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julius |
/* Decimal Number module for the decNumber C Library
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Copyright (C) 2005 Free Software Foundation, Inc.
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Contributed by IBM Corporation. Author Mike Cowlishaw.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 2, or (at your option) any later
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version.
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In addition to the permissions in the GNU General Public License,
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the Free Software Foundation gives you unlimited permission to link
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the compiled version of this file into combinations with other
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programs, and to distribute those combinations without any
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restriction coming from the use of this file. (The General Public
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License restrictions do apply in other respects; for example, they
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cover modification of the file, and distribution when not linked
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into a combine executable.)
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with GCC; see the file COPYING. If not, write to the Free
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
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02110-1301, USA. */
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/* ------------------------------------------------------------------ */
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/* This module comprises the routines for Standard Decimal Arithmetic */
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/* as defined in the specification which may be found on the */
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/* http://www2.hursley.ibm.com/decimal web pages. It implements both */
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/* the full ('extended') arithmetic and the simpler ('subset') */
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/* arithmetic. */
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/* */
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/* Usage notes: */
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/* */
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/* 1. This code is ANSI C89 except: */
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/* */
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/* a) Line comments (double forward slash) are used. (Most C */
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/* compilers accept these. If yours does not, a simple script */
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/* can be used to convert them to ANSI C comments.) */
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/* */
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/* b) Types from C99 stdint.h are used. If you do not have this */
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/* header file, see the User's Guide section of the decNumber */
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/* documentation; this lists the necessary definitions. */
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/* */
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/* c) If DECDPUN>4, non-ANSI 64-bit 'long long' types are used. */
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/* To avoid these, set DECDPUN <= 4 (see documentation). */
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/* */
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/* 2. The decNumber format which this library uses is optimized for */
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/* efficient processing of relatively short numbers; in particular */
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/* it allows the use of fixed sized structures and minimizes copy */
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/* and move operations. It does, however, support arbitrary */
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/* precision (up to 999,999,999 digits) and arbitrary exponent */
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/* range (Emax in the range 0 through 999,999,999 and Emin in the */
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/* range -999,999,999 through 0). */
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/* */
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/* 3. Operands to operator functions are never modified unless they */
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/* are also specified to be the result number (which is always */
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/* permitted). Other than that case, operands may not overlap. */
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/* */
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/* 4. Error handling: the type of the error is ORed into the status */
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/* flags in the current context (decContext structure). The */
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/* SIGFPE signal is then raised if the corresponding trap-enabler */
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/* flag in the decContext is set (is 1). */
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/* */
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/* It is the responsibility of the caller to clear the status */
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/* flags as required. */
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/* */
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/* The result of any routine which returns a number will always */
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/* be a valid number (which may be a special value, such as an */
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/* Infinity or NaN). */
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/* */
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/* 5. The decNumber format is not an exchangeable concrete */
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/* representation as it comprises fields which may be machine- */
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/* dependent (big-endian or little-endian, for example). */
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/* Canonical conversions to and from strings are provided; other */
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/* conversions are available in separate modules. */
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/* */
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/* 6. Normally, input operands are assumed to be valid. Set DECCHECK */
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/* to 1 for extended operand checking (including NULL operands). */
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/* Results are undefined if a badly-formed structure (or a NULL */
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/* NULL pointer to a structure) is provided, though with DECCHECK */
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/* enabled the operator routines are protected against exceptions. */
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/* (Except if the result pointer is NULL, which is unrecoverable.) */
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/* */
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/* However, the routines will never cause exceptions if they are */
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/* given well-formed operands, even if the value of the operands */
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/* is inappropriate for the operation and DECCHECK is not set. */
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/* */
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/* 7. Subset arithmetic is available only if DECSUBSET is set to 1. */
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/* ------------------------------------------------------------------ */
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/* Implementation notes for maintenance of this module: */
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/* */
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/* 1. Storage leak protection: Routines which use malloc are not */
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/* permitted to use return for fastpath or error exits (i.e., */
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/* they follow strict structured programming conventions). */
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/* Instead they have a do{}while(0); construct surrounding the */
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/* code which is protected -- break may be used from this. */
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/* Other routines are allowed to use the return statement inline. */
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/* */
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/* Storage leak accounting can be enabled using DECALLOC. */
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/* */
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/* 2. All loops use the for(;;) construct. Any do construct is for */
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/* protection as just described. */
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/* */
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/* 3. Setting status in the context must always be the very last */
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/* action in a routine, as non-0 status may raise a trap and hence */
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/* the call to set status may not return (if the handler uses long */
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/* jump). Therefore all cleanup must be done first. In general, */
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/* to achieve this we accumulate status and only finally apply it */
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/* by calling decContextSetStatus (via decStatus). */
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/* */
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/* Routines which allocate storage cannot, therefore, use the */
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/* 'top level' routines which could cause a non-returning */
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/* transfer of control. The decXxxxOp routines are safe (do not */
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/* call decStatus even if traps are set in the context) and should */
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/* be used instead (they are also a little faster). */
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/* */
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/* 4. Exponent checking is minimized by allowing the exponent to */
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/* grow outside its limits during calculations, provided that */
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/* the decFinalize function is called later. Multiplication and */
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/* division, and intermediate calculations in exponentiation, */
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/* require more careful checks because of the risk of 31-bit */
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/* overflow (the most negative valid exponent is -1999999997, for */
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/* a 999999999-digit number with adjusted exponent of -999999999). */
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/* */
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/* 5. Rounding is deferred until finalization of results, with any */
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/* 'off to the right' data being represented as a single digit */
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/* residue (in the range -1 through 9). This avoids any double- */
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/* rounding when more than one shortening takes place (for */
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/* example, when a result is subnormal). */
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/* */
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/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
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/* during many operations, so whole Units are handled and exact */
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/* accounting of digits is not needed. The correct digits value */
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/* is found by decGetDigits, which accounts for leading zeros. */
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/* This must be called before any rounding if the number of digits */
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/* is not known exactly. */
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/* */
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/* 7. We use the multiply-by-reciprocal 'trick' for partitioning */
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/* numbers up to four digits, using appropriate constants. This */
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/* is not useful for longer numbers because overflow of 32 bits */
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/* would lead to 4 multiplies, which is almost as expensive as */
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/* a divide (unless we assumed floating-point multiply available). */
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/* */
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/* 8. Unusual abbreviations possibly used in the commentary: */
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/* lhs -- left hand side (operand, of an operation) */
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/* lsd -- least significant digit (of coefficient) */
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/* lsu -- least significant Unit (of coefficient) */
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/* msd -- most significant digit (of coefficient) */
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/* msu -- most significant Unit (of coefficient) */
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/* rhs -- right hand side (operand, of an operation) */
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/* +ve -- positive */
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/* -ve -- negative */
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/* ------------------------------------------------------------------ */
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/* Some of glibc's string inlines cause warnings. Plus we'd rather
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rely on (and therefore test) GCC's string builtins. */
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#define __NO_STRING_INLINES
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#include <stdlib.h> /* for malloc, free, etc. */
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#include <stdio.h> /* for printf [if needed] */
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#include <string.h> /* for strcpy */
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#include <ctype.h> /* for lower */
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#include "config.h"
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#include "decNumber.h" /* base number library */
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#include "decNumberLocal.h" /* decNumber local types, etc. */
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/* Constants */
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/* Public constant array: powers of ten (powers[n]==10**n) */
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const uInt powers[] = { 1, 10, 100, 1000, 10000, 100000, 1000000,
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10000000, 100000000, 1000000000
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};
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/* Local constants */
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#define DIVIDE 0x80 /* Divide operators */
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#define REMAINDER 0x40 /* .. */
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#define DIVIDEINT 0x20 /* .. */
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#define REMNEAR 0x10 /* .. */
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#define COMPARE 0x01 /* Compare operators */
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#define COMPMAX 0x02 /* .. */
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#define COMPMIN 0x03 /* .. */
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#define COMPNAN 0x04 /* .. [NaN processing] */
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#define DEC_sNaN 0x40000000 /* local status: sNaN signal */
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#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */
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static Unit one[] = { 1 }; /* Unit array of 1, used for incrementing */
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/* Granularity-dependent code */
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#if DECDPUN<=4
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#define eInt Int /* extended integer */
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#define ueInt uInt /* unsigned extended integer */
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/* Constant multipliers for divide-by-power-of five using reciprocal */
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/* multiply, after removing powers of 2 by shifting, and final shift */
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/* of 17 [we only need up to **4] */
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static const uInt multies[] = { 131073, 26215, 5243, 1049, 210 };
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/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
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#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
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#else
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/* For DECDPUN>4 we currently use non-ANSI 64-bit types. These could */
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/* be replaced by subroutine calls later. */
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#ifdef long
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#undef long
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#endif
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typedef signed long long Long;
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typedef unsigned long long uLong;
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#define eInt Long /* extended integer */
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#define ueInt uLong /* unsigned extended integer */
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#endif
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/* Local routines */
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static decNumber *decAddOp (decNumber *, const decNumber *,
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const decNumber *, decContext *,
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uByte, uInt *);
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static void decApplyRound (decNumber *, decContext *, Int, uInt *);
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static Int decCompare (const decNumber * lhs, const decNumber * rhs);
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static decNumber *decCompareOp (decNumber *, const decNumber *, const decNumber *,
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decContext *, Flag, uInt *);
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static void decCopyFit (decNumber *, const decNumber *, decContext *,
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Int *, uInt *);
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static decNumber *decDivideOp (decNumber *, const decNumber *, const decNumber *,
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decContext *, Flag, uInt *);
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static void decFinalize (decNumber *, decContext *, Int *, uInt *);
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static Int decGetDigits (const Unit *, Int);
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#if DECSUBSET
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static Int decGetInt (const decNumber *, decContext *);
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#else
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static Int decGetInt (const decNumber *);
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#endif
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static decNumber *decMultiplyOp (decNumber *, const decNumber *,
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const decNumber *, decContext *, uInt *);
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static decNumber *decNaNs (decNumber *, const decNumber *, const decNumber *, uInt *);
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static decNumber *decQuantizeOp (decNumber *, const decNumber *,
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const decNumber *, decContext *, Flag, uInt *);
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static void decSetCoeff (decNumber *, decContext *, const Unit *,
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Int, Int *, uInt *);
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static void decSetOverflow (decNumber *, decContext *, uInt *);
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static void decSetSubnormal (decNumber *, decContext *, Int *, uInt *);
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static Int decShiftToLeast (Unit *, Int, Int);
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static Int decShiftToMost (Unit *, Int, Int);
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static void decStatus (decNumber *, uInt, decContext *);
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static Flag decStrEq (const char *, const char *);
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static void decToString (const decNumber *, char[], Flag);
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static decNumber *decTrim (decNumber *, Flag, Int *);
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static Int decUnitAddSub (const Unit *, Int, const Unit *, Int, Int, Unit *, Int);
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static Int decUnitCompare (const Unit *, Int, const Unit *, Int, Int);
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#if !DECSUBSET
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/* decFinish == decFinalize when no subset arithmetic needed */
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#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
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#else
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static void decFinish (decNumber *, decContext *, Int *, uInt *);
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static decNumber *decRoundOperand (const decNumber *, decContext *, uInt *);
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#endif
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/* Diagnostic macros, etc. */
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#if DECALLOC
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/* Handle malloc/free accounting. If enabled, our accountable routines */
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/* are used; otherwise the code just goes straight to the system malloc */
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/* and free routines. */
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#define malloc(a) decMalloc(a)
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#define free(a) decFree(a)
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#define DECFENCE 0x5a /* corruption detector */
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/* 'Our' malloc and free: */
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static void *decMalloc (size_t);
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static void decFree (void *);
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uInt decAllocBytes = 0; /* count of bytes allocated */
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/* Note that DECALLOC code only checks for storage buffer overflow. */
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/* To check for memory leaks, the decAllocBytes variable should be */
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/* checked to be 0 at appropriate times (e.g., after the test */
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/* harness completes a set of tests). This checking may be unreliable */
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/* if the testing is done in a multi-thread environment. */
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#endif
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#if DECCHECK
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/* Optional operand checking routines. Enabling these means that */
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/* decNumber and decContext operands to operator routines are checked */
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/* for correctness. This roughly doubles the execution time of the */
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/* fastest routines (and adds 600+ bytes), so should not normally be */
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/* used in 'production'. */
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#define DECUNUSED (void *)(0xffffffff)
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static Flag decCheckOperands (decNumber *, const decNumber *,
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const decNumber *, decContext *);
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static Flag decCheckNumber (const decNumber *, decContext *);
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#endif
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#if DECTRACE || DECCHECK
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/* Optional trace/debugging routines. */
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void decNumberShow (const decNumber *); /* displays the components of a number */
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static void decDumpAr (char, const Unit *, Int);
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#endif
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/* ================================================================== */
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/* Conversions */
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/* ================================================================== */
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152 |
jeremybenn |
/* The following two functions are copied from later versions, since */
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| 304 |
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/* they are needed by GDB which shares this library. */
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38 |
julius |
/* ------------------------------------------------------------------ */
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| 307 |
152 |
jeremybenn |
/* from-int32 -- conversion from Int or uInt */
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| 308 |
|
|
/* */
|
| 309 |
|
|
/* dn is the decNumber to receive the integer */
|
| 310 |
|
|
/* in or uin is the integer to be converted */
|
| 311 |
|
|
/* returns dn */
|
| 312 |
|
|
/* */
|
| 313 |
|
|
/* No error is possible. */
|
| 314 |
|
|
/* ------------------------------------------------------------------ */
|
| 315 |
|
|
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
|
| 316 |
|
|
uInt unsig;
|
| 317 |
|
|
if (in>=0) unsig=in;
|
| 318 |
|
|
else { /* negative (possibly BADINT) */
|
| 319 |
|
|
if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
|
| 320 |
|
|
else unsig=-in; /* invert */
|
| 321 |
|
|
}
|
| 322 |
|
|
/* in is now positive */
|
| 323 |
|
|
decNumberFromUInt32(dn, unsig);
|
| 324 |
|
|
if (in<0) dn->bits=DECNEG; /* sign needed */
|
| 325 |
|
|
return dn;
|
| 326 |
|
|
} /* decNumberFromInt32 */
|
| 327 |
|
|
|
| 328 |
|
|
decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
|
| 329 |
|
|
Unit *up; /* work pointer */
|
| 330 |
|
|
decNumberZero(dn); /* clean */
|
| 331 |
|
|
if (uin==0) return dn; /* [or decGetDigits bad call] */
|
| 332 |
|
|
for (up=dn->lsu; uin>0; up++) {
|
| 333 |
|
|
*up=(Unit)(uin%(DECDPUNMAX+1));
|
| 334 |
|
|
uin=uin/(DECDPUNMAX+1);
|
| 335 |
|
|
}
|
| 336 |
|
|
dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
|
| 337 |
|
|
return dn;
|
| 338 |
|
|
} /* decNumberFromUInt32 */
|
| 339 |
|
|
|
| 340 |
|
|
|
| 341 |
|
|
/* ------------------------------------------------------------------ */
|
| 342 |
38 |
julius |
/* to-scientific-string -- conversion to numeric string */
|
| 343 |
|
|
/* to-engineering-string -- conversion to numeric string */
|
| 344 |
|
|
/* */
|
| 345 |
|
|
/* decNumberToString(dn, string); */
|
| 346 |
|
|
/* decNumberToEngString(dn, string); */
|
| 347 |
|
|
/* */
|
| 348 |
|
|
/* dn is the decNumber to convert */
|
| 349 |
|
|
/* string is the string where the result will be laid out */
|
| 350 |
|
|
/* */
|
| 351 |
|
|
/* string must be at least dn->digits+14 characters long */
|
| 352 |
|
|
/* */
|
| 353 |
|
|
/* No error is possible, and no status can be set. */
|
| 354 |
|
|
/* ------------------------------------------------------------------ */
|
| 355 |
|
|
char *
|
| 356 |
|
|
decNumberToString (const decNumber * dn, char *string)
|
| 357 |
|
|
{
|
| 358 |
|
|
decToString (dn, string, 0);
|
| 359 |
|
|
return string;
|
| 360 |
|
|
}
|
| 361 |
|
|
|
| 362 |
|
|
char *
|
| 363 |
|
|
decNumberToEngString (const decNumber * dn, char *string)
|
| 364 |
|
|
{
|
| 365 |
|
|
decToString (dn, string, 1);
|
| 366 |
|
|
return string;
|
| 367 |
|
|
}
|
| 368 |
|
|
|
| 369 |
|
|
/* ------------------------------------------------------------------ */
|
| 370 |
|
|
/* to-number -- conversion from numeric string */
|
| 371 |
|
|
/* */
|
| 372 |
|
|
/* decNumberFromString -- convert string to decNumber */
|
| 373 |
|
|
/* dn -- the number structure to fill */
|
| 374 |
|
|
/* chars[] -- the string to convert ('\0' terminated) */
|
| 375 |
|
|
/* set -- the context used for processing any error, */
|
| 376 |
|
|
/* determining the maximum precision available */
|
| 377 |
|
|
/* (set.digits), determining the maximum and minimum */
|
| 378 |
|
|
/* exponent (set.emax and set.emin), determining if */
|
| 379 |
|
|
/* extended values are allowed, and checking the */
|
| 380 |
|
|
/* rounding mode if overflow occurs or rounding is */
|
| 381 |
|
|
/* needed. */
|
| 382 |
|
|
/* */
|
| 383 |
|
|
/* The length of the coefficient and the size of the exponent are */
|
| 384 |
|
|
/* checked by this routine, so the correct error (Underflow or */
|
| 385 |
|
|
/* Overflow) can be reported or rounding applied, as necessary. */
|
| 386 |
|
|
/* */
|
| 387 |
|
|
/* If bad syntax is detected, the result will be a quiet NaN. */
|
| 388 |
|
|
/* ------------------------------------------------------------------ */
|
| 389 |
|
|
decNumber *
|
| 390 |
|
|
decNumberFromString (decNumber * dn, const char chars[], decContext * set)
|
| 391 |
|
|
{
|
| 392 |
|
|
Int exponent = 0; /* working exponent [assume 0] */
|
| 393 |
|
|
uByte bits = 0; /* working flags [assume +ve] */
|
| 394 |
|
|
Unit *res; /* where result will be built */
|
| 395 |
|
|
Unit resbuff[D2U (DECBUFFER + 1)]; /* local buffer in case need temporary */
|
| 396 |
|
|
Unit *allocres = NULL; /* -> allocated result, iff allocated */
|
| 397 |
|
|
Int need; /* units needed for result */
|
| 398 |
|
|
Int d = 0; /* count of digits found in decimal part */
|
| 399 |
|
|
const char *dotchar = NULL; /* where dot was found */
|
| 400 |
|
|
const char *cfirst; /* -> first character of decimal part */
|
| 401 |
|
|
const char *last = NULL; /* -> last digit of decimal part */
|
| 402 |
|
|
const char *firstexp; /* -> first significant exponent digit */
|
| 403 |
|
|
const char *c; /* work */
|
| 404 |
|
|
Unit *up; /* .. */
|
| 405 |
|
|
#if DECDPUN>1
|
| 406 |
|
|
Int i; /* .. */
|
| 407 |
|
|
#endif
|
| 408 |
|
|
Int residue = 0; /* rounding residue */
|
| 409 |
|
|
uInt status = 0; /* error code */
|
| 410 |
|
|
|
| 411 |
|
|
#if DECCHECK
|
| 412 |
|
|
if (decCheckOperands (DECUNUSED, DECUNUSED, DECUNUSED, set))
|
| 413 |
|
|
return decNumberZero (dn);
|
| 414 |
|
|
#endif
|
| 415 |
|
|
|
| 416 |
|
|
do
|
| 417 |
|
|
{ /* status & malloc protection */
|
| 418 |
|
|
c = chars; /* -> input character */
|
| 419 |
|
|
if (*c == '-')
|
| 420 |
|
|
{ /* handle leading '-' */
|
| 421 |
|
|
bits = DECNEG;
|
| 422 |
|
|
c++;
|
| 423 |
|
|
}
|
| 424 |
|
|
else if (*c == '+')
|
| 425 |
|
|
c++; /* step over leading '+' */
|
| 426 |
|
|
/* We're at the start of the number [we think] */
|
| 427 |
|
|
cfirst = c; /* save */
|
| 428 |
|
|
for (;; c++)
|
| 429 |
|
|
{
|
| 430 |
|
|
if (*c >= '0' && *c <= '9')
|
| 431 |
|
|
{ /* test for Arabic digit */
|
| 432 |
|
|
last = c;
|
| 433 |
|
|
d++; /* count of real digits */
|
| 434 |
|
|
continue; /* still in decimal part */
|
| 435 |
|
|
}
|
| 436 |
|
|
if (*c != '.')
|
| 437 |
|
|
break; /* done with decimal part */
|
| 438 |
|
|
/* dot: record, check, and ignore */
|
| 439 |
|
|
if (dotchar != NULL)
|
| 440 |
|
|
{ /* two dots */
|
| 441 |
|
|
last = NULL; /* indicate bad */
|
| 442 |
|
|
break;
|
| 443 |
|
|
} /* .. and go report */
|
| 444 |
|
|
dotchar = c; /* offset into decimal part */
|
| 445 |
|
|
} /* c */
|
| 446 |
|
|
|
| 447 |
|
|
if (last == NULL)
|
| 448 |
|
|
{ /* no decimal digits, or >1 . */
|
| 449 |
|
|
#if DECSUBSET
|
| 450 |
|
|
/* If subset then infinities and NaNs are not allowed */
|
| 451 |
|
|
if (!set->extended)
|
| 452 |
|
|
{
|
| 453 |
|
|
status = DEC_Conversion_syntax;
|
| 454 |
|
|
break; /* all done */
|
| 455 |
|
|
}
|
| 456 |
|
|
else
|
| 457 |
|
|
{
|
| 458 |
|
|
#endif
|
| 459 |
|
|
/* Infinities and NaNs are possible, here */
|
| 460 |
|
|
decNumberZero (dn); /* be optimistic */
|
| 461 |
|
|
if (decStrEq (c, "Infinity") || decStrEq (c, "Inf"))
|
| 462 |
|
|
{
|
| 463 |
|
|
dn->bits = bits | DECINF;
|
| 464 |
|
|
break; /* all done */
|
| 465 |
|
|
}
|
| 466 |
|
|
else
|
| 467 |
|
|
{ /* a NaN expected */
|
| 468 |
|
|
/* 2003.09.10 NaNs are now permitted to have a sign */
|
| 469 |
|
|
status = DEC_Conversion_syntax; /* assume the worst */
|
| 470 |
|
|
dn->bits = bits | DECNAN; /* assume simple NaN */
|
| 471 |
|
|
if (*c == 's' || *c == 'S')
|
| 472 |
|
|
{ /* looks like an` sNaN */
|
| 473 |
|
|
c++;
|
| 474 |
|
|
dn->bits = bits | DECSNAN;
|
| 475 |
|
|
}
|
| 476 |
|
|
if (*c != 'n' && *c != 'N')
|
| 477 |
|
|
break; /* check caseless "NaN" */
|
| 478 |
|
|
c++;
|
| 479 |
|
|
if (*c != 'a' && *c != 'A')
|
| 480 |
|
|
break; /* .. */
|
| 481 |
|
|
c++;
|
| 482 |
|
|
if (*c != 'n' && *c != 'N')
|
| 483 |
|
|
break; /* .. */
|
| 484 |
|
|
c++;
|
| 485 |
|
|
/* now nothing, or nnnn, expected */
|
| 486 |
|
|
/* -> start of integer and skip leading 0s [including plain 0] */
|
| 487 |
|
|
for (cfirst = c; *cfirst == '0';)
|
| 488 |
|
|
cfirst++;
|
| 489 |
|
|
if (*cfirst == '\0')
|
| 490 |
|
|
{ /* "NaN" or "sNaN", maybe with all 0s */
|
| 491 |
|
|
status = 0; /* it's good */
|
| 492 |
|
|
break; /* .. */
|
| 493 |
|
|
}
|
| 494 |
|
|
/* something other than 0s; setup last and d as usual [no dots] */
|
| 495 |
|
|
for (c = cfirst;; c++, d++)
|
| 496 |
|
|
{
|
| 497 |
|
|
if (*c < '0' || *c > '9')
|
| 498 |
|
|
break; /* test for Arabic digit */
|
| 499 |
|
|
last = c;
|
| 500 |
|
|
}
|
| 501 |
|
|
if (*c != '\0')
|
| 502 |
|
|
break; /* not all digits */
|
| 503 |
|
|
if (d > set->digits)
|
| 504 |
|
|
break; /* too many digits */
|
| 505 |
|
|
/* good; drop through and convert the integer */
|
| 506 |
|
|
status = 0;
|
| 507 |
|
|
bits = dn->bits; /* for copy-back */
|
| 508 |
|
|
} /* NaN expected */
|
| 509 |
|
|
#if DECSUBSET
|
| 510 |
|
|
}
|
| 511 |
|
|
#endif
|
| 512 |
|
|
} /* last==NULL */
|
| 513 |
|
|
|
| 514 |
|
|
if (*c != '\0')
|
| 515 |
|
|
{ /* more there; exponent expected... */
|
| 516 |
|
|
Flag nege = 0; /* 1=negative exponent */
|
| 517 |
|
|
if (*c != 'e' && *c != 'E')
|
| 518 |
|
|
{
|
| 519 |
|
|
status = DEC_Conversion_syntax;
|
| 520 |
|
|
break;
|
| 521 |
|
|
}
|
| 522 |
|
|
|
| 523 |
|
|
/* Found 'e' or 'E' -- now process explicit exponent */
|
| 524 |
|
|
/* 1998.07.11: sign no longer required */
|
| 525 |
|
|
c++; /* to (expected) sign */
|
| 526 |
|
|
if (*c == '-')
|
| 527 |
|
|
{
|
| 528 |
|
|
nege = 1;
|
| 529 |
|
|
c++;
|
| 530 |
|
|
}
|
| 531 |
|
|
else if (*c == '+')
|
| 532 |
|
|
c++;
|
| 533 |
|
|
if (*c == '\0')
|
| 534 |
|
|
{
|
| 535 |
|
|
status = DEC_Conversion_syntax;
|
| 536 |
|
|
break;
|
| 537 |
|
|
}
|
| 538 |
|
|
|
| 539 |
|
|
for (; *c == '0' && *(c + 1) != '\0';)
|
| 540 |
|
|
c++; /* strip insignificant zeros */
|
| 541 |
|
|
firstexp = c; /* save exponent digit place */
|
| 542 |
|
|
for (;; c++)
|
| 543 |
|
|
{
|
| 544 |
|
|
if (*c < '0' || *c > '9')
|
| 545 |
|
|
break; /* not a digit */
|
| 546 |
|
|
exponent = X10 (exponent) + (Int) * c - (Int) '0';
|
| 547 |
|
|
} /* c */
|
| 548 |
|
|
/* if we didn't end on '\0' must not be a digit */
|
| 549 |
|
|
if (*c != '\0')
|
| 550 |
|
|
{
|
| 551 |
|
|
status = DEC_Conversion_syntax;
|
| 552 |
|
|
break;
|
| 553 |
|
|
}
|
| 554 |
|
|
|
| 555 |
|
|
/* (this next test must be after the syntax check) */
|
| 556 |
|
|
/* if it was too long the exponent may have wrapped, so check */
|
| 557 |
|
|
/* carefully and set it to a certain overflow if wrap possible */
|
| 558 |
|
|
if (c >= firstexp + 9 + 1)
|
| 559 |
|
|
{
|
| 560 |
|
|
if (c > firstexp + 9 + 1 || *firstexp > '1')
|
| 561 |
|
|
exponent = DECNUMMAXE * 2;
|
| 562 |
|
|
/* [up to 1999999999 is OK, for example 1E-1000000998] */
|
| 563 |
|
|
}
|
| 564 |
|
|
if (nege)
|
| 565 |
|
|
exponent = -exponent; /* was negative */
|
| 566 |
|
|
} /* had exponent */
|
| 567 |
|
|
/* Here when all inspected; syntax is good */
|
| 568 |
|
|
|
| 569 |
|
|
/* Handle decimal point... */
|
| 570 |
|
|
if (dotchar != NULL && dotchar < last) /* embedded . found, so */
|
| 571 |
|
|
exponent = exponent - (last - dotchar); /* .. adjust exponent */
|
| 572 |
|
|
/* [we can now ignore the .] */
|
| 573 |
|
|
|
| 574 |
|
|
/* strip leading zeros/dot (leave final if all 0's) */
|
| 575 |
|
|
for (c = cfirst; c < last; c++)
|
| 576 |
|
|
{
|
| 577 |
|
|
if (*c == '0')
|
| 578 |
|
|
d--; /* 0 stripped */
|
| 579 |
|
|
else if (*c != '.')
|
| 580 |
|
|
break;
|
| 581 |
|
|
cfirst++; /* step past leader */
|
| 582 |
|
|
} /* c */
|
| 583 |
|
|
|
| 584 |
|
|
#if DECSUBSET
|
| 585 |
|
|
/* We can now make a rapid exit for zeros if !extended */
|
| 586 |
|
|
if (*cfirst == '0' && !set->extended)
|
| 587 |
|
|
{
|
| 588 |
|
|
decNumberZero (dn); /* clean result */
|
| 589 |
|
|
break; /* [could be return] */
|
| 590 |
|
|
}
|
| 591 |
|
|
#endif
|
| 592 |
|
|
|
| 593 |
|
|
/* OK, the digits string is good. Copy to the decNumber, or to
|
| 594 |
|
|
a temporary decNumber if rounding is needed */
|
| 595 |
|
|
if (d <= set->digits)
|
| 596 |
|
|
res = dn->lsu; /* fits into given decNumber */
|
| 597 |
|
|
else
|
| 598 |
|
|
{ /* rounding needed */
|
| 599 |
|
|
need = D2U (d); /* units needed */
|
| 600 |
|
|
res = resbuff; /* assume use local buffer */
|
| 601 |
|
|
if (need * sizeof (Unit) > sizeof (resbuff))
|
| 602 |
|
|
{ /* too big for local */
|
| 603 |
|
|
allocres = (Unit *) malloc (need * sizeof (Unit));
|
| 604 |
|
|
if (allocres == NULL)
|
| 605 |
|
|
{
|
| 606 |
|
|
status |= DEC_Insufficient_storage;
|
| 607 |
|
|
break;
|
| 608 |
|
|
}
|
| 609 |
|
|
res = allocres;
|
| 610 |
|
|
}
|
| 611 |
|
|
}
|
| 612 |
|
|
/* res now -> number lsu, buffer, or allocated storage for Unit array */
|
| 613 |
|
|
|
| 614 |
|
|
/* Place the coefficient into the selected Unit array */
|
| 615 |
|
|
#if DECDPUN>1
|
| 616 |
|
|
i = d % DECDPUN; /* digits in top unit */
|
| 617 |
|
|
if (i == 0)
|
| 618 |
|
|
i = DECDPUN;
|
| 619 |
|
|
up = res + D2U (d) - 1; /* -> msu */
|
| 620 |
|
|
*up = 0;
|
| 621 |
|
|
for (c = cfirst;; c++)
|
| 622 |
|
|
{ /* along the digits */
|
| 623 |
|
|
if (*c == '.')
|
| 624 |
|
|
{ /* ignore . [don't decrement i] */
|
| 625 |
|
|
if (c != last)
|
| 626 |
|
|
continue;
|
| 627 |
|
|
break;
|
| 628 |
|
|
}
|
| 629 |
|
|
*up = (Unit) (X10 (*up) + (Int) * c - (Int) '0');
|
| 630 |
|
|
i--;
|
| 631 |
|
|
if (i > 0)
|
| 632 |
|
|
continue; /* more for this unit */
|
| 633 |
|
|
if (up == res)
|
| 634 |
|
|
break; /* just filled the last unit */
|
| 635 |
|
|
i = DECDPUN;
|
| 636 |
|
|
up--;
|
| 637 |
|
|
*up = 0;
|
| 638 |
|
|
} /* c */
|
| 639 |
|
|
#else
|
| 640 |
|
|
/* DECDPUN==1 */
|
| 641 |
|
|
up = res; /* -> lsu */
|
| 642 |
|
|
for (c = last; c >= cfirst; c--)
|
| 643 |
|
|
{ /* over each character, from least */
|
| 644 |
|
|
if (*c == '.')
