exp; /* working exponent */ - Int ideal; /* ideal (preferred) exponent */ - uInt needbytes; /* work */ - Int dropped; /* .. */ - - decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */ - /* buffer for f [needs +1 in case DECBUFFER 0] */ - uByte buff[sizeof (decNumber) + (D2U (DECBUFFER + 1) - 1) * sizeof (Unit)]; - /* buffer for a [needs +2 to match maxp] */ - uByte bufa[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)]; - /* buffer for temporary, b [must be same size as a] */ - uByte bufb[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)]; - decNumber *allocbuff = NULL; /* -> allocated buff, iff allocated */ - decNumber *allocbufa = NULL; /* -> allocated bufa, iff allocated */ - decNumber *allocbufb = NULL; /* -> allocated bufb, iff allocated */ - decNumber *f = (decNumber *) buff; /* reduced fraction */ - decNumber *a = (decNumber *) bufa; /* approximation to result */ - decNumber *b = (decNumber *) bufb; /* intermediate result */ - /* buffer for temporary variable, up to 3 digits */ - uByte buft[sizeof (decNumber) + (D2U (3) - 1) * sizeof (Unit)]; - decNumber *t = (decNumber *) 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 we keep them separate for clarity.] */ - rhs = allocrhs; - } - } -#endif - /* [following code does not require input rounding] */ - - /* handle infinities and NaNs */ - if (rhs->bits & DECSPECIAL) - { - if (decNumberIsInfinite (rhs)) - { /* an infinity */ - if (decNumberIsNegative (rhs)) - status |= DEC_Invalid_operation; - else - decNumberCopy (res, rhs); /* +Infinity */ - } - else - decNaNs (res, rhs, NULL, &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] */ - break; - } - - /* any other -x is an oops */ - if (decNumberIsNegative (rhs)) - { - status |= DEC_Invalid_operation; - break; - } - - /* we need space for three working variables */ - /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ - /* a -- Hull's approx -- precision, when assigned, is */ - /* currentprecision (we allow +2 for use as temporary) */ - /* b -- intermediate temporary result */ - /* if any is too long for local storage, then allocate */ - needbytes = - sizeof (decNumber) + (D2U (rhs->digits) - 1) * sizeof (Unit); - if (needbytes > 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 > 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 space */ - 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 contexts (the second is used for Numerical */ - /* Turing assignment) */ - decContextDefault (&workset, DEC_INIT_DECIMAL64); - decContextDefault (&approxset, DEC_INIT_DECIMAL64); - approxset.digits = set->digits; /* approx's length */ - - /* [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 = set->digits; /* 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 */ - /* assign to approx [round to length] */ - decAddOp (a, &dzero, a, &approxset, 0, &ignore); - if (workset.digits == maxp) - break; /* just did final */ - } /* loop */ - - /* a is now at currentprecision 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 */ - workset.digits--; /* maxp-1 is OK now */ - t->exponent = -set->digits - 1; /* make 0.5 ulp */ - decNumberCopy (b, a); - decAddOp (b, b, 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] */ - decAddOp (a, &dzero, a, &approxset, 0, &ignore); - } - else - { - decNumberCopy (b, a); - decAddOp (b, b, 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] */ - 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 [Hull] */ - a->exponent += exp / 2; /* set correct exponent */ - - /* Process Subnormals */ - decFinalize (a, set, &residue, &status); - - /* count dropable zeros [after any subnormal rounding] */ - decNumberCopy (b, a); - decTrim (b, 1, &dropped); /* [drops trailing zeros] */ - - /* Finally set Inexact and Rounded. The answer can only be exact if */ - /* it is short enough so that squaring it could fit in set->digits, */ - /* so this is the only (relatively rare) time we have to check */ - /* carefully */ - if (b->digits * 2 - 1 > set->digits) - { /* 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 != 0) - { /* result 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; - } - else - { /* is Exact */ - /* here, dropped is the count of trailing zeros in 'a' */ - /* use closest exponent to ideal... */ - Int todrop = ideal - a->exponent; /* most we can drop */ - - if (todrop < 0) - { /* ideally would add 0s */ - status |= DEC_Rounded; - } - else - { /* unrounded */ - if (dropped < todrop) - todrop = dropped; /* clamp to those available */ - if (todrop > 0) - { /* OK, some to drop */ - decShiftToLeast (a->lsu, D2U (a->digits), todrop); - a->exponent += todrop; /* maintain numerical value */ - a->digits -= todrop; /* new length */ - } - } - } - } - } - decNumberCopy (res, a); /* assume this is the result */ - } - while (0); /* end protected */ - - if (allocbuff != NULL) - free (allocbuff); /* drop any storage we used */ - if (allocbufa != NULL) - free (allocbufa); /* .. */ - if (allocbufb != NULL) - free (allocbufb); /* .. */ - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (status != 0) - decStatus (res, status, set); /* then report status */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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 operator and therefore treats */ -/* special values as valid, and also never sets Inexact. For finite */ -/* numbers it returns rescale(rhs, 0) if rhs->exponent is <0. */ -/* Otherwise the result is rhs (so no error is possible). */ -/* */ -/* The context is used for rounding mode and status after sNaN, but */ -/* the digits setting is ignored. */ -/* ------------------------------------------------------------------ */ -decNumber * -decNumberToIntegralValue (decNumber * res, const decNumber * rhs, decContext * set) -{ - decNumber dn; - decContext workset; /* working context */ - -#if DECCHECK - if (decCheckOperands (res, DECUNUSED, rhs, set)) - return res; -#endif - - /* handle infinities and NaNs */ - if (rhs->bits & DECSPECIAL) - { - uInt status = 0; - if (decNumberIsInfinite (rhs)) - decNumberCopy (res, rhs); /* an Infinity */ - else - decNaNs (res, rhs, NULL, &status); /* a NaN */ - if (status != 0) - decStatus (res, status, set); - return res; - } - - /* we have a