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Diffstat (limited to 'libdecnumber/decNumber.c')
| -rw-r--r-- | libdecnumber/decNumber.c | 5939 |
1 files changed, 5939 insertions, 0 deletions
diff --git a/libdecnumber/decNumber.c b/libdecnumber/decNumber.c new file mode 100644 index 00000000000..c2a89800680 --- /dev/null +++ b/libdecnumber/decNumber.c @@ -0,0 +1,5939 @@ +/* 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. + + 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, 59 Temple Place - Suite 330, Boston, MA + 02111-1307, 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 */ +/* ------------------------------------------------------------------ */ + +#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 "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 *, decNumber *, decNumber *, + decContext *, uByte, uInt *); +static void decApplyRound (decNumber *, decContext *, Int, uInt *); +static Int decCompare (decNumber * lhs, decNumber * rhs); +static decNumber *decCompareOp (decNumber *, decNumber *, decNumber *, + decContext *, Flag, uInt *); +static void decCopyFit (decNumber *, decNumber *, decContext *, + Int *, uInt *); +static decNumber *decDivideOp (decNumber *, decNumber *, decNumber *, + decContext *, Flag, uInt *); +static void decFinalize (decNumber *, decContext *, Int *, uInt *); +static Int decGetDigits (Unit *, Int); +#if DECSUBSET +static Int decGetInt (decNumber *, decContext *); +#else +static Int decGetInt (decNumber *); +#endif +static decNumber *decMultiplyOp (decNumber *, decNumber *, decNumber *, + decContext *, uInt *); +static decNumber *decNaNs (decNumber *, decNumber *, decNumber *, uInt *); +static decNumber *decQuantizeOp (decNumber *, decNumber *, decNumber *, + decContext *, Flag, uInt *); +static void decSetCoeff (decNumber *, decContext *, 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 (decNumber *, char[], Flag); +static decNumber *decTrim (decNumber *, Flag, Int *); +static Int decUnitAddSub (Unit *, Int, Unit *, Int, Int, Unit *, Int); +static Int decUnitCompare (Unit *, Int, 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 (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 *, decNumber *, decNumber *, + decContext *); +static Flag decCheckNumber (decNumber *, decContext *); +#endif + +#if DECTRACE || DECCHECK +/* Optional trace/debugging routines. */ +void decNumberShow (decNumber *); /* displays the components of a number */ +static void decDumpAr (char, 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 (decNumber * dn, char *string) +{ + decToString (dn, string, 0); + return string; +} + +char * +decNumberToEngString (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, 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 */ + char *dotchar = NULL; /* where dot was found */ + char *cfirst; /* -> first character of decimal part */ + char *last = NULL; /* -> last digit of decimal part */ + char *firstexp; /* -> first significant exponent digit */ + 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, 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, decNumber * lhs, 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, decNumber * lhs, 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, decNumber * lhs, + 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, decNumber * lhs, + 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, decNumber * lhs, 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, decNumber * lhs, 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, 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, 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, decNumber * lhs, + 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, 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, decNumber * lhs, + 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 */ + 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] */ + 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; + } + lhs = alloclhs; /* use the allocated space */ + } + else + lhs = (decNumber *) lhsbuff; /* use stack storage */ + /* [lhs now points to buffer or allocated storage] */ + decNumberCopy (lhs, dac); /* copy the 1/lhs */ + decNumberCopy (dac, &dnOne); /* restore acc=1 */ +#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, decNumber * lhs, + 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, decNumber * lhs, + 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, decNumber * lhs, + 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, decNumber * lhs, + 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, decNumber * lhs, 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, 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, decNumber * lhs, + 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, 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, 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 *s, *d, *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 (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] */ + 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, decNumber * lhs, + 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 */ + 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, + decNumber * lhs, 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 */ + + Unit *var2; /* -> var2 array */ + + Int var1units, var2units; /* actual lengths */ + Int var2ulen; /* logical length (units) */ + Int var1initpad = 0; /* var1 initial padding (digits) */ + Unit *msu1, *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, *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, *pv2, v2; /* units to compare */ + pv2 = msu2; /* -> msu */ + for (pv1 = msu1;; pv1--, pv2--) + { + /* v1=*pv1 -- always OK */ + v2 = 0; /* assume in padding */ + if (pv2 >= var2) + v2 = *pv2; /* in range */ + if (*pv1 != v2) + break; /* no longer the same */ + if (pv1 == var1) + break; /* done; leave pv1 as is */ + } + /* here when all inspected or a difference seen */ + if (*pv1 < v2) + break; /* var1 too low to subtract */ + if (*pv1 == v2) + { /* var1 == var2 */ + /* reach here if var1 and var2 are identical; subtraction */ + /* would increase digit by one, and the residue will be 0 so */ + /* 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, decNumber * lhs, + 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 */ + 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... */ + 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, decNumber * lhs, + decNumber * rhs, decContext * set, Flag quant, uInt * status) +{ + decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs = NULL; /* .., rhs */ + 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, decNumber * lhs, 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 */ + 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 (decNumber * lhs, 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 */ + 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 (Unit * a, Int alength, 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 */ + 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 (Unit * a, Int alength, + Unit * b, Int blength, Int bshift, Unit * c, Int m) +{ + 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 (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, 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, 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 *up, *target; /* 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 (decNumber * dn, decContext * set) +{ +#else +static Int +decGetInt (decNumber * dn) +{ +#endif + Int theInt; /* result accumulator */ + 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++) + { + if (*str1 == *str2) + { + if (*str1 == '\0') + break; + } + else + { + if (tolower (*str1) != tolower (*str2)) + 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, decNumber * lhs, 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 (Unit * uar, Int len) +{ + 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 (decNumber * dn) +{ + 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, Unit * ar, Int len) +{ + Int i; +#if DECDPUN==4 + char *spec = "%04d "; +#else + 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, decNumber * lhs, + 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 (decNumber * dn, decContext * set) +{ + 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 |