|
| 645 |
|
|
continue; /* ignore . [don't step b] */
|
| 646 |
|
|
*up = (Unit) ((Int) * c - (Int) '0');
|
| 647 |
|
|
up++;
|
| 648 |
|
|
} /* c */
|
| 649 |
|
|
#endif
|
| 650 |
|
|
|
| 651 |
|
|
dn->bits = bits;
|
| 652 |
|
|
dn->exponent = exponent;
|
| 653 |
|
|
dn->digits = d;
|
| 654 |
|
|
|
| 655 |
|
|
/* if not in number (too long) shorten into the number */
|
| 656 |
|
|
if (d > set->digits)
|
| 657 |
|
|
decSetCoeff (dn, set, res, d, &residue, &status);
|
| 658 |
|
|
|
| 659 |
|
|
/* Finally check for overflow or subnormal and round as needed */
|
| 660 |
|
|
decFinalize (dn, set, &residue, &status);
|
| 661 |
|
|
/* decNumberShow(dn); */
|
| 662 |
|
|
}
|
| 663 |
|
|
while (0); /* [for break] */
|
| 664 |
|
|
|
| 665 |
|
|
if (allocres != NULL)
|
| 666 |
|
|
free (allocres); /* drop any storage we used */
|
| 667 |
|
|
if (status != 0)
|
| 668 |
|
|
decStatus (dn, status, set);
|
| 669 |
|
|
return dn;
|
| 670 |
|
|
}
|
| 671 |
|
|
|
| 672 |
|
|
/* ================================================================== */
|
| 673 |
|
|
/* Operators */
|
| 674 |
|
|
/* ================================================================== */
|
| 675 |
|
|
|
| 676 |
|
|
/* ------------------------------------------------------------------ */
|
| 677 |
|
|
/* decNumberAbs -- absolute value operator */
|
| 678 |
|
|
/* */
|
| 679 |
|
|
/* This computes C = abs(A) */
|
| 680 |
|
|
/* */
|
| 681 |
|
|
/* res is C, the result. C may be A */
|
| 682 |
|
|
/* rhs is A */
|
| 683 |
|
|
/* set is the context */
|
| 684 |
|
|
/* */
|
| 685 |
|
|
/* C must have space for set->digits digits. */
|
| 686 |
|
|
/* ------------------------------------------------------------------ */
|
| 687 |
|
|
/* This has the same effect as decNumberPlus unless A is negative, */
|
| 688 |
|
|
/* in which case it has the same effect as decNumberMinus. */
|
| 689 |
|
|
/* ------------------------------------------------------------------ */
|
| 690 |
|
|
decNumber *
|
| 691 |
|
|
decNumberAbs (decNumber * res, const decNumber * rhs, decContext * set)
|
| 692 |
|
|
{
|
| 693 |
|
|
decNumber dzero; /* for 0 */
|
| 694 |
|
|
uInt status = 0; /* accumulator */
|
| 695 |
|
|
|
| 696 |
|
|
#if DECCHECK
|
| 697 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 698 |
|
|
return res;
|
| 699 |
|
|
#endif
|
| 700 |
|
|
|
| 701 |
|
|
decNumberZero (&dzero); /* set 0 */
|
| 702 |
|
|
dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
|
| 703 |
|
|
decAddOp (res, &dzero, rhs, set, (uByte) (rhs->bits & DECNEG), &status);
|
| 704 |
|
|
if (status != 0)
|
| 705 |
|
|
decStatus (res, status, set);
|
| 706 |
|
|
return res;
|
| 707 |
|
|
}
|
| 708 |
|
|
|
| 709 |
|
|
/* ------------------------------------------------------------------ */
|
| 710 |
|
|
/* decNumberAdd -- add two Numbers */
|
| 711 |
|
|
/* */
|
| 712 |
|
|
/* This computes C = A + B */
|
| 713 |
|
|
/* */
|
| 714 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 715 |
|
|
/* lhs is A */
|
| 716 |
|
|
/* rhs is B */
|
| 717 |
|
|
/* set is the context */
|
| 718 |
|
|
/* */
|
| 719 |
|
|
/* C must have space for set->digits digits. */
|
| 720 |
|
|
/* ------------------------------------------------------------------ */
|
| 721 |
|
|
/* This just calls the routine shared with Subtract */
|
| 722 |
|
|
decNumber *
|
| 723 |
|
|
decNumberAdd (decNumber * res, const decNumber * lhs,
|
| 724 |
|
|
const decNumber * rhs, decContext * set)
|
| 725 |
|
|
{
|
| 726 |
|
|
uInt status = 0; /* accumulator */
|
| 727 |
|
|
decAddOp (res, lhs, rhs, set, 0, &status);
|
| 728 |
|
|
if (status != 0)
|
| 729 |
|
|
decStatus (res, status, set);
|
| 730 |
|
|
return res;
|
| 731 |
|
|
}
|
| 732 |
|
|
|
| 733 |
|
|
/* ------------------------------------------------------------------ */
|
| 734 |
|
|
/* decNumberCompare -- compare two Numbers */
|
| 735 |
|
|
/* */
|
| 736 |
|
|
/* This computes C = A ? B */
|
| 737 |
|
|
/* */
|
| 738 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 739 |
|
|
/* lhs is A */
|
| 740 |
|
|
/* rhs is B */
|
| 741 |
|
|
/* set is the context */
|
| 742 |
|
|
/* */
|
| 743 |
|
|
/* C must have space for one digit. */
|
| 744 |
|
|
/* ------------------------------------------------------------------ */
|
| 745 |
|
|
decNumber *
|
| 746 |
|
|
decNumberCompare (decNumber * res, const decNumber * lhs,
|
| 747 |
|
|
const decNumber * rhs, decContext * set)
|
| 748 |
|
|
{
|
| 749 |
|
|
uInt status = 0; /* accumulator */
|
| 750 |
|
|
decCompareOp (res, lhs, rhs, set, COMPARE, &status);
|
| 751 |
|
|
if (status != 0)
|
| 752 |
|
|
decStatus (res, status, set);
|
| 753 |
|
|
return res;
|
| 754 |
|
|
}
|
| 755 |
|
|
|
| 756 |
|
|
/* ------------------------------------------------------------------ */
|
| 757 |
|
|
/* decNumberDivide -- divide one number by another */
|
| 758 |
|
|
/* */
|
| 759 |
|
|
/* This computes C = A / B */
|
| 760 |
|
|
/* */
|
| 761 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| 762 |
|
|
/* lhs is A */
|
| 763 |
|
|
/* rhs is B */
|
| 764 |
|
|
/* set is the context */
|
| 765 |
|
|
/* */
|
| 766 |
|
|
/* C must have space for set->digits digits. */
|
| 767 |
|
|
/* ------------------------------------------------------------------ */
|
| 768 |
|
|
decNumber *
|
| 769 |
|
|
decNumberDivide (decNumber * res, const decNumber * lhs,
|
| 770 |
|
|
const decNumber * rhs, decContext * set)
|
| 771 |
|
|
{
|
| 772 |
|
|
uInt status = 0; /* accumulator */
|
| 773 |
|
|
decDivideOp (res, lhs, rhs, set, DIVIDE, &status);
|
| 774 |
|
|
if (status != 0)
|
| 775 |
|
|
decStatus (res, status, set);
|
| 776 |
|
|
return res;
|
| 777 |
|
|
}
|
| 778 |
|
|
|
| 779 |
|
|
/* ------------------------------------------------------------------ */
|
| 780 |
|
|
/* decNumberDivideInteger -- divide and return integer quotient */
|
| 781 |
|
|
/* */
|
| 782 |
|
|
/* This computes C = A # B, where # is the integer divide operator */
|
| 783 |
|
|
/* */
|
| 784 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
|
| 785 |
|
|
/* lhs is A */
|
| 786 |
|
|
/* rhs is B */
|
| 787 |
|
|
/* set is the context */
|
| 788 |
|
|
/* */
|
| 789 |
|
|
/* C must have space for set->digits digits. */
|
| 790 |
|
|
/* ------------------------------------------------------------------ */
|
| 791 |
|
|
decNumber *
|
| 792 |
|
|
decNumberDivideInteger (decNumber * res, const decNumber * lhs,
|
| 793 |
|
|
const decNumber * rhs, decContext * set)
|
| 794 |
|
|
{
|
| 795 |
|
|
uInt status = 0; /* accumulator */
|
| 796 |
|
|
decDivideOp (res, lhs, rhs, set, DIVIDEINT, &status);
|
| 797 |
|
|
if (status != 0)
|
| 798 |
|
|
decStatus (res, status, set);
|
| 799 |
|
|
return res;
|
| 800 |
|
|
}
|
| 801 |
|
|
|
| 802 |
|
|
/* ------------------------------------------------------------------ */
|
| 803 |
|
|
/* decNumberMax -- compare two Numbers and return the maximum */
|
| 804 |
|
|
/* */
|
| 805 |
|
|
/* This computes C = A ? B, returning the maximum or A if equal */
|
| 806 |
|
|
/* */
|
| 807 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 808 |
|
|
/* lhs is A */
|
| 809 |
|
|
/* rhs is B */
|
| 810 |
|
|
/* set is the context */
|
| 811 |
|
|
/* */
|
| 812 |
|
|
/* C must have space for set->digits digits. */
|
| 813 |
|
|
/* ------------------------------------------------------------------ */
|
| 814 |
|
|
decNumber *
|
| 815 |
|
|
decNumberMax (decNumber * res, const decNumber * lhs,
|
| 816 |
|
|
const decNumber * rhs, decContext * set)
|
| 817 |
|
|
{
|
| 818 |
|
|
uInt status = 0; /* accumulator */
|
| 819 |
|
|
decCompareOp (res, lhs, rhs, set, COMPMAX, &status);
|
| 820 |
|
|
if (status != 0)
|
| 821 |
|
|
decStatus (res, status, set);
|
| 822 |
|
|
return res;
|
| 823 |
|
|
}
|
| 824 |
|
|
|
| 825 |
|
|
/* ------------------------------------------------------------------ */
|
| 826 |
|
|
/* decNumberMin -- compare two Numbers and return the minimum */
|
| 827 |
|
|
/* */
|
| 828 |
|
|
/* This computes C = A ? B, returning the minimum or A if equal */
|
| 829 |
|
|
/* */
|
| 830 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 831 |
|
|
/* lhs is A */
|
| 832 |
|
|
/* rhs is B */
|
| 833 |
|
|
/* set is the context */
|
| 834 |
|
|
/* */
|
| 835 |
|
|
/* C must have space for set->digits digits. */
|
| 836 |
|
|
/* ------------------------------------------------------------------ */
|
| 837 |
|
|
decNumber *
|
| 838 |
|
|
decNumberMin (decNumber * res, const decNumber * lhs,
|
| 839 |
|
|
const decNumber * rhs, decContext * set)
|
| 840 |
|
|
{
|
| 841 |
|
|
uInt status = 0; /* accumulator */
|
| 842 |
|
|
decCompareOp (res, lhs, rhs, set, COMPMIN, &status);
|
| 843 |
|
|
if (status != 0)
|
| 844 |
|
|
decStatus (res, status, set);
|
| 845 |
|
|
return res;
|
| 846 |
|
|
}
|
| 847 |
|
|
|
| 848 |
|
|
/* ------------------------------------------------------------------ */
|
| 849 |
|
|
/* decNumberMinus -- prefix minus operator */
|
| 850 |
|
|
/* */
|
| 851 |
|
|
/* This computes C = 0 - A */
|
| 852 |
|
|
/* */
|
| 853 |
|
|
/* res is C, the result. C may be A */
|
| 854 |
|
|
/* rhs is A */
|
| 855 |
|
|
/* set is the context */
|
| 856 |
|
|
/* */
|
| 857 |
|
|
/* C must have space for set->digits digits. */
|
| 858 |
|
|
/* ------------------------------------------------------------------ */
|
| 859 |
|
|
/* We simply use AddOp for the subtract, which will do the necessary. */
|
| 860 |
|
|
/* ------------------------------------------------------------------ */
|
| 861 |
|
|
decNumber *
|
| 862 |
|
|
decNumberMinus (decNumber * res, const decNumber * rhs, decContext * set)
|
| 863 |
|
|
{
|
| 864 |
|
|
decNumber dzero;
|
| 865 |
|
|
uInt status = 0; /* accumulator */
|
| 866 |
|
|
|
| 867 |
|
|
#if DECCHECK
|
| 868 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 869 |
|
|
return res;
|
| 870 |
|
|
#endif
|
| 871 |
|
|
|
| 872 |
|
|
decNumberZero (&dzero); /* make 0 */
|
| 873 |
|
|
dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
|
| 874 |
|
|
decAddOp (res, &dzero, rhs, set, DECNEG, &status);
|
| 875 |
|
|
if (status != 0)
|
| 876 |
|
|
decStatus (res, status, set);
|
| 877 |
|
|
return res;
|
| 878 |
|
|
}
|
| 879 |
|
|
|
| 880 |
|
|
/* ------------------------------------------------------------------ */
|
| 881 |
|
|
/* decNumberPlus -- prefix plus operator */
|
| 882 |
|
|
/* */
|
| 883 |
|
|
/* This computes C = 0 + A */
|
| 884 |
|
|
/* */
|
| 885 |
|
|
/* res is C, the result. C may be A */
|
| 886 |
|
|
/* rhs is A */
|
| 887 |
|
|
/* set is the context */
|
| 888 |
|
|
/* */
|
| 889 |
|
|
/* C must have space for set->digits digits. */
|
| 890 |
|
|
/* ------------------------------------------------------------------ */
|
| 891 |
|
|
/* We simply use AddOp; Add will take fast path after preparing A. */
|
| 892 |
|
|
/* Performance is a concern here, as this routine is often used to */
|
| 893 |
|
|
/* check operands and apply rounding and overflow/underflow testing. */
|
| 894 |
|
|
/* ------------------------------------------------------------------ */
|
| 895 |
|
|
decNumber *
|
| 896 |
|
|
decNumberPlus (decNumber * res, const decNumber * rhs, decContext * set)
|
| 897 |
|
|
{
|
| 898 |
|
|
decNumber dzero;
|
| 899 |
|
|
uInt status = 0; /* accumulator */
|
| 900 |
|
|
|
| 901 |
|
|
#if DECCHECK
|
| 902 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 903 |
|
|
return res;
|
| 904 |
|
|
#endif
|
| 905 |
|
|
|
| 906 |
|
|
decNumberZero (&dzero); /* make 0 */
|
| 907 |
|
|
dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
|
| 908 |
|
|
decAddOp (res, &dzero, rhs, set, 0, &status);
|
| 909 |
|
|
if (status != 0)
|
| 910 |
|
|
decStatus (res, status, set);
|
| 911 |
|
|
return res;
|
| 912 |
|
|
}
|
| 913 |
|
|
|
| 914 |
|
|
/* ------------------------------------------------------------------ */
|
| 915 |
|
|
/* decNumberMultiply -- multiply two Numbers */
|
| 916 |
|
|
/* */
|
| 917 |
|
|
/* This computes C = A x B */
|
| 918 |
|
|
/* */
|
| 919 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 920 |
|
|
/* lhs is A */
|
| 921 |
|
|
/* rhs is B */
|
| 922 |
|
|
/* set is the context */
|
| 923 |
|
|
/* */
|
| 924 |
|
|
/* C must have space for set->digits digits. */
|
| 925 |
|
|
/* ------------------------------------------------------------------ */
|
| 926 |
|
|
decNumber *
|
| 927 |
|
|
decNumberMultiply (decNumber * res, const decNumber * lhs,
|
| 928 |
|
|
const decNumber * rhs, decContext * set)
|
| 929 |
|
|
{
|
| 930 |
|
|
uInt status = 0; /* accumulator */
|
| 931 |
|
|
decMultiplyOp (res, lhs, rhs, set, &status);
|
| 932 |
|
|
if (status != 0)
|
| 933 |
|
|
decStatus (res, status, set);
|
| 934 |
|
|
return res;
|
| 935 |
|
|
}
|
| 936 |
|
|
|
| 937 |
|
|
/* ------------------------------------------------------------------ */
|
| 938 |
|
|
/* decNumberNormalize -- remove trailing zeros */
|
| 939 |
|
|
/* */
|
| 940 |
|
|
/* This computes C = 0 + A, and normalizes the result */
|
| 941 |
|
|
/* */
|
| 942 |
|
|
/* res is C, the result. C may be A */
|
| 943 |
|
|
/* rhs is A */
|
| 944 |
|
|
/* set is the context */
|
| 945 |
|
|
/* */
|
| 946 |
|
|
/* C must have space for set->digits digits. */
|
| 947 |
|
|
/* ------------------------------------------------------------------ */
|
| 948 |
|
|
decNumber *
|
| 949 |
|
|
decNumberNormalize (decNumber * res, const decNumber * rhs, decContext * set)
|
| 950 |
|
|
{
|
| 951 |
|
|
decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */
|
| 952 |
|
|
uInt status = 0; /* as usual */
|
| 953 |
|
|
Int residue = 0; /* as usual */
|
| 954 |
|
|
Int dropped; /* work */
|
| 955 |
|
|
|
| 956 |
|
|
#if DECCHECK
|
| 957 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 958 |
|
|
return res;
|
| 959 |
|
|
#endif
|
| 960 |
|
|
|
| 961 |
|
|
do
|
| 962 |
|
|
{ /* protect allocated storage */
|
| 963 |
|
|
#if DECSUBSET
|
| 964 |
|
|
if (!set->extended)
|
| 965 |
|
|
{
|
| 966 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 967 |
|
|
if (rhs->digits > set->digits)
|
| 968 |
|
|
{
|
| 969 |
|
|
allocrhs = decRoundOperand (rhs, set, &status);
|
| 970 |
|
|
if (allocrhs == NULL)
|
| 971 |
|
|
break;
|
| 972 |
|
|
rhs = allocrhs;
|
| 973 |
|
|
}
|
| 974 |
|
|
}
|
| 975 |
|
|
#endif
|
| 976 |
|
|
/* [following code does not require input rounding] */
|
| 977 |
|
|
|
| 978 |
|
|
/* specials copy through, except NaNs need care */
|
| 979 |
|
|
if (decNumberIsNaN (rhs))
|
| 980 |
|
|
{
|
| 981 |
|
|
decNaNs (res, rhs, NULL, &status);
|
| 982 |
|
|
break;
|
| 983 |
|
|
}
|
| 984 |
|
|
|
| 985 |
|
|
/* reduce result to the requested length and copy to result */
|
| 986 |
|
|
decCopyFit (res, rhs, set, &residue, &status); /* copy & round */
|
| 987 |
|
|
decFinish (res, set, &residue, &status); /* cleanup/set flags */
|
| 988 |
|
|
decTrim (res, 1, &dropped); /* normalize in place */
|
| 989 |
|
|
}
|
| 990 |
|
|
while (0); /* end protected */
|
| 991 |
|
|
|
| 992 |
|
|
if (allocrhs != NULL)
|
| 993 |
|
|
free (allocrhs); /* .. */
|
| 994 |
|
|
if (status != 0)
|
| 995 |
|
|
decStatus (res, status, set); /* then report status */
|
| 996 |
|
|
return res;
|
| 997 |
|
|
}
|
| 998 |
|
|
|
| 999 |
|
|
/* ------------------------------------------------------------------ */
|
| 1000 |
|
|
/* decNumberPower -- raise a number to an integer power */
|
| 1001 |
|
|
/* */
|
| 1002 |
|
|
/* This computes C = A ** B */
|
| 1003 |
|
|
/* */
|
| 1004 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
|
| 1005 |
|
|
/* lhs is A */
|
| 1006 |
|
|
/* rhs is B */
|
| 1007 |
|
|
/* set is the context */
|
| 1008 |
|
|
/* */
|
| 1009 |
|
|
/* C must have space for set->digits digits. */
|
| 1010 |
|
|
/* */
|
| 1011 |
|
|
/* Specification restriction: abs(n) must be <=999999999 */
|
| 1012 |
|
|
/* ------------------------------------------------------------------ */
|
| 1013 |
|
|
decNumber *
|
| 1014 |
|
|
decNumberPower (decNumber * res, const decNumber * lhs,
|
| 1015 |
|
|
const decNumber * rhs, decContext * set)
|
| 1016 |
|
|
{
|
| 1017 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 1018 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 1019 |
|
|
decNumber *allocdac = NULL; /* -> allocated acc buffer, iff used */
|
| 1020 |
|
|
const decNumber *inrhs = rhs; /* save original rhs */
|
| 1021 |
|
|
Int reqdigits = set->digits; /* requested DIGITS */
|
| 1022 |
|
|
Int n; /* RHS in binary */
|
| 1023 |
|
|
Int i; /* work */
|
| 1024 |
|
|
#if DECSUBSET
|
| 1025 |
|
|
Int dropped; /* .. */
|
| 1026 |
|
|
#endif
|
| 1027 |
|
|
uInt needbytes; /* buffer size needed */
|
| 1028 |
|
|
Flag seenbit; /* seen a bit while powering */
|
| 1029 |
|
|
Int residue = 0; /* rounding residue */
|
| 1030 |
|
|
uInt status = 0; /* accumulator */
|
| 1031 |
|
|
uByte bits = 0; /* result sign if errors */
|
| 1032 |
|
|
decContext workset; /* working context */
|
| 1033 |
|
|
decNumber dnOne; /* work value 1... */
|
| 1034 |
|
|
/* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
|
| 1035 |
|
|
uByte dacbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)];
|
| 1036 |
|
|
/* same again for possible 1/lhs calculation */
|
| 1037 |
|
|
uByte lhsbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)];
|
| 1038 |
|
|
decNumber *dac = (decNumber *) dacbuff; /* -> result accumulator */
|
| 1039 |
|
|
|
| 1040 |
|
|
#if DECCHECK
|
| 1041 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 1042 |
|
|
return res;
|
| 1043 |
|
|
#endif
|
| 1044 |
|
|
|
| 1045 |
|
|
do
|
| 1046 |
|
|
{ /* protect allocated storage */
|
| 1047 |
|
|
#if DECSUBSET
|
| 1048 |
|
|
if (!set->extended)
|
| 1049 |
|
|
{
|
| 1050 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 1051 |
|
|
if (lhs->digits > reqdigits)
|
| 1052 |
|
|
{
|
| 1053 |
|
|
alloclhs = decRoundOperand (lhs, set, &status);
|
| 1054 |
|
|
if (alloclhs == NULL)
|
| 1055 |
|
|
break;
|
| 1056 |
|
|
lhs = alloclhs;
|
| 1057 |
|
|
}
|
| 1058 |
|
|
/* rounding won't affect the result, but we might signal lostDigits */
|
| 1059 |
|
|
/* as well as the error for non-integer [x**y would need this too] */
|
| 1060 |
|
|
if (rhs->digits > reqdigits)
|
| 1061 |
|
|
{
|
| 1062 |
|
|
allocrhs = decRoundOperand (rhs, set, &status);
|
| 1063 |
|
|
if (allocrhs == NULL)
|
| 1064 |
|
|
break;
|
| 1065 |
|
|
rhs = allocrhs;
|
| 1066 |
|
|
}
|
| 1067 |
|
|
}
|
| 1068 |
|
|
#endif
|
| 1069 |
|
|
/* [following code does not require input rounding] */
|
| 1070 |
|
|
|
| 1071 |
|
|
/* handle rhs Infinity */
|
| 1072 |
|
|
if (decNumberIsInfinite (rhs))
|
| 1073 |
|
|
{
|
| 1074 |
|
|
status |= DEC_Invalid_operation; /* bad */
|
| 1075 |
|
|
break;
|
| 1076 |
|
|
}
|
| 1077 |
|
|
/* handle NaNs */
|
| 1078 |
|
|
if ((lhs->bits | rhs->bits) & (DECNAN | DECSNAN))
|
| 1079 |
|
|
{
|
| 1080 |
|
|
decNaNs (res, lhs, rhs, &status);
|
| 1081 |
|
|
break;
|
| 1082 |
|
|
}
|
| 1083 |
|
|
|
| 1084 |
|
|
/* Original rhs must be an integer that fits and is in range */
|
| 1085 |
|
|
#if DECSUBSET
|
| 1086 |
|
|
n = decGetInt (inrhs, set);
|
| 1087 |
|
|
#else
|
| 1088 |
|
|
n = decGetInt (inrhs);
|
| 1089 |
|
|
#endif
|
| 1090 |
|
|
if (n == BADINT || n > 999999999 || n < -999999999)
|
| 1091 |
|
|
{
|
| 1092 |
|
|
status |= DEC_Invalid_operation;
|
| 1093 |
|
|
break;
|
| 1094 |
|
|
}
|
| 1095 |
|
|
if (n < 0)
|
| 1096 |
|
|
{ /* negative */
|
| 1097 |
|
|
n = -n; /* use the absolute value */
|
| 1098 |
|
|
}
|
| 1099 |
|
|
if (decNumberIsNegative (lhs) /* -x .. */
|
| 1100 |
|
|
&& (n & 0x00000001))
|
| 1101 |
|
|
bits = DECNEG; /* .. to an odd power */
|
| 1102 |
|
|
|
| 1103 |
|
|
/* handle LHS infinity */
|
| 1104 |
|
|
if (decNumberIsInfinite (lhs))
|
| 1105 |
|
|
{ /* [NaNs already handled] */
|
| 1106 |
|
|
uByte rbits = rhs->bits; /* save */
|
| 1107 |
|
|
decNumberZero (res);
|
| 1108 |
|
|
if (n == 0)
|
| 1109 |
|
|
*res->lsu = 1; /* [-]Inf**0 => 1 */
|
| 1110 |
|
|
else
|
| 1111 |
|
|
{
|
| 1112 |
|
|
if (!(rbits & DECNEG))
|
| 1113 |
|
|
bits |= DECINF; /* was not a **-n */
|
| 1114 |
|
|
/* [otherwise will be 0 or -0] */
|
| 1115 |
|
|
res->bits = bits;
|
| 1116 |
|
|
}
|
| 1117 |
|
|
break;
|
| 1118 |
|
|
}
|
| 1119 |
|
|
|
| 1120 |
|
|
/* clone the context */
|
| 1121 |
|
|
workset = *set; /* copy all fields */
|
| 1122 |
|
|
/* calculate the working DIGITS */
|
| 1123 |
|
|
workset.digits = reqdigits + (inrhs->digits + inrhs->exponent) + 1;
|
| 1124 |
|
|
/* it's an error if this is more than we can handle */
|
| 1125 |
|
|
if (workset.digits > DECNUMMAXP)
|
| 1126 |
|
|
{
|
| 1127 |
|
|
status |= DEC_Invalid_operation;
|
| 1128 |
|
|
break;
|
| 1129 |
|
|
}
|
| 1130 |
|
|
|
| 1131 |
|
|
/* workset.digits is the count of digits for the accumulator we need */
|
| 1132 |
|
|
/* if accumulator is too long for local storage, then allocate */
|
| 1133 |
|
|
needbytes =
|
| 1134 |
|
|
sizeof (decNumber) + (D2U (workset.digits) - 1) * sizeof (Unit);
|
| 1135 |
|
|
/* [needbytes also used below if 1/lhs needed] */
|
| 1136 |
|
|
if (needbytes > sizeof (dacbuff))
|
| 1137 |
|
|
{
|
| 1138 |
|
|
allocdac = (decNumber *) malloc (needbytes);
|
| 1139 |
|
|
if (allocdac == NULL)
|
| 1140 |
|
|
{ /* hopeless -- abandon */
|
| 1141 |
|
|
status |= DEC_Insufficient_storage;
|
| 1142 |
|
|
break;
|
| 1143 |
|
|
}
|
| 1144 |
|
|
dac = allocdac; /* use the allocated space */
|
| 1145 |
|
|
}
|
| 1146 |
|
|
decNumberZero (dac); /* acc=1 */
|
| 1147 |
|
|
*dac->lsu = 1; /* .. */
|
| 1148 |
|
|
|
| 1149 |
|
|
if (n == 0)
|
| 1150 |
|
|
{ /* x**0 is usually 1 */
|
| 1151 |
|
|
/* 0**0 is bad unless subset, when it becomes 1 */
|
| 1152 |
|
|
if (ISZERO (lhs)
|
| 1153 |
|
|
#if DECSUBSET
|
| 1154 |
|
|
&& set->extended
|
| 1155 |
|
|
#endif
|
| 1156 |
|
|
)
|
| 1157 |
|
|
status |= DEC_Invalid_operation;
|
| 1158 |
|
|
else
|
| 1159 |
|
|
decNumberCopy (res, dac); /* copy the 1 */
|
| 1160 |
|
|
break;
|
| 1161 |
|
|
}
|
| 1162 |
|
|
|
| 1163 |
|
|
/* if a negative power we'll need the constant 1, and if not subset */
|
| 1164 |
|
|
/* we'll invert the lhs now rather than inverting the result later */
|
| 1165 |
|
|
if (decNumberIsNegative (rhs))
|
| 1166 |
|
|
{ /* was a **-n [hence digits>0] */
|
| 1167 |
|
|
decNumber * newlhs;
|
| 1168 |
|
|
decNumberCopy (&dnOne, dac); /* dnOne=1; [needed now or later] */
|
| 1169 |
|
|
#if DECSUBSET
|
| 1170 |
|
|
if (set->extended)
|
| 1171 |
|
|
{ /* need to calculate 1/lhs */
|
| 1172 |
|
|
#endif
|
| 1173 |
|
|
/* divide lhs into 1, putting result in dac [dac=1/dac] */
|
| 1174 |
|
|
decDivideOp (dac, &dnOne, lhs, &workset, DIVIDE, &status);
|
| 1175 |
|
|
if (alloclhs != NULL)
|
| 1176 |
|
|
{
|
| 1177 |
|
|
free (alloclhs); /* done with intermediate */
|
| 1178 |
|
|
alloclhs = NULL; /* indicate freed */
|
| 1179 |
|
|
}
|
| 1180 |
|
|
/* now locate or allocate space for the inverted lhs */
|
| 1181 |
|
|
if (needbytes > sizeof (lhsbuff))
|
| 1182 |
|
|
{
|
| 1183 |
|
|
alloclhs = (decNumber *) malloc (needbytes);
|
| 1184 |
|
|
if (alloclhs == NULL)
|
| 1185 |
|
|
{ /* hopeless -- abandon */
|
| 1186 |
|
|
status |= DEC_Insufficient_storage;
|
| 1187 |
|
|
break;
|
| 1188 |
|
|
}
|
| 1189 |
|
|
newlhs = alloclhs; /* use the allocated space */
|
| 1190 |
|
|
}
|
| 1191 |
|
|
else
|
| 1192 |
|
|
newlhs = (decNumber *) lhsbuff; /* use stack storage */
|
| 1193 |
|
|
/* [lhs now points to buffer or allocated storage] */
|
| 1194 |
|
|
decNumberCopy (newlhs, dac); /* copy the 1/lhs */
|
| 1195 |
|
|
decNumberCopy (dac, &dnOne); /* restore acc=1 */
|
| 1196 |
|
|
lhs = newlhs;
|
| 1197 |
|
|
#if DECSUBSET
|
| 1198 |
|
|
}
|
| 1199 |
|
|
#endif
|
| 1200 |
|
|
}
|
| 1201 |
|
|
|
| 1202 |
|
|
/* Raise-to-the-power loop... */
|
| 1203 |
|
|
seenbit = 0; /* set once we've seen a 1-bit */
|
| 1204 |
|
|
for (i = 1;; i++)
|
| 1205 |
|
|
{ /* for each bit [top bit ignored] */
|
| 1206 |
|
|
/* abandon if we have had overflow or terminal underflow */
|
| 1207 |
|
|
if (status & (DEC_Overflow | DEC_Underflow))
|
| 1208 |
|
|
{ /* interesting? */
|
| 1209 |
|
|
if (status & DEC_Overflow || ISZERO (dac))
|
| 1210 |
|
|
break;
|
| 1211 |
|
|
}
|
| 1212 |
|
|
/* [the following two lines revealed an optimizer bug in a C++ */
|
| 1213 |
|
|
/* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
|
| 1214 |
|
|
n = n << 1; /* move next bit to testable position */
|
| 1215 |
|
|
if (n < 0)
|
| 1216 |
|
|
{ /* top bit is set */
|
| 1217 |
|
|
seenbit = 1; /* OK, we're off */
|
| 1218 |
|
|
decMultiplyOp (dac, dac, lhs, &workset, &status); /* dac=dac*x */
|
| 1219 |
|
|
}
|
| 1220 |
|
|
if (i == 31)
|
| 1221 |
|
|
break; /* that was the last bit */
|
| 1222 |
|
|
if (!seenbit)
|
| 1223 |
|
|
continue; /* we don't have to square 1 */
|
| 1224 |
|
|
decMultiplyOp (dac, dac, dac, &workset, &status); /* dac=dac*dac [square] */
|
| 1225 |
|
|
} /*i *//* 32 bits */
|
| 1226 |
|
|
|
| 1227 |
|
|
/* complete internal overflow or underflow processing */
|
| 1228 |
|
|
if (status & (DEC_Overflow | DEC_Subnormal))
|
| 1229 |
|
|
{
|
| 1230 |
|
|
#if DECSUBSET
|
| 1231 |
|
|
/* If subset, and power was negative, reverse the kind of -erflow */
|
| 1232 |
|
|
/* [1/x not yet done] */
|
| 1233 |
|
|
if (!set->extended && decNumberIsNegative (rhs))
|
| 1234 |
|
|
{
|
| 1235 |
|
|
if (status & DEC_Overflow)
|
| 1236 |
|
|
status ^= DEC_Overflow | DEC_Underflow | DEC_Subnormal;
|
| 1237 |
|
|
else
|
| 1238 |
|
|
{ /* trickier -- Underflow may or may not be set */
|
| 1239 |
|
|
status &= ~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
|
| 1240 |
|
|
status |= DEC_Overflow;
|
| 1241 |
|
|
}
|
| 1242 |
|
|
}
|
| 1243 |
|
|
#endif
|
| 1244 |
|
|
dac->bits = (dac->bits & ~DECNEG) | bits; /* force correct sign */
|
| 1245 |
|
|
/* round subnormals [to set.digits rather than workset.digits] */
|
| 1246 |
|
|
/* or set overflow result similarly as required */
|
| 1247 |
|
|
decFinalize (dac, set, &residue, &status);
|
| 1248 |
|
|
decNumberCopy (res, dac); /* copy to result (is now OK length) */
|
| 1249 |
|
|
break;
|
| 1250 |
|
|
}
|
| 1251 |
|
|
|
| 1252 |
|
|
#if DECSUBSET
|
| 1253 |
|
|
if (!set->extended && /* subset math */
|
| 1254 |
|
|
decNumberIsNegative (rhs))
|
| 1255 |
|
|
{ /* was a **-n [hence digits>0] */
|
| 1256 |
|
|
/* so divide result into 1 [dac=1/dac] */
|
| 1257 |
|
|
decDivideOp (dac, &dnOne, dac, &workset, DIVIDE, &status);
|
| 1258 |
|
|
}
|
| 1259 |
|
|
#endif
|
| 1260 |
|
|
|
| 1261 |
|
|
/* reduce result to the requested length and copy to result */
|
| 1262 |
|
|
decCopyFit (res, dac, set, &residue, &status);
|
| 1263 |
|
|
decFinish (res, set, &residue, &status); /* final cleanup */
|
| 1264 |
|
|
#if DECSUBSET
|
| 1265 |
|
|
if (!set->extended)
|
| 1266 |
|
|
decTrim (res, 0, &dropped); /* trailing zeros */
|
| 1267 |
|
|
#endif
|
| 1268 |
|
|
}
|
| 1269 |
|
|
while (0); /* end protected */
|
| 1270 |
|
|
|
| 1271 |
|
|
if (allocdac != NULL)
|
| 1272 |
|
|
free (allocdac); /* drop any storage we used */
|
| 1273 |
|
|
if (allocrhs != NULL)
|
| 1274 |
|
|
free (allocrhs); /* .. */
|
| 1275 |
|
|
if (alloclhs != NULL)
|
| 1276 |
|
|
free (alloclhs); /* .. */
|
| 1277 |
|
|
if (status != 0)
|
| 1278 |
|
|
decStatus (res, status, set);
|
| 1279 |
|
|
return res;
|
| 1280 |
|
|
}
|
| 1281 |
|
|
|
| 1282 |
|
|
/* ------------------------------------------------------------------ */
|
| 1283 |
|
|
/* decNumberQuantize -- force exponent to requested value */
|
| 1284 |
|
|
/* */
|
| 1285 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 1286 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 1287 |
|
|
/* of C has exponent of B. The numerical value of C will equal A, */
|
| 1288 |
|
|
/* except for the effects of any rounding that occurred. */
|
| 1289 |
|
|
/* */
|
| 1290 |
|
|
/* res is C, the result. C may be A or B */
|
| 1291 |
|
|
/* lhs is A, the number to adjust */
|
| 1292 |
|
|
/* rhs is B, the number with exponent to match */
|
| 1293 |
|
|
/* set is the context */
|
| 1294 |
|
|
/* */
|
| 1295 |
|
|
/* C must have space for set->digits digits. */
|
| 1296 |
|
|
/* */
|
| 1297 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 1298 |
|
|
/* after the operation is guaranteed to be equal to that of B. */
|
| 1299 |
|
|
/* ------------------------------------------------------------------ */
|
| 1300 |
|
|
decNumber *
|
| 1301 |
|
|
decNumberQuantize (decNumber * res, const decNumber * lhs,
|
| 1302 |
|
|
const decNumber * rhs, decContext * set)
|
| 1303 |
|
|
{
|
| 1304 |
|
|
uInt status = 0; /* accumulator */
|
| 1305 |
|
|
decQuantizeOp (res, lhs, rhs, set, 1, &status);
|
| 1306 |
|
|
if (status != 0)
|
| 1307 |
|
|
decStatus (res, status, set);
|
| 1308 |
|
|
return res;
|
| 1309 |
|
|
}
|
| 1310 |
|
|
|
| 1311 |
|
|
/* ------------------------------------------------------------------ */
|
| 1312 |
|
|
/* decNumberRescale -- force exponent to requested value */
|
| 1313 |
|
|
/* */
|
| 1314 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 1315 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 1316 |
|
|
/* of C has the value B. The numerical value of C will equal A, */
|
| 1317 |
|
|
/* except for the effects of any rounding that occurred. */
|
| 1318 |
|
|
/* */
|
| 1319 |
|
|
/* res is C, the result. C may be A or B */
|
| 1320 |
|
|
/* lhs is A, the number to adjust */
|
| 1321 |
|
|
/* rhs is B, the requested exponent */
|
| 1322 |
|
|
/* set is the context */
|
| 1323 |
|
|
/* */
|
| 1324 |
|
|
/* C must have space for set->digits digits. */
|
| 1325 |
|
|
/* */
|
| 1326 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 1327 |
|
|
/* after the operation is guaranteed to be equal to B. */
|
| 1328 |
|
|
/* ------------------------------------------------------------------ */
|
| 1329 |
|
|
decNumber *
|
| 1330 |
|
|
decNumberRescale (decNumber * res, const decNumber * lhs,
|
| 1331 |
|
|
const decNumber * rhs, decContext * set)
|
| 1332 |
|
|
{
|
| 1333 |
|
|
uInt status = 0; /* accumulator */
|
| 1334 |
|
|
decQuantizeOp (res, lhs, rhs, set, 0, &status);
|
| 1335 |
|
|
if (status != 0)
|
| 1336 |
|
|
decStatus (res, status, set);
|
| 1337 |
|
|
return res;
|
| 1338 |
|
|
}
|
| 1339 |
|
|
|
| 1340 |
|
|
/* ------------------------------------------------------------------ */
|
| 1341 |
|
|
/* decNumberRemainder -- divide and return remainder */
|
| 1342 |
|
|
/* */
|
| 1343 |
|
|
/* This computes C = A % B */
|
| 1344 |
|
|
/* */
|
| 1345 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| 1346 |
|
|
/* lhs is A */
|
| 1347 |
|
|
/* rhs is B */
|
| 1348 |
|
|
/* set is the context */
|
| 1349 |
|
|
/* */
|
| 1350 |
|
|
/* C must have space for set->digits digits. */
|
| 1351 |
|
|
/* ------------------------------------------------------------------ */
|
| 1352 |
|
|
decNumber *
|
| 1353 |
|
|
decNumberRemainder (decNumber * res, const decNumber * lhs,
|
| 1354 |
|
|
const decNumber * rhs, decContext * set)
|
| 1355 |
|
|
{
|
| 1356 |
|
|
uInt status = 0; /* accumulator */
|
| 1357 |
|
|
decDivideOp (res, lhs, rhs, set, REMAINDER, &status);
|
| 1358 |
|
|
if (status != 0)
|
| 1359 |
|
|
decStatus (res, status, set);
|
| 1360 |
|
|
return res;
|
| 1361 |
|
|
}
|
| 1362 |
|
|
|
| 1363 |
|
|
/* ------------------------------------------------------------------ */
|
| 1364 |
|
|
/* decNumberRemainderNear -- divide and return remainder from nearest */
|
| 1365 |
|
|
/* */
|
| 1366 |
|
|
/* This computes C = A % B, where % is the IEEE remainder operator */
|
| 1367 |
|
|
/* */
|
| 1368 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| 1369 |
|
|
/* lhs is A */
|
| 1370 |
|
|
/* rhs is B */
|
| 1371 |
|
|
/* set is the context */
|
| 1372 |
|
|
/* */
|
| 1373 |
|
|
/* C must have space for set->digits digits. */
|
| 1374 |
|
|
/* ------------------------------------------------------------------ */
|
| 1375 |
|
|
decNumber *
|
| 1376 |
|
|
decNumberRemainderNear (decNumber * res, const decNumber * lhs,
|
| 1377 |
|
|
const decNumber * rhs, decContext * set)
|
| 1378 |
|
|
{
|
| 1379 |
|
|
uInt status = 0; /* accumulator */
|
| 1380 |
|
|
decDivideOp (res, lhs, rhs, set, REMNEAR, &status);
|
| 1381 |
|
|
if (status != 0)
|
| 1382 |
|
|
decStatus (res, status, set);
|
| 1383 |
|
|
return res;
|
| 1384 |
|
|
}
|
| 1385 |
|
|
|
| 1386 |
|
|
/* ------------------------------------------------------------------ */
|
| 1387 |
|
|
/* decNumberSameQuantum -- test for equal exponents */
|
| 1388 |
|
|
/* */
|
| 1389 |
|
|
/* res is the result number, which will contain either 0 or 1 */
|
| 1390 |
|
|
/* lhs is a number to test */
|
| 1391 |
|
|
/* rhs is the second (usually a pattern) */
|
| 1392 |
|
|
/* */
|
| 1393 |
|
|
/* No errors are possible and no context is needed. */
|
| 1394 |
|
|
/* ------------------------------------------------------------------ */
|
| 1395 |
|
|
decNumber *
|
| 1396 |
|
|
decNumberSameQuantum (decNumber * res, const decNumber * lhs, const decNumber * rhs)
|
| 1397 |
|
|
{
|
| 1398 |
|
|
uByte merged; /* merged flags */
|
| 1399 |
|
|
Unit ret = 0; /* return value */
|
| 1400 |
|
|
|
| 1401 |
|
|
#if DECCHECK
|
| 1402 |
|
|
if (decCheckOperands (res, lhs, rhs, DECUNUSED))
|
| 1403 |
|
|
return res;
|
| 1404 |
|
|
#endif
|
| 1405 |
|
|
|
| 1406 |
|
|
merged = (lhs->bits | rhs->bits) & DECSPECIAL;
|
| 1407 |
|
|
if (merged)
|
| 1408 |
|
|
{
|
| 1409 |
|
|
if (decNumberIsNaN (lhs) && decNumberIsNaN (rhs))
|
| 1410 |
|
|
ret = 1;
|
| 1411 |
|
|
else if (decNumberIsInfinite (lhs) && decNumberIsInfinite (rhs))
|
| 1412 |
|
|
ret = 1;
|
| 1413 |
|
|
/* [anything else with a special gives 0] */
|
| 1414 |
|
|
}
|
| 1415 |
|
|
else if (lhs->exponent == rhs->exponent)
|
| 1416 |
|
|
ret = 1;
|
| 1417 |
|
|
|
| 1418 |
|
|
decNumberZero (res); /* OK to overwrite an operand */
|
| 1419 |
|
|
*res->lsu = ret;
|
| 1420 |
|
|
return res;
|
| 1421 |
|
|
}
|
| 1422 |
|
|
|
| 1423 |
|
|
/* ------------------------------------------------------------------ */
|
| 1424 |
|
|
/* decNumberSquareRoot -- square root operator */
|
| 1425 |
|
|
/* */
|
| 1426 |
|
|
/* This computes C = squareroot(A) */
|
| 1427 |
|
|
/* */
|
| 1428 |
|
|
/* res is C, the result. C may be A */
|
| 1429 |
|
|
/* rhs is A */
|
| 1430 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 1431 |
|
|
/* */
|
| 1432 |
|
|
/* C must have space for set->digits digits. */
|
| 1433 |
|
|
/* ------------------------------------------------------------------ */
|
| 1434 |
|
|
/* This uses the following varying-precision algorithm in: */
|
| 1435 |
|
|
/* */
|
| 1436 |
|
|
/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
|
| 1437 |
|
|
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
|
| 1438 |
|
|
/* pp229-237, ACM, September 1985. */
|
| 1439 |
|
|
/* */
|
| 1440 |
|
|
/* % [Reformatted original Numerical Turing source code follows.] */
|
| 1441 |
|
|
/* function sqrt(x : real) : real */
|
| 1442 |
|
|
/* % sqrt(x) returns the properly rounded approximation to the square */
|
| 1443 |
|
|
/* % root of x, in the precision of the calling environment, or it */
|
| 1444 |
|
|
/* % fails if x < 0. */
|
| 1445 |
|
|
/* % t e hull and a abrham, august, 1984 */
|
| 1446 |
|
|
/* if x <= 0 then */
|
| 1447 |
|
|
/* if x < 0 then */
|
| 1448 |
|
|
/* assert false */
|
| 1449 |
|
|
/* else */
|
| 1450 |
|
|
/* result 0 */
|
| 1451 |
|
|
/* end if */
|
| 1452 |
|
|
/* end if */
|
| 1453 |
|
|
/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
|
| 1454 |
|
|
/* var e := getexp(x) % exponent part of x */
|
| 1455 |
|
|
/* var approx : real */
|
| 1456 |
|
|
/* if e mod 2 = 0 then */
|
| 1457 |
|
|
/* approx := .259 + .819 * f % approx to root of f */
|
| 1458 |
|
|
/* else */
|
| 1459 |
|
|
/* f := f/l0 % adjustments */
|
| 1460 |
|
|
/* e := e + 1 % for odd */
|
| 1461 |
|
|
/* approx := .0819 + 2.59 * f % exponent */
|
| 1462 |
|
|
/* end if */
|
| 1463 |
|
|
/* */
|
| 1464 |
|
|
/* var p:= 3 */
|
| 1465 |
|
|
/* const maxp := currentprecision + 2 */
|
| 1466 |
|
|
/* loop */
|
| 1467 |
|
|
/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
|
| 1468 |
|
|
/* precision p */
|
| 1469 |
|
|
/* approx := .5 * (approx + f/approx) */
|
| 1470 |
|
|
/* exit when p = maxp */
|
| 1471 |
|
|
/* end loop */
|
| 1472 |
|
|
/* */
|
| 1473 |
|
|
/* % approx is now within 1 ulp of the properly rounded square root */
|
| 1474 |
|
|
/* % of f; to ensure proper rounding, compare squares of (approx - */
|
| 1475 |
|
|
/* % l/2 ulp) and (approx + l/2 ulp) with f. */
|
| 1476 |
|
|
/* p := currentprecision */
|
| 1477 |
|
|
/* begin */
|
| 1478 |
|
|
/* precision p + 2 */
|
| 1479 |
|
|
/* const approxsubhalf := approx - setexp(.5, -p) */
|
| 1480 |
|
|
/* if mulru(approxsubhalf, approxsubhalf) > f then */
|
| 1481 |
|
|
/* approx := approx - setexp(.l, -p + 1) */
|
| 1482 |
|
|
/* else */
|
| 1483 |
|
|
/* const approxaddhalf := approx + setexp(.5, -p) */
|
| 1484 |
|
|
/* if mulrd(approxaddhalf, approxaddhalf) < f then */
|
| 1485 |
|
|
/* approx := approx + setexp(.l, -p + 1) */
|
| 1486 |
|
|
/* end if */
|
| 1487 |
|
|
/* end if */
|
| 1488 |
|
|
/* end */
|
| 1489 |
|
|
/* result setexp(approx, e div 2) % fix exponent */
|
| 1490 |
|
|
/* end sqrt */
|
| 1491 |
|
|
/* ------------------------------------------------------------------ */
|
| 1492 |
|
|
decNumber *
|
| 1493 |
|
|
decNumberSquareRoot (decNumber * res, const decNumber * rhs, decContext * set)
|
| 1494 |
|
|
{
|
| 1495 |
|
|
decContext workset, approxset; /* work contexts */
|
| 1496 |
|
|
decNumber dzero; /* used for constant zero */
|
| 1497 |
|
|
Int maxp = set->digits + 2; /* largest working precision */
|
| 1498 |
|
|
Int residue = 0; /* rounding residue */
|
| 1499 |
|
|
uInt status = 0, ignore = 0; /* status accumulators */
|
| 1500 |
|
|
Int exp; /* working exponent */
|
| 1501 |
|
|
Int ideal; /* ideal (preferred) exponent */
|
| 1502 |
|
|
uInt needbytes; /* work */
|
| 1503 |
|
|
Int dropped; /* .. */
|
| 1504 |
|
|
|
| 1505 |
|
|
decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */
|
| 1506 |
|
|
/* buffer for f [needs +1 in case DECBUFFER 0] */
|
| 1507 |
|
|
uByte buff[sizeof (decNumber) + (D2U (DECBUFFER + 1) - 1) * sizeof (Unit)];
|
| 1508 |
|
|
/* buffer for a [needs +2 to match maxp] */
|
| 1509 |
|
|
uByte bufa[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)];
|
| 1510 |
|
|
/* buffer for temporary, b [must be same size as a] */
|
| 1511 |
|
|
uByte bufb[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)];
|
| 1512 |
|
|
decNumber *allocbuff = NULL; /* -> allocated buff, iff allocated */
|
| 1513 |
|
|
decNumber *allocbufa = NULL; /* -> allocated bufa, iff allocated */
|
| 1514 |
|
|
decNumber *allocbufb = NULL; /* -> allocated bufb, iff allocated */
|
| 1515 |
|
|
decNumber *f = (decNumber *) buff; /* reduced fraction */
|
| 1516 |
|
|
decNumber *a = (decNumber *) bufa; /* approximation to result */
|
| 1517 |
|
|
decNumber *b = (decNumber *) bufb; /* intermediate result */
|
| 1518 |
|
|
/* buffer for temporary variable, up to 3 digits */
|
| 1519 |
|
|
uByte buft[sizeof (decNumber) + (D2U (3) - 1) * sizeof (Unit)];
|
| 1520 |
|
|
decNumber *t = (decNumber *) buft; /* up-to-3-digit constant or work */
|
| 1521 |
|
|
|
| 1522 |
|
|
#if DECCHECK
|
| 1523 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 1524 |
|
|
return res;
|
| 1525 |
|
|
#endif
|
| 1526 |
|
|
|
| 1527 |
|
|
do
|
| 1528 |
|
|
{ /* protect allocated storage */
|
| 1529 |
|
|
#if DECSUBSET
|
| 1530 |
|
|
if (!set->extended)
|
| 1531 |
|
|
{
|
| 1532 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 1533 |
|
|
if (rhs->digits > set->digits)
|
| 1534 |
|
|
{
|
| 1535 |
|
|
allocrhs = decRoundOperand (rhs, set, &status);
|
| 1536 |
|
|
if (allocrhs == NULL)
|
| 1537 |
|
|
break;
|
| 1538 |
|
|
/* [Note: 'f' allocation below could reuse this buffer if */
|
| 1539 |
|
|
/* used, but as this is rare we keep them separate for clarity.] */
|
| 1540 |
|
|
rhs = allocrhs;
|
| 1541 |
|
|
}
|
| 1542 |
|
|
}
|
| 1543 |
|
|
#endif
|
| 1544 |
|
|
/* [following code does not require input rounding] */
|
| 1545 |
|
|
|
| 1546 |
|
|
/* handle infinities and NaNs */
|
| 1547 |
|
|
if (rhs->bits & DECSPECIAL)
|
| 1548 |
|
|
{
|
| 1549 |
|
|
if (decNumberIsInfinite (rhs))
|
| 1550 |
|
|
{ /* an infinity */
|
| 1551 |
|
