| /* 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 |