finite number; no error possible */ - if (rhs->exponent >= 0) - return decNumberCopy (res, rhs); - /* that was easy, but if negative exponent we have 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 */ - return decNumberQuantize (res, rhs, &dn, &workset); -} - -/* ================================================================== */ -/* Utility routines */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* 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 */ - - /* We use explicit assignments here as structure assignment can copy */ - /* more than just the lsu (for small DECDPUN). This would not affect */ - /* the value of the results, but would 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 */ - Unit *d; /* work */ - const Unit *s, *smsup; /* work */ - /* 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; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ - return decTrim (dn, 0, &dropped); -} - -/* ------------------------------------------------------------------ */ -/* decNumberVersion -- return the name and version of this module */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -const char * -decNumberVersion (void) -{ - return DECVERSION; -} - -/* ------------------------------------------------------------------ */ -/* 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, DECUNUSED)) - return dn; -#endif - - dn->bits = 0; - dn->exponent = 0; - dn->digits = 1; - dn->lsu[0] = 0; - return dn; -} - -/* ================================================================== */ -/* 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 */ -/* */ -/* str 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. */ - -/* TODIGIT -- macro to remove the leading digit from the unsigned */ -/* integer u at column cut (counting from the right, LSD=0) and place */ -/* it as an ASCII character into the character pointed to by c. Note */ -/* that cut must be <= 9, and the maximum value for u is 2,000,000,000 */ -/* (as is needed for negative exponents of subnormals). The unsigned */ -/* integer pow is used as a temporary variable. */ -#define TODIGIT(u, cut, c) { \ - *(c)='0'; \ - pow=powers[cut]*2; \ - if ((u)>pow) { \ - pow*=4; \ - if ((u)>=pow) {(u)-=pow; *(c)+=8;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=4;} \ - pow/=2; \ - } \ - if ((u)>=pow) {(u)-=pow; *(c)+=2;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=1;} \ - } - -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 (DECUNUSED, dn, DECUNUSED, DECUNUSED)) - { - strcpy (string, "?"); - return; - } -#endif - - if (decNumberIsNegative (dn)) - { /* Negatives get a minus (except */ - *c = '-'; /* NaNs, which remove the '-' below) */ - c++; - } - if (dn->bits & DECSPECIAL) - { /* Is a special value */ - if (decNumberIsInfinite (dn)) - { - strcpy (c, "Infinity"); - 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 we have 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 = dn->digits % DECDPUN; - if (cut == 0) - cut = DECDPUN; /* msu is full */ - cut--; /* power of ten for digit */ - - if (exp == 0) - { /* simple integer [common fastpath, */ - /* used for NaNs, too] */ - 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); - 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)) - { /* may need to adjust */ - Int adj; /* adjustment */ - /* The C remainder operator is undefined for negative numbers, so */ - /* we must use positive remainder calculation here */ - if (e < 0) - { - adj = (-e) % 3; - if (adj != 0) - adj = 3 - adj; - } - else - { /* e>0 */ - adj = e % 3; - } - e = e - adj; - /* if we are dealing with zero we will use 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 */ - } - - /* lay out the digits of the coefficient, adding 0s and . as needed */ - u = *up; - if (pre > 0) - { /* xxx.xxx or xx00 (engineering) form */ - 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); - } - if (up > dn->lsu || (up == dn->lsu && cut >= 0)) - { /* 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); - } - } - 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); - } - } - - /* 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 subnormal 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 */ - } - /* layout the exponent (_itoa is not ANSI C) */ - for (cut = 9; cut >= 0; cut--) - { - TODIGIT (u, cut, c); - 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; -} - -/* ------------------------------------------------------------------ */ -/* 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. */ -/* ------------------------------------------------------------------ */ -/* If possible, we calculate the coefficient directly into C. */ -/* However, if: */ -/* -- we need a digits+1 calculation because 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 we must calculate into a temporary buffer. In this latter */ -/* case we use the local (stack) buffer if possible, and only if too */ -/* long for that do we resort to malloc. */ -/* */ -/* 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, so we take pains */ -/* to make returning as fast as possible, by flagging any allocation. */ -/* ------------------------------------------------------------------ */ -static decNumber * -decAddOp (decNumber * res, const decNumber * lhs, - const decNumber * rhs, decContext * set, uByte negate, uInt * status) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - 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[D2U (DECBUFFER + 1)]; /* local buffer [+1 is for possible */ - /* final carry digit or DECBUFFER=0] */ - Unit *allocacc = NULL; /* -> allocated acc buffer, iff allocated */ - Flag alloced = 0; /* set non-0 if any allocations */ - Int reqdigits = set->digits; /* local copy; requested DIGITS */ - uByte merged; /* merged flags */ - 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; - alloced = 1; - } - if (rhs->digits > reqdigits) - { - allocrhs = decRoundOperand (rhs, set, status); - if (allocrhs == NULL) - break; - rhs = allocrhs; - alloced = 1; - } - } -#endif - /* [following code does not require input rounding] */ - - /* note whether signs differ */ - diffsign = (Flag) ((lhs->bits ^ rhs->bits ^ negate) & DECNEG); - - /* handle infinities and NaNs */ - merged = (lhs->bits | rhs->bits) & DECSPECIAL; - if (merged) - { /* a special bit set */ - if (merged & (DECSNAN | DECNAN)) /* a NaN */ - decNaNs (res, lhs, rhs, 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; - } - /* [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 (rhs->digits <= DECDPUN && padding == 0 && rhs->exponent >= set->emin /* [some normals drop through] */ - && rhs->digits <= reqdigits && lhs->digits <= reqdigits) - { - Int partial = *lhs->lsu; - if (!diffsign) - { /* adding */ - Int maxv = DECDPUNMAX; /* highest no-overflow */ - if (lhs->digits < DECDPUN) - maxv = powers[lhs->digits] - 1; - partial += *rhs->lsu; - if (partial <= maxv) - { /* no carry */ - 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 we can add or subtract them, 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 or one and the highest of the other) we need to pad with up - to DIGITS-1 trailing zeros, and 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 needed */ - if (padding != 0) - { - /* some padding needed */ - /* We always pad the RHS, as we can then effect any required */ - /* padding by a 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 we 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 we 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 build direct */ - /* If destructive overlap, or the number is too long, or a carry or */ - /* borrow to DIGITS+1 might be possible we must use a buffer. */ - /* [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 */ - /* we'll need units for maxdigits digits, +1 Unit for carry or borrow */ - Int need = D2U (maxdigits) + 1; - acc = accbuff; /* assume use local buffer */ - if (need * sizeof (Unit) > sizeof (accbuff)) - { - allocacc = (Unit *) malloc (need * sizeof (Unit)); - if (allocacc == NULL) - { /* hopeless -- abandon */ - *status |= DEC_Insufficient_storage; - break; - } - acc = allocacc; - alloced = 1; - } - } - - 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: %d %d\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) - { /* we borrowed */ - res->digits = -res->digits; - res->bits ^= DECNEG; /* flip the sign */ - } -#if DECTRACE - decDumpAr ('+', acc, D2U (res->digits)); -#endif - - /* If we used a buffer we need to copy back, possibly shortening */ - /* (If we didn't use buffer it 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 we 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 */ - /* We may have an underestimate. This only occurs when both */ - /* numbers fit in DECDPUN digits and we are padding with a */ - /* negative multiple (-10, -100...) and the top digit(s) become */ - /* 0. (This only matters if we are 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 we 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; /* we did what we had to do */ - } - } /* 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 (alloced) - { - if (allocacc != NULL) - free (allocacc); /* drop any storage we used */ - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - } - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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) */ -/* */ -/* ------------------------------------------------------------------ */ -/* We need two working buffers during the long 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.*/ -/* ------------------------------------------------------------------ */ -static decNumber * -decDivideOp (decNumber * res, - const decNumber * lhs, const decNumber * rhs, - decContext * set, Flag op, uInt * status) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - Unit accbuff[D2U (DECBUFFER + DECDPUN)]; /* 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[D2U (DECBUFFER * 2 + DECDPUN) * sizeof (Unit)]; /* buffer for var1 */ - Unit *var1 = varbuff; /* -> var1 array for long subtraction */ - Unit *varalloc = NULL; /* -> allocated buffer, iff used */ - - const Unit *var2; /* -> var2 array */ - - Int var1units, var2units; /* actual lengths */ - Int var2ulen; /* logical length (units) */ - Int var1initpad = 0; /* var1 initial padding (digits) */ - Unit *msu1; /* -> msu of each var */ - const Unit *msu2; /* -> msu of each var */ - Int msu2plus; /* msu2 plus one [does not vary] */ - eInt msu2pair; /* msu2 pair plus one [does not vary] */ - 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 */ - uByte merged; /* merged flags */ - Unit *target; /* work */ - const Unit *source; /* work */ - uInt const *pow; /* .. */ - Int shift, cut; /* .. */ -#if DECSUBSET - Int dropped; /* work */ -#endif - -#if DECCHECK - if (decCheckOperands (res, lhs, rhs, set)) - return res; -#endif - - do - { /* protect allocated storage */ -#if DECSUBSET - if (!set->extended) - { - /* reduce operands and set lostDigits status, as needed */ - if (lhs->digits > reqdigits) - { - alloclhs = decRoundOperand (lhs, set, status); - if (alloclhs == NULL) - break; - lhs = alloclhs; - } - if (rhs->digits > reqdigits) - { - allocrhs = decRoundOperand (rhs, set, status); - if (allocrhs == NULL) - break; - rhs = allocrhs; - } - } -#endif - /* [following code does not require input rounding] */ - - bits = (lhs->bits ^ rhs->bits) & DECNEG; /* assumed sign for divisions */ - - /* handle infinities and NaNs */ - merged = (lhs->bits | rhs->bits) & DECSPECIAL; - if (merged) - { /* a special bit set */ - if (merged & (DECSNAN | DECNAN)) - { /* one or two NaNs */ - decNaNs (res, lhs, rhs, 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; - } - /* we can 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 */ - - /* We need long (slow) division; 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)) - { - 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 we need 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)) - { - 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 we can */ - /* subtract in place. The rhs (var2) has virtual padding */ - /* (implemented by decUnitAddSub). */ - /* We allocated one guard unit 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 we'll use for estimating the */ - /* multiplication factor. If these variables are not exact, we add */ - /* 1 to make sure that we never overestimate the multiplier. */ - 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 */ - } - - /* Since we are working in units, the units may have leading zeros, */ - /* but we calculated the exponent 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. */ - /* [We actually do this 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, we want to ensure */ - /* that the result will be Unit-aligned. To do this, we shift the */ - /* var1 accumulator towards least if need be. (It's much easier to */ - /* do this now than to reassemble the residue afterwards, if we are */ - /* doing a remainder.) Also ensure the exponent is not negative. */ - if (!