|
if (decNumberIsNegative (rhs))
|
| 1552 |
|
|
status |= DEC_Invalid_operation;
|
| 1553 |
|
|
else
|
| 1554 |
|
|
decNumberCopy (res, rhs); /* +Infinity */
|
| 1555 |
|
|
}
|
| 1556 |
|
|
else
|
| 1557 |
|
|
decNaNs (res, rhs, NULL, &status); /* a NaN */
|
| 1558 |
|
|
break;
|
| 1559 |
|
|
}
|
| 1560 |
|
|
|
| 1561 |
|
|
/* calculate the ideal (preferred) exponent [floor(exp/2)] */
|
| 1562 |
|
|
/* [We would like to write: ideal=rhs->exponent>>1, but this */
|
| 1563 |
|
|
/* generates a compiler warning. Generated code is the same.] */
|
| 1564 |
|
|
ideal = (rhs->exponent & ~1) / 2; /* target */
|
| 1565 |
|
|
|
| 1566 |
|
|
/* handle zeros */
|
| 1567 |
|
|
if (ISZERO (rhs))
|
| 1568 |
|
|
{
|
| 1569 |
|
|
decNumberCopy (res, rhs); /* could be 0 or -0 */
|
| 1570 |
|
|
res->exponent = ideal; /* use the ideal [safe] */
|
| 1571 |
|
|
break;
|
| 1572 |
|
|
}
|
| 1573 |
|
|
|
| 1574 |
|
|
/* any other -x is an oops */
|
| 1575 |
|
|
if (decNumberIsNegative (rhs))
|
| 1576 |
|
|
{
|
| 1577 |
|
|
status |= DEC_Invalid_operation;
|
| 1578 |
|
|
break;
|
| 1579 |
|
|
}
|
| 1580 |
|
|
|
| 1581 |
|
|
/* we need space for three working variables */
|
| 1582 |
|
|
/* f -- the same precision as the RHS, reduced to 0.01->0.99... */
|
| 1583 |
|
|
/* a -- Hull's approx -- precision, when assigned, is */
|
| 1584 |
|
|
/* currentprecision (we allow +2 for use as temporary) */
|
| 1585 |
|
|
/* b -- intermediate temporary result */
|
| 1586 |
|
|
/* if any is too long for local storage, then allocate */
|
| 1587 |
|
|
needbytes =
|
| 1588 |
|
|
sizeof (decNumber) + (D2U (rhs->digits) - 1) * sizeof (Unit);
|
| 1589 |
|
|
if (needbytes > sizeof (buff))
|
| 1590 |
|
|
{
|
| 1591 |
|
|
allocbuff = (decNumber *) malloc (needbytes);
|
| 1592 |
|
|
if (allocbuff == NULL)
|
| 1593 |
|
|
{ /* hopeless -- abandon */
|
| 1594 |
|
|
status |= DEC_Insufficient_storage;
|
| 1595 |
|
|
break;
|
| 1596 |
|
|
}
|
| 1597 |
|
|
f = allocbuff; /* use the allocated space */
|
| 1598 |
|
|
}
|
| 1599 |
|
|
/* a and b both need to be able to hold a maxp-length number */
|
| 1600 |
|
|
needbytes = sizeof (decNumber) + (D2U (maxp) - 1) * sizeof (Unit);
|
| 1601 |
|
|
if (needbytes > sizeof (bufa))
|
| 1602 |
|
|
{ /* [same applies to b] */
|
| 1603 |
|
|
allocbufa = (decNumber *) malloc (needbytes);
|
| 1604 |
|
|
allocbufb = (decNumber *) malloc (needbytes);
|
| 1605 |
|
|
if (allocbufa == NULL || allocbufb == NULL)
|
| 1606 |
|
|
{ /* hopeless */
|
| 1607 |
|
|
status |= DEC_Insufficient_storage;
|
| 1608 |
|
|
break;
|
| 1609 |
|
|
}
|
| 1610 |
|
|
a = allocbufa; /* use the allocated space */
|
| 1611 |
|
|
b = allocbufb; /* .. */
|
| 1612 |
|
|
}
|
| 1613 |
|
|
|
| 1614 |
|
|
/* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
|
| 1615 |
|
|
decNumberCopy (f, rhs);
|
| 1616 |
|
|
exp = f->exponent + f->digits; /* adjusted to Hull rules */
|
| 1617 |
|
|
f->exponent = -(f->digits); /* to range */
|
| 1618 |
|
|
|
| 1619 |
|
|
/* set up working contexts (the second is used for Numerical */
|
| 1620 |
|
|
/* Turing assignment) */
|
| 1621 |
|
|
decContextDefault (&workset, DEC_INIT_DECIMAL64);
|
| 1622 |
|
|
decContextDefault (&approxset, DEC_INIT_DECIMAL64);
|
| 1623 |
|
|
approxset.digits = set->digits; /* approx's length */
|
| 1624 |
|
|
|
| 1625 |
|
|
/* [Until further notice, no error is possible and status bits */
|
| 1626 |
|
|
/* (Rounded, etc.) should be ignored, not accumulated.] */
|
| 1627 |
|
|
|
| 1628 |
|
|
/* Calculate initial approximation, and allow for odd exponent */
|
| 1629 |
|
|
workset.digits = set->digits; /* p for initial calculation */
|
| 1630 |
|
|
t->bits = 0;
|
| 1631 |
|
|
t->digits = 3;
|
| 1632 |
|
|
a->bits = 0;
|
| 1633 |
|
|
a->digits = 3;
|
| 1634 |
|
|
if ((exp & 1) == 0)
|
| 1635 |
|
|
{ /* even exponent */
|
| 1636 |
|
|
/* Set t=0.259, a=0.819 */
|
| 1637 |
|
|
t->exponent = -3;
|
| 1638 |
|
|
a->exponent = -3;
|
| 1639 |
|
|
#if DECDPUN>=3
|
| 1640 |
|
|
t->lsu[0] = 259;
|
| 1641 |
|
|
a->lsu[0] = 819;
|
| 1642 |
|
|
#elif DECDPUN==2
|
| 1643 |
|
|
t->lsu[0] = 59;
|
| 1644 |
|
|
t->lsu[1] = 2;
|
| 1645 |
|
|
a->lsu[0] = 19;
|
| 1646 |
|
|
a->lsu[1] = 8;
|
| 1647 |
|
|
#else
|
| 1648 |
|
|
t->lsu[0] = 9;
|
| 1649 |
|
|
t->lsu[1] = 5;
|
| 1650 |
|
|
t->lsu[2] = 2;
|
| 1651 |
|
|
a->lsu[0] = 9;
|
| 1652 |
|
|
a->lsu[1] = 1;
|
| 1653 |
|
|
a->lsu[2] = 8;
|
| 1654 |
|
|
#endif
|
| 1655 |
|
|
}
|
| 1656 |
|
|
else
|
| 1657 |
|
|
{ /* odd exponent */
|
| 1658 |
|
|
/* Set t=0.0819, a=2.59 */
|
| 1659 |
|
|
f->exponent--; /* f=f/10 */
|
| 1660 |
|
|
exp++; /* e=e+1 */
|
| 1661 |
|
|
t->exponent = -4;
|
| 1662 |
|
|
a->exponent = -2;
|
| 1663 |
|
|
#if DECDPUN>=3
|
| 1664 |
|
|
t->lsu[0] = 819;
|
| 1665 |
|
|
a->lsu[0] = 259;
|
| 1666 |
|
|
#elif DECDPUN==2
|
| 1667 |
|
|
t->lsu[0] = 19;
|
| 1668 |
|
|
t->lsu[1] = 8;
|
| 1669 |
|
|
a->lsu[0] = 59;
|
| 1670 |
|
|
a->lsu[1] = 2;
|
| 1671 |
|
|
#else
|
| 1672 |
|
|
t->lsu[0] = 9;
|
| 1673 |
|
|
t->lsu[1] = 1;
|
| 1674 |
|
|
t->lsu[2] = 8;
|
| 1675 |
|
|
a->lsu[0] = 9;
|
| 1676 |
|
|
a->lsu[1] = 5;
|
| 1677 |
|
|
a->lsu[2] = 2;
|
| 1678 |
|
|
#endif
|
| 1679 |
|
|
}
|
| 1680 |
|
|
decMultiplyOp (a, a, f, &workset, &ignore); /* a=a*f */
|
| 1681 |
|
|
decAddOp (a, a, t, &workset, 0, &ignore); /* ..+t */
|
| 1682 |
|
|
/* [a is now the initial approximation for sqrt(f), calculated with */
|
| 1683 |
|
|
/* currentprecision, which is also a's precision.] */
|
| 1684 |
|
|
|
| 1685 |
|
|
/* the main calculation loop */
|
| 1686 |
|
|
decNumberZero (&dzero); /* make 0 */
|
| 1687 |
|
|
decNumberZero (t); /* set t = 0.5 */
|
| 1688 |
|
|
t->lsu[0] = 5; /* .. */
|
| 1689 |
|
|
t->exponent = -1; /* .. */
|
| 1690 |
|
|
workset.digits = 3; /* initial p */
|
| 1691 |
|
|
for (;;)
|
| 1692 |
|
|
{
|
| 1693 |
|
|
/* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
|
| 1694 |
|
|
workset.digits = workset.digits * 2 - 2;
|
| 1695 |
|
|
if (workset.digits > maxp)
|
| 1696 |
|
|
workset.digits = maxp;
|
| 1697 |
|
|
/* a = 0.5 * (a + f/a) */
|
| 1698 |
|
|
/* [calculated at p then rounded to currentprecision] */
|
| 1699 |
|
|
decDivideOp (b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
|
| 1700 |
|
|
decAddOp (b, b, a, &workset, 0, &ignore); /* b=b+a */
|
| 1701 |
|
|
decMultiplyOp (a, b, t, &workset, &ignore); /* a=b*0.5 */
|
| 1702 |
|
|
/* assign to approx [round to length] */
|
| 1703 |
|
|
decAddOp (a, &dzero, a, &approxset, 0, &ignore);
|
| 1704 |
|
|
if (workset.digits == maxp)
|
| 1705 |
|
|
break; /* just did final */
|
| 1706 |
|
|
} /* loop */
|
| 1707 |
|
|
|
| 1708 |
|
|
/* a is now at currentprecision and within 1 ulp of the properly */
|
| 1709 |
|
|
/* rounded square root of f; to ensure proper rounding, compare */
|
| 1710 |
|
|
/* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
|
| 1711 |
|
|
/* Here workset.digits=maxp and t=0.5 */
|
| 1712 |
|
|
workset.digits--; /* maxp-1 is OK now */
|
| 1713 |
|
|
t->exponent = -set->digits - 1; /* make 0.5 ulp */
|
| 1714 |
|
|
decNumberCopy (b, a);
|
| 1715 |
|
|
decAddOp (b, b, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
|
| 1716 |
|
|
workset.round = DEC_ROUND_UP;
|
| 1717 |
|
|
decMultiplyOp (b, b, b, &workset, &ignore); /* b = mulru(b, b) */
|
| 1718 |
|
|
decCompareOp (b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
|
| 1719 |
|
|
if (decNumberIsNegative (b))
|
| 1720 |
|
|
{ /* f < b [i.e., b > f] */
|
| 1721 |
|
|
/* this is the more common adjustment, though both are rare */
|
| 1722 |
|
|
t->exponent++; /* make 1.0 ulp */
|
| 1723 |
|
|
t->lsu[0] = 1; /* .. */
|
| 1724 |
|
|
decAddOp (a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
|
| 1725 |
|
|
/* assign to approx [round to length] */
|
| 1726 |
|
|
decAddOp (a, &dzero, a, &approxset, 0, &ignore);
|
| 1727 |
|
|
}
|
| 1728 |
|
|
else
|
| 1729 |
|
|
{
|
| 1730 |
|
|
decNumberCopy (b, a);
|
| 1731 |
|
|
decAddOp (b, b, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
|
| 1732 |
|
|
workset.round = DEC_ROUND_DOWN;
|
| 1733 |
|
|
decMultiplyOp (b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
|
| 1734 |
|
|
decCompareOp (b, b, f, &workset, COMPARE, &ignore); /* b ? f */
|
| 1735 |
|
|
if (decNumberIsNegative (b))
|
| 1736 |
|
|
{ /* b < f */
|
| 1737 |
|
|
t->exponent++; /* make 1.0 ulp */
|
| 1738 |
|
|
t->lsu[0] = 1; /* .. */
|
| 1739 |
|
|
decAddOp (a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
|
| 1740 |
|
|
/* assign to approx [round to length] */
|
| 1741 |
|
|
decAddOp (a, &dzero, a, &approxset, 0, &ignore);
|
| 1742 |
|
|
}
|
| 1743 |
|
|
}
|
| 1744 |
|
|
/* [no errors are possible in the above, and rounding/inexact during */
|
| 1745 |
|
|
/* estimation are irrelevant, so status was not accumulated] */
|
| 1746 |
|
|
|
| 1747 |
|
|
/* Here, 0.1 <= a < 1 [Hull] */
|
| 1748 |
|
|
a->exponent += exp / 2; /* set correct exponent */
|
| 1749 |
|
|
|
| 1750 |
|
|
/* Process Subnormals */
|
| 1751 |
|
|
decFinalize (a, set, &residue, &status);
|
| 1752 |
|
|
|
| 1753 |
|
|
/* count dropable zeros [after any subnormal rounding] */
|
| 1754 |
|
|
decNumberCopy (b, a);
|
| 1755 |
|
|
decTrim (b, 1, &dropped); /* [drops trailing zeros] */
|
| 1756 |
|
|
|
| 1757 |
|
|
/* Finally set Inexact and Rounded. The answer can only be exact if */
|
| 1758 |
|
|
/* it is short enough so that squaring it could fit in set->digits, */
|
| 1759 |
|
|
/* so this is the only (relatively rare) time we have to check */
|
| 1760 |
|
|
/* carefully */
|
| 1761 |
|
|
if (b->digits * 2 - 1 > set->digits)
|
| 1762 |
|
|
{ /* cannot fit */
|
| 1763 |
|
|
status |= DEC_Inexact | DEC_Rounded;
|
| 1764 |
|
|
}
|
| 1765 |
|
|
else
|
| 1766 |
|
|
{ /* could be exact/unrounded */
|
| 1767 |
|
|
uInt mstatus = 0; /* local status */
|
| 1768 |
|
|
decMultiplyOp (b, b, b, &workset, &mstatus); /* try the multiply */
|
| 1769 |
|
|
if (mstatus != 0)
|
| 1770 |
|
|
{ /* result won't fit */
|
| 1771 |
|
|
status |= DEC_Inexact | DEC_Rounded;
|
| 1772 |
|
|
}
|
| 1773 |
|
|
else
|
| 1774 |
|
|
{ /* plausible */
|
| 1775 |
|
|
decCompareOp (t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
|
| 1776 |
|
|
if (!ISZERO (t))
|
| 1777 |
|
|
{
|
| 1778 |
|
|
status |= DEC_Inexact | DEC_Rounded;
|
| 1779 |
|
|
}
|
| 1780 |
|
|
else
|
| 1781 |
|
|
{ /* is Exact */
|
| 1782 |
|
|
/* here, dropped is the count of trailing zeros in 'a' */
|
| 1783 |
|
|
/* use closest exponent to ideal... */
|
| 1784 |
|
|
Int todrop = ideal - a->exponent; /* most we can drop */
|
| 1785 |
|
|
|
| 1786 |
|
|
if (todrop < 0)
|
| 1787 |
|
|
{ /* ideally would add 0s */
|
| 1788 |
|
|
status |= DEC_Rounded;
|
| 1789 |
|
|
}
|
| 1790 |
|
|
else
|
| 1791 |
|
|
{ /* unrounded */
|
| 1792 |
|
|
if (dropped < todrop)
|
| 1793 |
|
|
todrop = dropped; /* clamp to those available */
|
| 1794 |
|
|
if (todrop > 0)
|
| 1795 |
|
|
{ /* OK, some to drop */
|
| 1796 |
|
|
decShiftToLeast (a->lsu, D2U (a->digits), todrop);
|
| 1797 |
|
|
a->exponent += todrop; /* maintain numerical value */
|
| 1798 |
|
|
a->digits -= todrop; /* new length */
|
| 1799 |
|
|
}
|
| 1800 |
|
|
}
|
| 1801 |
|
|
}
|
| 1802 |
|
|
}
|
| 1803 |
|
|
}
|
| 1804 |
|
|
decNumberCopy (res, a); /* assume this is the result */
|
| 1805 |
|
|
}
|
| 1806 |
|
|
while (0); /* end protected */
|
| 1807 |
|
|
|
| 1808 |
|
|
if (allocbuff != NULL)
|
| 1809 |
|
|
free (allocbuff); /* drop any storage we used */
|
| 1810 |
|
|
if (allocbufa != NULL)
|
| 1811 |
|
|
free (allocbufa); /* .. */
|
| 1812 |
|
|
if (allocbufb != NULL)
|
| 1813 |
|
|
free (allocbufb); /* .. */
|
| 1814 |
|
|
if (allocrhs != NULL)
|
| 1815 |
|
|
free (allocrhs); /* .. */
|
| 1816 |
|
|
if (status != 0)
|
| 1817 |
|
|
decStatus (res, status, set); /* then report status */
|
| 1818 |
|
|
return res;
|
| 1819 |
|
|
}
|
| 1820 |
|
|
|
| 1821 |
|
|
/* ------------------------------------------------------------------ */
|
| 1822 |
|
|
/* decNumberSubtract -- subtract two Numbers */
|
| 1823 |
|
|
/* */
|
| 1824 |
|
|
/* This computes C = A - B */
|
| 1825 |
|
|
/* */
|
| 1826 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
|
| 1827 |
|
|
/* lhs is A */
|
| 1828 |
|
|
/* rhs is B */
|
| 1829 |
|
|
/* set is the context */
|
| 1830 |
|
|
/* */
|
| 1831 |
|
|
/* C must have space for set->digits digits. */
|
| 1832 |
|
|
/* ------------------------------------------------------------------ */
|
| 1833 |
|
|
decNumber *
|
| 1834 |
|
|
decNumberSubtract (decNumber * res, const decNumber * lhs,
|
| 1835 |
|
|
const decNumber * rhs, decContext * set)
|
| 1836 |
|
|
{
|
| 1837 |
|
|
uInt status = 0; /* accumulator */
|
| 1838 |
|
|
|
| 1839 |
|
|
decAddOp (res, lhs, rhs, set, DECNEG, &status);
|
| 1840 |
|
|
if (status != 0)
|
| 1841 |
|
|
decStatus (res, status, set);
|
| 1842 |
|
|
return res;
|
| 1843 |
|
|
}
|
| 1844 |
|
|
|
| 1845 |
|
|
/* ------------------------------------------------------------------ */
|
| 1846 |
|
|
/* decNumberToIntegralValue -- round-to-integral-value */
|
| 1847 |
|
|
/* */
|
| 1848 |
|
|
/* res is the result */
|
| 1849 |
|
|
/* rhs is input number */
|
| 1850 |
|
|
/* set is the context */
|
| 1851 |
|
|
/* */
|
| 1852 |
|
|
/* res must have space for any value of rhs. */
|
| 1853 |
|
|
/* */
|
| 1854 |
|
|
/* This implements the IEEE special operator and therefore treats */
|
| 1855 |
|
|
/* special values as valid, and also never sets Inexact. For finite */
|
| 1856 |
|
|
/* numbers it returns rescale(rhs, 0) if rhs->exponent is <0. */
|
| 1857 |
|
|
/* Otherwise the result is rhs (so no error is possible). */
|
| 1858 |
|
|
/* */
|
| 1859 |
|
|
/* The context is used for rounding mode and status after sNaN, but */
|
| 1860 |
|
|
/* the digits setting is ignored. */
|
| 1861 |
|
|
/* ------------------------------------------------------------------ */
|
| 1862 |
|
|
decNumber *
|
| 1863 |
|
|
decNumberToIntegralValue (decNumber * res, const decNumber * rhs, decContext * set)
|
| 1864 |
|
|
{
|
| 1865 |
|
|
decNumber dn;
|
| 1866 |
|
|
decContext workset; /* working context */
|
| 1867 |
|
|
|
| 1868 |
|
|
#if DECCHECK
|
| 1869 |
|
|
if (decCheckOperands (res, DECUNUSED, rhs, set))
|
| 1870 |
|
|
return res;
|
| 1871 |
|
|
#endif
|
| 1872 |
|
|
|
| 1873 |
|
|
/* handle infinities and NaNs */
|
| 1874 |
|
|
if (rhs->bits & DECSPECIAL)
|
| 1875 |
|
|
{
|
| 1876 |
|
|
uInt status = 0;
|
| 1877 |
|
|
if (decNumberIsInfinite (rhs))
|
| 1878 |
|
|
decNumberCopy (res, rhs); /* an Infinity */
|
| 1879 |
|
|
else
|
| 1880 |
|
|
decNaNs (res, rhs, NULL, &status); /* a NaN */
|
| 1881 |
|
|
if (status != 0)
|
| 1882 |
|
|
decStatus (res, status, set);
|
| 1883 |
|
|
return res;
|
| 1884 |
|
|
}
|
| 1885 |
|
|
|
| 1886 |
|
|
/* we have a finite number; no error possible */
|
| 1887 |
|
|
if (rhs->exponent >= 0)
|
| 1888 |
|
|
return decNumberCopy (res, rhs);
|
| 1889 |
|
|
/* that was easy, but if negative exponent we have work to do... */
|
| 1890 |
|
|
workset = *set; /* clone rounding, etc. */
|
| 1891 |
|
|
workset.digits = rhs->digits; /* no length rounding */
|
| 1892 |
|
|
workset.traps = 0; /* no traps */
|
| 1893 |
|
|
decNumberZero (&dn); /* make a number with exponent 0 */
|
| 1894 |
|
|
return decNumberQuantize (res, rhs, &dn, &workset);
|
| 1895 |
|
|
}
|
| 1896 |
|
|
|
| 1897 |
|
|
/* ================================================================== */
|
| 1898 |
|
|
/* Utility routines */
|
| 1899 |
|
|
/* ================================================================== */
|
| 1900 |
|
|
|
| 1901 |
|
|
/* ------------------------------------------------------------------ */
|
| 1902 |
|
|
/* decNumberCopy -- copy a number */
|
| 1903 |
|
|
/* */
|
| 1904 |
|
|
/* dest is the target decNumber */
|
| 1905 |
|
|
/* src is the source decNumber */
|
| 1906 |
|
|
/* returns dest */
|
| 1907 |
|
|
/* */
|
| 1908 |
|
|
/* (dest==src is allowed and is a no-op) */
|
| 1909 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 1910 |
|
|
/* so special values are unchanged and no error is possible. */
|
| 1911 |
|
|
/* ------------------------------------------------------------------ */
|
| 1912 |
|
|
decNumber *
|
| 1913 |
|
|
decNumberCopy (decNumber * dest, const decNumber * src)
|
| 1914 |
|
|
{
|
| 1915 |
|
|
|
| 1916 |
|
|
#if DECCHECK
|
| 1917 |
|
|
if (src == NULL)
|
| 1918 |
|
|
return decNumberZero (dest);
|
| 1919 |
|
|
#endif
|
| 1920 |
|
|
|
| 1921 |
|
|
if (dest == src)
|
| 1922 |
|
|
return dest; /* no copy required */
|
| 1923 |
|
|
|
| 1924 |
|
|
/* We use explicit assignments here as structure assignment can copy */
|
| 1925 |
|
|
/* more than just the lsu (for small DECDPUN). This would not affect */
|
| 1926 |
|
|
/* the value of the results, but would disturb test harness spill */
|
| 1927 |
|
|
/* checking. */
|
| 1928 |
|
|
dest->bits = src->bits;
|
| 1929 |
|
|
dest->exponent = src->exponent;
|
| 1930 |
|
|
dest->digits = src->digits;
|
| 1931 |
|
|
dest->lsu[0] = src->lsu[0];
|
| 1932 |
|
|
if (src->digits > DECDPUN)
|
| 1933 |
|
|
{ /* more Units to come */
|
| 1934 |
|
|
Unit *d; /* work */
|
| 1935 |
|
|
const Unit *s, *smsup; /* work */
|
| 1936 |
|
|
/* memcpy for the remaining Units would be safe as they cannot */
|
| 1937 |
|
|
/* overlap. However, this explicit loop is faster in short cases. */
|
| 1938 |
|
|
d = dest->lsu + 1; /* -> first destination */
|
| 1939 |
|
|
smsup = src->lsu + D2U (src->digits); /* -> source msu+1 */
|
| 1940 |
|
|
for (s = src->lsu + 1; s < smsup; s++, d++)
|
| 1941 |
|
|
*d = *s;
|
| 1942 |
|
|
}
|
| 1943 |
|
|
return dest;
|
| 1944 |
|
|
}
|
| 1945 |
|
|
|
| 1946 |
|
|
/* ------------------------------------------------------------------ */
|
| 1947 |
|
|
/* decNumberTrim -- remove insignificant zeros */
|
| 1948 |
|
|
/* */
|
| 1949 |
|
|
/* dn is the number to trim */
|
| 1950 |
|
|
/* returns dn */
|
| 1951 |
|
|
/* */
|
| 1952 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 1953 |
|
|
/* so special values are unchanged and no error is possible. */
|
| 1954 |
|
|
/* ------------------------------------------------------------------ */
|
| 1955 |
|
|
decNumber *
|
| 1956 |
|
|
decNumberTrim (decNumber * dn)
|
| 1957 |
|
|
{
|
| 1958 |
|
|
Int dropped; /* work */
|
| 1959 |
|
|
return decTrim (dn, 0, &dropped);
|
| 1960 |
|
|
}
|
| 1961 |
|
|
|
| 1962 |
|
|
/* ------------------------------------------------------------------ */
|
| 1963 |
|
|
/* decNumberVersion -- return the name and version of this module */
|
| 1964 |
|
|
/* */
|
| 1965 |
|
|
/* No error is possible. */
|
| 1966 |
|
|
/* ------------------------------------------------------------------ */
|
| 1967 |
|
|
const char *
|
| 1968 |
|
|
decNumberVersion (void)
|
| 1969 |
|
|
{
|
| 1970 |
|
|
return DECVERSION;
|
| 1971 |
|
|
}
|
| 1972 |
|
|
|
| 1973 |
|
|
/* ------------------------------------------------------------------ */
|
| 1974 |
|
|
/* decNumberZero -- set a number to 0 */
|
| 1975 |
|
|
/* */
|
| 1976 |
|
|
/* dn is the number to set, with space for one digit */
|
| 1977 |
|
|
/* returns dn */
|
| 1978 |
|
|
/* */
|
| 1979 |
|
|
/* No error is possible. */
|
| 1980 |
|
|
/* ------------------------------------------------------------------ */
|
| 1981 |
|
|
/* Memset is not used as it is much slower in some environments. */
|
| 1982 |
|
|
decNumber *
|
| 1983 |
|
|
decNumberZero (decNumber * dn)
|
| 1984 |
|
|
{
|
| 1985 |
|
|
|
| 1986 |
|
|
#if DECCHECK
|
| 1987 |
|
|
if (decCheckOperands (dn, DECUNUSED, DECUNUSED, DECUNUSED))
|
| 1988 |
|
|
return dn;
|
| 1989 |
|
|
#endif
|
| 1990 |
|
|
|
| 1991 |
|
|
dn->bits = 0;
|
| 1992 |
|
|
dn->exponent = 0;
|
| 1993 |
|
|
dn->digits = 1;
|
| 1994 |
|
|
dn->lsu[0] = 0;
|
| 1995 |
|
|
return dn;
|
| 1996 |
|
|
}
|
| 1997 |
|
|
|
| 1998 |
|
|
/* ================================================================== */
|
| 1999 |
|
|
/* Local routines */
|
| 2000 |
|
|
/* ================================================================== */
|
| 2001 |
|
|
|
| 2002 |
|
|
/* ------------------------------------------------------------------ */
|
| 2003 |
|
|
/* decToString -- lay out a number into a string */
|
| 2004 |
|
|
/* */
|
| 2005 |
|
|
/* dn is the number to lay out */
|
| 2006 |
|
|
/* string is where to lay out the number */
|
| 2007 |
|
|
/* eng is 1 if Engineering, 0 if Scientific */
|
| 2008 |
|
|
/* */
|
| 2009 |
|
|
/* str must be at least dn->digits+14 characters long */
|
| 2010 |
|
|
/* No error is possible. */
|
| 2011 |
|
|
/* */
|
| 2012 |
|
|
/* Note that this routine can generate a -0 or 0.000. These are */
|
| 2013 |
|
|
/* never generated in subset to-number or arithmetic, but can occur */
|
| 2014 |
|
|
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
|
| 2015 |
|
|
/* ------------------------------------------------------------------ */
|
| 2016 |
|
|
/* If DECCHECK is enabled the string "?" is returned if a number is */
|
| 2017 |
|
|
/* invalid. */
|
| 2018 |
|
|
|
| 2019 |
|
|
/* TODIGIT -- macro to remove the leading digit from the unsigned */
|
| 2020 |
|
|
/* integer u at column cut (counting from the right, LSD=0) and place */
|
| 2021 |
|
|
/* it as an ASCII character into the character pointed to by c. Note */
|
| 2022 |
|
|
/* that cut must be <= 9, and the maximum value for u is 2,000,000,000 */
|
| 2023 |
|
|
/* (as is needed for negative exponents of subnormals). The unsigned */
|
| 2024 |
|
|
/* integer pow is used as a temporary variable. */
|
| 2025 |
|
|
#define TODIGIT(u, cut, c) { \
|
| 2026 |
|
|
*(c)='0'; \
|
| 2027 |
|
|
pow=powers[cut]*2; \
|
| 2028 |
|
|
if ((u)>pow) { \
|
| 2029 |
|
|
pow*=4; \
|
| 2030 |
|
|
if ((u)>=pow) {(u)-=pow; *(c)+=8;} \
|
| 2031 |
|
|
pow/=2; \
|
| 2032 |
|
|
if ((u)>=pow) {(u)-=pow; *(c)+=4;} \
|
| 2033 |
|
|
pow/=2; \
|
| 2034 |
|
|
} \
|
| 2035 |
|
|
if ((u)>=pow) {(u)-=pow; *(c)+=2;} \
|
| 2036 |
|
|
pow/=2; \
|
| 2037 |
|
|
if ((u)>=pow) {(u)-=pow; *(c)+=1;} \
|
| 2038 |
|
|
}
|
| 2039 |
|
|
|
| 2040 |
|
|
static void
|
| 2041 |
|
|
decToString (const decNumber * dn, char *string, Flag eng)
|
| 2042 |
|
|
{
|
| 2043 |
|
|
Int exp = dn->exponent; /* local copy */
|
| 2044 |
|
|
Int e; /* E-part value */
|
| 2045 |
|
|
Int pre; /* digits before the '.' */
|
| 2046 |
|
|
Int cut; /* for counting digits in a Unit */
|
| 2047 |
|
|
char *c = string; /* work [output pointer] */
|
| 2048 |
|
|
const Unit *up = dn->lsu + D2U (dn->digits) - 1; /* -> msu [input pointer] */
|
| 2049 |
|
|
uInt u, pow; /* work */
|
| 2050 |
|
|
|
| 2051 |
|
|
#if DECCHECK
|
| 2052 |
|
|
if (decCheckOperands (DECUNUSED, dn, DECUNUSED, DECUNUSED))
|
| 2053 |
|
|
{
|
| 2054 |
|
|
strcpy (string, "?");
|
| 2055 |
|
|
return;
|
| 2056 |
|
|
}
|
| 2057 |
|
|
#endif
|
| 2058 |
|
|
|
| 2059 |
|
|
if (decNumberIsNegative (dn))
|
| 2060 |
|
|
{ /* Negatives get a minus (except */
|
| 2061 |
|
|
*c = '-'; /* NaNs, which remove the '-' below) */
|
| 2062 |
|
|
c++;
|
| 2063 |
|
|
}
|
| 2064 |
|
|
if (dn->bits & DECSPECIAL)
|
| 2065 |
|
|
{ /* Is a special value */
|
| 2066 |
|
|
if (decNumberIsInfinite (dn))
|
| 2067 |
|
|
{
|
| 2068 |
|
|
strcpy (c, "Infinity");
|
| 2069 |
|
|
return;
|
| 2070 |
|
|
}
|
| 2071 |
|
|
/* a NaN */
|
| 2072 |
|
|
if (dn->bits & DECSNAN)
|
| 2073 |
|
|
{ /* signalling NaN */
|
| 2074 |
|
|
*c = 's';
|
| 2075 |
|
|
c++;
|
| 2076 |
|
|
}
|
| 2077 |
|
|
strcpy (c, "NaN");
|
| 2078 |
|
|
c += 3; /* step past */
|
| 2079 |
|
|
/* if not a clean non-zero coefficient, that's all we have in a */
|
| 2080 |
|
|
/* NaN string */
|
| 2081 |
|
|
if (exp != 0 || (*dn->lsu == 0 && dn->digits == 1))
|
| 2082 |
|
|
return;
|
| 2083 |
|
|
/* [drop through to add integer] */
|
| 2084 |
|
|
}
|
| 2085 |
|
|
|
| 2086 |
|
|
/* calculate how many digits in msu, and hence first cut */
|
| 2087 |
|
|
cut = dn->digits % DECDPUN;
|
| 2088 |
|
|
if (cut == 0)
|
| 2089 |
|
|
cut = DECDPUN; /* msu is full */
|
| 2090 |
|
|
cut--; /* power of ten for digit */
|
| 2091 |
|
|
|
| 2092 |
|
|
if (exp == 0)
|
| 2093 |
|
|
{ /* simple integer [common fastpath, */
|
| 2094 |
|
|
/* used for NaNs, too] */
|
| 2095 |
|
|
for (; up >= dn->lsu; up--)
|
| 2096 |
|
|
{ /* each Unit from msu */
|
| 2097 |
|
|
u = *up; /* contains DECDPUN digits to lay out */
|
| 2098 |
|
|
for (; cut >= 0; c++, cut--)
|
| 2099 |
|
|
TODIGIT (u, cut, c);
|
| 2100 |
|
|
cut = DECDPUN - 1; /* next Unit has all digits */
|
| 2101 |
|
|
}
|
| 2102 |
|
|
*c = '\0'; /* terminate the string */
|
| 2103 |
|
|
return;
|
| 2104 |
|
|
}
|
| 2105 |
|
|
|
| 2106 |
|
|
/* non-0 exponent -- assume plain form */
|
| 2107 |
|
|
pre = dn->digits + exp; /* digits before '.' */
|
| 2108 |
|
|
e = 0; /* no E */
|
| 2109 |
|
|
if ((exp > 0) || (pre < -5))
|
| 2110 |
|
|
{ /* need exponential form */
|
| 2111 |
|
|
e = exp + dn->digits - 1; /* calculate E value */
|
| 2112 |
|
|
pre = 1; /* assume one digit before '.' */
|
| 2113 |
|
|
if (eng && (e != 0))
|
| 2114 |
|
|
{ /* may need to adjust */
|
| 2115 |
|
|
Int adj; /* adjustment */
|
| 2116 |
|
|
/* The C remainder operator is undefined for negative numbers, so */
|
| 2117 |
|
|
/* we must use positive remainder calculation here */
|
| 2118 |
|
|
if (e < 0)
|
| 2119 |
|
|
{
|
| 2120 |
|
|
adj = (-e) % 3;
|
| 2121 |
|
|
if (adj != 0)
|
| 2122 |
|
|
adj = 3 - adj;
|
| 2123 |
|
|
}
|
| 2124 |
|
|
else
|
| 2125 |
|
|
{ /* e>0 */
|
| 2126 |
|
|
adj = e % 3;
|
| 2127 |
|
|
}
|
| 2128 |
|
|
e = e - adj;
|
| 2129 |
|
|
/* if we are dealing with zero we will use exponent which is a */
|
| 2130 |
|
|
/* multiple of three, as expected, but there will only be the */
|
| 2131 |
|
|
/* one zero before the E, still. Otherwise note the padding. */
|
| 2132 |
|
|
if (!ISZERO (dn))
|
| 2133 |
|
|
pre += adj;
|
| 2134 |
|
|
else
|
| 2135 |
|
|
{ /* is zero */
|
| 2136 |
|
|
if (adj != 0)
|
| 2137 |
|
|
{ /* 0.00Esnn needed */
|
| 2138 |
|
|
e = e + 3;
|
| 2139 |
|
|
pre = -(2 - adj);
|
| 2140 |
|
|
}
|
| 2141 |
|
|
} /* zero */
|
| 2142 |
|
|
} /* eng */
|
| 2143 |
|
|
}
|
| 2144 |
|
|
|
| 2145 |
|
|
/* lay out the digits of the coefficient, adding 0s and . as needed */
|
| 2146 |
|
|
u = *up;
|
| 2147 |
|
|
if (pre > 0)
|
| 2148 |
|
|
{ /* xxx.xxx or xx00 (engineering) form */
|
| 2149 |
|
|
for (; pre > 0; pre--, c++, cut--)
|
| 2150 |
|
|
{
|
| 2151 |
|
|
if (cut < 0)
|
| 2152 |
|
|
{ /* need new Unit */
|
| 2153 |
|
|
if (up == dn->lsu)
|
| 2154 |
|
|
break; /* out of input digits (pre>digits) */
|
| 2155 |
|
|
up--;
|
| 2156 |
|
|
cut = DECDPUN - 1;
|
| 2157 |
|
|
u = *up;
|
| 2158 |
|
|
}
|
| 2159 |
|
|
TODIGIT (u, cut, c);
|
| 2160 |
|
|
}
|
| 2161 |
|
|
if (up > dn->lsu || (up == dn->lsu && cut >= 0))
|
| 2162 |
|
|
{ /* more to come, after '.' */
|
| 2163 |
|
|
*c = '.';
|
| 2164 |
|
|
c++;
|
| 2165 |
|
|
for (;; c++, cut--)
|
| 2166 |
|
|
{
|
| 2167 |
|
|
if (cut < 0)
|
| 2168 |
|
|
{ /* need new Unit */
|
| 2169 |
|
|
if (up == dn->lsu)
|
| 2170 |
|
|
break; /* out of input digits */
|
| 2171 |
|
|
up--;
|
| 2172 |
|
|
cut = DECDPUN - 1;
|
| 2173 |
|
|
u = *up;
|
| 2174 |
|
|
}
|
| 2175 |
|
|
TODIGIT (u, cut, c);
|
| 2176 |
|
|
}
|
| 2177 |
|
|
}
|
| 2178 |
|
|
else
|
| 2179 |
|
|
for (; pre > 0; pre--, c++)
|
| 2180 |
|
|
*c = '0'; /* 0 padding (for engineering) needed */
|
| 2181 |
|
|
}
|
| 2182 |
|
|
else
|
| 2183 |
|
|
{ /* 0.xxx or 0.000xxx form */
|
| 2184 |
|
|
*c = '0';
|
| 2185 |
|
|
c++;
|
| 2186 |
|
|
*c = '.';
|
| 2187 |
|
|
c++;
|
| 2188 |
|
|
for (; pre < 0; pre++, c++)
|
| 2189 |
|
|
*c = '0'; /* add any 0's after '.' */
|
| 2190 |
|
|
for (;; c++, cut--)
|
| 2191 |
|
|
{
|
| 2192 |
|
|
if (cut < 0)
|
| 2193 |
|
|
{ /* need new Unit */
|
| 2194 |
|
|
if (up == dn->lsu)
|
| 2195 |
|
|
break; /* out of input digits */
|
| 2196 |
|
|
up--;
|
| 2197 |
|
|
cut = DECDPUN - 1;
|
| 2198 |
|
|
u = *up;
|
| 2199 |
|
|
}
|
| 2200 |
|
|
TODIGIT (u, cut, c);
|
| 2201 |
|
|
}
|
| 2202 |
|
|
}
|
| 2203 |
|
|
|
| 2204 |
|
|
/* Finally add the E-part, if needed. It will never be 0, has a
|
| 2205 |
|
|
base maximum and minimum of +999999999 through -999999999, but
|
| 2206 |
|
|
could range down to -1999999998 for subnormal numbers */
|
| 2207 |
|
|
if (e != 0)
|
| 2208 |
|
|
{
|
| 2209 |
|
|
Flag had = 0; /* 1=had non-zero */
|
| 2210 |
|
|
*c = 'E';
|
| 2211 |
|
|
c++;
|
| 2212 |
|
|
*c = '+';
|
| 2213 |
|
|
c++; /* assume positive */
|
| 2214 |
|
|
u = e; /* .. */
|
| 2215 |
|
|
if (e < 0)
|
| 2216 |
|
|
{
|
| 2217 |
|
|
*(c - 1) = '-'; /* oops, need - */
|
| 2218 |
|
|
u = -e; /* uInt, please */
|
| 2219 |
|
|
}
|
| 2220 |
|
|
/* layout the exponent (_itoa is not ANSI C) */
|
| 2221 |
|
|
for (cut = 9; cut >= 0; cut--)
|
| 2222 |
|
|
{
|
| 2223 |
|
|
TODIGIT (u, cut, c);
|
| 2224 |
|
|
if (*c == '0' && !had)
|
| 2225 |
|
|
continue; /* skip leading zeros */
|
| 2226 |
|
|
had = 1; /* had non-0 */
|
| 2227 |
|
|
c++; /* step for next */
|
| 2228 |
|
|
} /* cut */
|
| 2229 |
|
|
}
|
| 2230 |
|
|
*c = '\0'; /* terminate the string (all paths) */
|
| 2231 |
|
|
return;
|
| 2232 |
|
|
}
|
| 2233 |
|
|
|
| 2234 |
|
|
/* ------------------------------------------------------------------ */
|
| 2235 |
|
|
/* decAddOp -- add/subtract operation */
|
| 2236 |
|
|
/* */
|
| 2237 |
|
|
/* This computes C = A + B */
|
| 2238 |
|
|
/* */
|
| 2239 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 2240 |
|
|
/* lhs is A */
|
| 2241 |
|
|
/* rhs is B */
|
| 2242 |
|
|
/* set is the context */
|
| 2243 |
|
|
/* negate is DECNEG if rhs should be negated, or 0 otherwise */
|
| 2244 |
|
|
/* status accumulates status for the caller */
|
| 2245 |
|
|
/* */
|
| 2246 |
|
|
/* C must have space for set->digits digits. */
|
| 2247 |
|
|
/* ------------------------------------------------------------------ */
|
| 2248 |
|
|
/* If possible, we calculate the coefficient directly into C. */
|
| 2249 |
|
|
/* However, if: */
|
| 2250 |
|
|
/* -- we need a digits+1 calculation because numbers are unaligned */
|
| 2251 |
|
|
/* and span more than set->digits digits */
|
| 2252 |
|
|
/* -- a carry to digits+1 digits looks possible */
|
| 2253 |
|
|
/* -- C is the same as A or B, and the result would destructively */
|
| 2254 |
|
|
/* overlap the A or B coefficient */
|
| 2255 |
|
|
/* then we must calculate into a temporary buffer. In this latter */
|
| 2256 |
|
|
/* case we use the local (stack) buffer if possible, and only if too */
|
| 2257 |
|
|
/* long for that do we resort to malloc. */
|
| 2258 |
|
|
/* */
|
| 2259 |
|
|
/* Misalignment is handled as follows: */
|
| 2260 |
|
|
/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
|
| 2261 |
|
|
/* BPad: Apply the padding by a combination of shifting (whole */
|
| 2262 |
|
|
/* units) and multiplication (part units). */
|
| 2263 |
|
|
/* */
|
| 2264 |
|
|
/* Addition, especially x=x+1, is speed-critical, so we take pains */
|
| 2265 |
|
|
/* to make returning as fast as possible, by flagging any allocation. */
|
| 2266 |
|
|
/* ------------------------------------------------------------------ */
|
| 2267 |
|
|
static decNumber *
|
| 2268 |
|
|
decAddOp (decNumber * res, const decNumber * lhs,
|
| 2269 |
|
|
const decNumber * rhs, decContext * set, uByte negate, uInt * status)
|
| 2270 |
|
|
{
|
| 2271 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 2272 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 2273 |
|
|
Int rhsshift; /* working shift (in Units) */
|
| 2274 |
|
|
Int maxdigits; /* longest logical length */
|
| 2275 |
|
|
Int mult; /* multiplier */
|
| 2276 |
|
|
Int residue; /* rounding accumulator */
|
| 2277 |
|
|
uByte bits; /* result bits */
|
| 2278 |
|
|
Flag diffsign; /* non-0 if arguments have different sign */
|
| 2279 |
|
|
Unit *acc; /* accumulator for result */
|
| 2280 |
|
|
Unit accbuff[D2U (DECBUFFER + 1)]; /* local buffer [+1 is for possible */
|
| 2281 |
|
|
/* final carry digit or DECBUFFER=0] */
|
| 2282 |
|
|
Unit *allocacc = NULL; /* -> allocated acc buffer, iff allocated */
|
| 2283 |
|
|
Flag alloced = 0; /* set non-0 if any allocations */
|
| 2284 |
|
|
Int reqdigits = set->digits; /* local copy; requested DIGITS */
|
| 2285 |
|
|
uByte merged; /* merged flags */
|
| 2286 |
|
|
Int padding; /* work */
|
| 2287 |
|
|
|
| 2288 |
|
|
#if DECCHECK
|
| 2289 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 2290 |
|
|
return res;
|
| 2291 |
|
|
#endif
|
| 2292 |
|
|
|
| 2293 |
|
|
do
|
| 2294 |
|
|
{ /* protect allocated storage */
|
| 2295 |
|
|
#if DECSUBSET
|
| 2296 |
|
|
if (!set->extended)
|
| 2297 |
|
|
{
|
| 2298 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 2299 |
|
|
if (lhs->digits > reqdigits)
|
| 2300 |
|
|
{
|
| 2301 |
|
|
alloclhs = decRoundOperand (lhs, set, status);
|
| 2302 |
|
|
if (alloclhs == NULL)
|
| 2303 |
|
|
break;
|
| 2304 |
|
|
lhs = alloclhs;
|
| 2305 |
|
|
alloced = 1;
|
| 2306 |
|
|
}
|
| 2307 |
|
|
if (rhs->digits > reqdigits)
|
| 2308 |
|
|
{
|
| 2309 |
|
|
allocrhs = decRoundOperand (rhs, set, status);
|
| 2310 |
|
|
if (allocrhs == NULL)
|
| 2311 |
|
|
break;
|
| 2312 |
|
|
rhs = allocrhs;
|
| 2313 |
|
|
alloced = 1;
|
| 2314 |
|
|
}
|
| 2315 |
|
|
}
|
| 2316 |
|
|
#endif
|
| 2317 |
|
|
/* [following code does not require input rounding] */
|
| 2318 |
|
|
|
| 2319 |
|
|
/* note whether signs differ */
|
| 2320 |
|
|
diffsign = (Flag) ((lhs->bits ^ rhs->bits ^ negate) & DECNEG);
|
| 2321 |
|
|
|
| 2322 |
|
|
/* handle infinities and NaNs */
|
| 2323 |
|
|
merged = (lhs->bits | rhs->bits) & DECSPECIAL;
|
| 2324 |
|
|
if (merged)
|
| 2325 |
|
|
{ /* a special bit set */
|
| 2326 |
|
|
if (merged & (DECSNAN | DECNAN)) /* a NaN */
|
| 2327 |
|
|
decNaNs (res, lhs, rhs, status);
|
| 2328 |
|
|
else
|
| 2329 |
|
|
{ /* one or two infinities */
|
| 2330 |
|
|
if (decNumberIsInfinite (lhs))
|
| 2331 |
|
|
{ /* LHS is infinity */
|
| 2332 |
|
|
/* two infinities with different signs is invalid */
|
| 2333 |
|
|
if (decNumberIsInfinite (rhs) && diffsign)
|
| 2334 |
|
|
{
|
| 2335 |
|
|
*status |= DEC_Invalid_operation;
|
| 2336 |
|
|
break;
|
| 2337 |
|
|
}
|
| 2338 |
|
|
bits = lhs->bits & DECNEG; /* get sign from LHS */
|
| 2339 |
|
|
}
|
| 2340 |
|
|
else
|
| 2341 |
|
|
bits = (rhs->bits ^ negate) & DECNEG; /* RHS must be Infinity */
|
| 2342 |
|
|
bits |= DECINF;
|
| 2343 |
|
|
decNumberZero (res);
|
| 2344 |
|
|
res->bits = bits; /* set +/- infinity */
|
| 2345 |
|
|
} /* an infinity */
|
| 2346 |
|
|
break;
|
| 2347 |
|
|
}
|
| 2348 |
|
|
|
| 2349 |
|
|
/* Quick exit for add 0s; return the non-0, modified as need be */
|
| 2350 |
|
|
if (ISZERO (lhs))
|
| 2351 |
|
|
{
|
| 2352 |
|
|
Int adjust; /* work */
|
| 2353 |
|
|
Int lexp = lhs->exponent; /* save in case LHS==RES */
|
| 2354 |
|
|
bits = lhs->bits; /* .. */
|
| 2355 |
|
|
residue = 0; /* clear accumulator */
|
| 2356 |
|
|
decCopyFit (res, rhs, set, &residue, status); /* copy (as needed) */
|
| 2357 |
|
|
res->bits ^= negate; /* flip if rhs was negated */
|
| 2358 |
|
|
#if DECSUBSET
|
| 2359 |
|
|
if (set->extended)
|
| 2360 |
|
|
{ /* exponents on zeros count */
|
| 2361 |
|
|
#endif
|
| 2362 |
|
|
/* exponent will be the lower of the two */
|
| 2363 |
|
|
adjust = lexp - res->exponent; /* adjustment needed [if -ve] */
|
| 2364 |
|
|
if (ISZERO (res))
|
| 2365 |
|
|
{ /* both 0: special IEEE 854 rules */
|
| 2366 |
|
|
if (adjust < 0)
|
| 2367 |
|
|
res->exponent = lexp; /* set exponent */
|
| 2368 |
|
|
/* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
|
| 2369 |
|
|
if (diffsign)
|
| 2370 |
|
|
{
|
| 2371 |
|
|
if (set->round != DEC_ROUND_FLOOR)
|
| 2372 |
|
|
res->bits = 0;
|
| 2373 |
|
|
else
|
| 2374 |
|
|
res->bits = DECNEG; /* preserve 0 sign */
|
| 2375 |
|
|
}
|
| 2376 |
|
|
}
|
| 2377 |
|
|
else
|
| 2378 |
|
|
{ /* non-0 res */
|
| 2379 |
|
|
if (adjust < 0)
|
| 2380 |
|
|
{ /* 0-padding needed */
|
| 2381 |
|
|
if ((res->digits - adjust) > set->digits)
|
| 2382 |
|
|
{
|
| 2383 |
|
|
adjust = res->digits - set->digits; /* to fit exactly */
|
| 2384 |
|
|
*status |= DEC_Rounded; /* [but exact] */
|
| 2385 |
|
|
}
|
| 2386 |
|
|
res->digits =
|
| 2387 |
|
|
decShiftToMost (res->lsu, res->digits, -adjust);
|
| 2388 |
|
|
res->exponent += adjust; /* set the exponent. */
|
| 2389 |
|
|
}
|
| 2390 |
|
|
} /* non-0 res */
|
| 2391 |
|
|
#if DECSUBSET
|
| 2392 |
|
|
} /* extended */
|
| 2393 |
|
|
#endif
|
| 2394 |
|
|
decFinish (res, set, &residue, status); /* clean and finalize */
|
| 2395 |
|
|
break;
|
| 2396 |
|
|
}
|
| 2397 |
|
|
|
| 2398 |
|
|
if (ISZERO (rhs))
|
| 2399 |
|
|
{ /* [lhs is non-zero] */
|
| 2400 |
|
|
Int adjust; /* work */
|
| 2401 |
|
|
Int rexp = rhs->exponent; /* save in case RHS==RES */
|
| 2402 |
|
|
bits = rhs->bits; /* be clean */
|
| 2403 |
|
|
residue = 0; /* clear accumulator */
|
| 2404 |
|
|
decCopyFit (res, lhs, set, &residue, status); /* copy (as needed) */
|
| 2405 |
|
|
#if DECSUBSET
|
| 2406 |
|
|
if (set->extended)
|
| 2407 |
|
|
{ /* exponents on zeros count */
|
| 2408 |
|
|
#endif
|
| 2409 |
|
|
/* exponent will be the lower of the two */
|
| 2410 |
|
|
/* [0-0 case handled above] */
|
| 2411 |
|
|
adjust = rexp - res->exponent; /* adjustment needed [if -ve] */
|
| 2412 |
|
|
if (adjust < 0)
|
| 2413 |
|
|
{ /* 0-padding needed */
|
| 2414 |
|
|
if ((res->digits - adjust) > set->digits)
|
| 2415 |
|
|
{
|
| 2416 |
|
|
adjust = res->digits - set->digits; /* to fit exactly */
|
| 2417 |
|
|
*status |= DEC_Rounded; /* [but exact] */
|
| 2418 |
|
|
}
|
| 2419 |
|
|
res->digits =
|
| 2420 |
|
|
decShiftToMost (res->lsu, res->digits, -adjust);
|
| 2421 |
|
|
res->exponent += adjust; /* set the exponent. */
|
| 2422 |
|
|
}
|
| 2423 |
|
|
#if DECSUBSET
|
| 2424 |
|
|
} /* extended */
|
| 2425 |
|
|
#endif
|
| 2426 |
|
|
decFinish (res, set, &residue, status); /* clean and finalize */
|
| 2427 |
|
|
break;
|
| 2428 |
|
|
}
|
| 2429 |
|
|
/* [both fastpath and mainpath code below assume these cases */
|
| 2430 |
|
|
/* (notably 0-0) have already been handled] */
|
| 2431 |
|
|
|
| 2432 |
|
|
/* calculate the padding needed to align the operands */
|
| 2433 |
|
|
padding = rhs->exponent - lhs->exponent;
|
| 2434 |
|
|
|
| 2435 |
|
|
/* Fastpath cases where the numbers are aligned and normal, the RHS */
|
| 2436 |
|
|
/* is all in one unit, no operand rounding is needed, and no carry, */
|
| 2437 |
|
|
/* lengthening, or borrow is needed */
|
| 2438 |
|
|
if (rhs->digits <= DECDPUN && padding == 0 && rhs->exponent >= set->emin /* [some normals drop through] */
|
| 2439 |
|
|
&& rhs->digits <= reqdigits && lhs->digits <= reqdigits)
|
| 2440 |
|
|
{
|
| 2441 |
|
|
Int partial = *lhs->lsu;
|
| 2442 |
|
|
if (!diffsign)
|
| 2443 |
|
|
{ /* adding */
|
| 2444 |
|
|
Int maxv = DECDPUNMAX; /* highest no-overflow */
|
| 2445 |
|
|
if (lhs->digits < DECDPUN)
|
| 2446 |
|
|
maxv = powers[lhs->digits] - 1;
|
| 2447 |
|
|
partial += *rhs->lsu;
|
| 2448 |
|
|
if (partial <= maxv)
|
| 2449 |
|
|
{ /* no carry */
|
| 2450 |
|
|
if (res != lhs)
|
| 2451 |
|
|
decNumberCopy (res, lhs); /* not in place */
|
| 2452 |
|
|
*res->lsu = (Unit) partial; /* [copy could have overwritten RHS] */
|
| 2453 |
|
|
break;
|
| 2454 |
|
|
}
|
| 2455 |
|
|
/* else drop out for careful add */
|
| 2456 |
|
|
}
|
| 2457 |
|
|
else
|
| 2458 |
|
|
{ /* signs differ */
|
| 2459 |
|
|
partial -= *rhs->lsu;
|
| 2460 |
|
|
if (partial > 0)
|
| 2461 |
|
|
{ /* no borrow needed, and non-0 result */
|
| 2462 |
|
|
if (res != lhs)
|
| 2463 |
|
|
decNumberCopy (res, lhs); /* not in place */
|
| 2464 |
|
|
*res->lsu = (Unit) partial;
|
| 2465 |
|
|
/* this could have reduced digits [but result>0] */
|
| 2466 |
|
|
res->digits = decGetDigits (res->lsu, D2U (res->digits));
|
| 2467 |
|
|
break;
|
| 2468 |
|
|
}
|
| 2469 |
|
|
/* else drop out for careful subtract */
|
| 2470 |
|
|
}
|
| 2471 |
|
|
}
|
| 2472 |
|
|
|
| 2473 |
|
|
/* Now align (pad) the lhs or rhs so we can add or subtract them, as
|
| 2474 |
|
|
necessary. If one number is much larger than the other (that is,
|
| 2475 |
|
|
if in plain form there is a least one digit between the lowest
|
| 2476 |
|
|
digit or one and the highest of the other) we need to pad with up
|
| 2477 |
|
|
to DIGITS-1 trailing zeros, and then apply rounding (as exotic
|
| 2478 |
|
|
rounding modes may be affected by the residue).
|
| 2479 |
|
|
*/
|
| 2480 |
|
|
rhsshift = 0; /* rhs shift to left (padding) in Units */
|
| 2481 |
|
|
bits = lhs->bits; /* assume sign is that of LHS */
|
| 2482 |
|
|
mult = 1; /* likely multiplier */
|
| 2483 |
|
|
|
| 2484 |
|
|
/* if padding==0 the operands are aligned; no padding needed */
|
| 2485 |
|
|
if (padding != 0)
|
| 2486 |
|
|
{
|
| 2487 |
|
|
/* some padding needed */
|
| 2488 |
|
|
/* We always pad the RHS, as we can then effect any required */
|
| 2489 |
|
|
/* padding by a combination of shifts and a multiply */
|
| 2490 |
|
|
Flag swapped = 0;
|
| 2491 |
|
|
if (padding < 0)
|
| 2492 |
|
|
{ /* LHS needs the padding */
|
| 2493 |
|
|
const decNumber *t;
|
| 2494 |
|
|
padding = -padding; /* will be +ve */
|
| 2495 |
|
|
bits = (uByte) (rhs->bits ^ negate); /* assumed sign is now that of RHS */
|
| 2496 |
|
|
t = lhs;
|
| 2497 |
|
|
lhs = rhs;
|
| 2498 |
|
|
rhs = t;
|
| 2499 |
|
|
swapped = 1;
|
| 2500 |
|
|
}
|
| 2501 |
|
|
|
| 2502 |
|
|
/* If, after pad, rhs would be longer than lhs by digits+1 or */
|
| 2503 |
|
|
/* more then lhs cannot affect the answer, except as a residue, */
|
| 2504 |
|
|
/* so we only need to pad up to a length of DIGITS+1. */
|
| 2505 |
|
|
if (rhs->digits + padding > lhs->digits + reqdigits + 1)
|
| 2506 |
|
|
{
|
| 2507 |
|
|
/* The RHS is sufficient */
|
| 2508 |
|
|
/* for residue we use the relative sign indication... */
|
| 2509 |
|
|
Int shift = reqdigits - rhs->digits; /* left shift needed */
|
| 2510 |
|
|
residue = 1; /* residue for rounding */
|
| 2511 |
|
|
if (diffsign)
|
| 2512 |
|
|
residue = -residue; /* signs differ */
|
| 2513 |
|
|
/* copy, shortening if necessary */
|
| 2514 |
|
|
decCopyFit (res, rhs, set, &residue, status);
|
| 2515 |
|
|
/* if it was already shorter, then need to pad with zeros */
|
| 2516 |
|
|
if (shift > 0)
|
| 2517 |
|
|
{
|
| 2518 |
|
|
res->digits = decShiftToMost (res->lsu, res->digits, shift);
|
| 2519 |
|
|
res->exponent -= shift; /* adjust the exponent. */
|
| 2520 |
|
|
}
|
| 2521 |
|
|
/* flip the result sign if unswapped and rhs was negated */
|
| 2522 |
|
|
if (!swapped)
|
| 2523 |
|
|
res->bits ^= negate;
|
| 2524 |
|
|
decFinish (res, set, &residue, status); /* done */
|
| 2525 |
|
|
break;
|
| 2526 |
|
|
}
|
| 2527 |
|
|
|
| 2528 |
|
|
/* LHS digits may affect result */
|
| 2529 |
|
|
rhsshift = D2U (padding + 1) - 1; /* this much by Unit shift .. */
|
| 2530 |
|
|
mult = powers[padding - (rhsshift * DECDPUN)]; /* .. this by multiplication */
|
| 2531 |
|
|
} /* padding needed */
|
| 2532 |
|
|
|
| 2533 |
|
|
if (diffsign)
|
| 2534 |
|
|
mult = -mult; /* signs differ */
|
| 2535 |
|
|
|
| 2536 |
|
|
/* determine the longer operand */
|
| 2537 |
|
|
maxdigits = rhs->digits + padding; /* virtual length of RHS */
|
| 2538 |
|
|
if (lhs->digits > maxdigits)
|
| 2539 |
|
|
maxdigits = lhs->digits;
|
| 2540 |
|
|
|
| 2541 |
|
|
/* Decide on the result buffer to use; if possible place directly */
|
| 2542 |
|
|
/* into result. */
|
| 2543 |
|
|
acc = res->lsu; /* assume build direct */
|
| 2544 |
|
|
/* If destructive overlap, or the number is too long, or a carry or */
|
| 2545 |
|
|
/* borrow to DIGITS+1 might be possible we must use a buffer. */
|
| 2546 |
|
|
/* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
|
| 2547 |
|
|
if ((maxdigits >= reqdigits) /* is, or could be, too large */
|
| 2548 |
|
|
|| (res == rhs && rhsshift > 0))
|
| 2549 |
|
|
{ /* destructive overlap */
|
| 2550 |
|
|
/* buffer needed; choose it */
|
| 2551 |
|
|
/* we'll need units for maxdigits digits, +1 Unit for carry or borrow */
|
| 2552 |
|
|
Int need = D2U (maxdigits) + 1;
|
| 2553 |
|
|
acc = accbuff; /* assume use local buffer */
|
| 2554 |
|
|
if (need * sizeof (Unit) > sizeof (accbuff))
|
| 2555 |
|
|
{
|
| 2556 |
|
|
allocacc = (Unit *) malloc (need * sizeof (Unit));
|
| 2557 |
|
|
if (allocacc == NULL)
|
| 2558 |
|
|
{ /* hopeless -- abandon */
|
| 2559 |
|
|
*status |= DEC_Insufficient_storage;
|
| 2560 |
|
|
break;
|
| 2561 |
|
|
}
|
| 2562 |
|
|
acc = allocacc;
|
| 2563 |
|
|
alloced = 1;
|
| 2564 |
|
|
}
|
| 2565 |
|
|
}
|
| 2566 |
|
|
|
| 2567 |
|
|
res->bits = (uByte) (bits & DECNEG); /* it's now safe to overwrite.. */
|
| 2568 |
|
|
res->exponent = lhs->exponent; /* .. operands (even if aliased) */
|
| 2569 |
|
|
|
| 2570 |
|
|
#if DECTRACE
|
| 2571 |
|
|
decDumpAr ('A', lhs->lsu, D2U (lhs->digits));
|
| 2572 |
|
|
decDumpAr ('B', rhs->lsu, D2U (rhs->digits));
|
| 2573 |
|
|
printf (" :h: %d %d\n", rhsshift, mult);
|
| 2574 |
|
|
#endif
|
| 2575 |
|
|
|
| 2576 |
|
|
/* add [A+B*m] or subtract [A+B*(-m)] */
|
| 2577 |
|
|
res->digits = decUnitAddSub (lhs->lsu, D2U (lhs->digits), rhs->lsu, D2U (rhs->digits), rhsshift, acc, mult) * DECDPUN; /* [units -> digits] */
|
| 2578 |
|
|
if (res->digits < 0)
|
| 2579 |
|
|
{ /* we borrowed */
|
| 2580 |
|
|
res->digits = -res->digits;
|
| 2581 |
|
|
res->bits ^= DECNEG; /* flip the sign */
|
| 2582 |
|
|
}
|
| 2583 |
|
|
#if DECTRACE
|
| 2584 |
|
|
decDumpAr ('+', acc, D2U (res->digits));
|
| 2585 |
|
|
#endif
|
| 2586 |
|
|
|
| 2587 |
|
|
/* If we used a buffer we need to copy back, possibly shortening */
|
| 2588 |
|
|
/* (If we didn't use buffer it must have fit, so can't need rounding */
|
| 2589 |
|
|
/* and residue must be 0.) */
|
| 2590 |
|
|
residue = 0; /* clear accumulator */
|
| 2591 |
|
|
if (acc != res->lsu)
|
| 2592 |
|
|
{
|
| 2593 |
|
|
#if DECSUBSET
|
| 2594 |
|
|
if (set->extended)
|
| 2595 |
|
|
{ /* round from first significant digit */
|
| 2596 |
|
|
#endif
|
| 2597 |
|
|
/* remove leading zeros that we added due to rounding up to */
|
| 2598 |
|
|
/* integral Units -- before the test for rounding. */
|
| 2599 |
|
|
if (res->digits > reqdigits)
|
| 2600 |
|
|
res->digits = decGetDigits (acc, D2U (res->digits));
|
| 2601 |
|
|
decSetCoeff (res, set, acc, res->digits, &residue, status);
|
| 2602 |
|
|
#if DECSUBSET
|
| 2603 |
|
|
}
|
| 2604 |
|
|
else
|
| 2605 |
|
|
{ /* subset arithmetic rounds from original significant digit */
|
| 2606 |
|
|
/* We may have an underestimate. This only occurs when both */
|
| 2607 |
|
|
/* numbers fit in DECDPUN digits and we are padding with a */
|
| 2608 |
|
|
/* negative multiple (-10, -100...) and the top digit(s) become */
|
| 2609 |
|
|
/* 0. (This only matters if we are using X3.274 rules where the */
|
| 2610 |
|
|
/* leading zero could be included in the rounding.) */
|
| 2611 |
|
|
if (res->digits < maxdigits)
|
| 2612 |
|
|
{
|
| 2613 |
|
|
*(acc + D2U (res->digits)) = 0; /* ensure leading 0 is there */
|
| 2614 |
|
|
res->digits = maxdigits;
|
| 2615 |
|
|
}
|
| 2616 |
|
|
else
|
| 2617 |
|
|
{
|
| 2618 |
|
|
/* remove leading zeros that we added due to rounding up to */
|
| 2619 |
|
|
/* integral Units (but only those in excess of the original */
|
| 2620 |
|
|
/* maxdigits length, unless extended) before test for rounding. */
|
| 2621 |
|
|
if (res->digits > reqdigits)
|
| 2622 |
|
|
{
|
| 2623 |
|
|
res->digits = decGetDigits (acc, D2U (res->digits));
|
| 2624 |
|
|
if (res->digits < maxdigits)
|
| 2625 |
|
|
res->digits = maxdigits;
|
| 2626 |
|
|
}
|
| 2627 |
|
|
}
|
| 2628 |
|
|
decSetCoeff (res, set, acc, res->digits, &residue, status);
|
| 2629 |
|
|
/* Now apply rounding if needed before removing leading zeros. */
|
| 2630 |
|
|
/* This is safe because subnormals are not a possibility */
|
| 2631 |
|
|
if (residue != 0)
|
| 2632 |
|
|
{
|
| 2633 |
|
|
decApplyRound (res, set, residue, status);
|
| 2634 |
|
|
residue = 0; /* we did what we had to do */
|
| 2635 |
|
|
}
|
| 2636 |
|
|
} /* subset */
|
| 2637 |
|
|
#endif
|
| 2638 |
|
|
} /* used buffer */
|
| 2639 |
|
|
|
| 2640 |
|
|
/* strip leading zeros [these were left on in case of subset subtract] */
|
| 2641 |
|
|
res->digits = decGetDigits (res->lsu, D2U (res->digits));
|
| 2642 |
|
|
|
| 2643 |
|
|
/* apply checks and rounding */
|
| 2644 |
|
|
decFinish (res, set, &residue, status);
|
| 2645 |
|
|
|
| 2646 |
|
|
/* "When the sum of two operands with opposite signs is exactly */
|
| 2647 |
|
|
/* zero, the sign of that sum shall be '+' in all rounding modes */
|
| 2648 |
|
|
/* except round toward -Infinity, in which mode that sign shall be */
|
| 2649 |
|
|
/* '-'." [Subset zeros also never have '-', set by decFinish.] */
|
| 2650 |
|
|
if (ISZERO (res) && diffsign
|
| 2651 |
|
|
#if DECSUBSET
|
| 2652 |
|
|
&& set->extended
|
| 2653 |
|
|
#endif
|
| 2654 |
|
|
&& (*status & DEC_Inexact) == 0)
|
| 2655 |
|
|
{
|
| 2656 |
|
|
if (set->round == DEC_ROUND_FLOOR)
|
| 2657 |
|
|
res->bits |= DECNEG; /* sign - */
|
| 2658 |
|
|
else
|
| 2659 |
|
|
res->bits &= ~DECNEG; /* sign + */
|
| 2660 |
|
|
}
|
| 2661 |
|
|
}
|
| 2662 |
|
|
while (0); /* end protected */
|
| 2663 |
|
|
|
| 2664 |
|
|
if (alloced)
|
| 2665 |
|
|
{
|
| 2666 |
|
|
if (allocacc != NULL)
|
| 2667 |
|
|
free (allocacc); /* drop any storage we used */
|
| 2668 |
|
|
if (allocrhs != NULL)
|
| 2669 |
|
|
free (allocrhs); /* .. */
|
| 2670 |
|
|
if (alloclhs != NULL)
|
| 2671 |
|
|
free (alloclhs); /* .. */
|
| 2672 |
|
|
}
|
| 2673 |
|
|
return res;
|
| 2674 |
|
|
}
|
| 2675 |
|
|
|
| 2676 |
|
|
/* ------------------------------------------------------------------ */
|
| 2677 |
|
|
/* decDivideOp -- division operation */
|
| 2678 |
|
|
/* */
|
| 2679 |
|
|
/* This routine performs the calculations for all four division */
|
| 2680 |
|
|
/* operators (divide, divideInteger, remainder, remainderNear). */
|
| 2681 |
|
|
/* */
|
| 2682 |
|
|
/* C=A op B */
|
| 2683 |
|
|
/* */
|
| 2684 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| 2685 |
|
|
/* lhs is A */
|
| 2686 |
|
|
/* rhs is B */
|
| 2687 |
|
|
/* set is the context */
|
| 2688 |
|
|
/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
|
| 2689 |
|
|
/* status is the usual accumulator */
|
| 2690 |
|
|
/* */
|
| 2691 |
|
|
/* C must have space for set->digits digits. */
|
| 2692 |
|
|
/* */
|
| 2693 |
|
|
/* ------------------------------------------------------------------ */
|
| 2694 |
|
|
/* The underlying algorithm of this routine is the same as in the */
|
| 2695 |
|
|
/* 1981 S/370 implementation, that is, non-restoring long division */
|
| 2696 |
|
|
/* with bi-unit (rather than bi-digit) estimation for each unit */
|
| 2697 |
|
|
/* multiplier. In this pseudocode overview, complications for the */
|
| 2698 |
|
|
/* Remainder operators and division residues for exact rounding are */
|
| 2699 |
|
|
/* omitted for clarity. */
|
| 2700 |
|
|
/* */
|
| 2701 |
|
|
/* Prepare operands and handle special values */
|
| 2702 |
|
|
/* Test for x/0 and then 0/x */
|
| 2703 |
|
|
/* Exp =Exp1 - Exp2 */
|
| 2704 |
|
|
/* Exp =Exp +len(var1) -len(var2) */
|
| 2705 |
|
|
/* Sign=Sign1 * Sign2 */
|
| 2706 |
|
|
/* Pad accumulator (Var1) to double-length with 0's (pad1) */
|
| 2707 |
|
|
/* Pad Var2 to same length as Var1 */
|
| 2708 |
|
|
/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
|
| 2709 |
|
|
/* have=0 */
|
| 2710 |
|
|
/* Do until (have=digits+1 OR residue=0) */
|
| 2711 |
|
|
/* if exp<0 then if integer divide/residue then leave */
|
| 2712 |
|
|
/* this_unit=0 */
|
| 2713 |
|
|
/* Do forever */
|
| 2714 |
|
|
/* compare numbers */
|
| 2715 |
|
|
/* if <0 then leave inner_loop */
|
| 2716 |
|
|
/* if =0 then (* quick exit without subtract *) do */
|
| 2717 |
|
|
/* this_unit=this_unit+1; output this_unit */
|
| 2718 |
|
|
/* leave outer_loop; end */
|
| 2719 |
|
|
/* Compare lengths of numbers (mantissae): */
|
| 2720 |
|
|
/* If same then tops2=msu2pair -- {units 1&2 of var2} */
|
| 2721 |
|
|
/* else tops2=msu2plus -- {0, unit 1 of var2} */
|
| 2722 |
|
|
/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
|
| 2723 |
|
|
/* mult=tops1/tops2 -- Good and safe guess at divisor */
|
| 2724 |
|
|
/* if mult=0 then mult=1 */
|
| 2725 |
|
|
/* this_unit=this_unit+mult */
|
| 2726 |
|
|
/* subtract */
|
| 2727 |
|
|
/* end inner_loop */
|
| 2728 |
|
|
/* if have\=0 | this_unit\=0 then do */
|
| 2729 |
|
|
/* output this_unit */
|
| 2730 |
|
|
/* have=have+1; end */
|
| 2731 |
|
|
/* var2=var2/10 */
|
| 2732 |
|
|
/* exp=exp-1 */
|
| 2733 |
|
|
/* end outer_loop */
|
| 2734 |
|
|
/* exp=exp+1 -- set the proper exponent */
|
| 2735 |
|
|
/* if have=0 then generate answer=0 */
|
| 2736 |
|
|
/* Return (Result is defined by Var1) */
|
| 2737 |
|
|
/* */
|
| 2738 |
|
|
/* ------------------------------------------------------------------ */
|
| 2739 |
|
|
/* We need two working buffers during the long division; one (digits+ */
|
| 2740 |
|
|
/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
|
| 2741 |
|
|
/* long subtractions. These are acc and var1 respectively. */
|
| 2742 |
|
|
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
|
| 2743 |
|
|
/* ------------------------------------------------------------------ */
|
| 2744 |
|
|
static decNumber *
|
| 2745 |
|
|
decDivideOp (decNumber * res,
|
| 2746 |
|
|
const decNumber * lhs, const decNumber * rhs,
|
| 2747 |
|
|
decContext * set, Flag op, uInt * status)
|
| 2748 |
|
|
{
|
| 2749 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 2750 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 2751 |
|
|
Unit accbuff[D2U (DECBUFFER + DECDPUN)]; /* local buffer */
|
| 2752 |
|
|
Unit *acc = accbuff; /* -> accumulator array for result */
|
| 2753 |
|
|
Unit *allocacc = NULL; /* -> allocated buffer, iff allocated */
|
| 2754 |
|
|
Unit *accnext; /* -> where next digit will go */
|
| 2755 |
|
|
Int acclength; /* length of acc needed [Units] */
|
| 2756 |
|
|
Int accunits; /* count of units accumulated */
|
| 2757 |
|
|
Int accdigits; /* count of digits accumulated */
|
| 2758 |
|
|
|
| 2759 |
|
|
Unit varbuff[D2U (DECBUFFER * 2 + DECDPUN) * sizeof (Unit)]; /* buffer for var1 */
|
| 2760 |
|
|
Unit *var1 = varbuff; /* -> var1 array for long subtraction */
|
| 2761 |
|
|
Unit *varalloc = NULL; /* -> allocated buffer, iff used */
|
| 2762 |
|
|
|
| 2763 |
|
|
const Unit *var2; /* -> var2 array */
|
| 2764 |
|
|
|
| 2765 |
|
|
Int var1units, var2units; /* actual lengths */
|
| 2766 |
|
|
Int var2ulen; /* logical length (units) */
|
| 2767 |
|
|
Int var1initpad = 0; /* var1 initial padding (digits) */
|
| 2768 |
|
|
Unit *msu1; /* -> msu of each var */
|
| 2769 |
|
|
const Unit *msu2; /* -> msu of each var */
|
| 2770 |
|
|
Int msu2plus; /* msu2 plus one [does not vary] */
|
| 2771 |
|
|
eInt msu2pair; /* msu2 pair plus one [does not vary] */
|
| 2772 |
|
|
Int maxdigits; /* longest LHS or required acc length */
|
| 2773 |
|
|
Int mult; /* multiplier for subtraction */
|
| 2774 |
|
|
Unit thisunit; /* current unit being accumulated */
|
| 2775 |
|
|
Int residue; /* for rounding */
|
| 2776 |
|
|
Int reqdigits = set->digits; /* requested DIGITS */
|
| 2777 |
|
|
Int exponent; /* working exponent */
|
| 2778 |
|
|
Int maxexponent = 0; /* DIVIDE maximum exponent if unrounded */
|
| 2779 |
|
|
uByte bits; /* working sign */
|
| 2780 |
|
|
uByte merged; /* merged flags */
|
| 2781 |
|
|
Unit *target; /* work */
|
| 2782 |
|
|
const Unit *source; /* work */
|
| 2783 |
|
|
uInt const *pow; /* .. */
|
| 2784 |
|
|
Int shift, cut; /* .. */
|
| 2785 |
|
|
#if DECSUBSET
|
| 2786 |
|
|
Int dropped; /* work */
|
| 2787 |
|
|
#endif
|
| 2788 |
|
|
|
| 2789 |
|
|
#if DECCHECK
|
| 2790 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 2791 |
|
|
return res;
|
| 2792 |
|
|
#endif
|
| 2793 |
|
|
|
| 2794 |
|
|
do
|
| 2795 |
|
|
{ /* protect allocated storage */
|
| 2796 |
|
|
#if DECSUBSET
|
| 2797 |
|
|
if (!set->extended)
|
| 2798 |
|
|
{
|
| 2799 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 2800 |
|
|
if (lhs->digits > reqdigits)
|
| 2801 |
|
|
{
|
| 2802 |
|
|
alloclhs = decRoundOperand (lhs, set, status);
|
| 2803 |
|
|
if (alloclhs == NULL)
|
| 2804 |
|
|
break;
|
| 2805 |
|
|
lhs = alloclhs;
|
| 2806 |
|
|
}
|
| 2807 |
|
|
if (rhs->digits > reqdigits)
|
| 2808 |
|
|
{
|
| 2809 |
|
|
allocrhs = decRoundOperand (rhs, set, status);
|
| 2810 |
|
|
if (allocrhs == NULL)
|
| 2811 |
|
|
break;
|
| 2812 |
|
|
rhs = allocrhs;
|
| 2813 |
|
|
}
|
| 2814 |
|
|
}
|
| 2815 |
|
|
#endif
|
| 2816 |
|
|
/* [following code does not require input rounding] */
|
| 2817 |
|
|
|
| 2818 |
|
|
bits = (lhs->bits ^ rhs->bits) & DECNEG; /* assumed sign for divisions */
|
| 2819 |
|
|
|
| 2820 |
|
|
/* handle infinities and NaNs */
|
| 2821 |
|
|
merged = (lhs->bits | rhs->bits) & DECSPECIAL;
|
| 2822 |
|
|
if (merged)
|
| 2823 |
|
|
{ /* a special bit set */
|
| 2824 |
|
|
if (merged & (DECSNAN | DECNAN))
|
| 2825 |
|
|
{ /* one or two NaNs */
|
| 2826 |
|
|
decNaNs (res, lhs, rhs, status);
|
| 2827 |
|
|
break;
|
| 2828 |
|
|
}
|
| 2829 |
|
|
/* one or two infinities */
|
| 2830 |
|
|
if (decNumberIsInfinite (lhs))
|
| 2831 |
|
|
{ /* LHS (dividend) is infinite */
|
| 2832 |
|
|
if (decNumberIsInfinite (rhs) || /* two infinities are invalid .. */
|
| 2833 |
|
|
op & (REMAINDER | REMNEAR))
|
| 2834 |
|
|
{ /* as is remainder of infinity */
|
| 2835 |
|
|
*status |= DEC_Invalid_operation;
|
| 2836 |
|
|
break;
|
| 2837 |
|
|
}
|
| 2838 |
|
|
/* [Note that infinity/0 raises no exceptions] */
|
| 2839 |
|
|
decNumberZero (res);
|
| 2840 |
|
|
res->bits = bits | DECINF; /* set +/- infinity */
|
| 2841 |
|
|
break;
|
| 2842 |
|
|
}
|
| 2843 |
|
|
else
|
| 2844 |
|
|
{ /* RHS (divisor) is infinite */
|
| 2845 |
|
|
residue = 0;
|
| 2846 |
|
|
if (op & (REMAINDER | REMNEAR))
|
| 2847 |
|
|
{
|
| 2848 |
|
|
/* result is [finished clone of] lhs */
|
| 2849 |
|
|
decCopyFit (res, lhs, set, &residue, status);
|
| 2850 |
|
|
}
|
| 2851 |
|
|
else
|
| 2852 |
|
|
{ /* a division */
|
| 2853 |
|
|
decNumberZero (res);
|
| 2854 |
|
|
res->bits = bits; /* set +/- zero */
|
| 2855 |
|
|
/* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
|
| 2856 |
|
|
/* is a 0 with infinitely negative exponent, clamped to minimum */
|
| 2857 |
|
|
if (op & DIVIDE)
|
| 2858 |
|
|
{
|
| 2859 |
|
|
res->exponent = set->emin - set->digits + 1;
|
| 2860 |
|
|
*status |= DEC_Clamped;
|
| 2861 |
|
|
}
|
| 2862 |
|
|
}
|
| 2863 |
|
|
decFinish (res, set, &residue, status);
|
| 2864 |
|
|
break;
|
| 2865 |
|
|
}
|
| 2866 |
|
|
}
|
| 2867 |
|
|
|
| 2868 |
|
|
/* handle 0 rhs (x/0) */
|
| 2869 |
|
|
if (ISZERO (rhs))
|
| 2870 |
|
|
{ /* x/0 is always exceptional */
|
| 2871 |
|
|
if (ISZERO (lhs))
|
| 2872 |
|
|
{
|
| 2873 |
|
|
decNumberZero (res); /* [after lhs test] */
|
| 2874 |
|
|
*status |= DEC_Division_undefined; /* 0/0 will become NaN */
|
| 2875 |
|
|
}
|
| 2876 |
|
|
else
|
| 2877 |
|
|
{
|
| 2878 |
|
|
decNumberZero (res);
|
| 2879 |
|
|
if (op & (REMAINDER | REMNEAR))
|
| 2880 |
|
|
*status |= DEC_Invalid_operation;
|
| 2881 |
|
|
else
|
| 2882 |
|
|
{
|
| 2883 |
|
|
*status |= DEC_Division_by_zero; /* x/0 */
|
| 2884 |
|
|
res->bits = bits | DECINF; /* .. is +/- Infinity */
|
| 2885 |
|
|
}
|
| 2886 |
|
|
}
|
| 2887 |
|
|
break;
|
| 2888 |
|
|
}
|
| 2889 |
|
|
|
| 2890 |
|
|
/* handle 0 lhs (0/x) */
|
| 2891 |
|
|
if (ISZERO (lhs))
|
| 2892 |
|
|
{ /* 0/x [x!=0] */
|
| 2893 |
|
|
#if DECSUBSET
|
| 2894 |
|
|
if (!set->extended)
|
| 2895 |
|
|
decNumberZero (res);
|
| 2896 |
|
|
else
|
| 2897 |
|
|
{
|
| 2898 |
|
|
#endif
|
| 2899 |
|
|
if (op & DIVIDE)
|
| 2900 |
|
|
{
|
| 2901 |
|
|
residue = 0;
|
| 2902 |
|
|
exponent = lhs->exponent - rhs->exponent; /* ideal exponent */
|
| 2903 |
|
|
decNumberCopy (res, lhs); /* [zeros always fit] */
|
| 2904 |
|
|
res->bits = bits; /* sign as computed */
|
| 2905 |
|
|
res->exponent = exponent; /* exponent, too */
|
| 2906 |
|
|
decFinalize (res, set, &residue, status); /* check exponent */
|
| 2907 |
|
|
}
|
| 2908 |
|
|
else if (op & DIVIDEINT)
|
| 2909 |
|
|
{
|
| 2910 |
|
|
decNumberZero (res); /* integer 0 */
|
| 2911 |
|
|
res->bits = bits; /* sign as computed */
|
| 2912 |
|
|
}
|
| 2913 |
|
|
else
|
| 2914 |
|
|
{ /* a remainder */
|
| 2915 |
|
|
exponent = rhs->exponent; /* [save in case overwrite] */
|
| 2916 |
|
|
decNumberCopy (res, lhs); /* [zeros always fit] */
|
| 2917 |
|
|
if (exponent < res->exponent)
|
| 2918 |
|
|
res->exponent = exponent; /* use lower */
|
| 2919 |
|
|
}
|
| 2920 |
|
|
#if DECSUBSET
|
| 2921 |
|
|
}
|
| 2922 |
|
|
#endif
|
| 2923 |
|
|
break;
|
| 2924 |
|
|
}
|
| 2925 |
|
|
|
| 2926 |
|
|
/* Precalculate exponent. This starts off adjusted (and hence fits */
|
| 2927 |
|
|
/* in 31 bits) and becomes the usual unadjusted exponent as the */
|
| 2928 |
|
|
/* division proceeds. The order of evaluation is important, here, */
|
| 2929 |
|
|
/* to avoid wrap. */
|
| 2930 |
|
|
exponent =
|
| 2931 |
|
|
(lhs->exponent + lhs->digits) - (rhs->exponent + rhs->digits);
|
| 2932 |
|
|
|
| 2933 |
|
|
/* If the working exponent is -ve, then some quick exits are */
|
| 2934 |
|
|
/* possible because the quotient is known to be <1 */
|
| 2935 |
|
|
/* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
|
| 2936 |
|
|
if (exponent < 0 && !(op == DIVIDE))
|
| 2937 |
|
|
{
|
| 2938 |
|
|
if (op & DIVIDEINT)
|
| 2939 |
|
|
{
|
| 2940 |
|
|
decNumberZero (res); /* integer part is 0 */
|
| 2941 |
|
|
#if DECSUBSET
|
| 2942 |
|
|
if (set->extended)
|
| 2943 |
|
|
#endif
|
| 2944 |
|
|
res->bits = bits; /* set +/- zero */
|
| 2945 |
|
|
break;
|
| 2946 |
|
|
}
|
| 2947 |
|
|
/* we can fastpath remainders so long as the lhs has the */
|
| 2948 |
|
|
/* smaller (or equal) exponent */
|
| 2949 |
|
|
if (lhs->exponent <= rhs->exponent)
|
| 2950 |
|
|
{
|
| 2951 |
|
|
if (op & REMAINDER || exponent < -1)
|
| 2952 |
|
|
{
|
| 2953 |
|
|
/* It is REMAINDER or safe REMNEAR; result is [finished */
|
| 2954 |
|
|
/* clone of] lhs (r = x - 0*y) */
|
| 2955 |
|
|
residue = 0;
|
| 2956 |
|
|
decCopyFit (res, lhs, set, &residue, status);
|
| 2957 |
|
|
decFinish (res, set, &residue, status);
|
| 2958 |
|
|
break;
|
| 2959 |
|
|
}
|
| 2960 |
|
|
/* [unsafe REMNEAR drops through] */
|
| 2961 |
|
|
}
|
| 2962 |
|
|
} /* fastpaths */
|
| 2963 |
|
|
|
| 2964 |
|
|
/* We need long (slow) division; roll up the sleeves... */
|
| 2965 |
|
|
|
| 2966 |
|
|
/* The accumulator will hold the quotient of the division. */
|
| 2967 |
|
|
/* If it needs to be too long for stack storage, then allocate. */
|
| 2968 |
|
|
acclength = D2U (reqdigits + DECDPUN); /* in Units */
|
| 2969 |
|
|
if (acclength * sizeof (Unit) > sizeof (accbuff))
|
| 2970 |
|
|
{
|
| 2971 |
|
|
allocacc = (Unit *) malloc (acclength * sizeof (Unit));
|
| 2972 |
|
|
if (allocacc == NULL)
|
| 2973 |
|
|
{ /* hopeless -- abandon */
|
| 2974 |
|
|
*status |= DEC_Insufficient_storage;
|
| 2975 |
|
|
break;
|
| 2976 |
|
|
}
|
| 2977 |
|
|
acc = allocacc; /* use the allocated space */
|
| 2978 |
|
|
}
|
| 2979 |
|
|
|
| 2980 |
|
|
/* var1 is the padded LHS ready for subtractions. */
|
| 2981 |
|
|
/* If it needs to be too long for stack storage, then allocate. */
|
| 2982 |
|
|
/* The maximum units we need for var1 (long subtraction) is: */
|
| 2983 |
|
|
/* Enough for */
|
| 2984 |
|
|
/* (rhs->digits+reqdigits-1) -- to allow full slide to right */
|
| 2985 |
|
|
/* or (lhs->digits) -- to allow for long lhs */
|
| 2986 |
|
|
/* whichever is larger */
|
| 2987 |
|
|
/* +1 -- for rounding of slide to right */
|
| 2988 |
|
|
/* +1 -- for leading 0s */
|
| 2989 |
|
|
/* +1 -- for pre-adjust if a remainder or DIVIDEINT */
|
| 2990 |
|
|
/* [Note: unused units do not participate in decUnitAddSub data] */
|
| 2991 |
|
|
maxdigits = rhs->digits + reqdigits - 1;
|
| 2992 |
|
|
if (lhs->digits > maxdigits)
|
| 2993 |
|
|
maxdigits = lhs->digits;
|
| 2994 |
|
|
var1units = D2U (maxdigits) + 2;
|
| 2995 |
|
|
/* allocate a guard unit above msu1 for REMAINDERNEAR */
|
| 2996 |
|
|
if (!(op & DIVIDE))
|
| 2997 |
|
|
var1units++;
|
| 2998 |
|
|
if ((var1units + 1) * sizeof (Unit) > sizeof (varbuff))
|
| 2999 |
|
|
{
|
| 3000 |
|
|
varalloc = (Unit *) malloc ((var1units + 1) * sizeof (Unit));
|
| 3001 |
|
|
if (varalloc == NULL)
|
| 3002 |
|
|
{ /* hopeless -- abandon */
|
| 3003 |
|
|
*status |= DEC_Insufficient_storage;
|
| 3004 |
|
|
break;
|
| 3005 |
|
|
}
|
| 3006 |
|
|
var1 = varalloc; /* use the allocated space */
|
| 3007 |
|
|
}
|
| 3008 |
|
|
|
| 3009 |
|
|
/* Extend the lhs and rhs to full long subtraction length. The lhs */
|
| 3010 |
|
|
/* is truly extended into the var1 buffer, with 0 padding, so we can */
|
| 3011 |
|
|
/* subtract in place. The rhs (var2) has virtual padding */
|
| 3012 |
|
|
/* (implemented by decUnitAddSub). */
|
| 3013 |
|
|
/* We allocated one guard unit above msu1 for rem=rem+rem in REMAINDERNEAR */
|
| 3014 |
|
|
msu1 = var1 + var1units - 1; /* msu of var1 */
|
| 3015 |
|
|
source = lhs->lsu + D2U (lhs->digits) - 1; /* msu of input array */
|
| 3016 |
|
|
for (target = msu1; source >= lhs->lsu; source--, target--)
|
| 3017 |
|
|
*target = *source;
|
| 3018 |
|
|
for (; target >= var1; target--)
|
| 3019 |
|
|
*target = 0;
|
| 3020 |
|
|
|
| 3021 |
|
|
/* rhs (var2) is left-aligned with var1 at the start */
|
| 3022 |
|
|
var2ulen = var1units; /* rhs logical length (units) */
|
| 3023 |
|
|
var2units = D2U (rhs->digits); /* rhs actual length (units) */
|
| 3024 |
|
|
var2 = rhs->lsu; /* -> rhs array */
|
| 3025 |
|
|
msu2 = var2 + var2units - 1; /* -> msu of var2 [never changes] */
|
| 3026 |
|
|
/* now set up the variables which we'll use for estimating the */
|
| 3027 |
|
|
/* multiplication factor. If these variables are not exact, we add */
|
| 3028 |
|
|
/* 1 to make sure that we never overestimate the multiplier. */
|
| 3029 |
|
|
msu2plus = *msu2; /* it's value .. */
|
| 3030 |
|
|
if (var2units > 1)
|
| 3031 |
|
|
msu2plus++; /* .. +1 if any more */
|
| 3032 |
|
|
msu2pair = (eInt) * msu2 * (DECDPUNMAX + 1); /* top two pair .. */
|
| 3033 |
|
|
if (var2units > 1)
|
| 3034 |
|
|
{ /* .. [else treat 2nd as 0] */
|
| 3035 |
|
|
msu2pair += *(msu2 - 1); /* .. */
|
| 3036 |
|
|
if (var2units > 2)
|
| 3037 |
|
|
msu2pair++; /* .. +1 if any more */
|
| 3038 |
|
|
}
|
| 3039 |
|
|
|
| 3040 |
|
|
/* Since we are working in units, the units may have leading zeros, */
|
| 3041 |
|
|
/* but we calculated the exponent on the assumption that they are */
|
| 3042 |
|
|
/* both left-aligned. Adjust the exponent to compensate: add the */
|
| 3043 |
|
|
/* number of leading zeros in var1 msu and subtract those in var2 msu. */
|
| 3044 |
|
|
/* [We actually do this by counting the digits and negating, as */
|
| 3045 |
|
|
/* lead1=DECDPUN-digits1, and similarly for lead2.] */
|
| 3046 |
|
|
for (pow = &powers[1]; *msu1 >= *pow; pow++)
|
| 3047 |
|
|
exponent--;
|
| 3048 |
|
|
for (pow = &powers[1]; *msu2 >= *pow; pow++)
|
| 3049 |
|
|
exponent++;
|
| 3050 |
|
|
|
| 3051 |
|
|
/* Now, if doing an integer divide or remainder, we want to ensure */
|
| 3052 |
|
|
/* that the result will be Unit-aligned. To do this, we shift the */
|
| 3053 |
|
|
/* var1 accumulator towards least if need be. (It's much easier to */
|
| 3054 |
|
|
/* do this now than to reassemble the residue afterwards, if we are */
|
| 3055 |
|
|
/* doing a remainder.) Also ensure the exponent is not negative. */
|
| 3056 |
|
|
if (!(op & DIVIDE))
|
| 3057 |
|
|
{
|
| 3058 |
|
|
Unit *u;
|
| 3059 |
|
|
/* save the initial 'false' padding of var1, in digits */
|
| 3060 |
|
|
var1initpad = (var1units - D2U (lhs->digits)) * DECDPUN;
|
| 3061 |
|
|
/* Determine the shift to do. */
|
| 3062 |
|
|
if (exponent < 0)
|
| 3063 |
|
|
cut = -exponent;
|
| 3064 |
|
|
else
|
| 3065 |
|
|
cut = DECDPUN - exponent % DECDPUN;
|
| 3066 |
|
|
decShiftToLeast (var1, var1units, cut);
|
| 3067 |
|
|
exponent += cut; /* maintain numerical value */
|
| 3068 |
|
|
var1initpad -= cut; /* .. and reduce padding */
|
| 3069 |
|
|
/* clean any most-significant units we just emptied */
|
| 3070 |
|
|
for (u = msu1; cut >= DECDPUN; cut -= DECDPUN, u--)
|
| 3071 |
|
|
*u = 0;
|
| 3072 |
|
|
} /* align */
|
| 3073 |
|
|
else
|
| 3074 |
|
|
{ /* is DIVIDE */
|
| 3075 |
|
|
maxexponent = lhs->exponent - rhs->exponent; /* save */
|
| 3076 |
|
|
/* optimization: if the first iteration will just produce 0, */
|
| 3077 |
|
|
/* preadjust to skip it [valid for DIVIDE only] */
|
| 3078 |
|
|
if (*msu1 < *msu2)
|
| 3079 |
|
|
{
|
| 3080 |
|
|
var2ulen--; /* shift down */
|
| 3081 |
|
|
exponent -= DECDPUN; /* update the exponent */
|
| 3082 |
|
|
}
|
| 3083 |
|
|
}
|
| 3084 |
|
|
|
| 3085 |
|
|
/* ---- start the long-division loops ------------------------------ */
|
| 3086 |
|
|
accunits = 0; /* no units accumulated yet */
|
| 3087 |
|
|
accdigits = 0; /* .. or digits */
|
| 3088 |
|
|
accnext = acc + acclength - 1; /* -> msu of acc [NB: allows digits+1] */
|
| 3089 |
|
|
for (;;)
|
| 3090 |
|
|
{ /* outer forever loop */
|
| 3091 |
|
|
thisunit = 0; /* current unit assumed 0 */
|
| 3092 |
|
|
/* find the next unit */
|
| 3093 |
|
|
for (;;)
|
| 3094 |
|
|
{ /* inner forever loop */
|
| 3095 |
|
|
/* strip leading zero units [from either pre-adjust or from */
|
| 3096 |
|
|
/* subtract last time around]. Leave at least one unit. */
|
| 3097 |
|
|
for (; *msu1 == 0 && msu1 > var1; msu1--)
|
| 3098 |
|
|
var1units--;
|
| 3099 |
|
|
|
| 3100 |
|
|
if (var1units < var2ulen)
|
| 3101 |
|
|
break; /* var1 too low for subtract */
|
| 3102 |
|
|
if (var1units == var2ulen)
|
| 3103 |
|
|
{ /* unit-by-unit compare needed */
|
| 3104 |
|
|
/* compare the two numbers, from msu */
|
| 3105 |
|
|
Unit *pv1, v2; /* units to compare */
|
| 3106 |
|
|
const Unit *pv2; /* units to compare */
|
| 3107 |
|
|
pv2 = msu2; /* -> msu */
|
| 3108 |
|
|
for (pv1 = msu1;; pv1--, pv2--)
|
| 3109 |
|
|
{
|
| 3110 |
|
|