(op & DIVIDE)) - { - Unit *u; - /* 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 we 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 */ - Unit *pv1, v2; /* units to compare */ - const Unit *pv2; /* 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 */ - /* we are done; leave the loop with residue set to 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 we can only use one unit for var2. */ - 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 we are in place */ - shift = var2ulen - var2units; -#if DECTRACE - decDumpAr ('1', &var1[shift], var1units - shift); - decDumpAr ('2', var2, var2units); - printf ("m=%d\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 */ - - /* We have the next unit; unless it's a leading zero, add to acc */ - if (accunits != 0 || thisunit != 0) - { /* put the unit we got */ - *accnext = thisunit; /* store in accumulator */ - /* account exactly for the digits we got */ - 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; /* we have all we need */ - } - - /* if the residue is zero, we're done (unless divide or */ - /* divideInteger and we haven't got 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] */ - } - /* we've also done enough if calculating remainder or integer */ - /* divide and we 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 we collected in acc */ - if (accunits == 0) - { /* acc is 0 */ - accunits = 1; /* show we have one .. */ - 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 */ - /* We 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 we adjusted var1 */ - /* appropriately.] */ - Int postshift; /* work */ - Flag wasodd = 0; /* integer was odd */ - Unit *quotlsu; /* for save */ - Int quotdigits; /* .. */ - - /* 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 */ - 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; - bits = lhs->bits; /* remainder sign is always as lhs */ - - /* Now correct the result if we are 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 we must now compare 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; we know the */ - /* lsu is 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; - } - - /* we need rem-rhs; the sign will invert. Again we can */ - /* safely use var1 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, 0, &dropped); -#endif - } - while (0); /* end protected */ - - if (varalloc != NULL) - free (varalloc); /* drop any storage we used */ - if (allocacc != NULL) - free (allocacc); /* .. */ - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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. */ -/* */ -/* ------------------------------------------------------------------ */ -/* Note: We use 'long' multiplication rather than Karatsuba, as the */ -/* latter would give only a minor improvement for the short numbers */ -/* we expect to handle most (and uses much more memory). */ -/* */ -/* We always have to use a buffer for the accumulator. */ -/* ------------------------------------------------------------------ */ -static decNumber * -decMultiplyOp (decNumber * res, const decNumber * lhs, - const decNumber * rhs, decContext * set, uInt * status) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - Unit accbuff[D2U (DECBUFFER * 2 + 1)]; /* local buffer (+1 in case DECBUFFER==0) */ - Unit *acc = accbuff; /* -> accumulator array for exact result */ - Unit *allocacc = NULL; /* -> allocated buffer, iff allocated */ - const Unit *mer, *mermsup; /* work */ - Int accunits; /* Units of accumulator in use */ - Int madlength; /* Units in multiplicand */ - Int shift; /* Units to shift multiplicand by */ - Int need; /* Accumulator units needed */ - Int exponent; /* work */ - Int residue = 0; /* rounding residue */ - uByte bits; /* result sign */ - uByte merged; /* merged flags */ - -#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) - 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] */ - - /* precalculate result sign */ - bits = (uByte) ((lhs->bits ^ rhs->bits) & DECNEG); - - /* handle infinities and NaNs */ - merged = (lhs->bits | rhs->bits) & DECSPECIAL; - if (merged) - { /* a special bit set */ - if (merged & (DECSNAN | DECNAN)) - { /* one or two NaNs */ - decNaNs (res, lhs, rhs, status); - break; - } - /* one or two infinities. Infinity * 0 is invalid */ - if (((lhs->bits & DECSPECIAL) == 0 && ISZERO (lhs)) - || ((rhs->bits & DECSPECIAL) == 0 && ISZERO (rhs))) - { - *status |= DEC_Invalid_operation; - break; - } - decNumberZero (res); - res->bits = bits | DECINF; /* infinity */ - break; - } - - /* For best speed, as in DMSRCN, we use the shorter number as the */ - /* multiplier (rhs) and the longer as the multiplicand (lhs) */ - if (lhs->digits < rhs->digits) - { /* swap... */ - const decNumber *hold = lhs; - lhs = rhs; - rhs = hold; - } - - /* if accumulator is too long for local storage, then allocate */ - need = D2U (lhs->digits) + D2U (rhs->digits); /* maximum units in result */ - if (need * sizeof (Unit) > sizeof (accbuff)) - { - allocacc = (Unit *) malloc (need * sizeof (Unit)); - if (allocacc == NULL) - { - *status |= DEC_Insufficient_storage; - break; - } - acc = 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 we 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); /* we know 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; we'll use it shortly */ - /* [this avoids length of <=0 later] */ - *(acc + accunits) = 0; - accunits++; - } - /* multiply multiplicand by 10**DECDPUN for next Unit to left */ - shift++; /* add this for 'logical length' */ - } /* n */ -#if DECTRACE - /* Show exact result */ - decDumpAr ('*', acc, accunits); -#endif - - /* acc now