/* v1=*pv1 -- always OK */
|
| 3111 |
|
|
v2 = 0; /* assume in padding */
|
| 3112 |
|
|
if (pv2 >= var2)
|
| 3113 |
|
|
v2 = *pv2; /* in range */
|
| 3114 |
|
|
if (*pv1 != v2)
|
| 3115 |
|
|
break; /* no longer the same */
|
| 3116 |
|
|
if (pv1 == var1)
|
| 3117 |
|
|
break; /* done; leave pv1 as is */
|
| 3118 |
|
|
}
|
| 3119 |
|
|
/* here when all inspected or a difference seen */
|
| 3120 |
|
|
if (*pv1 < v2)
|
| 3121 |
|
|
break; /* var1 too low to subtract */
|
| 3122 |
|
|
if (*pv1 == v2)
|
| 3123 |
|
|
{ /* var1 == var2 */
|
| 3124 |
|
|
/* reach here if var1 and var2 are identical; subtraction */
|
| 3125 |
|
|
/* would increase digit by one, and the residue will be 0 so */
|
| 3126 |
|
|
/* we are done; leave the loop with residue set to 0. */
|
| 3127 |
|
|
thisunit++; /* as though subtracted */
|
| 3128 |
|
|
*var1 = 0; /* set var1 to 0 */
|
| 3129 |
|
|
var1units = 1; /* .. */
|
| 3130 |
|
|
break; /* from inner */
|
| 3131 |
|
|
} /* var1 == var2 */
|
| 3132 |
|
|
/* *pv1>v2. Prepare for real subtraction; the lengths are equal */
|
| 3133 |
|
|
/* Estimate the multiplier (there's always a msu1-1)... */
|
| 3134 |
|
|
/* Bring in two units of var2 to provide a good estimate. */
|
| 3135 |
|
|
mult =
|
| 3136 |
|
|
(Int) (((eInt) * msu1 * (DECDPUNMAX + 1) +
|
| 3137 |
|
|
*(msu1 - 1)) / msu2pair);
|
| 3138 |
|
|
} /* lengths the same */
|
| 3139 |
|
|
else
|
| 3140 |
|
|
{ /* var1units > var2ulen, so subtraction is safe */
|
| 3141 |
|
|
/* The var2 msu is one unit towards the lsu of the var1 msu, */
|
| 3142 |
|
|
/* so we can only use one unit for var2. */
|
| 3143 |
|
|
mult =
|
| 3144 |
|
|
(Int) (((eInt) * msu1 * (DECDPUNMAX + 1) +
|
| 3145 |
|
|
*(msu1 - 1)) / msu2plus);
|
| 3146 |
|
|
}
|
| 3147 |
|
|
if (mult == 0)
|
| 3148 |
|
|
mult = 1; /* must always be at least 1 */
|
| 3149 |
|
|
/* subtraction needed; var1 is > var2 */
|
| 3150 |
|
|
thisunit = (Unit) (thisunit + mult); /* accumulate */
|
| 3151 |
|
|
/* subtract var1-var2, into var1; only the overlap needs */
|
| 3152 |
|
|
/* processing, as we are in place */
|
| 3153 |
|
|
shift = var2ulen - var2units;
|
| 3154 |
|
|
#if DECTRACE
|
| 3155 |
|
|
decDumpAr ('1', &var1[shift], var1units - shift);
|
| 3156 |
|
|
decDumpAr ('2', var2, var2units);
|
| 3157 |
|
|
printf ("m=%d\n", -mult);
|
| 3158 |
|
|
#endif
|
| 3159 |
|
|
decUnitAddSub (&var1[shift], var1units - shift,
|
| 3160 |
|
|
var2, var2units, 0, &var1[shift], -mult);
|
| 3161 |
|
|
#if DECTRACE
|
| 3162 |
|
|
decDumpAr ('#', &var1[shift], var1units - shift);
|
| 3163 |
|
|
#endif
|
| 3164 |
|
|
/* var1 now probably has leading zeros; these are removed at the */
|
| 3165 |
|
|
/* top of the inner loop. */
|
| 3166 |
|
|
} /* inner loop */
|
| 3167 |
|
|
|
| 3168 |
|
|
/* We have the next unit; unless it's a leading zero, add to acc */
|
| 3169 |
|
|
if (accunits != 0 || thisunit != 0)
|
| 3170 |
|
|
{ /* put the unit we got */
|
| 3171 |
|
|
*accnext = thisunit; /* store in accumulator */
|
| 3172 |
|
|
/* account exactly for the digits we got */
|
| 3173 |
|
|
if (accunits == 0)
|
| 3174 |
|
|
{
|
| 3175 |
|
|
accdigits++; /* at least one */
|
| 3176 |
|
|
for (pow = &powers[1]; thisunit >= *pow; pow++)
|
| 3177 |
|
|
accdigits++;
|
| 3178 |
|
|
}
|
| 3179 |
|
|
else
|
| 3180 |
|
|
accdigits += DECDPUN;
|
| 3181 |
|
|
accunits++; /* update count */
|
| 3182 |
|
|
accnext--; /* ready for next */
|
| 3183 |
|
|
if (accdigits > reqdigits)
|
| 3184 |
|
|
break; /* we have all we need */
|
| 3185 |
|
|
}
|
| 3186 |
|
|
|
| 3187 |
|
|
/* if the residue is zero, we're done (unless divide or */
|
| 3188 |
|
|
/* divideInteger and we haven't got enough digits yet) */
|
| 3189 |
|
|
if (*var1 == 0 && var1units == 1)
|
| 3190 |
|
|
{ /* residue is 0 */
|
| 3191 |
|
|
if (op & (REMAINDER | REMNEAR))
|
| 3192 |
|
|
break;
|
| 3193 |
|
|
if ((op & DIVIDE) && (exponent <= maxexponent))
|
| 3194 |
|
|
break;
|
| 3195 |
|
|
/* [drop through if divideInteger] */
|
| 3196 |
|
|
}
|
| 3197 |
|
|
/* we've also done enough if calculating remainder or integer */
|
| 3198 |
|
|
/* divide and we just did the last ('units') unit */
|
| 3199 |
|
|
if (exponent == 0 && !(op & DIVIDE))
|
| 3200 |
|
|
break;
|
| 3201 |
|
|
|
| 3202 |
|
|
/* to get here, var1 is less than var2, so divide var2 by the per- */
|
| 3203 |
|
|
/* Unit power of ten and go for the next digit */
|
| 3204 |
|
|
var2ulen--; /* shift down */
|
| 3205 |
|
|
exponent -= DECDPUN; /* update the exponent */
|
| 3206 |
|
|
} /* outer loop */
|
| 3207 |
|
|
|
| 3208 |
|
|
/* ---- division is complete --------------------------------------- */
|
| 3209 |
|
|
/* here: acc has at least reqdigits+1 of good results (or fewer */
|
| 3210 |
|
|
/* if early stop), starting at accnext+1 (its lsu) */
|
| 3211 |
|
|
/* var1 has any residue at the stopping point */
|
| 3212 |
|
|
/* accunits is the number of digits we collected in acc */
|
| 3213 |
|
|
if (accunits == 0)
|
| 3214 |
|
|
{ /* acc is 0 */
|
| 3215 |
|
|
accunits = 1; /* show we have one .. */
|
| 3216 |
|
|
accdigits = 1; /* .. */
|
| 3217 |
|
|
*accnext = 0; /* .. whose value is 0 */
|
| 3218 |
|
|
}
|
| 3219 |
|
|
else
|
| 3220 |
|
|
accnext++; /* back to last placed */
|
| 3221 |
|
|
/* accnext now -> lowest unit of result */
|
| 3222 |
|
|
|
| 3223 |
|
|
residue = 0; /* assume no residue */
|
| 3224 |
|
|
if (op & DIVIDE)
|
| 3225 |
|
|
{
|
| 3226 |
|
|
/* record the presence of any residue, for rounding */
|
| 3227 |
|
|
if (*var1 != 0 || var1units > 1)
|
| 3228 |
|
|
residue = 1;
|
| 3229 |
|
|
else
|
| 3230 |
|
|
{ /* no residue */
|
| 3231 |
|
|
/* We had an exact division; clean up spurious trailing 0s. */
|
| 3232 |
|
|
/* There will be at most DECDPUN-1, from the final multiply, */
|
| 3233 |
|
|
/* and then only if the result is non-0 (and even) and the */
|
| 3234 |
|
|
/* exponent is 'loose'. */
|
| 3235 |
|
|
#if DECDPUN>1
|
| 3236 |
|
|
Unit lsu = *accnext;
|
| 3237 |
|
|
if (!(lsu & 0x01) && (lsu != 0))
|
| 3238 |
|
|
{
|
| 3239 |
|
|
/* count the trailing zeros */
|
| 3240 |
|
|
Int drop = 0;
|
| 3241 |
|
|
for (;; drop++)
|
| 3242 |
|
|
{ /* [will terminate because lsu!=0] */
|
| 3243 |
|
|
if (exponent >= maxexponent)
|
| 3244 |
|
|
break; /* don't chop real 0s */
|
| 3245 |
|
|
#if DECDPUN<=4
|
| 3246 |
|
|
if ((lsu - QUOT10 (lsu, drop + 1)
|
| 3247 |
|
|
* powers[drop + 1]) != 0)
|
| 3248 |
|
|
break; /* found non-0 digit */
|
| 3249 |
|
|
#else
|
| 3250 |
|
|
if (lsu % powers[drop + 1] != 0)
|
| 3251 |
|
|
break; /* found non-0 digit */
|
| 3252 |
|
|
#endif
|
| 3253 |
|
|
exponent++;
|
| 3254 |
|
|
}
|
| 3255 |
|
|
if (drop > 0)
|
| 3256 |
|
|
{
|
| 3257 |
|
|
accunits = decShiftToLeast (accnext, accunits, drop);
|
| 3258 |
|
|
accdigits = decGetDigits (accnext, accunits);
|
| 3259 |
|
|
accunits = D2U (accdigits);
|
| 3260 |
|
|
/* [exponent was adjusted in the loop] */
|
| 3261 |
|
|
}
|
| 3262 |
|
|
} /* neither odd nor 0 */
|
| 3263 |
|
|
#endif
|
| 3264 |
|
|
} /* exact divide */
|
| 3265 |
|
|
} /* divide */
|
| 3266 |
|
|
else /* op!=DIVIDE */
|
| 3267 |
|
|
{
|
| 3268 |
|
|
/* check for coefficient overflow */
|
| 3269 |
|
|
if (accdigits + exponent > reqdigits)
|
| 3270 |
|
|
{
|
| 3271 |
|
|
*status |= DEC_Division_impossible;
|
| 3272 |
|
|
break;
|
| 3273 |
|
|
}
|
| 3274 |
|
|
if (op & (REMAINDER | REMNEAR))
|
| 3275 |
|
|
{
|
| 3276 |
|
|
/* [Here, the exponent will be 0, because we adjusted var1 */
|
| 3277 |
|
|
/* appropriately.] */
|
| 3278 |
|
|
Int postshift; /* work */
|
| 3279 |
|
|
Flag wasodd = 0; /* integer was odd */
|
| 3280 |
|
|
Unit *quotlsu; /* for save */
|
| 3281 |
|
|
Int quotdigits; /* .. */
|
| 3282 |
|
|
|
| 3283 |
|
|
/* Fastpath when residue is truly 0 is worthwhile [and */
|
| 3284 |
|
|
/* simplifies the code below] */
|
| 3285 |
|
|
if (*var1 == 0 && var1units == 1)
|
| 3286 |
|
|
{ /* residue is 0 */
|
| 3287 |
|
|
Int exp = lhs->exponent; /* save min(exponents) */
|
| 3288 |
|
|
if (rhs->exponent < exp)
|
| 3289 |
|
|
exp = rhs->exponent;
|
| 3290 |
|
|
decNumberZero (res); /* 0 coefficient */
|
| 3291 |
|
|
#if DECSUBSET
|
| 3292 |
|
|
if (set->extended)
|
| 3293 |
|
|
#endif
|
| 3294 |
|
|
res->exponent = exp; /* .. with proper exponent */
|
| 3295 |
|
|
break;
|
| 3296 |
|
|
}
|
| 3297 |
|
|
/* note if the quotient was odd */
|
| 3298 |
|
|
if (*accnext & 0x01)
|
| 3299 |
|
|
wasodd = 1; /* acc is odd */
|
| 3300 |
|
|
quotlsu = accnext; /* save in case need to reinspect */
|
| 3301 |
|
|
quotdigits = accdigits; /* .. */
|
| 3302 |
|
|
|
| 3303 |
|
|
/* treat the residue, in var1, as the value to return, via acc */
|
| 3304 |
|
|
/* calculate the unused zero digits. This is the smaller of: */
|
| 3305 |
|
|
/* var1 initial padding (saved above) */
|
| 3306 |
|
|
/* var2 residual padding, which happens to be given by: */
|
| 3307 |
|
|
postshift =
|
| 3308 |
|
|
var1initpad + exponent - lhs->exponent + rhs->exponent;
|
| 3309 |
|
|
/* [the 'exponent' term accounts for the shifts during divide] */
|
| 3310 |
|
|
if (var1initpad < postshift)
|
| 3311 |
|
|
postshift = var1initpad;
|
| 3312 |
|
|
|
| 3313 |
|
|
/* shift var1 the requested amount, and adjust its digits */
|
| 3314 |
|
|
var1units = decShiftToLeast (var1, var1units, postshift);
|
| 3315 |
|
|
accnext = var1;
|
| 3316 |
|
|
accdigits = decGetDigits (var1, var1units);
|
| 3317 |
|
|
accunits = D2U (accdigits);
|
| 3318 |
|
|
|
| 3319 |
|
|
exponent = lhs->exponent; /* exponent is smaller of lhs & rhs */
|
| 3320 |
|
|
if (rhs->exponent < exponent)
|
| 3321 |
|
|
exponent = rhs->exponent;
|
| 3322 |
|
|
bits = lhs->bits; /* remainder sign is always as lhs */
|
| 3323 |
|
|
|
| 3324 |
|
|
/* Now correct the result if we are doing remainderNear; if it */
|
| 3325 |
|
|
/* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
|
| 3326 |
|
|
/* the integer was odd then the result should be rem-rhs. */
|
| 3327 |
|
|
if (op & REMNEAR)
|
| 3328 |
|
|
{
|
| 3329 |
|
|
Int compare, tarunits; /* work */
|
| 3330 |
|
|
Unit *up; /* .. */
|
| 3331 |
|
|
|
| 3332 |
|
|
|
| 3333 |
|
|
/* calculate remainder*2 into the var1 buffer (which has */
|
| 3334 |
|
|
/* 'headroom' of an extra unit and hence enough space) */
|
| 3335 |
|
|
/* [a dedicated 'double' loop would be faster, here] */
|
| 3336 |
|
|
tarunits =
|
| 3337 |
|
|
decUnitAddSub (accnext, accunits, accnext, accunits, 0,
|
| 3338 |
|
|
accnext, 1);
|
| 3339 |
|
|
/* decDumpAr('r', accnext, tarunits); */
|
| 3340 |
|
|
|
| 3341 |
|
|
/* Here, accnext (var1) holds tarunits Units with twice the */
|
| 3342 |
|
|
/* remainder's coefficient, which we must now compare to the */
|
| 3343 |
|
|
/* RHS. The remainder's exponent may be smaller than the RHS's. */
|
| 3344 |
|
|
compare =
|
| 3345 |
|
|
decUnitCompare (accnext, tarunits, rhs->lsu,
|
| 3346 |
|
|
D2U (rhs->digits),
|
| 3347 |
|
|
rhs->exponent - exponent);
|
| 3348 |
|
|
if (compare == BADINT)
|
| 3349 |
|
|
{ /* deep trouble */
|
| 3350 |
|
|
*status |= DEC_Insufficient_storage;
|
| 3351 |
|
|
break;
|
| 3352 |
|
|
}
|
| 3353 |
|
|
|
| 3354 |
|
|
/* now restore the remainder by dividing by two; we know the */
|
| 3355 |
|
|
/* lsu is even. */
|
| 3356 |
|
|
for (up = accnext; up < accnext + tarunits; up++)
|
| 3357 |
|
|
{
|
| 3358 |
|
|
Int half; /* half to add to lower unit */
|
| 3359 |
|
|
half = *up & 0x01;
|
| 3360 |
|
|
*up /= 2; /* [shift] */
|
| 3361 |
|
|
if (!half)
|
| 3362 |
|
|
continue;
|
| 3363 |
|
|
*(up - 1) += (DECDPUNMAX + 1) / 2;
|
| 3364 |
|
|
}
|
| 3365 |
|
|
/* [accunits still describes the original remainder length] */
|
| 3366 |
|
|
|
| 3367 |
|
|
if (compare > 0 || (compare == 0 && wasodd))
|
| 3368 |
|
|
{ /* adjustment needed */
|
| 3369 |
|
|
Int exp, expunits, exprem; /* work */
|
| 3370 |
|
|
/* This is effectively causing round-up of the quotient, */
|
| 3371 |
|
|
/* so if it was the rare case where it was full and all */
|
| 3372 |
|
|
/* nines, it would overflow and hence division-impossible */
|
| 3373 |
|
|
/* should be raised */
|
| 3374 |
|
|
Flag allnines = 0; /* 1 if quotient all nines */
|
| 3375 |
|
|
if (quotdigits == reqdigits)
|
| 3376 |
|
|
{ /* could be borderline */
|
| 3377 |
|
|
for (up = quotlsu;; up++)
|
| 3378 |
|
|
{
|
| 3379 |
|
|
if (quotdigits > DECDPUN)
|
| 3380 |
|
|
{
|
| 3381 |
|
|
if (*up != DECDPUNMAX)
|
| 3382 |
|
|
break; /* non-nines */
|
| 3383 |
|
|
}
|
| 3384 |
|
|
else
|
| 3385 |
|
|
{ /* this is the last Unit */
|
| 3386 |
|
|
if (*up == powers[quotdigits] - 1)
|
| 3387 |
|
|
allnines = 1;
|
| 3388 |
|
|
break;
|
| 3389 |
|
|
}
|
| 3390 |
|
|
quotdigits -= DECDPUN; /* checked those digits */
|
| 3391 |
|
|
} /* up */
|
| 3392 |
|
|
} /* borderline check */
|
| 3393 |
|
|
if (allnines)
|
| 3394 |
|
|
{
|
| 3395 |
|
|
*status |= DEC_Division_impossible;
|
| 3396 |
|
|
break;
|
| 3397 |
|
|
}
|
| 3398 |
|
|
|
| 3399 |
|
|
/* we need rem-rhs; the sign will invert. Again we can */
|
| 3400 |
|
|
/* safely use var1 for the working Units array. */
|
| 3401 |
|
|
exp = rhs->exponent - exponent; /* RHS padding needed */
|
| 3402 |
|
|
/* Calculate units and remainder from exponent. */
|
| 3403 |
|
|
expunits = exp / DECDPUN;
|
| 3404 |
|
|
exprem = exp % DECDPUN;
|
| 3405 |
|
|
/* subtract [A+B*(-m)]; the result will always be negative */
|
| 3406 |
|
|
accunits = -decUnitAddSub (accnext, accunits,
|
| 3407 |
|
|
rhs->lsu, D2U (rhs->digits),
|
| 3408 |
|
|
expunits, accnext,
|
| 3409 |
|
|
-(Int) powers[exprem]);
|
| 3410 |
|
|
accdigits = decGetDigits (accnext, accunits); /* count digits exactly */
|
| 3411 |
|
|
accunits = D2U (accdigits); /* and recalculate the units for copy */
|
| 3412 |
|
|
/* [exponent is as for original remainder] */
|
| 3413 |
|
|
bits ^= DECNEG; /* flip the sign */
|
| 3414 |
|
|
}
|
| 3415 |
|
|
} /* REMNEAR */
|
| 3416 |
|
|
} /* REMAINDER or REMNEAR */
|
| 3417 |
|
|
} /* not DIVIDE */
|
| 3418 |
|
|
|
| 3419 |
|
|
/* Set exponent and bits */
|
| 3420 |
|
|
res->exponent = exponent;
|
| 3421 |
|
|
res->bits = (uByte) (bits & DECNEG); /* [cleaned] */
|
| 3422 |
|
|
|
| 3423 |
|
|
/* Now the coefficient. */
|
| 3424 |
|
|
decSetCoeff (res, set, accnext, accdigits, &residue, status);
|
| 3425 |
|
|
|
| 3426 |
|
|
decFinish (res, set, &residue, status); /* final cleanup */
|
| 3427 |
|
|
|
| 3428 |
|
|
#if DECSUBSET
|
| 3429 |
|
|
/* If a divide then strip trailing zeros if subset [after round] */
|
| 3430 |
|
|
if (!set->extended && (op == DIVIDE))
|
| 3431 |
|
|
decTrim (res, 0, &dropped);
|
| 3432 |
|
|
#endif
|
| 3433 |
|
|
}
|
| 3434 |
|
|
while (0); /* end protected */
|
| 3435 |
|
|
|
| 3436 |
|
|
if (varalloc != NULL)
|
| 3437 |
|
|
free (varalloc); /* drop any storage we used */
|
| 3438 |
|
|
if (allocacc != NULL)
|
| 3439 |
|
|
free (allocacc); /* .. */
|
| 3440 |
|
|
if (allocrhs != NULL)
|
| 3441 |
|
|
free (allocrhs); /* .. */
|
| 3442 |
|
|
if (alloclhs != NULL)
|
| 3443 |
|
|
free (alloclhs); /* .. */
|
| 3444 |
|
|
return res;
|
| 3445 |
|
|
}
|
| 3446 |
|
|
|
| 3447 |
|
|
/* ------------------------------------------------------------------ */
|
| 3448 |
|
|
/* decMultiplyOp -- multiplication operation */
|
| 3449 |
|
|
/* */
|
| 3450 |
|
|
/* This routine performs the multiplication C=A x B. */
|
| 3451 |
|
|
/* */
|
| 3452 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
|
| 3453 |
|
|
/* lhs is A */
|
| 3454 |
|
|
/* rhs is B */
|
| 3455 |
|
|
/* set is the context */
|
| 3456 |
|
|
/* status is the usual accumulator */
|
| 3457 |
|
|
/* */
|
| 3458 |
|
|
/* C must have space for set->digits digits. */
|
| 3459 |
|
|
/* */
|
| 3460 |
|
|
/* ------------------------------------------------------------------ */
|
| 3461 |
|
|
/* Note: We use 'long' multiplication rather than Karatsuba, as the */
|
| 3462 |
|
|
/* latter would give only a minor improvement for the short numbers */
|
| 3463 |
|
|
/* we expect to handle most (and uses much more memory). */
|
| 3464 |
|
|
/* */
|
| 3465 |
|
|
/* We always have to use a buffer for the accumulator. */
|
| 3466 |
|
|
/* ------------------------------------------------------------------ */
|
| 3467 |
|
|
static decNumber *
|
| 3468 |
|
|
decMultiplyOp (decNumber * res, const decNumber * lhs,
|
| 3469 |
|
|
const decNumber * rhs, decContext * set, uInt * status)
|
| 3470 |
|
|
{
|
| 3471 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 3472 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 3473 |
|
|
Unit accbuff[D2U (DECBUFFER * 2 + 1)]; /* local buffer (+1 in case DECBUFFER==0) */
|
| 3474 |
|
|
Unit *acc = accbuff; /* -> accumulator array for exact result */
|
| 3475 |
|
|
Unit *allocacc = NULL; /* -> allocated buffer, iff allocated */
|
| 3476 |
|
|
const Unit *mer, *mermsup; /* work */
|
| 3477 |
|
|
Int accunits; /* Units of accumulator in use */
|
| 3478 |
|
|
Int madlength; /* Units in multiplicand */
|
| 3479 |
|
|
Int shift; /* Units to shift multiplicand by */
|
| 3480 |
|
|
Int need; /* Accumulator units needed */
|
| 3481 |
|
|
Int exponent; /* work */
|
| 3482 |
|
|
Int residue = 0; /* rounding residue */
|
| 3483 |
|
|
uByte bits; /* result sign */
|
| 3484 |
|
|
uByte merged; /* merged flags */
|
| 3485 |
|
|
|
| 3486 |
|
|
#if DECCHECK
|
| 3487 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 3488 |
|
|
return res;
|
| 3489 |
|
|
#endif
|
| 3490 |
|
|
|
| 3491 |
|
|
do
|
| 3492 |
|
|
{ /* protect allocated storage */
|
| 3493 |
|
|
#if DECSUBSET
|
| 3494 |
|
|
if (!set->extended)
|
| 3495 |
|
|
{
|
| 3496 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 3497 |
|
|
if (lhs->digits > set->digits)
|
| 3498 |
|
|
{
|
| 3499 |
|
|
alloclhs = decRoundOperand (lhs, set, status);
|
| 3500 |
|
|
if (alloclhs == NULL)
|
| 3501 |
|
|
break;
|
| 3502 |
|
|
lhs = alloclhs;
|
| 3503 |
|
|
}
|
| 3504 |
|
|
if (rhs->digits > set->digits)
|
| 3505 |
|
|
{
|
| 3506 |
|
|
allocrhs = decRoundOperand (rhs, set, status);
|
| 3507 |
|
|
if (allocrhs == NULL)
|
| 3508 |
|
|
break;
|
| 3509 |
|
|
rhs = allocrhs;
|
| 3510 |
|
|
}
|
| 3511 |
|
|
}
|
| 3512 |
|
|
#endif
|
| 3513 |
|
|
/* [following code does not require input rounding] */
|
| 3514 |
|
|
|
| 3515 |
|
|
/* precalculate result sign */
|
| 3516 |
|
|
bits = (uByte) ((lhs->bits ^ rhs->bits) & DECNEG);
|
| 3517 |
|
|
|
| 3518 |
|
|
/* handle infinities and NaNs */
|
| 3519 |
|
|
merged = (lhs->bits | rhs->bits) & DECSPECIAL;
|
| 3520 |
|
|
if (merged)
|
| 3521 |
|
|
{ /* a special bit set */
|
| 3522 |
|
|
if (merged & (DECSNAN | DECNAN))
|
| 3523 |
|
|
{ /* one or two NaNs */
|
| 3524 |
|
|
decNaNs (res, lhs, rhs, status);
|
| 3525 |
|
|
break;
|
| 3526 |
|
|
}
|
| 3527 |
|
|
/* one or two infinities. Infinity * 0 is invalid */
|
| 3528 |
|
|
if (((lhs->bits & DECSPECIAL) == 0 && ISZERO (lhs))
|
| 3529 |
|
|
|| ((rhs->bits & DECSPECIAL) == 0 && ISZERO (rhs)))
|
| 3530 |
|
|
{
|
| 3531 |
|
|
*status |= DEC_Invalid_operation;
|
| 3532 |
|
|
break;
|
| 3533 |
|
|
}
|
| 3534 |
|
|
decNumberZero (res);
|
| 3535 |
|
|
res->bits = bits | DECINF; /* infinity */
|
| 3536 |
|
|
break;
|
| 3537 |
|
|
}
|
| 3538 |
|
|
|
| 3539 |
|
|
/* For best speed, as in DMSRCN, we use the shorter number as the */
|
| 3540 |
|
|
/* multiplier (rhs) and the longer as the multiplicand (lhs) */
|
| 3541 |
|
|
if (lhs->digits < rhs->digits)
|
| 3542 |
|
|
{ /* swap... */
|
| 3543 |
|
|
const decNumber *hold = lhs;
|
| 3544 |
|
|
lhs = rhs;
|
| 3545 |
|
|
rhs = hold;
|
| 3546 |
|
|
}
|
| 3547 |
|
|
|
| 3548 |
|
|
/* if accumulator is too long for local storage, then allocate */
|
| 3549 |
|
|
need = D2U (lhs->digits) + D2U (rhs->digits); /* maximum units in result */
|
| 3550 |
|
|
if (need * sizeof (Unit) > sizeof (accbuff))
|
| 3551 |
|
|
{
|
| 3552 |
|
|
allocacc = (Unit *) malloc (need * sizeof (Unit));
|
| 3553 |
|
|
if (allocacc == NULL)
|
| 3554 |
|
|
{
|
| 3555 |
|
|
*status |= DEC_Insufficient_storage;
|
| 3556 |
|
|
break;
|
| 3557 |
|
|
}
|
| 3558 |
|
|
acc = allocacc; /* use the allocated space */
|
| 3559 |
|
|
}
|
| 3560 |
|
|
|
| 3561 |
|
|
/* Now the main long multiplication loop */
|
| 3562 |
|
|
/* Unlike the equivalent in the IBM Java implementation, there */
|
| 3563 |
|
|
/* is no advantage in calculating from msu to lsu. So we do it */
|
| 3564 |
|
|
/* by the book, as it were. */
|
| 3565 |
|
|
/* Each iteration calculates ACC=ACC+MULTAND*MULT */
|
| 3566 |
|
|
accunits = 1; /* accumulator starts at '0' */
|
| 3567 |
|
|
*acc = 0; /* .. (lsu=0) */
|
| 3568 |
|
|
shift = 0; /* no multiplicand shift at first */
|
| 3569 |
|
|
madlength = D2U (lhs->digits); /* we know this won't change */
|
| 3570 |
|
|
mermsup = rhs->lsu + D2U (rhs->digits); /* -> msu+1 of multiplier */
|
| 3571 |
|
|
|
| 3572 |
|
|
for (mer = rhs->lsu; mer < mermsup; mer++)
|
| 3573 |
|
|
{
|
| 3574 |
|
|
/* Here, *mer is the next Unit in the multiplier to use */
|
| 3575 |
|
|
/* If non-zero [optimization] add it... */
|
| 3576 |
|
|
if (*mer != 0)
|
| 3577 |
|
|
{
|
| 3578 |
|
|
accunits =
|
| 3579 |
|
|
decUnitAddSub (&acc[shift], accunits - shift, lhs->lsu,
|
| 3580 |
|
|
madlength, 0, &acc[shift], *mer) + shift;
|
| 3581 |
|
|
}
|
| 3582 |
|
|
else
|
| 3583 |
|
|
{ /* extend acc with a 0; we'll use it shortly */
|
| 3584 |
|
|
/* [this avoids length of <=0 later] */
|
| 3585 |
|
|
*(acc + accunits) = 0;
|
| 3586 |
|
|
accunits++;
|
| 3587 |
|
|
}
|
| 3588 |
|
|
/* multiply multiplicand by 10**DECDPUN for next Unit to left */
|
| 3589 |
|
|
shift++; /* add this for 'logical length' */
|
| 3590 |
|
|
} /* n */
|
| 3591 |
|
|
#if DECTRACE
|
| 3592 |
|
|
/* Show exact result */
|
| 3593 |
|
|
decDumpAr ('*', acc, accunits);
|
| 3594 |
|
|
#endif
|
| 3595 |
|
|
|
| 3596 |
|
|
/* acc now contains the exact result of the multiplication */
|
| 3597 |
|
|
/* Build a decNumber from it, noting if any residue */
|
| 3598 |
|
|
res->bits = bits; /* set sign */
|
| 3599 |
|
|
res->digits = decGetDigits (acc, accunits); /* count digits exactly */
|
| 3600 |
|
|
|
| 3601 |
|
|
/* We might have a 31-bit wrap in calculating the exponent. */
|
| 3602 |
|
|
/* This can only happen if both input exponents are negative and */
|
| 3603 |
|
|
/* both their magnitudes are large. If we did wrap, we set a safe */
|
| 3604 |
|
|
/* very negative exponent, from which decFinalize() will raise a */
|
| 3605 |
|
|
/* hard underflow. */
|
| 3606 |
|
|
exponent = lhs->exponent + rhs->exponent; /* calculate exponent */
|
| 3607 |
|
|
if (lhs->exponent < 0 && rhs->exponent < 0 && exponent > 0)
|
| 3608 |
|
|
exponent = -2 * DECNUMMAXE; /* force underflow */
|
| 3609 |
|
|
res->exponent = exponent; /* OK to overwrite now */
|
| 3610 |
|
|
|
| 3611 |
|
|
/* Set the coefficient. If any rounding, residue records */
|
| 3612 |
|
|
decSetCoeff (res, set, acc, res->digits, &residue, status);
|
| 3613 |
|
|
|
| 3614 |
|
|
decFinish (res, set, &residue, status); /* final cleanup */
|
| 3615 |
|
|
}
|
| 3616 |
|
|
while (0); /* end protected */
|
| 3617 |
|
|
|
| 3618 |
|
|
if (allocacc != NULL)
|
| 3619 |
|
|
free (allocacc); /* drop any storage we used */
|
| 3620 |
|
|
if (allocrhs != NULL)
|
| 3621 |
|
|
free (allocrhs); /* .. */
|
| 3622 |
|
|
if (alloclhs != NULL)
|
| 3623 |
|
|
free (alloclhs); /* .. */
|
| 3624 |
|
|
return res;
|
| 3625 |
|
|
}
|
| 3626 |
|
|
|
| 3627 |
|
|
/* ------------------------------------------------------------------ */
|
| 3628 |
|
|
/* decQuantizeOp -- force exponent to requested value */
|
| 3629 |
|
|
/* */
|
| 3630 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 3631 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 3632 |
|
|
/* of C has the value B or matches the exponent of B. */
|
| 3633 |
|
|
/* The numerical value of C will equal A, except for the effects of */
|
| 3634 |
|
|
/* any rounding that occurred. */
|
| 3635 |
|
|
/* */
|
| 3636 |
|
|
/* res is C, the result. C may be A or B */
|
| 3637 |
|
|
/* lhs is A, the number to adjust */
|
| 3638 |
|
|
/* rhs is B, the requested exponent */
|
| 3639 |
|
|
/* set is the context */
|
| 3640 |
|
|
/* quant is 1 for quantize or 0 for rescale */
|
| 3641 |
|
|
/* status is the status accumulator (this can be called without */
|
| 3642 |
|
|
/* risk of control loss) */
|
| 3643 |
|
|
/* */
|
| 3644 |
|
|
/* C must have space for set->digits digits. */
|
| 3645 |
|
|
/* */
|
| 3646 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 3647 |
|
|
/* after the operation is guaranteed to be that requested. */
|
| 3648 |
|
|
/* ------------------------------------------------------------------ */
|
| 3649 |
|
|
static decNumber *
|
| 3650 |
|
|
decQuantizeOp (decNumber * res, const decNumber * lhs,
|
| 3651 |
|
|
const decNumber * rhs, decContext * set, Flag quant, uInt * status)
|
| 3652 |
|
|
{
|
| 3653 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 3654 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 3655 |
|
|
const decNumber *inrhs = rhs; /* save original rhs */
|
| 3656 |
|
|
Int reqdigits = set->digits; /* requested DIGITS */
|
| 3657 |
|
|
Int reqexp; /* requested exponent [-scale] */
|
| 3658 |
|
|
Int residue = 0; /* rounding residue */
|
| 3659 |
|
|
uByte merged; /* merged flags */
|
| 3660 |
|
|
Int etiny = set->emin - (set->digits - 1);
|
| 3661 |
|
|
|
| 3662 |
|
|
#if DECCHECK
|
| 3663 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 3664 |
|
|
return res;
|
| 3665 |
|
|
#endif
|
| 3666 |
|
|
|
| 3667 |
|
|
do
|
| 3668 |
|
|
{ /* protect allocated storage */
|
| 3669 |
|
|
#if DECSUBSET
|
| 3670 |
|
|
if (!set->extended)
|
| 3671 |
|
|
{
|
| 3672 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 3673 |
|
|
if (lhs->digits > reqdigits)
|
| 3674 |
|
|
{
|
| 3675 |
|
|
alloclhs = decRoundOperand (lhs, set, status);
|
| 3676 |
|
|
if (alloclhs == NULL)
|
| 3677 |
|
|
break;
|
| 3678 |
|
|
lhs = alloclhs;
|
| 3679 |
|
|
}
|
| 3680 |
|
|
if (rhs->digits > reqdigits)
|
| 3681 |
|
|
{ /* [this only checks lostDigits] */
|
| 3682 |
|
|
allocrhs = decRoundOperand (rhs, set, status);
|
| 3683 |
|
|
if (allocrhs == NULL)
|
| 3684 |
|
|
break;
|
| 3685 |
|
|
rhs = allocrhs;
|
| 3686 |
|
|
}
|
| 3687 |
|
|
}
|
| 3688 |
|
|
#endif
|
| 3689 |
|
|
/* [following code does not require input rounding] */
|
| 3690 |
|
|
|
| 3691 |
|
|
/* Handle special values */
|
| 3692 |
|
|
merged = (lhs->bits | rhs->bits) & DECSPECIAL;
|
| 3693 |
|
|
if ((lhs->bits | rhs->bits) & DECSPECIAL)
|
| 3694 |
|
|
{
|
| 3695 |
|
|
/* NaNs get usual processing */
|
| 3696 |
|
|
if (merged & (DECSNAN | DECNAN))
|
| 3697 |
|
|
decNaNs (res, lhs, rhs, status);
|
| 3698 |
|
|
/* one infinity but not both is bad */
|
| 3699 |
|
|
else if ((lhs->bits ^ rhs->bits) & DECINF)
|
| 3700 |
|
|
*status |= DEC_Invalid_operation;
|
| 3701 |
|
|
/* both infinity: return lhs */
|
| 3702 |
|
|
else
|
| 3703 |
|
|
decNumberCopy (res, lhs); /* [nop if in place] */
|
| 3704 |
|
|
break;
|
| 3705 |
|
|
}
|
| 3706 |
|
|
|
| 3707 |
|
|
/* set requested exponent */
|
| 3708 |
|
|
if (quant)
|
| 3709 |
|
|
reqexp = inrhs->exponent; /* quantize -- match exponents */
|
| 3710 |
|
|
else
|
| 3711 |
|
|
{ /* rescale -- use value of rhs */
|
| 3712 |
|
|
/* Original rhs must be an integer that fits and is in range */
|
| 3713 |
|
|
#if DECSUBSET
|
| 3714 |
|
|
reqexp = decGetInt (inrhs, set);
|
| 3715 |
|
|
#else
|
| 3716 |
|
|
reqexp = decGetInt (inrhs);
|
| 3717 |
|
|
#endif
|
| 3718 |
|
|
}
|
| 3719 |
|
|
|
| 3720 |
|
|
#if DECSUBSET
|
| 3721 |
|
|
if (!set->extended)
|
| 3722 |
|
|
etiny = set->emin; /* no subnormals */
|
| 3723 |
|
|
#endif
|
| 3724 |
|
|
|
| 3725 |
|
|
if (reqexp == BADINT /* bad (rescale only) or .. */
|
| 3726 |
|
|
|| (reqexp < etiny) /* < lowest */
|
| 3727 |
|
|
|| (reqexp > set->emax))
|
| 3728 |
|
|
{ /* > Emax */
|
| 3729 |
|
|
*status |= DEC_Invalid_operation;
|
| 3730 |
|
|
break;
|
| 3731 |
|
|
}
|
| 3732 |
|
|
|
| 3733 |
|
|
/* we've processed the RHS, so we can overwrite it now if necessary */
|
| 3734 |
|
|
if (ISZERO (lhs))
|
| 3735 |
|
|
{ /* zero coefficient unchanged */
|
| 3736 |
|
|
decNumberCopy (res, lhs); /* [nop if in place] */
|
| 3737 |
|
|
res->exponent = reqexp; /* .. just set exponent */
|
| 3738 |
|
|
#if DECSUBSET
|
| 3739 |
|
|
if (!set->extended)
|
| 3740 |
|
|
res->bits = 0; /* subset specification; no -0 */
|
| 3741 |
|
|
#endif
|
| 3742 |
|
|
}
|
| 3743 |
|
|
else
|
| 3744 |
|
|
{ /* non-zero lhs */
|
| 3745 |
|
|
Int adjust = reqexp - lhs->exponent; /* digit adjustment needed */
|
| 3746 |
|
|
/* if adjusted coefficient will not fit, give up now */
|
| 3747 |
|
|
if ((lhs->digits - adjust) > reqdigits)
|
| 3748 |
|
|
{
|
| 3749 |
|
|
*status |= DEC_Invalid_operation;
|
| 3750 |
|
|
break;
|
| 3751 |
|
|
}
|
| 3752 |
|
|
|
| 3753 |
|
|
if (adjust > 0)
|
| 3754 |
|
|
{ /* increasing exponent */
|
| 3755 |
|
|
/* this will decrease the length of the coefficient by adjust */
|
| 3756 |
|
|
/* digits, and must round as it does so */
|
| 3757 |
|
|
decContext workset; /* work */
|
| 3758 |
|
|
workset = *set; /* clone rounding, etc. */
|
| 3759 |
|
|
workset.digits = lhs->digits - adjust; /* set requested length */
|
| 3760 |
|
|
/* [note that the latter can be <1, here] */
|
| 3761 |
|
|
decCopyFit (res, lhs, &workset, &residue, status); /* fit to result */
|
| 3762 |
|
|
decApplyRound (res, &workset, residue, status); /* .. and round */
|
| 3763 |
|
|
residue = 0; /* [used] */
|
| 3764 |
|
|
/* If we rounded a 999s case, exponent will be off by one; */
|
| 3765 |
|
|
/* adjust back if so. */
|
| 3766 |
|
|
if (res->exponent > reqexp)
|
| 3767 |
|
|
{
|
| 3768 |
|
|
res->digits = decShiftToMost (res->lsu, res->digits, 1); /* shift */