contains the exact result of the multiplication */ - /* Build a decNumber from it, noting if any residue */ - res->bits = bits; /* set sign */ - res->digits = decGetDigits (acc, accunits); /* count digits exactly */ - - /* We might have 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 we did wrap, we set a safe */ - /* very negative exponent, from which decFinalize() will raise a */ - /* hard underflow. */ - 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 we used */ - if (allocrhs != NULL) - free (allocrhs); /* .. */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - const decNumber *inrhs = rhs; /* save original rhs */ - Int reqdigits = set->digits; /* requested DIGITS */ - Int reqexp; /* requested exponent [-scale] */ - Int residue = 0; /* rounding residue */ - uByte merged; /* merged flags */ - Int etiny = set->emin - (set->digits - 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 */ - merged = (lhs->bits | rhs->bits) & DECSPECIAL; - if ((lhs->bits | rhs->bits) & DECSPECIAL) - { - /* NaNs get usual processing */ - if (merged & (DECSNAN | DECNAN)) - decNaNs (res, lhs, rhs, 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 */ -#if DECSUBSET - reqexp = decGetInt (inrhs, set); -#else - reqexp = decGetInt (inrhs); -#endif - } - -#if DECSUBSET - if (!set->extended) - etiny = set->emin; /* no subnormals */ -#endif - - if (reqexp == BADINT /* bad (rescale only) or .. */ - || (reqexp < etiny) /* < lowest */ - || (reqexp > set->emax)) - { /* > Emax */ - *status |= DEC_Invalid_operation; - break; - } - - /* we've processed the RHS, so we can overwrite it 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 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 we rounded a 999s case, exponent will be off by one; */ - /* adjust back if so. */ - if (res->exponent > reqexp) - { - 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 trailing zeros. */ - 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 (allocrhs != NULL) - free (allocrhs); /* drop any storage we used */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* decCompareOp -- compare, min, or max two Numbers */ -/* */ -/* This computes C = A ? B and returns the signum (as a Number) */ -/* for COMPARE or the maximum or minimum (for COMPMAX and COMPMIN). */ -/* */ -/* 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 and COMPMIN. */ -/* ------------------------------------------------------------------ */ -/* The emphasis here is on speed for common cases, and avoiding */ -/* coefficient comparison if possible. */ -/* ------------------------------------------------------------------ */ -decNumber * -decCompareOp (decNumber * res, const decNumber * lhs, const decNumber * rhs, - decContext * set, Flag op, uInt * status) -{ - decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ - decNumber *allocrhs = NULL; /* .., rhs */ - Int result = 0; /* default result value */ - uByte merged; /* merged flags */ - uByte bits = 0; /* non-0 for NaN */ - -#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] */ - - /* handle NaNs now; let infinities drop through */ - /* +++ review sNaN handling with 754r, for now assumes sNaN */ - /* (even just one) leads to NaN. */ - merged = (lhs->bits | rhs->bits) & (DECSNAN | DECNAN); - if (merged) - { /* a NaN bit set */ - if (op == COMPARE); - else if (merged & DECSNAN); - else - { /* 754r rules for MIN and MAX ignore single NaN */ - /* here if MIN or MAX, and one or two quiet NaNs */ - if (lhs->bits & rhs->bits & DECNAN); - else - { /* just one quiet 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; - } - } - op = COMPNAN; /* use special path */ - decNaNs (res, lhs, rhs, status); - break; - } - - result = decCompare (lhs, rhs); /* we have numbers */ - } - while (0); /* end protected */ - - if (result == BADINT) - *status |= DEC_Insufficient_storage; /* rare */ - else - { - if (op == COMPARE) - { /* return signum */ - decNumberZero (res); /* [always a valid result] */ - if (result == 0) - res->bits = bits; /* (maybe qNaN) */ - else - { - *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, we 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 */ - if (op == COMPMIN) - result = -result; /* reverse if looking for MIN */ - 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 (allocrhs != NULL) - free (allocrhs); /* free any storage we used */ - if (alloclhs != NULL) - free (alloclhs); /* .. */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* */ -/* 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) */ -/* ------------------------------------------------------------------ */ -/* This could be merged into decCompareOp */ -static Int -decCompare (const decNumber * lhs, const decNumber * rhs) -{ - Int result; /* result value */ - Int sigr; /* rhs signum */ - Int compare; /* work */ - result = 1; /* assume signum(lhs) */ - if (ISZERO (lhs)) - result = 0; - else if (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; /* R < L, return -1 */ - - /* signums are the same */ - if (result == 0) - return 0; /* both 0 */ - /* Both non-zero */ - if ((lhs->bits | rhs->bits) & DECINF) - { /* one or more infinities */ - if (lhs->bits == rhs->bits) - result = 0; /* both the same */ - else if (decNumberIsInfinite (rhs)) - result = -result; - return result; - } - - /* we 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; /* what we got */ -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* */ -/* 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 -decUnitCompare (const Unit * a, Int alength, const Unit * b, Int blength, Int exp) -{ - Unit *acc; /* accumulator for result */ - Unit accbuff[D2U (DECBUFFER + 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 we can return easily */ - if (alength > blength + (Int) D2U (exp)) - return 1; - if (alength + 1 < blength + (Int) D2U (exp)) - return -1; - - /* We need to do a real subtract. For this, we need a result buffer */ - /* even though we only are interested in the sign. 