|
| 3769 |
|
|
res->exponent--; /* (re)adjust the exponent. */
|
| 3770 |
|
|
}
|
| 3771 |
|
|
#if DECSUBSET
|
| 3772 |
|
|
if (ISZERO (res) && !set->extended)
|
| 3773 |
|
|
res->bits = 0; /* subset; no -0 */
|
| 3774 |
|
|
#endif
|
| 3775 |
|
|
} /* increase */
|
| 3776 |
|
|
else /* adjust<=0 */
|
| 3777 |
|
|
{ /* decreasing or = exponent */
|
| 3778 |
|
|
/* this will increase the length of the coefficient by -adjust */
|
| 3779 |
|
|
/* digits, by adding trailing zeros. */
|
| 3780 |
|
|
decNumberCopy (res, lhs); /* [it will fit] */
|
| 3781 |
|
|
/* if padding needed (adjust<0), add it now... */
|
| 3782 |
|
|
if (adjust < 0)
|
| 3783 |
|
|
{
|
| 3784 |
|
|
res->digits =
|
| 3785 |
|
|
decShiftToMost (res->lsu, res->digits, -adjust);
|
| 3786 |
|
|
res->exponent += adjust; /* adjust the exponent */
|
| 3787 |
|
|
}
|
| 3788 |
|
|
} /* decrease */
|
| 3789 |
|
|
} /* non-zero */
|
| 3790 |
|
|
|
| 3791 |
|
|
/* Check for overflow [do not use Finalize in this case, as an */
|
| 3792 |
|
|
/* overflow here is a "don't fit" situation] */
|
| 3793 |
|
|
if (res->exponent > set->emax - res->digits + 1)
|
| 3794 |
|
|
{ /* too big */
|
| 3795 |
|
|
*status |= DEC_Invalid_operation;
|
| 3796 |
|
|
break;
|
| 3797 |
|
|
}
|
| 3798 |
|
|
else
|
| 3799 |
|
|
{
|
| 3800 |
|
|
decFinalize (res, set, &residue, status); /* set subnormal flags */
|
| 3801 |
|
|
*status &= ~DEC_Underflow; /* suppress Underflow [754r] */
|
| 3802 |
|
|
}
|
| 3803 |
|
|
}
|
| 3804 |
|
|
while (0); /* end protected */
|
| 3805 |
|
|
|
| 3806 |
|
|
if (allocrhs != NULL)
|
| 3807 |
|
|
free (allocrhs); /* drop any storage we used */
|
| 3808 |
|
|
if (alloclhs != NULL)
|
| 3809 |
|
|
free (alloclhs); /* .. */
|
| 3810 |
|
|
return res;
|
| 3811 |
|
|
}
|
| 3812 |
|
|
|
| 3813 |
|
|
/* ------------------------------------------------------------------ */
|
| 3814 |
|
|
/* decCompareOp -- compare, min, or max two Numbers */
|
| 3815 |
|
|
/* */
|
| 3816 |
|
|
/* This computes C = A ? B and returns the signum (as a Number) */
|
| 3817 |
|
|
/* for COMPARE or the maximum or minimum (for COMPMAX and COMPMIN). */
|
| 3818 |
|
|
/* */
|
| 3819 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 3820 |
|
|
/* lhs is A */
|
| 3821 |
|
|
/* rhs is B */
|
| 3822 |
|
|
/* set is the context */
|
| 3823 |
|
|
/* op is the operation flag */
|
| 3824 |
|
|
/* status is the usual accumulator */
|
| 3825 |
|
|
/* */
|
| 3826 |
|
|
/* C must have space for one digit for COMPARE or set->digits for */
|
| 3827 |
|
|
/* COMPMAX and COMPMIN. */
|
| 3828 |
|
|
/* ------------------------------------------------------------------ */
|
| 3829 |
|
|
/* The emphasis here is on speed for common cases, and avoiding */
|
| 3830 |
|
|
/* coefficient comparison if possible. */
|
| 3831 |
|
|
/* ------------------------------------------------------------------ */
|
| 3832 |
|
|
decNumber *
|
| 3833 |
|
|
decCompareOp (decNumber * res, const decNumber * lhs, const decNumber * rhs,
|
| 3834 |
|
|
decContext * set, Flag op, uInt * status)
|
| 3835 |
|
|
{
|
| 3836 |
|
|
decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
|
| 3837 |
|
|
decNumber *allocrhs = NULL; /* .., rhs */
|
| 3838 |
|
|
Int result = 0; /* default result value */
|
| 3839 |
|
|
uByte merged; /* merged flags */
|
| 3840 |
|
|
uByte bits = 0; /* non-0 for NaN */
|
| 3841 |
|
|
|
| 3842 |
|
|
#if DECCHECK
|
| 3843 |
|
|
if (decCheckOperands (res, lhs, rhs, set))
|
| 3844 |
|
|
return res;
|
| 3845 |
|
|
#endif
|
| 3846 |
|
|
|
| 3847 |
|
|
do
|
| 3848 |
|
|
{ /* protect allocated storage */
|
| 3849 |
|
|
#if DECSUBSET
|
| 3850 |
|
|
if (!set->extended)
|
| 3851 |
|
|
{
|
| 3852 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 3853 |
|
|
if (lhs->digits > set->digits)
|
| 3854 |
|
|
{
|
| 3855 |
|
|
alloclhs = decRoundOperand (lhs, set, status);
|
| 3856 |
|
|
if (alloclhs == NULL)
|
| 3857 |
|
|
{
|
| 3858 |
|
|
result = BADINT;
|
| 3859 |
|
|
break;
|
| 3860 |
|
|
}
|
| 3861 |
|
|
lhs = alloclhs;
|
| 3862 |
|
|
}
|
| 3863 |
|
|
if (rhs->digits > set->digits)
|
| 3864 |
|
|
{
|
| 3865 |
|
|
allocrhs = decRoundOperand (rhs, set, status);
|
| 3866 |
|
|
if (allocrhs == NULL)
|
| 3867 |
|
|
{
|
| 3868 |
|
|
result = BADINT;
|
| 3869 |
|
|
break;
|
| 3870 |
|
|
}
|
| 3871 |
|
|
rhs = allocrhs;
|
| 3872 |
|
|
}
|
| 3873 |
|
|
}
|
| 3874 |
|
|
#endif
|
| 3875 |
|
|
/* [following code does not require input rounding] */
|
| 3876 |
|
|
|
| 3877 |
|
|
/* handle NaNs now; let infinities drop through */
|
| 3878 |
|
|
/* +++ review sNaN handling with 754r, for now assumes sNaN */
|
| 3879 |
|
|
/* (even just one) leads to NaN. */
|
| 3880 |
|
|
merged = (lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
|
| 3881 |
|
|
if (merged)
|
| 3882 |
|
|
{ /* a NaN bit set */
|
| 3883 |
|
|
if (op == COMPARE);
|
| 3884 |
|
|
else if (merged & DECSNAN);
|
| 3885 |
|
|
else
|
| 3886 |
|
|
{ /* 754r rules for MIN and MAX ignore single NaN */
|
| 3887 |
|
|
/* here if MIN or MAX, and one or two quiet NaNs */
|
| 3888 |
|
|
if (lhs->bits & rhs->bits & DECNAN);
|
| 3889 |
|
|
else
|
| 3890 |
|
|
{ /* just one quiet NaN */
|
| 3891 |
|
|
/* force choice to be the non-NaN operand */
|
| 3892 |
|
|
op = COMPMAX;
|
| 3893 |
|
|
if (lhs->bits & DECNAN)
|
| 3894 |
|
|
result = -1; /* pick rhs */
|
| 3895 |
|
|
else
|
| 3896 |
|
|
result = +1; /* pick lhs */
|
| 3897 |
|
|
break;
|
| 3898 |
|
|
}
|
| 3899 |
|
|
}
|
| 3900 |
|
|
op = COMPNAN; /* use special path */
|
| 3901 |
|
|
decNaNs (res, lhs, rhs, status);
|
| 3902 |
|
|
break;
|
| 3903 |
|
|
}
|
| 3904 |
|
|
|
| 3905 |
|
|
result = decCompare (lhs, rhs); /* we have numbers */
|
| 3906 |
|
|
}
|
| 3907 |
|
|
while (0); /* end protected */
|
| 3908 |
|
|
|
| 3909 |
|
|
if (result == BADINT)
|
| 3910 |
|
|
*status |= DEC_Insufficient_storage; /* rare */
|
| 3911 |
|
|
else
|
| 3912 |
|
|
{
|
| 3913 |
|
|
if (op == COMPARE)
|
| 3914 |
|
|
{ /* return signum */
|
| 3915 |
|
|
decNumberZero (res); /* [always a valid result] */
|
| 3916 |
|
|
if (result == 0)
|
| 3917 |
|
|
res->bits = bits; /* (maybe qNaN) */
|
| 3918 |
|
|
else
|
| 3919 |
|
|
{
|
| 3920 |
|
|
*res->lsu = 1;
|
| 3921 |
|
|
if (result < 0)
|
| 3922 |
|
|
res->bits = DECNEG;
|
| 3923 |
|
|
}
|
| 3924 |
|
|
}
|
| 3925 |
|
|
else if (op == COMPNAN); /* special, drop through */
|
| 3926 |
|
|
else
|
| 3927 |
|
|
{ /* MAX or MIN, non-NaN result */
|
| 3928 |
|
|
Int residue = 0; /* rounding accumulator */
|
| 3929 |
|
|
/* choose the operand for the result */
|
| 3930 |
|
|
const decNumber *choice;
|
| 3931 |
|
|
if (result == 0)
|
| 3932 |
|
|
{ /* operands are numerically equal */
|
| 3933 |
|
|
/* choose according to sign then exponent (see 754r) */
|
| 3934 |
|
|
uByte slhs = (lhs->bits & DECNEG);
|
| 3935 |
|
|
uByte srhs = (rhs->bits & DECNEG);
|
| 3936 |
|
|
#if DECSUBSET
|
| 3937 |
|
|
if (!set->extended)
|
| 3938 |
|
|
{ /* subset: force left-hand */
|
| 3939 |
|
|
op = COMPMAX;
|
| 3940 |
|
|
result = +1;
|
| 3941 |
|
|
}
|
| 3942 |
|
|
else
|
| 3943 |
|
|
#endif
|
| 3944 |
|
|
if (slhs != srhs)
|
| 3945 |
|
|
{ /* signs differ */
|
| 3946 |
|
|
if (slhs)
|
| 3947 |
|
|
result = -1; /* rhs is max */
|
| 3948 |
|
|
else
|
| 3949 |
|
|
result = +1; /* lhs is max */
|
| 3950 |
|
|
}
|
| 3951 |
|
|
else if (slhs && srhs)
|
| 3952 |
|
|
{ /* both negative */
|
| 3953 |
|
|
if (lhs->exponent < rhs->exponent)
|
| 3954 |
|
|
result = +1;
|
| 3955 |
|
|
else
|
| 3956 |
|
|
result = -1;
|
| 3957 |
|
|
/* [if equal, we use lhs, technically identical] */
|
| 3958 |
|
|
}
|
| 3959 |
|
|
else
|
| 3960 |
|
|
{ /* both positive */
|
| 3961 |
|
|
if (lhs->exponent > rhs->exponent)
|
| 3962 |
|
|
result = +1;
|
| 3963 |
|
|
else
|
| 3964 |
|
|
result = -1;
|
| 3965 |
|
|
/* [ditto] */
|
| 3966 |
|
|
}
|
| 3967 |
|
|
} /* numerically equal */
|
| 3968 |
|
|
/* here result will be non-0 */
|
| 3969 |
|
|
if (op == COMPMIN)
|
| 3970 |
|
|
result = -result; /* reverse if looking for MIN */
|
| 3971 |
|
|
choice = (result > 0 ? lhs : rhs); /* choose */
|
| 3972 |
|
|
/* copy chosen to result, rounding if need be */
|
| 3973 |
|
|
decCopyFit (res, choice, set, &residue, status);
|
| 3974 |
|
|
decFinish (res, set, &residue, status);
|
| 3975 |
|
|
}
|
| 3976 |
|
|
}
|
| 3977 |
|
|
if (allocrhs != NULL)
|
| 3978 |
|
|
free (allocrhs); /* free any storage we used */
|
| 3979 |
|
|
if (alloclhs != NULL)
|
| 3980 |
|
|
free (alloclhs); /* .. */
|
| 3981 |
|
|
return res;
|
| 3982 |
|
|
}
|
| 3983 |
|
|
|
| 3984 |
|
|
/* ------------------------------------------------------------------ */
|
| 3985 |
|
|
/* decCompare -- compare two decNumbers by numerical value */
|
| 3986 |
|
|
/* */
|
| 3987 |
|
|
/* This routine compares A ? B without altering them. */
|
| 3988 |
|
|
/* */
|
| 3989 |
|
|
/* Arg1 is A, a decNumber which is not a NaN */
|
| 3990 |
|
|
/* Arg2 is B, a decNumber which is not a NaN */
|
| 3991 |
|
|
/* */
|
| 3992 |
|
|
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| 3993 |
|
|
/* (the only possible failure is an allocation error) */
|
| 3994 |
|
|
/* ------------------------------------------------------------------ */
|
| 3995 |
|
|
/* This could be merged into decCompareOp */
|
| 3996 |
|
|
static Int
|
| 3997 |
|
|
decCompare (const decNumber * lhs, const decNumber * rhs)
|
| 3998 |
|
|
{
|
| 3999 |
|
|
Int result; /* result value */
|
| 4000 |
|
|
Int sigr; /* rhs signum */
|
| 4001 |
|
|
Int compare; /* work */
|
| 4002 |
|
|
result = 1; /* assume signum(lhs) */
|
| 4003 |
|
|
if (ISZERO (lhs))
|
| 4004 |
|
|
result = 0;
|
| 4005 |
|
|
else if (decNumberIsNegative (lhs))
|
| 4006 |
|
|
result = -1;
|
| 4007 |
|
|
sigr = 1; /* compute signum(rhs) */
|
| 4008 |
|
|
if (ISZERO (rhs))
|
| 4009 |
|
|
sigr = 0;
|
| 4010 |
|
|
else if (decNumberIsNegative (rhs))
|
| 4011 |
|
|
sigr = -1;
|
| 4012 |
|
|
if (result > sigr)
|
| 4013 |
|
|
return +1; /* L > R, return 1 */
|
| 4014 |
|
|
if (result < sigr)
|
| 4015 |
|
|
return -1; /* R < L, return -1 */
|
| 4016 |
|
|
|
| 4017 |
|
|
/* signums are the same */
|
| 4018 |
|
|
if (result == 0)
|
| 4019 |
|
|
return 0; /* both 0 */
|
| 4020 |
|
|
/* Both non-zero */
|
| 4021 |
|
|
if ((lhs->bits | rhs->bits) & DECINF)
|
| 4022 |
|
|
{ /* one or more infinities */
|
| 4023 |
|
|
if (lhs->bits == rhs->bits)
|
| 4024 |
|
|
result = 0; /* both the same */
|
| 4025 |
|
|
else if (decNumberIsInfinite (rhs))
|
| 4026 |
|
|
result = -result;
|
| 4027 |
|
|
return result;
|
| 4028 |
|
|
}
|
| 4029 |
|
|
|
| 4030 |
|
|
/* we must compare the coefficients, allowing for exponents */
|
| 4031 |
|
|
if (lhs->exponent > rhs->exponent)
|
| 4032 |
|
|
{ /* LHS exponent larger */
|
| 4033 |
|
|
/* swap sides, and sign */
|
| 4034 |
|
|
const decNumber *temp = lhs;
|
| 4035 |
|
|
lhs = rhs;
|
| 4036 |
|
|
rhs = temp;
|
| 4037 |
|
|
result = -result;
|
| 4038 |
|
|
}
|
| 4039 |
|
|
|
| 4040 |
|
|
compare = decUnitCompare (lhs->lsu, D2U (lhs->digits),
|
| 4041 |
|
|
rhs->lsu, D2U (rhs->digits),
|
| 4042 |
|
|
rhs->exponent - lhs->exponent);
|
| 4043 |
|
|
|
| 4044 |
|
|
if (compare != BADINT)
|
| 4045 |
|
|
compare *= result; /* comparison succeeded */
|
| 4046 |
|
|
return compare; /* what we got */
|
| 4047 |
|
|
}
|
| 4048 |
|
|
|
| 4049 |
|
|
/* ------------------------------------------------------------------ */
|
| 4050 |
|
|
/* decUnitCompare -- compare two >=0 integers in Unit arrays */
|
| 4051 |
|
|
/* */
|
| 4052 |
|
|
/* This routine compares A ? B*10**E where A and B are unit arrays */
|
| 4053 |
|
|
/* A is a plain integer */
|
| 4054 |
|
|
/* B has an exponent of E (which must be non-negative) */
|
| 4055 |
|
|
/* */
|
| 4056 |
|
|
/* Arg1 is A first Unit (lsu) */
|
| 4057 |
|
|
/* Arg2 is A length in Units */
|
| 4058 |
|
|
/* Arg3 is B first Unit (lsu) */
|
| 4059 |
|
|
/* Arg4 is B length in Units */
|
| 4060 |
|
|
/* Arg5 is E */
|
| 4061 |
|
|
/* */
|
| 4062 |
|
|
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| 4063 |
|
|
/* (the only possible failure is an allocation error) */
|
| 4064 |
|
|
/* ------------------------------------------------------------------ */
|
| 4065 |
|
|
static Int
|
| 4066 |
|
|
decUnitCompare (const Unit * a, Int alength, const Unit * b, Int blength, Int exp)
|
| 4067 |
|
|
{
|
| 4068 |
|
|
Unit *acc; /* accumulator for result */
|
| 4069 |
|
|
Unit accbuff[D2U (DECBUFFER + 1)]; /* local buffer */
|
| 4070 |
|
|
Unit *allocacc = NULL; /* -> allocated acc buffer, iff allocated */
|
| 4071 |
|
|
Int accunits, need; /* units in use or needed for acc */
|
| 4072 |
|
|
const Unit *l, *r, *u; /* work */
|
| 4073 |
|
|
Int expunits, exprem, result; /* .. */
|
| 4074 |
|
|
|
| 4075 |
|
|
if (exp == 0)
|
| 4076 |
|
|
{ /* aligned; fastpath */
|
| 4077 |
|
|
if (alength > blength)
|
| 4078 |
|
|
return 1;
|
| 4079 |
|
|
if (alength < blength)
|
| 4080 |
|
|
return -1;
|
| 4081 |
|
|
/* same number of units in both -- need unit-by-unit compare */
|
| 4082 |
|
|
l = a + alength - 1;
|
| 4083 |
|
|
r = b + alength - 1;
|
| 4084 |
|
|
for (; l >= a; l--, r--)
|
| 4085 |
|
|
{
|
| 4086 |
|
|
if (*l > *r)
|
| 4087 |
|
|
return 1;
|
| 4088 |
|
|
if (*l < *r)
|
| 4089 |
|
|
return -1;
|
| 4090 |
|
|
}
|
| 4091 |
|
|
return 0; /* all units match */
|
| 4092 |
|
|
} /* aligned */
|
| 4093 |
|
|
|
| 4094 |
|
|
/* Unaligned. If one is >1 unit longer than the other, padded */
|
| 4095 |
|
|
/* approximately, then we can return easily */
|
| 4096 |
|
|
if (alength > blength + (Int) D2U (exp))
|
| 4097 |
|
|
return 1;
|
| 4098 |
|
|
if (alength + 1 < blength + (Int) D2U (exp))
|
| 4099 |
|
|
return -1;
|
| 4100 |
|
|
|
| 4101 |
|
|
/* We need to do a real subtract. For this, we need a result buffer */
|
| 4102 |
|
|
/* even though we only are interested in the sign. Its length needs */
|
| 4103 |
|
|
/* to be the larger of alength and padded blength, +2 */
|
| 4104 |
|
|
need = blength + D2U (exp); /* maximum real length of B */
|
| 4105 |
|
|
if (need < alength)
|
| 4106 |
|
|
need = alength;
|
| 4107 |
|
|
need += 2;
|
| 4108 |
|
|
acc = accbuff; /* assume use local buffer */
|
| 4109 |
|
|
if (need * sizeof (Unit) > sizeof (accbuff))
|
| 4110 |
|
|
{
|
| 4111 |
|
|
allocacc = (Unit *) malloc (need * sizeof (Unit));
|
| 4112 |
|
|
if (allocacc == NULL)
|
| 4113 |
|
|
return BADINT; /* hopeless -- abandon */
|
| 4114 |
|
|
acc = allocacc;
|
| 4115 |
|
|
}
|
| 4116 |
|
|
/* Calculate units and remainder from exponent. */
|
| 4117 |
|
|
expunits = exp / DECDPUN;
|
| 4118 |
|
|
exprem = exp % DECDPUN;
|
| 4119 |
|
|
/* subtract [A+B*(-m)] */
|
| 4120 |
|
|
accunits = decUnitAddSub (a, alength, b, blength, expunits, acc,
|
| 4121 |
|
|
-(Int) powers[exprem]);
|
| 4122 |
|
|
/* [UnitAddSub result may have leading zeros, even on zero] */
|
| 4123 |
|
|
if (accunits < 0)
|
| 4124 |
|
|
result = -1; /* negative result */
|
| 4125 |
|
|
else
|
| 4126 |
|
|
{ /* non-negative result */
|
| 4127 |
|
|
/* check units of the result before freeing any storage */
|
| 4128 |
|
|
for (u = acc; u < acc + accunits - 1 && *u == 0;)
|
| 4129 |
|
|
u++;
|
| 4130 |
|
|
result = (*u == 0 ? 0 : +1);
|
| 4131 |
|
|
}
|
| 4132 |
|
|
/* clean up and return the result */
|
| 4133 |
|
|
if (allocacc != NULL)
|
| 4134 |
|
|
free (allocacc); /* drop any storage we used */
|
| 4135 |
|
|
return result;
|
| 4136 |
|
|
}
|
| 4137 |
|
|
|
| 4138 |
|
|
/* ------------------------------------------------------------------ */
|
| 4139 |
|
|
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
|
| 4140 |
|
|
/* */
|
| 4141 |
|
|
/* This routine performs the calculation: */
|
| 4142 |
|
|
/* */
|
| 4143 |
|
|
/* C=A+(B*M) */
|
| 4144 |
|
|
/* */
|
| 4145 |
|
|
/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
|
| 4146 |
|
|
/* */
|
| 4147 |
|
|
/* A may be shorter or longer than B. */
|
| 4148 |
|
|
/* */
|
| 4149 |
|
|
/* Leading zeros are not removed after a calculation. The result is */
|
| 4150 |
|
|
/* either the same length as the longer of A and B (adding any */
|
| 4151 |
|
|
/* shift), or one Unit longer than that (if a Unit carry occurred). */
|
| 4152 |
|
|
/* */
|
| 4153 |
|
|
/* A and B content are not altered unless C is also A or B. */
|
| 4154 |
|
|
/* C may be the same array as A or B, but only if no zero padding is */
|
| 4155 |
|
|
/* requested (that is, C may be B only if bshift==0). */
|
| 4156 |
|
|
/* C is filled from the lsu; only those units necessary to complete */
|
| 4157 |
|
|
/* the calculation are referenced. */
|
| 4158 |
|
|
/* */
|
| 4159 |
|
|
/* Arg1 is A first Unit (lsu) */
|
| 4160 |
|
|
/* Arg2 is A length in Units */
|
| 4161 |
|
|
/* Arg3 is B first Unit (lsu) */
|
| 4162 |
|
|
/* Arg4 is B length in Units */
|
| 4163 |
|
|
/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
|
| 4164 |
|
|
/* Arg6 is C first Unit (lsu) */
|
| 4165 |
|
|
/* Arg7 is M, the multiplier */
|
| 4166 |
|
|
/* */
|
| 4167 |
|
|
/* returns the count of Units written to C, which will be non-zero */
|
| 4168 |
|
|
/* and negated if the result is negative. That is, the sign of the */
|
| 4169 |
|
|
/* returned Int is the sign of the result (positive for zero) and */
|
| 4170 |
|
|
/* the absolute value of the Int is the count of Units. */
|
| 4171 |
|
|
/* */
|
| 4172 |
|
|
/* It is the caller's responsibility to make sure that C size is */
|
| 4173 |
|
|
/* safe, allowing space if necessary for a one-Unit carry. */
|
| 4174 |
|
|
/* */
|
| 4175 |
|
|
/* This routine is severely performance-critical; *any* change here */
|
| 4176 |
|
|
/* must be measured (timed) to assure no performance degradation. */
|
| 4177 |
|
|
/* In particular, trickery here tends to be counter-productive, as */
|
| 4178 |
|
|
/* increased complexity of code hurts register optimizations on */
|
| 4179 |
|
|
/* register-poor architectures. Avoiding divisions is nearly */
|
| 4180 |
|
|
/* always a Good Idea, however. */
|
| 4181 |
|
|
/* */
|
| 4182 |
|
|
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
|
| 4183 |
|
|
/* (IBM Warwick, UK) for some of the ideas used in this routine. */
|
| 4184 |
|
|
/* ------------------------------------------------------------------ */
|
| 4185 |
|
|
static Int
|
| 4186 |
|
|
decUnitAddSub (const Unit * a, Int alength,
|
| 4187 |
|
|
const Unit * b, Int blength, Int bshift, Unit * c, Int m)
|
| 4188 |
|
|
{
|
| 4189 |
|
|
const Unit *alsu = a; /* A lsu [need to remember it] */
|
| 4190 |
|
|
Unit *clsu = c; /* C ditto */
|
| 4191 |
|
|
Unit *minC; /* low water mark for C */
|
| 4192 |
|
|
Unit *maxC; /* high water mark for C */
|
| 4193 |
|
|
eInt carry = 0; /* carry integer (could be Long) */
|
| 4194 |
|
|
Int add; /* work */
|
| 4195 |
|
|
#if DECDPUN==4 /* myriadal */
|
| 4196 |
|
|
Int est; /* estimated quotient */
|
| 4197 |
|
|
#endif
|
| 4198 |
|
|
|
| 4199 |
|
|
#if DECTRACE
|
| 4200 |
|
|
if (alength < 1 || blength < 1)
|
| 4201 |
|
|
printf ("decUnitAddSub: alen blen m %d %d [%d]\n", alength, blength, m);
|
| 4202 |
|
|
#endif
|
| 4203 |
|
|
|
| 4204 |
|
|
maxC = c + alength; /* A is usually the longer */
|
| 4205 |
|
|
minC = c + blength; /* .. and B the shorter */
|
| 4206 |
|
|
if (bshift != 0)
|
| 4207 |
|
|
{ /* B is shifted; low As copy across */
|
| 4208 |
|
|
minC += bshift;
|
| 4209 |
|
|
/* if in place [common], skip copy unless there's a gap [rare] */
|
| 4210 |
|
|
if (a == c && bshift <= alength)
|
| 4211 |
|
|
{
|
| 4212 |
|
|
c += bshift;
|
| 4213 |
|
|
a += bshift;
|
| 4214 |
|
|
}
|
| 4215 |
|
|
else
|
| 4216 |
|
|
for (; c < clsu + bshift; a++, c++)
|
| 4217 |
|
|
{ /* copy needed */
|
| 4218 |
|
|
if (a < alsu + alength)
|
| 4219 |
|
|
*c = *a;
|
| 4220 |
|
|
else
|
| 4221 |
|
|
*c = 0;
|
| 4222 |
|
|
}
|
| 4223 |
|
|
}
|
| 4224 |
|
|
if (minC > maxC)
|
| 4225 |
|
|
{ /* swap */
|
| 4226 |
|
|
Unit *hold = minC;
|
| 4227 |
|
|
minC = maxC;
|
| 4228 |
|
|
maxC = hold;
|
| 4229 |
|
|
}
|
| 4230 |
|
|
|
| 4231 |
|
|
/* For speed, we do the addition as two loops; the first where both A */
|
| 4232 |
|
|
/* and B contribute, and the second (if necessary) where only one or */
|
| 4233 |
|
|
/* other of the numbers contribute. */
|
| 4234 |
|
|
/* Carry handling is the same (i.e., duplicated) in each case. */
|
| 4235 |
|
|
for (; c < minC; c++)
|
| 4236 |
|
|
{
|
| 4237 |
|
|
carry += *a;
|
| 4238 |
|
|
a++;
|
| 4239 |
|
|
carry += ((eInt) * b) * m; /* [special-casing m=1/-1 */
|
| 4240 |
|
|
b++; /* here is not a win] */
|
| 4241 |
|
|
/* here carry is new Unit of digits; it could be +ve or -ve */
|
| 4242 |
|
|
if ((ueInt) carry <= DECDPUNMAX)
|
| 4243 |
|
|
{ /* fastpath 0-DECDPUNMAX */
|
| 4244 |
|
|
*c = (Unit) carry;
|
| 4245 |
|
|
carry = 0;
|
| 4246 |
|
|
continue;
|
| 4247 |
|
|
}
|
| 4248 |
|
|
/* remainder operator is undefined if negative, so we must test */
|
| 4249 |
|
|
#if DECDPUN==4 /* use divide-by-multiply */
|
| 4250 |
|
|
if (carry >= 0)
|
| 4251 |
|
|
{
|
| 4252 |
|
|
est = (((ueInt) carry >> 11) * 53687) >> 18;
|
| 4253 |
|
|
*c = (Unit) (carry - est * (DECDPUNMAX + 1)); /* remainder */
|
| 4254 |
|
|
carry = est; /* likely quotient [89%] */
|
| 4255 |
|
|
if (*c < DECDPUNMAX + 1)
|
| 4256 |
|
|
continue; /* estimate was correct */
|
| 4257 |
|
|
carry++;
|
| 4258 |
|
|
*c -= DECDPUNMAX + 1;
|
| 4259 |
|
|
continue;
|
| 4260 |
|
|
}
|
| 4261 |
|
|
/* negative case */
|
| 4262 |
|
|
carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
|
| 4263 |
|
|
est = (((ueInt) carry >> 11) * 53687) >> 18;
|
| 4264 |
|
|
*c = (Unit) (carry - est * (DECDPUNMAX + 1));
|
| 4265 |
|
|
carry = est - (DECDPUNMAX + 1); /* correctly negative */
|
| 4266 |
|
|
if (*c < DECDPUNMAX + 1)
|
| 4267 |
|
|
continue; /* was OK */
|
| 4268 |
|
|
carry++;
|
| 4269 |
|
|
*c -= DECDPUNMAX + 1;
|
| 4270 |
|
|
#else
|
| 4271 |
|
|
if ((ueInt) carry < (DECDPUNMAX + 1) * 2)
|
| 4272 |
|
|
{ /* fastpath carry +1 */
|
| 4273 |
|
|
*c = (Unit) (carry - (DECDPUNMAX + 1)); /* [helps additions] */
|
| 4274 |
|
|
carry = 1;
|
| 4275 |
|
|
continue;
|
| 4276 |
|
|
}
|
| 4277 |
|
|
if (carry >= 0)
|
| 4278 |
|
|
{
|
| 4279 |
|
|
*c = (Unit) (carry % (DECDPUNMAX + 1));
|
| 4280 |
|
|
carry = carry / (DECDPUNMAX + 1);
|
| 4281 |
|
|
continue;
|
| 4282 |
|
|
}
|
| 4283 |
|
|
/* negative case */
|
| 4284 |
|
|
carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
|
| 4285 |
|
|
*c = (Unit) (carry % (DECDPUNMAX + 1));
|
| 4286 |
|
|
carry = carry / (DECDPUNMAX + 1) - (DECDPUNMAX + 1);
|
| 4287 |
|
|
#endif
|
| 4288 |
|
|
} /* c */
|
| 4289 |
|
|
|
| 4290 |
|
|
/* we now may have one or other to complete */
|
| 4291 |
|
|
/* [pretest to avoid loop setup/shutdown] */
|
| 4292 |
|
|
if (c < maxC)
|
| 4293 |
|
|
for (; c < maxC; c++)
|
| 4294 |
|
|
{
|
| 4295 |
|
|
if (a < alsu + alength)
|
| 4296 |
|
|
{ /* still in A */
|
| 4297 |
|
|
carry += *a;
|
| 4298 |
|
|
a++;
|
| 4299 |
|
|
}
|
| 4300 |
|
|
else
|
| 4301 |
|
|
{ /* inside B */
|
| 4302 |
|
|
carry += ((eInt) * b) * m;
|
| 4303 |
|
|
b++;
|
| 4304 |
|
|
}
|
| 4305 |
|
|
/* here carry is new Unit of digits; it could be +ve or -ve and */
|
| 4306 |
|
|
/* magnitude up to DECDPUNMAX squared */
|
| 4307 |
|
|
if ((ueInt) carry <= DECDPUNMAX)
|
| 4308 |
|
|
{ /* fastpath 0-DECDPUNMAX */
|
| 4309 |
|
|
*c = (Unit) carry;
|
| 4310 |
|
|
carry = 0;
|
| 4311 |
|
|
continue;
|
| 4312 |
|
|
}
|
| 4313 |
|
|
/* result for this unit is negative or >DECDPUNMAX */
|
| 4314 |
|
|
#if DECDPUN==4 /* use divide-by-multiply */
|
| 4315 |
|
|
/* remainder is undefined if negative, so we must test */
|
| 4316 |
|
|
if (carry >= 0)
|
| 4317 |
|
|
{
|
| 4318 |
|
|
est = (((ueInt) carry >> 11) * 53687) >> 18;
|
| 4319 |
|
|
*c = (Unit) (carry - est * (DECDPUNMAX + 1)); /* remainder */
|
| 4320 |
|
|
carry = est; /* likely quotient [79.7%] */
|
| 4321 |
|
|
if (*c < DECDPUNMAX + 1)
|
| 4322 |
|
|
continue; /* estimate was correct */
|
| 4323 |
|
|
carry++;
|
| 4324 |
|
|
*c -= DECDPUNMAX + 1;
|
| 4325 |
|
|
continue;
|
| 4326 |
|
|
}
|
| 4327 |
|
|
/* negative case */
|
| 4328 |
|
|
carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
|
| 4329 |
|
|
est = (((ueInt) carry >> 11) * 53687) >> 18;
|
| 4330 |
|
|
*c = (Unit) (carry - est * (DECDPUNMAX + 1));
|
| 4331 |
|
|
carry = est - (DECDPUNMAX + 1); /* correctly negative */
|
| 4332 |
|
|
if (*c < DECDPUNMAX + 1)
|
| 4333 |
|
|
continue; /* was OK */
|
| 4334 |
|
|
carry++;
|
| 4335 |
|
|
*c -= DECDPUNMAX + 1;
|
| 4336 |
|
|
#else
|
| 4337 |
|
|
if ((ueInt) carry < (DECDPUNMAX + 1) * 2)
|
| 4338 |
|
|
{ /* fastpath carry 1 */
|
| 4339 |
|
|
*c = (Unit) (carry - (DECDPUNMAX + 1));
|
| 4340 |
|
|
carry = 1;
|
| 4341 |
|
|
continue;
|
| 4342 |
|
|
}
|
| 4343 |
|
|
/* remainder is undefined if negative, so we must test */
|
| 4344 |
|
|
if (carry >= 0)
|
| 4345 |
|
|
{
|
| 4346 |
|
|
*c = (Unit) (carry % (DECDPUNMAX + 1));
|
| 4347 |
|
|
carry = carry / (DECDPUNMAX + 1);
|
| 4348 |
|
|
continue;
|
| 4349 |
|
|
}
|
| 4350 |
|
|
/* negative case */
|
| 4351 |
|
|
carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
|
| 4352 |
|
|
*c = (Unit) (carry % (DECDPUNMAX + 1));
|
| 4353 |
|
|
carry = carry / (DECDPUNMAX + 1) - (DECDPUNMAX + 1);
|
| 4354 |
|
|
#endif
|
| 4355 |
|
|
} /* c */
|
| 4356 |
|
|
|
| 4357 |
|
|
/* OK, all A and B processed; might still have carry or borrow */
|
| 4358 |
|
|
/* return number of Units in the result, negated if a borrow */
|
| 4359 |
|
|
if (carry == 0)
|
| 4360 |
|
|
return c - clsu; /* no carry, we're done */
|
| 4361 |
|
|
if (carry > 0)
|
| 4362 |
|
|
{ /* positive carry */
|
| 4363 |
|
|
*c = (Unit) carry; /* place as new unit */
|
| 4364 |
|
|
c++; /* .. */
|
| 4365 |
|
|
return c - clsu;
|
| 4366 |
|
|
}
|
| 4367 |
|
|
/* -ve carry: it's a borrow; complement needed */
|
| 4368 |
|
|
add = 1; /* temporary carry... */
|
| 4369 |
|
|
for (c = clsu; c < maxC; c++)
|
| 4370 |
|
|
{
|
| 4371 |
|
|
add = DECDPUNMAX + add - *c;
|
| 4372 |
|
|
if (add <= DECDPUNMAX)
|
| 4373 |
|
|
{
|
| 4374 |
|
|
*c = (Unit) add;
|
| 4375 |
|
|
add = 0;
|
| 4376 |
|
|
}
|
| 4377 |
|
|
else
|
| 4378 |
|
|
{
|
| 4379 |
|
|
*c = 0;
|
| 4380 |
|
|
add = 1;
|
| 4381 |
|
|
}
|
| 4382 |
|
|
}
|
| 4383 |
|
|
/* add an extra unit iff it would be non-zero */
|
| 4384 |
|
|
#if DECTRACE
|
| 4385 |
|
|
printf ("UAS borrow: add %d, carry %d\n", add, carry);
|
| 4386 |
|
|
#endif
|
| 4387 |
|
|
if ((add - carry - 1) != 0)
|
| 4388 |
|
|
{
|
| 4389 |
|
|
*c = (Unit) (add - carry - 1);
|
| 4390 |
|
|
c++; /* interesting, include it */
|
| 4391 |
|
|
}
|
| 4392 |
|
|
return clsu - c; /* -ve result indicates borrowed */
|
| 4393 |
|
|
}
|
| 4394 |
|
|
|
| 4395 |
|
|
/* ------------------------------------------------------------------ */
|
| 4396 |
|
|
/* decTrim -- trim trailing zeros or normalize */
|
| 4397 |
|
|
/* */
|
| 4398 |
|
|
/* dn is the number to trim or normalize */
|
| 4399 |
|
|
/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
|
| 4400 |
|
|
/* dropped returns the number of discarded trailing zeros */
|
| 4401 |
|
|
/* returns dn */
|
| 4402 |
|
|
/* */
|
| 4403 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 4404 |
|
|
/* so special values are unchanged and no error is possible. */
|
| 4405 |
|
|
/* ------------------------------------------------------------------ */
|
| 4406 |
|
|
static decNumber *
|
| 4407 |
|
|
decTrim (decNumber * dn, Flag all, Int * dropped)
|
| 4408 |
|
|
{
|
| 4409 |
|
|
Int d, exp; /* work */
|
| 4410 |
|
|
uInt cut; /* .. */
|
| 4411 |
|
|
Unit *up; /* -> current Unit */
|
| 4412 |
|
|
|
| 4413 |
|
|
#if DECCHECK
|
| 4414 |
|
|
if (decCheckOperands (dn, DECUNUSED, DECUNUSED, DECUNUSED))
|
| 4415 |
|
|
return dn;
|
| 4416 |
|
|
#endif
|
| 4417 |
|
|
|
| 4418 |
|
|
*dropped = 0; /* assume no zeros dropped */
|
| 4419 |
|
|
if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
|
| 4420 |
|
|
|| (*dn->lsu & 0x01))
|
| 4421 |
|
|
return dn; /* .. or odd */
|
| 4422 |
|
|
if (ISZERO (dn))
|
| 4423 |
|
|
{ /* .. or 0 */
|
| 4424 |
|
|
dn->exponent = 0; /* (sign is preserved) */
|
| 4425 |
|
|
return dn;
|
| 4426 |
|
|
}
|
| 4427 |
|
|
|
| 4428 |
|
|
/* we have a finite number which is even */
|
| 4429 |
|
|
exp = dn->exponent;
|
| 4430 |
|
|
cut = 1; /* digit (1-DECDPUN) in Unit */
|
| 4431 |
|
|
up = dn->lsu; /* -> current Unit */
|
| 4432 |
|
|
for (d = 0; d < dn->digits - 1; d++)
|
| 4433 |
|
|
{ /* [don't strip the final digit] */
|
| 4434 |
|
|
/* slice by powers */
|
| 4435 |
|
|
#if DECDPUN<=4
|
| 4436 |
|
|
uInt quot = QUOT10 (*up, cut);
|
| 4437 |
|
|
if ((*up - quot * powers[cut]) != 0)
|
| 4438 |
|
|
break; /* found non-0 digit */
|
| 4439 |
|
|
#else
|
| 4440 |
|
|
if (*up % powers[cut] != 0)
|
| 4441 |
|
|
break; /* found non-0 digit */
|
| 4442 |
|
|
#endif
|
| 4443 |
|
|
/* have a trailing 0 */
|
| 4444 |
|
|
if (!all)
|
| 4445 |
|
|
{ /* trimming */
|
| 4446 |
|
|
/* [if exp>0 then all trailing 0s are significant for trim] */
|
| 4447 |
|
|
if (exp <= 0)
|
| 4448 |
|
|
{ /* if digit might be significant */
|
| 4449 |
|
|
if (exp == 0)
|
| 4450 |
|
|
break; /* then quit */
|
| 4451 |
|
|
exp++; /* next digit might be significant */
|
| 4452 |
|
|
}
|
| 4453 |
|
|
}
|
| 4454 |
|
|
cut++; /* next power */
|
| 4455 |
|
|
if (cut > DECDPUN)
|
| 4456 |
|
|
{ /* need new Unit */
|
| 4457 |
|
|
up++;
|
| 4458 |
|
|
cut = 1;
|
| 4459 |
|
|
}
|
| 4460 |
|
|
} /* d */
|
| 4461 |
|
|
if (d == 0)
|
| 4462 |
|
|
return dn; /* none dropped */
|
| 4463 |
|
|
|
| 4464 |
|
|
/* effect the drop */
|
| 4465 |
|
|
decShiftToLeast (dn->lsu, D2U (dn->digits), d);
|
| 4466 |
|
|
dn->exponent += d; /* maintain numerical value */
|
| 4467 |
|
|
dn->digits -= d; /* new length */
|
| 4468 |
|
|
*dropped = d; /* report the count */
|
| 4469 |
|
|
return dn;
|
| 4470 |
|
|
}
|
| 4471 |
|
|
|
| 4472 |
|
|
/* ------------------------------------------------------------------ */
|
| 4473 |
|
|
/* decShiftToMost -- shift digits in array towards most significant */
|
| 4474 |
|
|
/* */
|
| 4475 |
|
|
/* uar is the array */
|
| 4476 |
|
|
/* digits is the count of digits in use in the array */
|
| 4477 |
|
|
/* shift is the number of zeros to pad with (least significant); */
|
| 4478 |
|
|
/* it must be zero or positive */
|
| 4479 |
|
|
/* */
|
| 4480 |
|
|
/* returns the new length of the integer in the array, in digits */
|
| 4481 |
|
|
/* */
|
| 4482 |
|
|
/* No overflow is permitted (that is, the uar array must be known to */
|
| 4483 |
|
|
/* be large enough to hold the result, after shifting). */
|
| 4484 |
|
|
/* ------------------------------------------------------------------ */
|
| 4485 |
|
|
static Int
|
| 4486 |
|
|
decShiftToMost (Unit * uar, Int digits, Int shift)
|
| 4487 |
|
|
{
|
| 4488 |
|
|
Unit *target, *source, *first; /* work */
|
| 4489 |
|
|
uInt rem; /* for division */
|
| 4490 |
|
|
Int cut; /* odd 0's to add */
|
| 4491 |
|
|
uInt next; /* work */
|
| 4492 |
|
|
|
| 4493 |
|
|
if (shift == 0)
|
| 4494 |
|
|
return digits; /* [fastpath] nothing to do */
|
| 4495 |
|
|
if ((digits + shift) <= DECDPUN)
|
| 4496 |
|
|
{ /* [fastpath] single-unit case */
|
| 4497 |
|
|
*uar = (Unit) (*uar * powers[shift]);
|
| 4498 |
|
|
return digits + shift;
|
| 4499 |
|
|
}
|
| 4500 |
|
|
|
| 4501 |
|
|
cut = (DECDPUN - shift % DECDPUN) % DECDPUN;
|
| 4502 |
|
|
source = uar + D2U (digits) - 1; /* where msu comes from */
|
| 4503 |
|
|
first = uar + D2U (digits + shift) - 1; /* where msu of source will end up */
|
| 4504 |
|
|
target = source + D2U (shift); /* where upper part of first cut goes */
|
| 4505 |
|
|
next = 0;
|
| 4506 |
|
|
|
| 4507 |
|
|
for (; source >= uar; source--, target--)
|
| 4508 |
|
|
{
|
| 4509 |
|
|
/* split the source Unit and accumulate remainder for next */
|
| 4510 |
|
|
#if DECDPUN<=4
|
| 4511 |
|
|
uInt quot = QUOT10 (*source, cut);
|
| 4512 |
|
|
rem = *source - quot * powers[cut];
|
| 4513 |
|
|
next += quot;
|
| 4514 |
|
|
#else
|
| 4515 |
|
|
rem = *source % powers[cut];
|
| 4516 |
|
|
next += *source / powers[cut];
|
| 4517 |
|
|
#endif
|
| 4518 |
|
|
if (target <= first)
|
| 4519 |
|
|
*target = (Unit) next; /* write to target iff valid */
|
| 4520 |
|
|
next = rem * powers[DECDPUN - cut]; /* save remainder for next Unit */
|
| 4521 |
|
|
}
|
| 4522 |
|
|
/* propagate to one below and clear the rest */
|
| 4523 |
|
|
for (; target >= uar; target--)
|
| 4524 |
|
|
{
|
| 4525 |
|
|
*target = (Unit) next;
|
| 4526 |
|
|
next = 0;
|
| 4527 |
|
|
}
|
| 4528 |
|
|
return digits + shift;
|
| 4529 |
|
|
}
|
| 4530 |
|
|
|
| 4531 |
|
|
/* ------------------------------------------------------------------ */
|
| 4532 |
|
|
/* decShiftToLeast -- shift digits in array towards least significant */
|
| 4533 |
|
|
/* */
|
| 4534 |
|
|
/* uar is the array */
|
| 4535 |
|
|
/* units is length of the array, in units */
|
| 4536 |
|
|
/* shift is the number of digits to remove from the lsu end; it */
|
| 4537 |
|
|
/* must be zero or positive and less than units*DECDPUN. */
|
| 4538 |
|
|
/* */
|
| 4539 |
|
|
/* returns the new length of the integer in the array, in units */
|
| 4540 |
|
|
/* */
|
| 4541 |
|
|
/* Removed digits are discarded (lost). Units not required to hold */
|
| 4542 |
|
|
/* the final result are unchanged. */
|
| 4543 |
|
|
/* ------------------------------------------------------------------ */
|
| 4544 |
|
|
static Int
|
| 4545 |
|
|
decShiftToLeast (Unit * uar, Int units, Int shift)
|
| 4546 |
|
|
{
|
| 4547 |
|
|
Unit *target, *up; /* work */
|
| 4548 |
|
|
Int cut, count; /* work */
|
| 4549 |
|
|
Int quot, rem; /* for division */
|
| 4550 |
|
|
|
| 4551 |
|
|
if (shift == 0)
|
| 4552 |
|
|
return units; /* [fastpath] nothing to do */
|
| 4553 |
|
|
|
| 4554 |
|
|
up = uar + shift / DECDPUN; /* source; allow for whole Units */
|
| 4555 |
|
|
cut = shift % DECDPUN; /* odd 0's to drop */
|
| 4556 |
|
|
target = uar; /* both paths */
|
| 4557 |
|
|
if (cut == 0)
|
| 4558 |
|
|
{ /* whole units shift */
|
| 4559 |
|
|
for (; up < uar + units; target++, up++)
|
| 4560 |
|
|
*target = *up;
|
| 4561 |
|
|
return target - uar;
|
| 4562 |
|
|
}
|
| 4563 |
|
|
/* messier */
|
| 4564 |
|
|
count = units * DECDPUN - shift; /* the maximum new length */
|
| 4565 |
|
|
#if DECDPUN<=4
|
| 4566 |
|
|
quot = QUOT10 (*up, cut);
|
| 4567 |
|
|
#else
|
| 4568 |
|
|
quot = *up / powers[cut];
|
| 4569 |
|
|
#endif
|
| 4570 |
|
|
for (;; target++)
|
| 4571 |
|
|
{
|
| 4572 |
|
|
*target = (Unit) quot;
|
| 4573 |
|
|
count -= (DECDPUN - cut);
|
| 4574 |
|
|
if (count <= 0)
|
| 4575 |
|
|
break;
|
| 4576 |
|
|
up++;
|
| 4577 |
|
|
quot = *up;
|
| 4578 |
|
|
#if DECDPUN<=4
|
| 4579 |
|
|
quot = QUOT10 (quot, cut);
|
| 4580 |
|
|
rem = *up - quot * powers[cut];
|
| 4581 |
|
|
#else
|
| 4582 |
|
|
rem = quot % powers[cut];
|
| 4583 |
|
|
quot = quot / powers[cut];
|
| 4584 |
|
|
#endif
|
| 4585 |
|
|
*target = (Unit) (*target + rem * powers[DECDPUN - cut]);
|
| 4586 |
|
|
count -= cut;
|
| 4587 |
|
|
if (count <= 0)
|
| 4588 |
|
|
break;
|
| 4589 |
|
|
}
|
| 4590 |
|
|
return target - uar + 1;
|
| 4591 |
|
|
}
|
| 4592 |
|
|
|
| 4593 |
|
|
#if DECSUBSET
|
| 4594 |
|
|
/* ------------------------------------------------------------------ */
|
| 4595 |
|
|
/* decRoundOperand -- round an operand [used for subset only] */
|
| 4596 |
|
|
/* */
|
| 4597 |
|
|
/* dn is the number to round (dn->digits is > set->digits) */
|
| 4598 |
|
|
/* set is the relevant context */
|
| 4599 |
|
|
/* status is the status accumulator */
|
| 4600 |
|
|
/* */
|
| 4601 |
|
|
/* returns an allocated decNumber with the rounded result. */
|
| 4602 |
|
|
/* */
|
| 4603 |
|
|
/* lostDigits and other status may be set by this. */
|
| 4604 |
|
|
/* */
|
| 4605 |
|
|
/* Since the input is an operand, we are not permitted to modify it. */
|
| 4606 |
|
|
/* We therefore return an allocated decNumber, rounded as required. */
|
| 4607 |
|
|
/* It is the caller's responsibility to free the allocated storage. */
|
| 4608 |
|
|
/* */
|
| 4609 |
|
|
/* If no storage is available then the result cannot be used, so NULL */
|
| 4610 |
|
|
/* is returned. */
|
| 4611 |
|
|
/* ------------------------------------------------------------------ */
|
| 4612 |
|
|
static decNumber *
|
| 4613 |
|
|
decRoundOperand (const decNumber * dn, decContext * set, uInt * status)
|
| 4614 |
|
|
{
|
| 4615 |
|
|
decNumber *res; /* result structure */
|
| 4616 |
|
|
uInt newstatus = 0; /* status from round */
|
| 4617 |
|
|
Int residue = 0; /* rounding accumulator */
|
| 4618 |
|
|
|
| 4619 |
|
|
/* Allocate storage for the returned decNumber, big enough for the */
|
| 4620 |
|
|
/* length specified by the context */
|
| 4621 |
|
|
res = (decNumber *) malloc (sizeof (decNumber)
|
| 4622 |
|
|
+ (D2U (set->digits) - 1) * sizeof (Unit));
|
| 4623 |
|
|
if (res == NULL)
|
| 4624 |
|
|
{
|
| 4625 |
|
|
*status |= DEC_Insufficient_storage;
|
| 4626 |
|
|
return NULL;
|
| 4627 |
|
|
}
|
| 4628 |
|
|
decCopyFit (res, dn, set, &residue, &newstatus);
|
| 4629 |
|
|
decApplyRound (res, set, residue, &newstatus);
|
| 4630 |
|
|
|
| 4631 |
|
|
/* If that set Inexact then we "lost digits" */
|
| 4632 |
|
|
if (newstatus & DEC_Inexact)
|
| 4633 |
|
|
newstatus |= DEC_Lost_digits;
|
| 4634 |
|
|
*status |= newstatus;
|
| 4635 |
|
|
return res;
|
| 4636 |
|
|
}
|
| 4637 |
|
|
#endif
|
| 4638 |
|
|
|
| 4639 |
|
|
/* ------------------------------------------------------------------ */
|
| 4640 |
|
|
/* decCopyFit -- copy a number, shortening the coefficient if needed */
|
| 4641 |
|
|
/* */
|
| 4642 |
|
|
/* dest is the target decNumber */
|
| 4643 |
|
|
/* src is the source decNumber */
|
| 4644 |
|
|
/* set is the context [used for length (digits) and rounding mode] */
|
| 4645 |
|
|
/* residue is the residue accumulator */
|
| 4646 |
|
|
/* status contains the current status to be updated */
|
| 4647 |
|
|
/* */
|
| 4648 |
|
|
/* (dest==src is allowed and will be a no-op if fits) */
|
| 4649 |
|
|
/* All fields are updated as required. */
|
| 4650 |
|
|
/* ------------------------------------------------------------------ */
|
| 4651 |
|
|
static void
|
| 4652 |
|
|
decCopyFit (decNumber * dest, const decNumber * src, decContext * set,
|
| 4653 |
|
|
Int * residue, uInt * status)
|
| 4654 |
|
|
{
|
| 4655 |
|
|
dest->bits = src->bits;
|
| 4656 |
|
|
dest->exponent = src->exponent;
|
| 4657 |
|
|
decSetCoeff (dest, set, src->lsu, src->digits, residue, status);
|
| 4658 |
|
|
}
|
| 4659 |
|
|
|
| 4660 |
|
|
/* ------------------------------------------------------------------ */
|
| 4661 |
|
|
/* decSetCoeff -- set the coefficient of a number */
|
| 4662 |
|
|
/* */
|
| 4663 |
|
|
/* dn is the number whose coefficient array is to be set. */
|
| 4664 |
|
|
/* It must have space for set->digits digits */
|
| 4665 |
|
|
/* set is the context [for size] */
|
| 4666 |
|
|
/* lsu -> lsu of the source coefficient [may be dn->lsu] */
|
| 4667 |
|
|
/* len is digits in the source coefficient [may be dn->digits] */
|
| 4668 |
|
|
/* residue is the residue accumulator. This has values as in */
|
| 4669 |
|
|
/* decApplyRound, and will be unchanged unless the */
|
| 4670 |
|
|
/* target size is less than len. In this case, the */
|
| 4671 |
|
|
/* coefficient is truncated and the residue is updated to */
|
| 4672 |
|
|
/* reflect the previous residue and the dropped digits. */
|
| 4673 |
|
|
/* status is the status accumulator, as usual */
|
| 4674 |
|
|
/* */
|
| 4675 |
|
|
/* The coefficient may already be in the number, or it can be an */
|
| 4676 |
|
|
/* external intermediate array. If it is in the number, lsu must == */
|
| 4677 |
|
|
/* dn->lsu and len must == dn->digits. */
|
| 4678 |
|
|
/* */
|
| 4679 |
|
|
/* Note that the coefficient length (len) may be < set->digits, and */
|
| 4680 |
|
|
/* in this case this merely copies the coefficient (or is a no-op */
|
| 4681 |
|
|
/* if dn->lsu==lsu). */
|
| 4682 |
|
|
/* */
|
| 4683 |
|
|
/* Note also that (only internally, from decNumberRescale and */
|
| 4684 |
|
|
/* decSetSubnormal) the value of set->digits may be less than one, */
|
| 4685 |
|
|
/* indicating a round to left. */
|
| 4686 |
|
|
/* This routine handles that case correctly; caller ensures space. */
|
| 4687 |
|
|
/* */
|
| 4688 |
|
|
/* dn->digits, dn->lsu (and as required), and dn->exponent are */
|
| 4689 |
|
|
/* updated as necessary. dn->bits (sign) is unchanged. */
|
| 4690 |
|
|
/* */
|
| 4691 |
|
|
/* DEC_Rounded status is set if any digits are discarded. */
|
| 4692 |
|
|
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
|
| 4693 |
|
|
/* incoming residue was non-0 (implies rounded) */
|
| 4694 |
|
|
/* ------------------------------------------------------------------ */
|
| 4695 |
|
|
/* mapping array: maps 0-9 to canonical residues, so that we can */
|
| 4696 |
|
|
/* adjust by a residue in range [-1, +1] and achieve correct rounding */
|
| 4697 |
|
|
/* 0 1 2 3 4 5 6 7 8 9 */
|
| 4698 |
|
|
static const uByte resmap[10] = { 0, 3, 3, 3, 3, 5, 7, 7, 7, 7 };
|
| 4699 |
|
|
static void
|
| 4700 |
|
|
decSetCoeff (decNumber * dn, decContext * set, const Unit * lsu,
|
| 4701 |
|
|
Int len, Int * residue, uInt * status)
|
| 4702 |
|
|
{
|
| 4703 |
|
|
Int discard; /* number of digits to discard */
|
| 4704 |
|
|
uInt discard1; /* first discarded digit */
|
| 4705 |
|
|
uInt cut; /* cut point in Unit */
|
| 4706 |
|
|
uInt quot, rem; /* for divisions */
|
| 4707 |
|
|
Unit *target; /* work */
|
| 4708 |
|
|
const Unit *up; /* work */
|
| 4709 |
|
|
Int count; /* .. */
|
| 4710 |
|
|
#if DECDPUN<=4
|
| 4711 |
|
|
uInt temp; /* .. */
|
| 4712 |
|
|
#endif
|
| 4713 |
|
|
|
| 4714 |
|
|
discard = len - set->digits; /* digits to discard */
|
| 4715 |
|
|
if (discard <= 0)
|
| 4716 |
|
|
{ /* no digits are being discarded */
|
| 4717 |
|
|
if (dn->lsu != lsu)
|
| 4718 |
|
|
{ /* copy needed */
|
| 4719 |
|
|
/* copy the coefficient array to the result number; no shift needed */
|
| 4720 |
|
|
up = lsu;
|
| 4721 |
|
|
for (target = dn->lsu; target < dn->lsu + D2U (len); target++, up++)
|
| 4722 |
|
|
{
|
| 4723 |
|
|
*target = *up;
|
| 4724 |
|
|
}
|
| 4725 |
|
|
dn->digits = len; /* set the new length */
|
| 4726 |
|
|
}
|
| 4727 |
|
|
/* dn->exponent and residue are unchanged */
|
| 4728 |
|
|
if (*residue != 0)
|
| 4729 |
|
|
*status |= (DEC_Inexact | DEC_Rounded); /* record inexactitude */
|
| 4730 |
|
|
return;
|
| 4731 |
|
|
}
|
| 4732 |
|
|
|
| 4733 |
|
|
/* we have to discard some digits */
|
| 4734 |
|
|
*status |= DEC_Rounded; /* accumulate Rounded status */
|
| 4735 |
|
|
if (*residue > 1)
|
| 4736 |
|
|
*residue = 1; /* previous residue now to right, so -1 to +1 */
|
| 4737 |
|
|
|
| 4738 |
|
|
if (discard > len)
|
| 4739 |
|
|
{ /* everything, +1, is being discarded */
|
| 4740 |
|
|
/* guard digit is 0 */
|
| 4741 |
|
|
/* residue is all the number [NB could be all 0s] */
|
| 4742 |
|
|
if (*residue <= 0)
|
| 4743 |
|
|
for (up = lsu + D2U (len) - 1; up >= lsu; up--)
|
| 4744 |
|
|
{
|
| 4745 |
|
|
if (*up != 0)
|
| 4746 |
|
|
{ /* found a non-0 */
|
| 4747 |
|
|
*residue = 1;
|
| 4748 |
|
|
break; /* no need to check any others */
|
| 4749 |
|
|
}
|
| 4750 |
|
|
}
|
| 4751 |
|
|
if (*residue != 0)
|
| 4752 |
|
|
*status |= DEC_Inexact; /* record inexactitude */
|
| 4753 |
|
|
*dn->lsu = 0; /* coefficient will now be 0 */
|
| 4754 |
|
|
dn->digits = 1; /* .. */
|
| 4755 |
|
|
dn->exponent += discard; /* maintain numerical value */
|
| 4756 |
|
|
return;
|
| 4757 |
|
|
} /* total discard */
|
| 4758 |
|
|
|
| 4759 |
|
|
/* partial discard [most common case] */
|
| 4760 |
|
|
/* here, at least the first (most significant) discarded digit exists */
|
| 4761 |
|
|
|
| 4762 |
|
|
/* spin up the number, noting residue as we pass, until we get to */
|
| 4763 |
|
|
/* the Unit with the first discarded digit. When we get there, */
|
| 4764 |
|
|
/* extract it and remember where we're at */
|
| 4765 |
|
|
count = 0;
|
| 4766 |
|
|
for (up = lsu;; up++)
|
| 4767 |
|
|
{
|
| 4768 |
|
|
count += DECDPUN;
|
| 4769 |
|
|
if (count >= discard)
|
| 4770 |
|
|
break; /* full ones all checked */
|
| 4771 |
|
|
if (*up != 0)
|
| 4772 |
|
|
*residue = 1;
|
| 4773 |
|
|
} /* up */
|
| 4774 |
|
|
|
| 4775 |
|
|
/* here up -> Unit with discarded digit */
|
| 4776 |
|
|
cut = discard - (count - DECDPUN) - 1;
|
| 4777 |
|
|
if (cut == DECDPUN - 1)
|
| 4778 |
|
|
{ /* discard digit is at top */
|
| 4779 |
|
|
#if DECDPUN<=4
|
| 4780 |
|
|
discard1 = QUOT10 (*up, DECDPUN - 1);
|
| 4781 |
|
|
rem = *up - discard1 * powers[DECDPUN - 1];
|
| 4782 |
|
|
#else
|
| 4783 |
|
|
rem = *up % powers[DECDPUN - 1];
|
| 4784 |
|
|
discard1 = *up / powers[DECDPUN - 1];
|
| 4785 |
|
|
#endif
|
| 4786 |
|
|
if (rem != 0)
|
| 4787 |
|
|
*residue = 1;
|
| 4788 |
|
|
up++; /* move to next */
|
| 4789 |
|
|
cut = 0; /* bottom digit of result */
|
| 4790 |
|
|
quot = 0; /* keep a certain compiler happy */
|
| 4791 |
|
|
}
|
| 4792 |
|
|
else
|
| 4793 |
|
|
{
|
| 4794 |
|
|
/* discard digit is in low digit(s), not top digit */
|
| 4795 |
|
|
if (cut == 0)
|
| 4796 |
|
|
quot = *up;
|
| 4797 |
|
|
else /* cut>0 */
|
| 4798 |
|
|
{ /* it's not at bottom of Unit */
|
| 4799 |
|
|
#if DECDPUN<=4
|
| 4800 |
|
|
quot = QUOT10 (*up, cut);
|
| 4801 |
|
|
rem = *up - quot * powers[cut];
|
| 4802 |
|
|
#else
|
| 4803 |
|
|
rem = *up % powers[cut];
|
| 4804 |
|
|
quot = *up / powers[cut];
|
| 4805 |
|
|
#endif
|
| 4806 |
|
|
if (rem != 0)
|
| 4807 |
|
|
*residue = 1;
|
| 4808 |
|
|
}
|
| 4809 |
|
|
/* discard digit is now at bottom of quot */
|
| 4810 |
|
|
#if DECDPUN<=4
|
| 4811 |
|
|
temp = (quot * 6554) >> 16; /* fast /10 */
|
| 4812 |
|
|
/* Vowels algorithm here not a win (9 instructions) */
|
| 4813 |
|
|
discard1 = quot - X10 (temp);
|
| 4814 |
|
|
quot = temp;
|
| 4815 |
|
|
#else
|
| 4816 |
|
|
discard1 = quot % 10;
|
| 4817 |
|
|
quot = quot / 10;
|
| 4818 |
|
|
#endif
|
| 4819 |
|
|
cut++; /* update cut */
|
| 4820 |
|
|
}
|
| 4821 |
|
|
|
| 4822 |
|
|
/* here: up -> Unit of the array with discarded digit */
|
| 4823 |
|
|
/* cut is the division point for each Unit */
|
| 4824 |
|
|
/* quot holds the uncut high-order digits for the current */
|
| 4825 |
|
|
/* Unit, unless cut==0 in which case it's still in *up */
|
| 4826 |
|
|
/* copy the coefficient array to the result number, shifting as we go */
|
| 4827 |
|
|
count = set->digits; /* digits to end up with */
|
| 4828 |
|
|
if (count <= 0)
|
| 4829 |
|
|
{ /* special for Rescale/Subnormal :-( */
|
| 4830 |
|
|
*dn->lsu = 0; /* .. result is 0 */
|
| 4831 |
|
|
dn->digits = 1; /* .. */
|
| 4832 |
|
|
}
|
| 4833 |
|
|
else
|
| 4834 |
|
|
{ /* shift to least */
|
| 4835 |
|
|
/* [this is similar to decShiftToLeast code, with copy] */
|
| 4836 |
|
|
dn->digits = count; /* set the new length */
|
| 4837 |
|
|
if (cut == 0)
|
| 4838 |
|
|
{
|
| 4839 |
|
|
/* on unit boundary, so simple shift down copy loop suffices */
|
| 4840 |
|
|
for (target = dn->lsu; target < dn->lsu + D2U (count);
|
| 4841 |
|
|
target++, up++)
|
| 4842 |
|
|
{
|
| 4843 |
|
|
*target = *up;
|
| 4844 |
|
|
}
|
| 4845 |
|
|
}
|
| 4846 |
|
|
else
|
| 4847 |
|
|
for (target = dn->lsu;; target++)
|
| 4848 |
|
|
{
|
| 4849 |
|
|
*target = (Unit) quot;
|
| 4850 |
|
|
count -= (DECDPUN - cut);
|
| 4851 |
|
|
if (count <= 0)
|
| 4852 |
|
|
break;
|
| 4853 |
|
|
up++;
|
| 4854 |
|
|
quot = *up;
|
| 4855 |
|
|
#if DECDPUN<=4
|
| 4856 |
|
|
quot = QUOT10 (quot, cut);
|
| 4857 |
|
|
rem = *up - quot * powers[cut];
|
| 4858 |
|
|
#else
|
| 4859 |
|
|
rem = quot % powers[cut];
|
| 4860 |
|
|
quot = quot / powers[cut];
|
| 4861 |
|
|
#endif
|
| 4862 |
|
|
*target = (Unit) (*target + rem * powers[DECDPUN - cut]);
|
| 4863 |
|
|
count -= cut;
|
| 4864 |
|
|
if (count <= 0)
|
| 4865 |
|
|
break;
|
| 4866 |
|
|
}
|
| 4867 |
|
|
} /* shift to least needed */
|
| 4868 |
|
|
dn->exponent += discard; /* maintain numerical value */
|
| 4869 |
|
|
|
| 4870 |
|
|
/* here, discard1 is the guard digit, and residue is everything else */
|
| 4871 |
|
|
/* [use mapping to accumulate residue safely] */
|
| 4872 |
|
|
*residue += resmap[discard1];
|
| 4873 |
|
|
|
| 4874 |
|
|
if (*residue != 0)
|
| 4875 |
|
|
*status |= DEC_Inexact; /* record inexactitude */
|
| 4876 |
|
|
return;
|
| 4877 |
|
|
}
|
| 4878 |
|
|
|
| 4879 |
|
|
/* ------------------------------------------------------------------ */
|
| 4880 |
|
|
/* decApplyRound -- apply pending rounding to a number */
|
| 4881 |
|
|
/* */
|
| 4882 |
|
|
/* dn is the number, with space for set->digits digits */
|
| 4883 |
|
|
/* set is the context [for size and rounding mode] */
|
| 4884 |
|
|
/* residue indicates pending rounding, being any accumulated */
|
| 4885 |
|
|
/* guard and sticky information. It may be: */
|
| 4886 |
|
|
/* 6-9: rounding digit is >5 */
|
| 4887 |
|
|
/* 5: rounding digit is exactly half-way */
|
| 4888 |
|
|
/* 1-4: rounding digit is <5 and >0 */
|
| 4889 |
|
|
/* 0: the coefficient is exact */
|
| 4890 |
|
|
/* -1: as 1, but the hidden digits are subtractive, that */
|
| 4891 |
|
|
/* is, of the opposite sign to dn. In this case the */
|
| 4892 |
|
|
/* coefficient must be non-0. */
|
| 4893 |
|
|
/* status is the status accumulator, as usual */
|
| 4894 |
|
|
/* */
|
| 4895 |
|
|
/* This routine applies rounding while keeping the length of the */
|
| 4896 |
|
|
/* coefficient constant. The exponent and status are unchanged */
|
| 4897 |
|
|
/* except if: */
|
| 4898 |
|
|
/* */
|
| 4899 |
|
|
/* -- the coefficient was increased and is all nines (in which */
|
| 4900 |
|
|
/* case Overflow could occur, and is handled directly here so */
|
| 4901 |
|
|
/* the caller does not need to re-test for overflow) */
|
| 4902 |
|
|
/* */
|
| 4903 |
|
|
/* -- the coefficient was decreased and becomes all nines (in which */
|
| 4904 |
|
|
/* case Underflow could occur, and is also handled directly). */
|
| 4905 |
|
|
/* */
|
| 4906 |
|
|
/* All fields in dn are updated as required. */
|
| 4907 |
|
|
/* */
|
| 4908 |
|
|
/* ------------------------------------------------------------------ */
|
| 4909 |
|
|
static void
|
| 4910 |
|
|
decApplyRound (decNumber * dn, decContext * set, Int residue, uInt * status)
|
| 4911 |
|
|
{
|
| 4912 |
|
|
Int bump; /* 1 if coefficient needs to be incremented */
|
| 4913 |
|
|
/* -1 if coefficient needs to be decremented */
|
| 4914 |
|
|
|
| 4915 |
|
|
if (residue == 0)
|
| 4916 |
|
|
return; /* nothing to apply */
|
| 4917 |
|
|
|
| 4918 |
|
|
bump = 0; /* assume a smooth ride */
|
| 4919 |
|
|
|
| 4920 |
|
|
/* now decide whether, and how, to round, depending on mode */
|
| 4921 |
|
|
switch (set->round)
|
| 4922 |
|
|
{
|
| 4923 |
|
|
case DEC_ROUND_DOWN:
|
| 4924 |
|
|
{
|
| 4925 |
|
|
/* no change, except if negative residue */
|
| 4926 |
|
|
if (residue < 0)
|
| 4927 |
|
|
bump = -1;
|
| 4928 |
|
|
break;
|
| 4929 |
|
|
} /* r-d */
|
| 4930 |
|
|
|
| 4931 |
|
|
case DEC_ROUND_HALF_DOWN:
|
| 4932 |
|
|
{
|
| 4933 |
|
|
if (residue > 5)
|
| 4934 |
|
|
bump = 1;
|
| 4935 |
|
|
break;
|
| 4936 |
|
|
} /* r-h-d */
|
| 4937 |
|
|
|
| 4938 |
|
|
case DEC_ROUND_HALF_EVEN:
|
| 4939 |
|
|
{
|
| 4940 |
|
|
if (residue > 5)
|
| 4941 |
|
|
bump = 1; /* >0.5 goes up */
|
| 4942 |
|
|
else if (residue == 5)
|
| 4943 |
|
|
{ /* exactly 0.5000... */
|
| 4944 |
|
|
/* 0.5 goes up iff [new] lsd is odd */
|
| 4945 |
|
|
if (*dn->lsu & 0x01)
|
| 4946 |
|
|
bump = 1;
|
| 4947 |
|
|
}
|
| 4948 |
|
|
break;
|
| 4949 |
|
|
} /* r-h-e */
|
| 4950 |
|
|
|
| 4951 |
|
|
case DEC_ROUND_HALF_UP:
|
| 4952 |
|
|
{
|
| 4953 |
|
|
if (residue >= 5)
|
| 4954 |
|
|
bump = 1;
|
| 4955 |
|
|
break;
|
| 4956 |
|
|
} /* r-h-u */
|
| 4957 |
|
|
|
| 4958 |
|
|
case DEC_ROUND_UP:
|
| 4959 |
|
|
{
|
| 4960 |
|
|
if (residue > 0)
|
| 4961 |
|
|
bump = 1;
|
| 4962 |
|
|
break;
|
| 4963 |
|
|
} /* r-u */
|
| 4964 |
|
|
|
| 4965 |
|
|
case DEC_ROUND_CEILING:
|
| 4966 |
|
|
{
|
| 4967 |
|
|
/* same as _UP for positive numbers, and as _DOWN for negatives */
|
| 4968 |
|
|
/* [negative residue cannot occur on 0] */
|
| 4969 |
|
|
if (decNumberIsNegative (dn))
|
| 4970 |
|
|
{
|
| 4971 |
|
|
if (residue < 0)
|
| 4972 |
|
|
bump = -1;
|
| 4973 |
|
|
}
|
| 4974 |
|
|
else
|
| 4975 |
|
|
{
|
| 4976 |
|
|
if (residue > 0)
|
| 4977 |
|
|
bump = 1;
|
| 4978 |
|
|
}
|
| 4979 |
|
|
break;
|
| 4980 |
|
|
} /* r-c */
|
| 4981 |
|
|
|
| 4982 |
|
|
case DEC_ROUND_FLOOR:
|
| 4983 |
|
|
{
|
| 4984 |
|
|
/* same as _UP for negative numbers, and as _DOWN for positive */
|
| 4985 |
|
|
/* [negative residue cannot occur on 0] */
|
| 4986 |
|
|
if (!decNumberIsNegative (dn))
|
| 4987 |
|
|
{
|
| 4988 |
|
|
if (residue < 0)
|
| 4989 |
|
|
bump = -1;
|
| 4990 |
|
|
}
|
| 4991 |
|
|
else
|
| 4992 |
|
|
{
|
| 4993 |
|
|
if (residue > 0)
|
| 4994 |
|
|
bump = 1;
|
| 4995 |
|
|
}
|
| 4996 |
|
|
break;
|
| 4997 |
|
|
} /* r-f */
|
| 4998 |
|
|
|
| 4999 |
|
|
default:
|
| 5000 |
|
|
{ /* e.g., DEC_ROUND_MAX */
|
| 5001 |
|
|
*status |= DEC_Invalid_context;
|
| 5002 |
|
|
#if DECTRACE
|
| 5003 |
|
|
printf ("Unknown rounding mode: %d\n", set->round);
|
| 5004 |
|
|
#endif
|
| 5005 |
|
|
break;
|
| 5006 |
|
|
}
|
| 5007 |
|
|
} /* switch */
|
| 5008 |
|
|
|
| 5009 |
|
|
/* now bump the number, up or down, if need be */
|
| 5010 |
|
|
if (bump == 0)
|
| 5011 |
|
|
return; /* no action required */
|
| 5012 |
|
|
|
| 5013 |
|
|
/* Simply use decUnitAddSub unless we are bumping up and the number */
|
| 5014 |
|
|
/* is all nines. In this special case we set to 1000... and adjust */
|
| 5015 |
|
|
/* the exponent by one (as otherwise we could overflow the array) */
|
| 5016 |
|
|
/* Similarly handle all-nines result if bumping down. */
|
| 5017 |
|
|
if (bump > 0)
|
| 5018 |
|
|
{
|
| 5019 |
|
|
Unit *up; /* work */
|
| 5020 |
|
|
uInt count = dn->digits; /* digits to be checked */
|
| 5021 |
|
|
for (up = dn->lsu;; up++)
|
| 5022 |
|
|
{
|
| 5023 |
|
|
if (count <= DECDPUN)
|
| 5024 |
|
|
{
|
| 5025 |
|
|
/* this is the last Unit (the msu) */
|
| 5026 |
|
|
if (*up != powers[count] - 1)
|
| 5027 |
|
|
break; /* not still 9s */
|
| 5028 |
|
|
/* here if it, too, is all nines */
|
| 5029 |
|
|
*up = (Unit) powers[count - 1]; /* here 999 -> 100 etc. */
|
| 5030 |
|
|
for (up = up - 1; up >= dn->lsu; up--)
|
| 5031 |
|
|
*up = 0; /* others all to 0 */
|
| 5032 |
|
|
dn->exponent++; /* and bump exponent */
|
| 5033 |
|
|
/* [which, very rarely, could cause Overflow...] */
|
| 5034 |
|
|
if ((dn->exponent + dn->digits) > set->emax + 1)
|
| 5035 |
|
|
{
|
| 5036 |
|
|
decSetOverflow (dn, set, status);
|
| 5037 |
|
|
}
|
| 5038 |
|
|
return; /* done */
|
| 5039 |
|
|
}
|
| 5040 |
|
|
/* a full unit to check, with more to come */
|
| 5041 |
|
|
if (*up != DECDPUNMAX)
|
| 5042 |
|
|
break; /* not still 9s */
|
| 5043 |
|
|
count -= DECDPUN;
|
| 5044 |
|
|
} /* up */
|
| 5045 |
|
|
} /* bump>0 */
|
| 5046 |
|
|
else
|
| 5047 |
|
|
{ /* -1 */
|
| 5048 |
|
|
/* here we are lookng for a pre-bump of 1000... (leading 1, */
|
| 5049 |
|
|
/* all other digits zero) */
|
| 5050 |
|
|
Unit *up, *sup; /* work */
|
| 5051 |
|
|
uInt count = dn->digits; /* digits to be checked */
|
| 5052 |
|
|
for (up = dn->lsu;; up++)
|
| 5053 |
|
|
{
|
| 5054 |
|
|
if (count <= DECDPUN)
|
| 5055 |
|
|
{
|
| 5056 |
|
|
/* this is the last Unit (the msu) */
|
| 5057 |
|
|
if (*up != powers[count - 1])
|
| 5058 |
|
|
break; /* not 100.. */
|
| 5059 |
|
|
/* here if we have the 1000... case */
|
| 5060 |
|
|
sup = up; /* save msu pointer */
|
| 5061 |
|
|
*up = (Unit) powers[count] - 1; /* here 100 in msu -> 999 */
|
| 5062 |
|
|
/* others all to all-nines, too */
|
| 5063 |
|
|
for (up = up - 1; up >= dn->lsu; up--)
|
| 5064 |
|
|
*up = (Unit) powers[DECDPUN] - 1;
|
| 5065 |
|
|
dn->exponent--; /* and bump exponent */
|
| 5066 |
|
|
|
| 5067 |
|
|
/* iff the number was at the subnormal boundary (exponent=etiny) */
|
| 5068 |
|
|
/* then the exponent is now out of range, so it will in fact get */
|
| 5069 |
|
|
/* clamped to etiny and the final 9 dropped. */
|
| 5070 |
|
|
/* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
|
| 5071 |
|
|
/* dn->exponent, set->digits); */
|
| 5072 |
|
|
if (dn->exponent + 1 == set->emin - set->digits + 1)
|
| 5073 |
|
|
{
|
| 5074 |
|
|
if (count == 1 && dn->digits == 1)
|
| 5075 |
|
|
*sup = 0; /* here 9 -> 0[.9] */
|
| 5076 |
|
|
else
|
| 5077 |
|
|
{
|
| 5078 |
|
|
*sup = (Unit) powers[count - 1] - 1; /* here 999.. in msu -> 99.. */
|
| 5079 |
|
|
dn->digits--;
|
| 5080 |
|
|
}
|
| 5081 |
|
|
dn->exponent++;
|
| 5082 |
|
|
*status |=
|
| 5083 |
|
|
DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| 5084 |
|
|
}
|
| 5085 |
|
|
return; /* done */
|
| 5086 |
|
|
}
|
| 5087 |
|
|
|
| 5088 |
|
|
/* a full unit to check, with more to come */
|
| 5089 |
|
|
if (*up != 0)
|
| 5090 |
|
|
break; /* not still 0s */
|
| 5091 |
|
|
count -= DECDPUN;
|
| 5092 |
|
|
} /* up */
|
| 5093 |
|
|
|
| 5094 |
|
|
} /* bump<0 */
|
| 5095 |
|
|
|
| 5096 |
|
|
/* Actual bump needed. Do it. */
|
| 5097 |
|
|
decUnitAddSub (dn->lsu, D2U (dn->digits), one, 1, 0, dn->lsu, bump);
|
| 5098 |
|
|
}
|
| 5099 |
|
|
|
| 5100 |
|
|
#if DECSUBSET
|
| 5101 |
|
|
/* ------------------------------------------------------------------ */
|
| 5102 |
|
|
/* decFinish -- finish processing a number */
|
| 5103 |
|
|
/* */
|
| 5104 |
|
|
/* dn is the number */
|
| 5105 |
|
|
/* set is the context */
|
| 5106 |
|
|
/* residue is the rounding accumulator (as in decApplyRound) */
|
| 5107 |
|
|
/* status is the accumulator */
|
| 5108 |
|
|
/* */
|
| 5109 |
|
|
/* This finishes off the current number by: */
|
| 5110 |
|
|
/* 1. If not extended: */
|
| 5111 |
|
|
/* a. Converting a zero result to clean '0' */
|
| 5112 |
|
|
/* b. Reducing positive exponents to 0, if would fit in digits */
|
| 5113 |
|
|
/* 2. Checking for overflow and subnormals (always) */
|
| 5114 |
|
|
/* Note this is just Finalize when no subset arithmetic. */
|
| 5115 |
|
|
/* All fields are updated as required. */
|
| 5116 |
|
|
/* ------------------------------------------------------------------ */
|
| 5117 |
|
|
static void
|
| 5118 |
|
|
decFinish (decNumber * dn, decContext * set, Int * residue, uInt * status)
|
| 5119 |
|
|
{
|
| 5120 |
|
|
if (!set->extended)
|
| 5121 |
|
|
{
|
| 5122 |
|
|
if ISZERO
|
| 5123 |
|
|
(dn)
|
| 5124 |
|
|
{ /* value is zero */
|
| 5125 |
|
|
dn->exponent = 0; /* clean exponent .. */
|
| 5126 |
|
|
dn->bits = 0; /* .. and sign */
|
| 5127 |
|
|
return; /* no error possible */
|
| 5128 |
|
|
}
|
| 5129 |
|
|
if (dn->exponent >= 0)
|
| 5130 |
|
|
{ /* non-negative exponent */
|
| 5131 |
|
|
/* >0; reduce to integer if possible */
|
| 5132 |
|
|
if (set->digits >= (dn->exponent + dn->digits))
|
| 5133 |
|
|
{
|
| 5134 |
|
|
dn->digits = decShiftToMost (dn->lsu, dn->digits, dn->exponent);
|
| 5135 |
|
|
dn->exponent = 0;
|
| 5136 |
|
|
}
|
| 5137 |
|
|
}
|
| 5138 |
|
|
} /* !extended */
|
| 5139 |
|
|
|
| 5140 |
|
|
decFinalize (dn, set, residue, status);
|
| 5141 |
|
|
}
|
| 5142 |
|
|
#endif
|
| 5143 |
|
|
|
| 5144 |
|
|
/* ------------------------------------------------------------------ */
|
| 5145 |
|
|