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 we used */ - return result; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ - Int est; /* estimated quotient */ -#endif - -#if DECTRACE - if (alength < 1 || blength < 1) - printf ("decUnitAddSub: alen blen m %d %d [%d]\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, we 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; - } - /* remainder operator is undefined if negative, so we must test */ -#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; -#else - 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 */ - - /* we 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 */ - /* remainder is undefined if negative, so we must test */ - 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; -#else - if ((ueInt) carry < (DECDPUNMAX + 1) * 2) - { /* fastpath carry 1 */ - *c = (Unit) (carry - (DECDPUNMAX + 1)); - carry = 1; - continue; - } - /* remainder is undefined if negative, so we 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, we're done */ - 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 %d, carry %d\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 */ -} - -/* ------------------------------------------------------------------ */ -/* decTrim -- trim trailing zeros or normalize */ -/* */ -/* dn is the number to trim or normalize */ -/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ -/* dropped returns the number of discarded trailing zeros */ -/* returns dn */ -/* */ -/* 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, Flag all, Int * dropped) -{ - Int d, exp; /* work */ - uInt cut; /* .. */ - Unit *up; /* -> current Unit */ - -#if DECCHECK - if (decCheckOperands (dn, DECUNUSED, DECUNUSED, DECUNUSED)) - 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; - } - - /* we 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 dropped */ - - /* 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; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ - uInt rem; /* for division */ - 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; - } - - cut = (DECDPUN - shift % DECDPUN) % DECDPUN; - source = uar + D2U (digits) - 1; /* where msu comes from */ - first = uar + D2U (digits + shift) - 1; /* where msu of source will end up */ - target = source + D2U (shift); /* where upper part of first cut goes */ - next = 0; - - for (; source >= uar; source--, target--) - { - /* split the source Unit and accumulate remainder for next */ -#if DECDPUN<=4 - uInt quot = QUOT10 (*source, cut); - rem = *source - quot * powers[cut]; - next += quot; -#else - 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 */ - } - /* propagate to one below and clear the rest */ - for (; target >= uar; target--) - { - *target = (Unit) next; - next = 0; - } - return digits + shift; -} - -/* ------------------------------------------------------------------ */ -/* 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 less 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 */ - - up = uar + shift / DECDPUN; /* source; allow for whole Units */ - cut = shift % DECDPUN; /* odd 0's to drop */ - target = uar; /* both paths */ - if (cut == 0) - { /* whole units shift */ - for (; up < uar + units; target++, up++) - *target = *up; - return target - uar; - } - /* messier */ - 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; -} - -#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, we are not permitted to modify it. */ -/* We therefore 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 we "lost digits" */ - if (newstatus & DEC_Inexact) - newstatus |= DEC_Lost_digits; - *status |= newstatus; - return res; -} -#endif - -/* ------------------------------------------------------------------ */ -/* decCopyFit -- copy a number, shortening 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); -} - -/* ------------------------------------------------------------------ */ -/* 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 decNumberRescale 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 we can */ -/* adjust by a residue in 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 discard1; /* first discarded digit */ - uInt cut; /* cut point in Unit */ - uInt quot, rem; /* for divisions */ - Unit *target; /* work */ - const Unit *up; /* work */ - 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 */ - up = lsu; - for (target = dn->lsu; target < dn->lsu + D2U (len); target++, up++) - { - *target = *up; - } - dn->digits = len; /* set the new length */ - } - /* dn->exponent and residue are unchanged */ - if (*residue != 0) - *status |= (DEC_Inexact | DEC_Rounded); /* record inexactitude */ - return; - } - - /* we have to discard some digits */ - *status |= DEC_Rounded; /* accumulate Rounded status */ - if (*residue > 1) - *residue = 1; /* previous residue now to right, so -1 to +1 */ - - 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) - for (up = lsu + D2U (len) - 1; up >= lsu; up--) - { - if (*up != 0) - { /* found a 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; /* .. */ - dn->exponent += discard; /* maintain numerical value */ - return; - } /* total discard */ - - /* partial discard [most common case] */ - /* here, at least the first (most significant) discarded digit exists */ - - /* spin up the number, noting residue as we pass, until we get to */ - /* the Unit with the first discarded digit. When we get there, */ - /* extract it and remember where we're at */ - 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 discarded digit */ - cut = discard - (count - DECDPUN) - 1; - if (cut == DECDPUN - 1) - { /* discard digit is at top */ -#if DECDPUN<=4 - discard1 = QUOT10 (*up, DECDPUN - 1); - rem = *up - discard1 * powers[DECDPUN - 1]; -#else - rem = *up % powers[DECDPUN - 1]; - discard1 = *up / powers[DECDPUN - 1]; -#endif - if (rem != 0) - *residue = 1; - up++; /* move to next */ - cut = 0; /* bottom digit of result */ - quot = 0; /* keep a certain compiler happy */ - } - else - { - /* discard digit is in low digit(s), not top digit */ - if (cut == 0) - quot = *up; - 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 - cut++; /* update cut */ - } - - /* here: up -> Unit of the array with discarded digit */ - /* cut is the division point for each Unit */ - /* quot holds the uncut high-order digits for the current */ - /* Unit, unless cut==0 in which case it's still in *up */ - /* copy the coefficient array to the result number, shifting as we go */ - count = set->digits; /* digits to end up with */ - if (count <= 0) - { /* special for Rescale/Subnormal :-( */ - *dn->lsu = 0; /* .. result is 0 */ - dn->digits = 1; /* .. */ - } - else - { /* shift to least */ - /* [this is similar to decShiftToLeast code, with copy] */ - dn->digits = count; /* set the new length */ - if (cut == 0) - { - /* on unit boundary, so simple shift down copy loop suffices */ - for (target = dn->lsu; target < dn->lsu + D2U (count); - target++, up++) - { - *target = *up; - } - } - else - 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 to least needed */ - dn->exponent += discard; /* maintain numerical value */ - - /* here, discard1 is the guard digit, and residue is everything else */ - /* [use mapping to accumulate residue safely] */ - *residue += resmap[discard1]; - - if (*residue != 0) - *status |= DEC_Inexact; /* record inexactitude */ - return; -} - -/* ------------------------------------------------------------------ */ -/* 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. */ -/* 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_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 - 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 we are bumping up and the number */ - /* is all nines. In this special case we set to 1000... and adjust */ - /* the exponent by one (as otherwise we 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 we are lookng 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 we 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), one, 1, 0, dn->lsu, bump); -} - -#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); -} -#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 */ - - /* We have to be careful 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 < 0 /* negative exponent */ - && (dn->exponent < set->emin - dn->digits + 1)) - { - /* Go handle subnormals; this will apply round if needed. */ - 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 we 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 we 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; -} - -/* ------------------------------------------------------------------ */ -/* 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] */ -/* 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 therounding 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_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) - { - 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; /* we filled those digits */ - } /* up */ - dn->bits = sign; /* sign */ - dn->exponent = set->emax - set->digits + 1; - } - else - dn->bits = sign | DECINF; /* Value is +/-Infinity */ - *status |= DEC_Overflow | DEC_Inexact | DEC_Rounded; -} - -/* ------------------------------------------------------------------ */ -/* 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 %d\n", *residue); - *status |= DEC_Invalid_operation; - } -#endif - if (dn->exponent < etiny) - { /* clamp required */ - dn->exponent = etiny; - *status |= DEC_Clamped; - } - return; - } - - *status |= DEC_Subnormal; /* we 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, so fast-path out */ -#if DECCHECK - if (*residue != 0) - { - printf ("++ Subnormal no-adjust residue %d\n", *residue); - *status |= DEC_Invalid_operation; - } -#endif - /* it may already be inexact (from setting the coefficient) */ - if (*status & DEC_Inexact) - *status |= DEC_Underflow; - return; - } - - /* adjust>0. we 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 we rounded up a 999s case, exponent will be off by one; adjust */ - /* back if so [it will fit, because we shortened] */ - if (dn->exponent > etiny) - { - dn->digits = decShiftToMost (dn->lsu, dn->digits, 1); - dn->exponent--; /* (re)adjust the exponent. */ - } -} - -/* ------------------------------------------------------------------ */ -/* decGetInt -- get integer from a number */ -/* */ -/* dn is the number [which will not be altered] */ -/* set is the context [requested digits], subset only */ -/* returns the converted integer, or BADINT if error */ -/* */ -/* This checks and gets a whole number from the input decNumber. */ -/* The magnitude of the integer must be <2^31. */ -/* Any discarded fractional part must be 0. */ -/* If subset it must also fit in set->digits */ -/* ------------------------------------------------------------------ */ -#if DECSUBSET -static Int -decGetInt (const decNumber * dn, decContext * set) -{ -#else -static Int -decGetInt (const decNumber * dn) -{ -#endif - Int theInt; /* result accumulator */ - const Unit *up; /* work */ - Int got; /* digits (real or not) processed */ - Int ilength = dn->digits + dn->exponent; /* integral length */ - - /* 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 */ - if (ilength > 10) - return BADINT; /* always too big */ -#if DECSUBSET - if (!set->extended && ilength > set->digits) - return BADINT; -#endif - - 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 we get to 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 */ - /* OK, we're good */ - got = DECDPUN - count; /* number of digits so far */ - up++; /* ready for next */ - } - } - /* collect the rest */ - for (; got < ilength; up++) - { - theInt += *up * powers[got]; - got += DECDPUN; - } - if ((ilength == 10) /* check no wrap */ - && (theInt / (Int) powers[got - DECDPUN] != *(up - 1))) - return BADINT; - /* [that test also disallows the BADINT result case] */ - - /* apply any sign and return */ - if (decNumberIsNegative (dn)) - theInt = -theInt; - return theInt; -} - -/* ------------------------------------------------------------------ */ -/* decStrEq -- caseless comparison of strings */ -/* */ -/* str1 is one of the strings to compare */ -/* str2 is the other */ -/* */ -/* returns 1 if strings caseless-compare equal, 0 otherwise */ -/* */ -/* Note that the strings must be the same length if they are to */ -/* compare equal; there is no padding. */ -/* ------------------------------------------------------------------ */ -/* [strcmpi is not in ANSI C] */ -static Flag -decStrEq (const char *str1, const char *str2) -{ - for (;; str1++, str2++) - { - unsigned char u1 = (unsigned char) *str1; - unsigned char u2 = (unsigned char) *str2; - if (u1 == u2) - { - if (u1 == '\0') - break; - } - else - { - if (tolower (u1) != tolower (u2)) - return 0; - } - } /* stepping */ - return 1; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* 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, 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; - - decNumberCopy (res, lhs); - res->bits &= ~DECSNAN; /* convert any sNaN to NaN, while */ - res->bits |= DECNAN; /* .. preserving sign */ - res->exponent = 0; /* clean exponent */ - /* [coefficient was copied] */ - return res; -} - -/* ------------------------------------------------------------------ */ -/* 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); - return; -} - -/* ------------------------------------------------------------------ */ -/* 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 */ -/* */ -/* 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 (const Unit * uar, Int len) -{ - const Unit *up = uar + len - 1; /* -> msu */ - Int digits = len * DECDPUN; /* maximum possible digits */ - uInt const *pow; /* work */ - - for (; up >= uar; up--) - { - digits -= DECDPUN; - if (*up == 0) - { /* unit is 0 */ - if (digits != 0) - continue; /* more to check */ - /* all units were 0 */ - digits++; /* .. so bump digits to 1 */ - break; - } - /* found the first non-zero Unit */ - digits++; - if (*up < 10) - break; /* fastpath 1-9 */ - digits++; - for (pow = &powers[2]; *up >= *pow; pow++) - digits++; - break; - } /* up */ - - return digits; -} - - -#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, we're done */ - 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 ("%d", *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 ("%d", d); - } /* cut */ - } /* up */ - if (dn->exponent != 0) - { - char esign = '+'; - if (dn->exponent < 0) - esign = '-'; - printf (" E%c%d", esign, abs (dn->exponent)); - } - printf (" [%d]\n", dn->digits); -} -#endif - -#if DECTRACE || DECCHECK -/* ------------------------------------------------------------------ */ -/* decDumpAr -- display a unit array [debug 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; -#if DECDPUN==4 - const char *spec = "%04d "; -#else - const char *spec = "%d "; -#endif - printf (" :%c: ", name); - for (i = len - 1; i >= 0; i--) - { - if (i == len - 1) - printf ("%d ", 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 DECUNUSED) */ -/* rhs is the second (may be DECUNUSED) */ -/* set is the context (may be DECUNUSED) */ -/* 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 - printf ("Context is NULL.\n"); -#endif - bad = 1; - return 1; - } - else if (set != DECUNUSED - && (set->digits < 1 || set->round < 0 - || set->round >= DEC_ROUND_MAX)) - { - bad = 1; -#if DECTRACE - printf ("Bad context [digits=%d round=%d].\n", set->digits, set->round); -#endif - } - else - { - if (res == NULL) - { - bad = 1; -#if DECTRACE - printf ("Bad result [is NULL].\n"); -#endif - } - if (!bad && lhs != DECUNUSED) - bad = (decCheckNumber (lhs, set)); - if (!bad && rhs != DECUNUSED) - bad = (decCheckNumber (rhs, set)); - } - if (bad) - { - if (set != DECUNUSED) - decContextSetStatus (set, DEC_Invalid_operation); - if (res != DECUNUSED && res != NULL) - { - decNumberZero (res); - res->bits = DECNAN; /* qNaN */ - } - } - return bad; -} - -/* ------------------------------------------------------------------ */ -/* decCheckNumber -- check a number */ -/* dn is the number to check */ -/* set is the context (may be DECUNUSED) */ -/* 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 (not necessarily the current one). */ -/* ------------------------------------------------------------------ */ -Flag -decCheckNumber (const decNumber * dn, decContext * set) -{ - const Unit *up; /* work */ - uInt maxuint; /* .. */ - Int ae, d, digits; /* .. */ - Int emin, emax; /* .. */ - - if (dn == NULL) - { /* hopeless */ -#if DECTRACE - printf ("Reference to decNumber is NULL.\n"); -#endif - return 1; - } - - /* check special values */ - if (dn->bits & DECSPECIAL) - { - if (dn->exponent != 0) - { -#if DECTRACE - printf ("Exponent %d (not 0) for a special value.\n", dn->exponent); -#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 - printf ("Digits %d (not 1) for an infinity.\n", dn->digits); -#endif - return 1; - } - if (*dn->lsu != 0) - { -#if DECTRACE - printf ("LSU %d (not 0) for an infinity.\n", *dn->lsu); -#endif - return 1; - } - } /* Inf */ - /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ - /* concrete formats (decimal64, etc.), though they are */ - /* never visible in strings. */ - return 0; - - /* if ((dn->bits & DECINF) || (dn->bits & DECNEG)==0) return 0; */ - /* #if DECTRACE */ - /* printf("Negative NaN in number.\n"); */ - /* #endif */ - /* return 1; */ - } - - /* check the coefficient */ - if (dn->digits < 1 || dn->digits > DECNUMMAXP) - { -#if DECTRACE - printf ("Digits %d in number.\n", dn->digits); -#endif - return 1; - } - - d = dn->digits; - - for (up = dn->lsu; d > 0; up++) - { - if (d > DECDPUN) - maxuint = DECDPUNMAX; - else - { /* we are at the msu */ - maxuint = powers[d] - 1; - if (dn->digits > 1 && *up < powers[d - 1]) - { -#if DECTRACE - printf ("Leading 0 in number.\n"); - decNumberShow (dn); -#endif - return 1; - } - } - if (*up > maxuint) - { -#if DECTRACE - printf ("Bad Unit [%08x] in number at offset %d [maxuint %d].\n", - *up, up - dn->lsu, 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 - printf ("Adjusted exponent underflow [%d].\n", ae); - decNumberShow (dn); -#endif - return 1; - } - if (ae > +emax) - { -#if DECTRACE - printf ("Adjusted exponent overflow [%d].\n", ae); - decNumberShow (dn); -#endif - return 1; - } - - return 0; /* it's OK */ -} -#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 (uInt 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(%d)\n", 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 */ -} - -/* ------------------------------------------------------------------ */ -/* 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 %d ===\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 %d, n=%d ===\n", *b, - b - b0 - 8, (Int) b0, n); - free (b0); /* drop the storage */ - decAllocBytes -= n; /* account for storage */ -} -#endif |