/* decFinalize -- final check, clamp, and round of a number */
|
| 5146 |
|
|
/* */
|
| 5147 |
|
|
/* dn is the number */
|
| 5148 |
|
|
/* set is the context */
|
| 5149 |
|
|
/* residue is the rounding accumulator (as in decApplyRound) */
|
| 5150 |
|
|
/* status is the status accumulator */
|
| 5151 |
|
|
/* */
|
| 5152 |
|
|
/* This finishes off the current number by checking for subnormal */
|
| 5153 |
|
|
/* results, applying any pending rounding, checking for overflow, */
|
| 5154 |
|
|
/* and applying any clamping. */
|
| 5155 |
|
|
/* Underflow and overflow conditions are raised as appropriate. */
|
| 5156 |
|
|
/* All fields are updated as required. */
|
| 5157 |
|
|
/* ------------------------------------------------------------------ */
|
| 5158 |
|
|
static void
|
| 5159 |
|
|
decFinalize (decNumber * dn, decContext * set, Int * residue, uInt * status)
|
| 5160 |
|
|
{
|
| 5161 |
|
|
Int shift; /* shift needed if clamping */
|
| 5162 |
|
|
|
| 5163 |
|
|
/* We have to be careful when checking the exponent as the adjusted */
|
| 5164 |
|
|
/* exponent could overflow 31 bits [because it may already be up */
|
| 5165 |
|
|
/* to twice the expected]. */
|
| 5166 |
|
|
|
| 5167 |
|
|
/* First test for subnormal. This must be done before any final */
|
| 5168 |
|
|
/* round as the result could be rounded to Nmin or 0. */
|
| 5169 |
|
|
if (dn->exponent < 0 /* negative exponent */
|
| 5170 |
|
|
&& (dn->exponent < set->emin - dn->digits + 1))
|
| 5171 |
|
|
{
|
| 5172 |
|
|
/* Go handle subnormals; this will apply round if needed. */
|
| 5173 |
|
|
decSetSubnormal (dn, set, residue, status);
|
| 5174 |
|
|
return;
|
| 5175 |
|
|
}
|
| 5176 |
|
|
|
| 5177 |
|
|
/* now apply any pending round (this could raise overflow). */
|
| 5178 |
|
|
if (*residue != 0)
|
| 5179 |
|
|
decApplyRound (dn, set, *residue, status);
|
| 5180 |
|
|
|
| 5181 |
|
|
/* Check for overflow [redundant in the 'rare' case] or clamp */
|
| 5182 |
|
|
if (dn->exponent <= set->emax - set->digits + 1)
|
| 5183 |
|
|
return; /* neither needed */
|
| 5184 |
|
|
|
| 5185 |
|
|
/* here when we might have an overflow or clamp to do */
|
| 5186 |
|
|
if (dn->exponent > set->emax - dn->digits + 1)
|
| 5187 |
|
|
{ /* too big */
|
| 5188 |
|
|
decSetOverflow (dn, set, status);
|
| 5189 |
|
|
return;
|
| 5190 |
|
|
}
|
| 5191 |
|
|
/* here when the result is normal but in clamp range */
|
| 5192 |
|
|
if (!set->clamp)
|
| 5193 |
|
|
return;
|
| 5194 |
|
|
|
| 5195 |
|
|
/* here when we need to apply the IEEE exponent clamp (fold-down) */
|
| 5196 |
|
|
shift = dn->exponent - (set->emax - set->digits + 1);
|
| 5197 |
|
|
|
| 5198 |
|
|
/* shift coefficient (if non-zero) */
|
| 5199 |
|
|
if (!ISZERO (dn))
|
| 5200 |
|
|
{
|
| 5201 |
|
|
dn->digits = decShiftToMost (dn->lsu, dn->digits, shift);
|
| 5202 |
|
|
}
|
| 5203 |
|
|
dn->exponent -= shift; /* adjust the exponent to match */
|
| 5204 |
|
|
*status |= DEC_Clamped; /* and record the dirty deed */
|
| 5205 |
|
|
return;
|
| 5206 |
|
|
}
|
| 5207 |
|
|
|
| 5208 |
|
|
/* ------------------------------------------------------------------ */
|
| 5209 |
|
|
/* decSetOverflow -- set number to proper overflow value */
|
| 5210 |
|
|
/* */
|
| 5211 |
|
|
/* dn is the number (used for sign [only] and result) */
|
| 5212 |
|
|
/* set is the context [used for the rounding mode] */
|
| 5213 |
|
|
/* status contains the current status to be updated */
|
| 5214 |
|
|
/* */
|
| 5215 |
|
|
/* This sets the sign of a number and sets its value to either */
|
| 5216 |
|
|
/* Infinity or the maximum finite value, depending on the sign of */
|
| 5217 |
|
|
/* dn and therounding mode, following IEEE 854 rules. */
|
| 5218 |
|
|
/* ------------------------------------------------------------------ */
|
| 5219 |
|
|
static void
|
| 5220 |
|
|
decSetOverflow (decNumber * dn, decContext * set, uInt * status)
|
| 5221 |
|
|
{
|
| 5222 |
|
|
Flag needmax = 0; /* result is maximum finite value */
|
| 5223 |
|
|
uByte sign = dn->bits & DECNEG; /* clean and save sign bit */
|
| 5224 |
|
|
|
| 5225 |
|
|
if (ISZERO (dn))
|
| 5226 |
|
|
{ /* zero does not overflow magnitude */
|
| 5227 |
|
|
Int emax = set->emax; /* limit value */
|
| 5228 |
|
|
if (set->clamp)
|
| 5229 |
|
|
emax -= set->digits - 1; /* lower if clamping */
|
| 5230 |
|
|
if (dn->exponent > emax)
|
| 5231 |
|
|
{ /* clamp required */
|
| 5232 |
|
|
dn->exponent = emax;
|
| 5233 |
|
|
*status |= DEC_Clamped;
|
| 5234 |
|
|
}
|
| 5235 |
|
|
return;
|
| 5236 |
|
|
}
|
| 5237 |
|
|
|
| 5238 |
|
|
decNumberZero (dn);
|
| 5239 |
|
|
switch (set->round)
|
| 5240 |
|
|
{
|
| 5241 |
|
|
case DEC_ROUND_DOWN:
|
| 5242 |
|
|
{
|
| 5243 |
|
|
needmax = 1; /* never Infinity */
|
| 5244 |
|
|
break;
|
| 5245 |
|
|
} /* r-d */
|
| 5246 |
|
|
case DEC_ROUND_CEILING:
|
| 5247 |
|
|
{
|
| 5248 |
|
|
if (sign)
|
| 5249 |
|
|
needmax = 1; /* Infinity if non-negative */
|
| 5250 |
|
|
break;
|
| 5251 |
|
|
} /* r-c */
|
| 5252 |
|
|
case DEC_ROUND_FLOOR:
|
| 5253 |
|
|
{
|
| 5254 |
|
|
if (!sign)
|
| 5255 |
|
|
needmax = 1; /* Infinity if negative */
|
| 5256 |
|
|
break;
|
| 5257 |
|
|
} /* r-f */
|
| 5258 |
|
|
default:
|
| 5259 |
|
|
break; /* Infinity in all other cases */
|
| 5260 |
|
|
}
|
| 5261 |
|
|
if (needmax)
|
| 5262 |
|
|
{
|
| 5263 |
|
|
Unit *up; /* work */
|
| 5264 |
|
|
Int count = set->digits; /* nines to add */
|
| 5265 |
|
|
dn->digits = count;
|
| 5266 |
|
|
/* fill in all nines to set maximum value */
|
| 5267 |
|
|
for (up = dn->lsu;; up++)
|
| 5268 |
|
|
{
|
| 5269 |
|
|
if (count > DECDPUN)
|
| 5270 |
|
|
*up = DECDPUNMAX; /* unit full o'nines */
|
| 5271 |
|
|
else
|
| 5272 |
|
|
{ /* this is the msu */
|
| 5273 |
|
|
*up = (Unit) (powers[count] - 1);
|
| 5274 |
|
|
break;
|
| 5275 |
|
|
}
|
| 5276 |
|
|
count -= DECDPUN; /* we filled those digits */
|
| 5277 |
|
|
} /* up */
|
| 5278 |
|
|
dn->bits = sign; /* sign */
|
| 5279 |
|
|
dn->exponent = set->emax - set->digits + 1;
|
| 5280 |
|
|
}
|
| 5281 |
|
|
else
|
| 5282 |
|
|
dn->bits = sign | DECINF; /* Value is +/-Infinity */
|
| 5283 |
|
|
*status |= DEC_Overflow | DEC_Inexact | DEC_Rounded;
|
| 5284 |
|
|
}
|
| 5285 |
|
|
|
| 5286 |
|
|
/* ------------------------------------------------------------------ */
|
| 5287 |
|
|
/* decSetSubnormal -- process value whose exponent is <Emin */
|
| 5288 |
|
|
/* */
|
| 5289 |
|
|
/* dn is the number (used as input as well as output; it may have */
|
| 5290 |
|
|
/* an allowed subnormal value, which may need to be rounded) */
|
| 5291 |
|
|
/* set is the context [used for the rounding mode] */
|
| 5292 |
|
|
/* residue is any pending residue */
|
| 5293 |
|
|
/* status contains the current status to be updated */
|
| 5294 |
|
|
/* */
|
| 5295 |
|
|
/* If subset mode, set result to zero and set Underflow flags. */
|
| 5296 |
|
|
/* */
|
| 5297 |
|
|
/* Value may be zero with a low exponent; this does not set Subnormal */
|
| 5298 |
|
|
/* but the exponent will be clamped to Etiny. */
|
| 5299 |
|
|
/* */
|
| 5300 |
|
|
/* Otherwise ensure exponent is not out of range, and round as */
|
| 5301 |
|
|
/* necessary. Underflow is set if the result is Inexact. */
|
| 5302 |
|
|
/* ------------------------------------------------------------------ */
|
| 5303 |
|
|
static void
|
| 5304 |
|
|
decSetSubnormal (decNumber * dn, decContext * set,
|
| 5305 |
|
|
Int * residue, uInt * status)
|
| 5306 |
|
|
{
|
| 5307 |
|
|
decContext workset; /* work */
|
| 5308 |
|
|
Int etiny, adjust; /* .. */
|
| 5309 |
|
|
|
| 5310 |
|
|
#if DECSUBSET
|
| 5311 |
|
|
/* simple set to zero and 'hard underflow' for subset */
|
| 5312 |
|
|
if (!set->extended)
|
| 5313 |
|
|
{
|
| 5314 |
|
|
decNumberZero (dn);
|
| 5315 |
|
|
/* always full overflow */
|
| 5316 |
|
|
*status |= DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| 5317 |
|
|
return;
|
| 5318 |
|
|
}
|
| 5319 |
|
|
#endif
|
| 5320 |
|
|
|
| 5321 |
|
|
/* Full arithmetic -- allow subnormals, rounded to minimum exponent */
|
| 5322 |
|
|
/* (Etiny) if needed */
|
| 5323 |
|
|
etiny = set->emin - (set->digits - 1); /* smallest allowed exponent */
|
| 5324 |
|
|
|
| 5325 |
|
|
if ISZERO
|
| 5326 |
|
|
(dn)
|
| 5327 |
|
|
{ /* value is zero */
|
| 5328 |
|
|
/* residue can never be non-zero here */
|
| 5329 |
|
|
#if DECCHECK
|
| 5330 |
|
|
if (*residue != 0)
|
| 5331 |
|
|
{
|
| 5332 |
|
|
printf ("++ Subnormal 0 residue %d\n", *residue);
|
| 5333 |
|
|
*status |= DEC_Invalid_operation;
|
| 5334 |
|
|
}
|
| 5335 |
|
|
#endif
|
| 5336 |
|
|
if (dn->exponent < etiny)
|
| 5337 |
|
|
{ /* clamp required */
|
| 5338 |
|
|
dn->exponent = etiny;
|
| 5339 |
|
|
*status |= DEC_Clamped;
|
| 5340 |
|
|
}
|
| 5341 |
|
|
return;
|
| 5342 |
|
|
}
|
| 5343 |
|
|
|
| 5344 |
|
|
*status |= DEC_Subnormal; /* we have a non-zero subnormal */
|
| 5345 |
|
|
|
| 5346 |
|
|
adjust = etiny - dn->exponent; /* calculate digits to remove */
|
| 5347 |
|
|
if (adjust <= 0)
|
| 5348 |
|
|
{ /* not out of range; unrounded */
|
| 5349 |
|
|
/* residue can never be non-zero here, so fast-path out */
|
| 5350 |
|
|
#if DECCHECK
|
| 5351 |
|
|
if (*residue != 0)
|
| 5352 |
|
|
{
|
| 5353 |
|
|
printf ("++ Subnormal no-adjust residue %d\n", *residue);
|
| 5354 |
|
|
*status |= DEC_Invalid_operation;
|
| 5355 |
|
|
}
|
| 5356 |
|
|
#endif
|
| 5357 |
|
|
/* it may already be inexact (from setting the coefficient) */
|
| 5358 |
|
|
if (*status & DEC_Inexact)
|
| 5359 |
|
|
*status |= DEC_Underflow;
|
| 5360 |
|
|
return;
|
| 5361 |
|
|
}
|
| 5362 |
|
|
|
| 5363 |
|
|
/* adjust>0. we need to rescale the result so exponent becomes Etiny */
|
| 5364 |
|
|
/* [this code is similar to that in rescale] */
|
| 5365 |
|
|
workset = *set; /* clone rounding, etc. */
|
| 5366 |
|
|
workset.digits = dn->digits - adjust; /* set requested length */
|
| 5367 |
|
|
workset.emin -= adjust; /* and adjust emin to match */
|
| 5368 |
|
|
/* [note that the latter can be <1, here, similar to Rescale case] */
|
| 5369 |
|
|
decSetCoeff (dn, &workset, dn->lsu, dn->digits, residue, status);
|
| 5370 |
|
|
decApplyRound (dn, &workset, *residue, status);
|
| 5371 |
|
|
|
| 5372 |
|
|
/* Use 754R/854 default rule: Underflow is set iff Inexact */
|
| 5373 |
|
|
/* [independent of whether trapped] */
|
| 5374 |
|
|
if (*status & DEC_Inexact)
|
| 5375 |
|
|
*status |= DEC_Underflow;
|
| 5376 |
|
|
|
| 5377 |
|
|
/* if we rounded up a 999s case, exponent will be off by one; adjust */
|
| 5378 |
|
|
/* back if so [it will fit, because we shortened] */
|
| 5379 |
|
|
if (dn->exponent > etiny)
|
| 5380 |
|
|
{
|
| 5381 |
|
|
dn->digits = decShiftToMost (dn->lsu, dn->digits, 1);
|
| 5382 |
|
|
dn->exponent--; /* (re)adjust the exponent. */
|
| 5383 |
|
|
}
|
| 5384 |
|
|
}
|
| 5385 |
|
|
|
| 5386 |
|
|
/* ------------------------------------------------------------------ */
|
| 5387 |
|
|
/* decGetInt -- get integer from a number */
|
| 5388 |
|
|
/* */
|
| 5389 |
|
|
/* dn is the number [which will not be altered] */
|
| 5390 |
|
|
/* set is the context [requested digits], subset only */
|
| 5391 |
|
|
/* returns the converted integer, or BADINT if error */
|
| 5392 |
|
|
/* */
|
| 5393 |
|
|
/* This checks and gets a whole number from the input decNumber. */
|
| 5394 |
|
|
/* The magnitude of the integer must be <2^31. */
|
| 5395 |
|
|
/* Any discarded fractional part must be 0. */
|
| 5396 |
|
|
/* If subset it must also fit in set->digits */
|
| 5397 |
|
|
/* ------------------------------------------------------------------ */
|
| 5398 |
|
|
#if DECSUBSET
|
| 5399 |
|
|
static Int
|
| 5400 |
|
|
decGetInt (const decNumber * dn, decContext * set)
|
| 5401 |
|
|
{
|
| 5402 |
|
|
#else
|
| 5403 |
|
|
static Int
|
| 5404 |
|
|
decGetInt (const decNumber * dn)
|
| 5405 |
|
|
{
|
| 5406 |
|
|
#endif
|
| 5407 |
|
|
Int theInt; /* result accumulator */
|
| 5408 |
|
|
const Unit *up; /* work */
|
| 5409 |
|
|
Int got; /* digits (real or not) processed */
|
| 5410 |
|
|
Int ilength = dn->digits + dn->exponent; /* integral length */
|
| 5411 |
|
|
|
| 5412 |
|
|
/* The number must be an integer that fits in 10 digits */
|
| 5413 |
|
|
/* Assert, here, that 10 is enough for any rescale Etiny */
|
| 5414 |
|
|
#if DEC_MAX_EMAX > 999999999
|
| 5415 |
|
|
#error GetInt may need updating [for Emax]
|
| 5416 |
|
|
#endif
|
| 5417 |
|
|
#if DEC_MIN_EMIN < -999999999
|
| 5418 |
|
|
#error GetInt may need updating [for Emin]
|
| 5419 |
|
|
#endif
|
| 5420 |
|
|
if (ISZERO (dn))
|
| 5421 |
|
|
return 0; /* zeros are OK, with any exponent */
|
| 5422 |
|
|
if (ilength > 10)
|
| 5423 |
|
|
return BADINT; /* always too big */
|
| 5424 |
|
|
#if DECSUBSET
|
| 5425 |
|
|
if (!set->extended && ilength > set->digits)
|
| 5426 |
|
|
return BADINT;
|
| 5427 |
|
|
#endif
|
| 5428 |
|
|
|
| 5429 |
|
|
up = dn->lsu; /* ready for lsu */
|
| 5430 |
|
|
theInt = 0; /* ready to accumulate */
|
| 5431 |
|
|
if (dn->exponent >= 0)
|
| 5432 |
|
|
{ /* relatively easy */
|
| 5433 |
|
|
/* no fractional part [usual]; allow for positive exponent */
|
| 5434 |
|
|
got = dn->exponent;
|
| 5435 |
|
|
}
|
| 5436 |
|
|
else
|
| 5437 |
|
|
{ /* -ve exponent; some fractional part to check and discard */
|
| 5438 |
|
|
Int count = -dn->exponent; /* digits to discard */
|
| 5439 |
|
|
/* spin up whole units until we get to the Unit with the unit digit */
|
| 5440 |
|
|
for (; count >= DECDPUN; up++)
|
| 5441 |
|
|
{
|
| 5442 |
|
|
if (*up != 0)
|
| 5443 |
|
|
return BADINT; /* non-zero Unit to discard */
|
| 5444 |
|
|
count -= DECDPUN;
|
| 5445 |
|
|
}
|
| 5446 |
|
|
if (count == 0)
|
| 5447 |
|
|
got = 0; /* [a multiple of DECDPUN] */
|
| 5448 |
|
|
else
|
| 5449 |
|
|
{ /* [not multiple of DECDPUN] */
|
| 5450 |
|
|
Int rem; /* work */
|
| 5451 |
|
|
/* slice off fraction digits and check for non-zero */
|
| 5452 |
|
|
#if DECDPUN<=4
|
| 5453 |
|
|
theInt = QUOT10 (*up, count);
|
| 5454 |
|
|
rem = *up - theInt * powers[count];
|
| 5455 |
|
|
#else
|
| 5456 |
|
|
rem = *up % powers[count]; /* slice off discards */
|
| 5457 |
|
|
theInt = *up / powers[count];
|
| 5458 |
|
|
#endif
|
| 5459 |
|
|
if (rem != 0)
|
| 5460 |
|
|
return BADINT; /* non-zero fraction */
|
| 5461 |
|
|
/* OK, we're good */
|
| 5462 |
|
|
got = DECDPUN - count; /* number of digits so far */
|
| 5463 |
|
|
up++; /* ready for next */
|
| 5464 |
|
|
}
|
| 5465 |
|
|
}
|
| 5466 |
|
|
/* collect the rest */
|
| 5467 |
|
|
for (; got < ilength; up++)
|
| 5468 |
|
|
{
|
| 5469 |
|
|
theInt += *up * powers[got];
|
| 5470 |
|
|
got += DECDPUN;
|
| 5471 |
|
|
}
|
| 5472 |
|
|
if ((ilength == 10) /* check no wrap */
|
| 5473 |
|
|
&& (theInt / (Int) powers[got - DECDPUN] != *(up - 1)))
|
| 5474 |
|
|
return BADINT;
|
| 5475 |
|
|
/* [that test also disallows the BADINT result case] */
|
| 5476 |
|
|
|
| 5477 |
|
|
/* apply any sign and return */
|
| 5478 |
|
|
if (decNumberIsNegative (dn))
|
| 5479 |
|
|
theInt = -theInt;
|
| 5480 |
|
|
return theInt;
|
| 5481 |
|
|
}
|
| 5482 |
|
|
|
| 5483 |
|
|
/* ------------------------------------------------------------------ */
|
| 5484 |
|
|
/* decStrEq -- caseless comparison of strings */
|
| 5485 |
|
|
/* */
|
| 5486 |
|
|
/* str1 is one of the strings to compare */
|
| 5487 |
|
|
/* str2 is the other */
|
| 5488 |
|
|
/* */
|
| 5489 |
|
|
/* returns 1 if strings caseless-compare equal, 0 otherwise */
|
| 5490 |
|
|
/* */
|
| 5491 |
|
|
/* Note that the strings must be the same length if they are to */
|
| 5492 |
|
|
/* compare equal; there is no padding. */
|
| 5493 |
|
|
/* ------------------------------------------------------------------ */
|
| 5494 |
|
|
/* [strcmpi is not in ANSI C] */
|
| 5495 |
|
|
static Flag
|
| 5496 |
|
|
decStrEq (const char *str1, const char *str2)
|
| 5497 |
|
|
{
|
| 5498 |
|
|
for (;; str1++, str2++)
|
| 5499 |
|
|
{
|
| 5500 |
|
|
unsigned char u1 = (unsigned char) *str1;
|
| 5501 |
|
|
unsigned char u2 = (unsigned char) *str2;
|
| 5502 |
|
|
if (u1 == u2)
|
| 5503 |
|
|
{
|
| 5504 |
|
|
if (u1 == '\0')
|
| 5505 |
|
|
break;
|
| 5506 |
|
|
}
|
| 5507 |
|
|
else
|
| 5508 |
|
|
{
|
| 5509 |
|
|
if (tolower (u1) != tolower (u2))
|
| 5510 |
|
|
return 0;
|
| 5511 |
|
|
}
|
| 5512 |
|
|
} /* stepping */
|
| 5513 |
|
|
return 1;
|
| 5514 |
|
|
}
|
| 5515 |
|
|
|
| 5516 |
|
|
/* ------------------------------------------------------------------ */
|
| 5517 |
|
|
/* decNaNs -- handle NaN operand or operands */
|
| 5518 |
|
|
/* */
|
| 5519 |
|
|
/* res is the result number */
|
| 5520 |
|
|
/* lhs is the first operand */
|
| 5521 |
|
|
/* rhs is the second operand, or NULL if none */
|
| 5522 |
|
|
/* status contains the current status */
|
| 5523 |
|
|
/* returns res in case convenient */
|
| 5524 |
|
|
/* */
|
| 5525 |
|
|
/* Called when one or both operands is a NaN, and propagates the */
|
| 5526 |
|
|
/* appropriate result to res. When an sNaN is found, it is changed */
|
| 5527 |
|
|
/* to a qNaN and Invalid operation is set. */
|
| 5528 |
|
|
/* ------------------------------------------------------------------ */
|
| 5529 |
|
|
static decNumber *
|
| 5530 |
|
|
decNaNs (decNumber * res, const decNumber * lhs, const decNumber * rhs, uInt * status)
|
| 5531 |
|
|
{
|
| 5532 |
|
|
/* This decision tree ends up with LHS being the source pointer, */
|
| 5533 |
|
|
/* and status updated if need be */
|
| 5534 |
|
|
if (lhs->bits & DECSNAN)
|
| 5535 |
|
|
*status |= DEC_Invalid_operation | DEC_sNaN;
|
| 5536 |
|
|
else if (rhs == NULL);
|
| 5537 |
|
|
else if (rhs->bits & DECSNAN)
|
| 5538 |
|
|
{
|
| 5539 |
|
|
lhs = rhs;
|
| 5540 |
|
|
*status |= DEC_Invalid_operation | DEC_sNaN;
|
| 5541 |
|
|
}
|
| 5542 |
|
|
else if (lhs->bits & DECNAN);
|
| 5543 |
|
|
else
|
| 5544 |
|
|
lhs = rhs;
|
| 5545 |
|
|
|
| 5546 |
|
|
decNumberCopy (res, lhs);
|
| 5547 |
|
|
res->bits &= ~DECSNAN; /* convert any sNaN to NaN, while */
|
| 5548 |
|
|
res->bits |= DECNAN; /* .. preserving sign */
|
| 5549 |
|
|
res->exponent = 0; /* clean exponent */
|
| 5550 |
|
|
/* [coefficient was copied] */
|
| 5551 |
|
|
return res;
|
| 5552 |
|
|
}
|
| 5553 |
|
|
|
| 5554 |
|
|
/* ------------------------------------------------------------------ */
|
| 5555 |
|
|
/* decStatus -- apply non-zero status */
|
| 5556 |
|
|
/* */
|
| 5557 |
|
|
/* dn is the number to set if error */
|
| 5558 |
|
|
/* status contains the current status (not yet in context) */
|
| 5559 |
|
|
/* set is the context */
|
| 5560 |
|
|
/* */
|
| 5561 |
|
|
/* If the status is an error status, the number is set to a NaN, */
|
| 5562 |
|
|
/* unless the error was an overflow, divide-by-zero, or underflow, */
|
| 5563 |
|
|
/* in which case the number will have already been set. */
|
| 5564 |
|
|
/* */
|
| 5565 |
|
|
/* The context status is then updated with the new status. Note that */
|
| 5566 |
|
|
/* this may raise a signal, so control may never return from this */
|
| 5567 |
|
|
/* routine (hence resources must be recovered before it is called). */
|
| 5568 |
|
|
/* ------------------------------------------------------------------ */
|
| 5569 |
|
|
static void
|
| 5570 |
|
|
decStatus (decNumber * dn, uInt status, decContext * set)
|
| 5571 |
|
|
{
|
| 5572 |
|
|
if (status & DEC_NaNs)
|
| 5573 |
|
|
{ /* error status -> NaN */
|
| 5574 |
|
|
/* if cause was an sNaN, clear and propagate [NaN is already set up] */
|
| 5575 |
|
|
if (status & DEC_sNaN)
|
| 5576 |
|
|
status &= ~DEC_sNaN;
|
| 5577 |
|
|
else
|
| 5578 |
|
|
{
|
| 5579 |
|
|
decNumberZero (dn); /* other error: clean throughout */
|
| 5580 |
|
|
dn->bits = DECNAN; /* and make a quiet NaN */
|
| 5581 |
|
|
}
|
| 5582 |
|
|
}
|
| 5583 |
|
|
decContextSetStatus (set, status);
|
| 5584 |
|
|
return;
|
| 5585 |
|
|
}
|
| 5586 |
|
|
|
| 5587 |
|
|
/* ------------------------------------------------------------------ */
|
| 5588 |
|
|
/* decGetDigits -- count digits in a Units array */
|
| 5589 |
|
|
/* */
|
| 5590 |
|
|
/* uar is the Unit array holding the number [this is often an */
|
| 5591 |
|
|
/* accumulator of some sort] */
|
| 5592 |
|
|
/* len is the length of the array in units */
|
| 5593 |
|
|
/* */
|
| 5594 |
|
|
/* returns the number of (significant) digits in the array */
|
| 5595 |
|
|
/* */
|
| 5596 |
|
|
/* All leading zeros are excluded, except the last if the array has */
|
| 5597 |
|
|
/* only zero Units. */
|
| 5598 |
|
|
/* ------------------------------------------------------------------ */
|
| 5599 |
|
|
/* This may be called twice during some operations. */
|
| 5600 |
|
|
static Int
|
| 5601 |
|
|
decGetDigits (const Unit * uar, Int len)
|
| 5602 |
|
|
{
|
| 5603 |
|
|
const Unit *up = uar + len - 1; /* -> msu */
|
| 5604 |
|
|
Int digits = len * DECDPUN; /* maximum possible digits */
|
| 5605 |
|
|
uInt const *pow; /* work */
|
| 5606 |
|
|
|
| 5607 |
|
|
for (; up >= uar; up--)
|
| 5608 |
|
|
{
|
| 5609 |
|
|
digits -= DECDPUN;
|
| 5610 |
|
|
if (*up == 0)
|
| 5611 |
|
|
{ /* unit is 0 */
|
| 5612 |
|
|
if (digits != 0)
|
| 5613 |
|
|
continue; /* more to check */
|
| 5614 |
|
|
/* all units were 0 */
|
| 5615 |
|
|
digits++; /* .. so bump digits to 1 */
|
| 5616 |
|
|
break;
|
| 5617 |
|
|
}
|
| 5618 |
|
|
/* found the first non-zero Unit */
|
| 5619 |
|
|
digits++;
|
| 5620 |
|
|
if (*up < 10)
|
| 5621 |
|
|
break; /* fastpath 1-9 */
|
| 5622 |
|
|
digits++;
|
| 5623 |
|
|
for (pow = &powers[2]; *up >= *pow; pow++)
|
| 5624 |
|
|
digits++;
|
| 5625 |
|
|
break;
|
| 5626 |
|
|
} /* up */
|
| 5627 |
|
|
|
| 5628 |
|
|
return digits;
|
| 5629 |
|
|
}
|
| 5630 |
|
|
|
| 5631 |
|
|
|
| 5632 |
|
|
#if DECTRACE | DECCHECK
|
| 5633 |
|
|
/* ------------------------------------------------------------------ */
|
| 5634 |
|
|
/* decNumberShow -- display a number [debug aid] */
|
| 5635 |
|
|
/* dn is the number to show */
|
| 5636 |
|
|
/* */
|
| 5637 |
|
|
/* Shows: sign, exponent, coefficient (msu first), digits */
|
| 5638 |
|
|
/* or: sign, special-value */
|
| 5639 |
|
|
/* ------------------------------------------------------------------ */
|
| 5640 |
|
|
/* this is public so other modules can use it */
|
| 5641 |
|
|
void
|
| 5642 |
|
|
decNumberShow (const decNumber * dn)
|
| 5643 |
|
|
{
|
| 5644 |
|
|
const Unit *up; /* work */
|
| 5645 |
|
|
uInt u, d; /* .. */
|
| 5646 |
|
|
Int cut; /* .. */
|
| 5647 |
|
|
char isign = '+'; /* main sign */
|
| 5648 |
|
|
if (dn == NULL)
|
| 5649 |
|
|
{
|
| 5650 |
|
|
printf ("NULL\n");
|
| 5651 |
|
|
return;
|
| 5652 |
|
|
}
|
| 5653 |
|
|
if (decNumberIsNegative (dn))
|
| 5654 |
|
|
isign = '-';
|
| 5655 |
|
|
printf (" >> %c ", isign);
|
| 5656 |
|
|
if (dn->bits & DECSPECIAL)
|
| 5657 |
|
|
{ /* Is a special value */
|
| 5658 |
|
|
if (decNumberIsInfinite (dn))
|
| 5659 |
|
|
printf ("Infinity");
|
| 5660 |
|
|
else
|
| 5661 |
|
|
{ /* a NaN */
|
| 5662 |
|
|
if (dn->bits & DECSNAN)
|
| 5663 |
|
|
printf ("sNaN"); /* signalling NaN */
|
| 5664 |
|
|
else
|
| 5665 |
|
|
printf ("NaN");
|
| 5666 |
|
|
}
|
| 5667 |
|
|
/* if coefficient and exponent are 0, we're done */
|
| 5668 |
|
|
if (dn->exponent == 0 && dn->digits == 1 && *dn->lsu == 0)
|
| 5669 |
|
|
{
|
| 5670 |
|
|
printf ("\n");
|
| 5671 |
|
|
return;
|
| 5672 |
|
|
}
|
| 5673 |
|
|
/* drop through to report other information */
|
| 5674 |
|
|
printf (" ");
|
| 5675 |
|
|
}
|
| 5676 |
|
|
|
| 5677 |
|
|
/* now carefully display the coefficient */
|
| 5678 |
|
|
up = dn->lsu + D2U (dn->digits) - 1; /* msu */
|
| 5679 |
|
|
printf ("%d", *up);
|
| 5680 |
|
|
for (up = up - 1; up >= dn->lsu; up--)
|
| 5681 |
|
|
{
|
| 5682 |
|
|
u = *up;
|
| 5683 |
|
|
printf (":");
|
| 5684 |
|
|
for (cut = DECDPUN - 1; cut >= 0; cut--)
|
| 5685 |
|
|
{
|
| 5686 |
|
|
d = u / powers[cut];
|
| 5687 |
|
|
u -= d * powers[cut];
|
| 5688 |
|
|
printf ("%d", d);
|
| 5689 |
|
|
} /* cut */
|
| 5690 |
|
|
} /* up */
|
| 5691 |
|
|
if (dn->exponent != 0)
|
| 5692 |
|
|
{
|
| 5693 |
|
|
char esign = '+';
|
| 5694 |
|
|
if (dn->exponent < 0)
|
| 5695 |
|
|
esign = '-';
|
| 5696 |
|
|
printf (" E%c%d", esign, abs (dn->exponent));
|
| 5697 |
|
|
}
|
| 5698 |
|
|
printf (" [%d]\n", dn->digits);
|
| 5699 |
|
|
}
|
| 5700 |
|
|
#endif
|
| 5701 |
|
|
|
| 5702 |
|
|
#if DECTRACE || DECCHECK
|
| 5703 |
|
|
/* ------------------------------------------------------------------ */
|
| 5704 |
|
|
/* decDumpAr -- display a unit array [debug aid] */
|
| 5705 |
|
|
/* name is a single-character tag name */
|
| 5706 |
|
|
/* ar is the array to display */
|
| 5707 |
|
|
/* len is the length of the array in Units */
|
| 5708 |
|
|
/* ------------------------------------------------------------------ */
|
| 5709 |
|
|
static void
|
| 5710 |
|
|
decDumpAr (char name, const Unit * ar, Int len)
|
| 5711 |
|
|
{
|
| 5712 |
|
|
Int i;
|
| 5713 |
|
|
#if DECDPUN==4
|
| 5714 |
|
|
const char *spec = "%04d ";
|
| 5715 |
|
|
#else
|
| 5716 |
|
|
const char *spec = "%d ";
|
| 5717 |
|
|
#endif
|
| 5718 |
|
|
printf (" :%c: ", name);
|
| 5719 |
|
|
for (i = len - 1; i >= 0; i--)
|
| 5720 |
|
|
{
|
| 5721 |
|
|
if (i == len - 1)
|
| 5722 |
|
|
printf ("%d ", ar[i]);
|
| 5723 |
|
|
else
|
| 5724 |
|
|
printf (spec, ar[i]);
|
| 5725 |
|
|
}
|
| 5726 |
|
|
printf ("\n");
|
| 5727 |
|
|
return;
|
| 5728 |
|
|
}
|
| 5729 |
|
|
#endif
|
| 5730 |
|
|
|
| 5731 |
|
|
#if DECCHECK
|
| 5732 |
|
|
/* ------------------------------------------------------------------ */
|
| 5733 |
|
|
/* decCheckOperands -- check operand(s) to a routine */
|
| 5734 |
|
|
/* res is the result structure (not checked; it will be set to */
|
| 5735 |
|
|
/* quiet NaN if error found (and it is not NULL)) */
|
| 5736 |
|
|
/* lhs is the first operand (may be DECUNUSED) */
|
| 5737 |
|
|
/* rhs is the second (may be DECUNUSED) */
|
| 5738 |
|
|
/* set is the context (may be DECUNUSED) */
|
| 5739 |
|
|
/* returns 0 if both operands, and the context are clean, or 1 */
|
| 5740 |
|
|
/* otherwise (in which case the context will show an error, */
|
| 5741 |
|
|
/* unless NULL). Note that res is not cleaned; caller should */
|
| 5742 |
|
|
/* handle this so res=NULL case is safe. */
|
| 5743 |
|
|
/* The caller is expected to abandon immediately if 1 is returned. */
|
| 5744 |
|
|
/* ------------------------------------------------------------------ */
|
| 5745 |
|
|
static Flag
|
| 5746 |
|
|
decCheckOperands (decNumber * res, const decNumber * lhs,
|
| 5747 |
|
|
const decNumber * rhs, decContext * set)
|
| 5748 |
|
|
{
|
| 5749 |
|
|
Flag bad = 0;
|
| 5750 |
|
|
if (set == NULL)
|
| 5751 |
|
|
{ /* oops; hopeless */
|
| 5752 |
|
|
#if DECTRACE
|
| 5753 |
|
|
printf ("Context is NULL.\n");
|
| 5754 |
|
|
#endif
|
| 5755 |
|
|
bad = 1;
|
| 5756 |
|
|
return 1;
|
| 5757 |
|
|
}
|
| 5758 |
|
|
else if (set != DECUNUSED
|
| 5759 |
|
|
&& (set->digits < 1 || set->round < 0
|
| 5760 |
|
|
|| set->round >= DEC_ROUND_MAX))
|
| 5761 |
|
|
{
|
| 5762 |
|
|
bad = 1;
|
| 5763 |
|
|
#if DECTRACE
|
| 5764 |
|
|
printf ("Bad context [digits=%d round=%d].\n", set->digits, set->round);
|
| 5765 |
|
|
#endif
|
| 5766 |
|
|
}
|
| 5767 |
|
|
else
|
| 5768 |
|
|
{
|
| 5769 |
|
|
if (res == NULL)
|
| 5770 |
|
|
{
|
| 5771 |
|
|
bad = 1;
|
| 5772 |
|
|
#if DECTRACE
|
| 5773 |
|
|
printf ("Bad result [is NULL].\n");
|
| 5774 |
|
|
#endif
|
| 5775 |
|
|
}
|
| 5776 |
|
|
if (!bad && lhs != DECUNUSED)
|
| 5777 |
|
|
bad = (decCheckNumber (lhs, set));
|
| 5778 |
|
|
if (!bad && rhs != DECUNUSED)
|
| 5779 |
|
|
bad = (decCheckNumber (rhs, set));
|
| 5780 |
|
|
}
|
| 5781 |
|
|
if (bad)
|
| 5782 |
|
|
{
|
| 5783 |
|
|
if (set != DECUNUSED)
|
| 5784 |
|
|
decContextSetStatus (set, DEC_Invalid_operation);
|
| 5785 |
|
|
if (res != DECUNUSED && res != NULL)
|
| 5786 |
|
|
{
|
| 5787 |
|
|
decNumberZero (res);
|
| 5788 |
|
|
res->bits = DECNAN; /* qNaN */
|
| 5789 |
|
|
}
|
| 5790 |
|
|
}
|
| 5791 |
|
|
return bad;
|
| 5792 |
|
|
}
|
| 5793 |
|
|
|
| 5794 |
|
|
/* ------------------------------------------------------------------ */
|
| 5795 |
|
|
/* decCheckNumber -- check a number */
|
| 5796 |
|
|
/* dn is the number to check */
|
| 5797 |
|
|
/* set is the context (may be DECUNUSED) */
|
| 5798 |
|
|
/* returns 0 if the number is clean, or 1 otherwise */
|
| 5799 |
|
|
/* */
|
| 5800 |
|
|
/* The number is considered valid if it could be a result from some */
|
| 5801 |
|
|
/* operation in some valid context (not necessarily the current one). */
|
| 5802 |
|
|
/* ------------------------------------------------------------------ */
|
| 5803 |
|
|
Flag
|
| 5804 |
|
|
decCheckNumber (const decNumber * dn, decContext * set)
|
| 5805 |
|
|
{
|
| 5806 |
|
|
const Unit *up; /* work */
|
| 5807 |
|
|
uInt maxuint; /* .. */
|
| 5808 |
|
|
Int ae, d, digits; /* .. */
|
| 5809 |
|
|
Int emin, emax; /* .. */
|
| 5810 |
|
|
|
| 5811 |
|
|
if (dn == NULL)
|
| 5812 |
|
|
{ /* hopeless */
|
| 5813 |
|
|
#if DECTRACE
|
| 5814 |
|
|
printf ("Reference to decNumber is NULL.\n");
|
| 5815 |
|
|
#endif
|
| 5816 |
|
|
return 1;
|
| 5817 |
|
|
}
|
| 5818 |
|
|
|
| 5819 |
|
|
/* check special values */
|
| 5820 |
|
|
if (dn->bits & DECSPECIAL)
|
| 5821 |
|
|
{
|
| 5822 |
|
|
if (dn->exponent != 0)
|
| 5823 |
|
|
{
|
| 5824 |
|
|
#if DECTRACE
|
| 5825 |
|
|
printf ("Exponent %d (not 0) for a special value.\n", dn->exponent);
|
| 5826 |
|
|
#endif
|
| 5827 |
|
|
return 1;
|
| 5828 |
|
|
}
|
| 5829 |
|
|
|
| 5830 |
|
|
/* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
|
| 5831 |
|
|
if (decNumberIsInfinite (dn))
|
| 5832 |
|
|
{
|
| 5833 |
|
|
if (dn->digits != 1)
|
| 5834 |
|
|
{
|
| 5835 |
|
|
#if DECTRACE
|
| 5836 |
|
|
printf ("Digits %d (not 1) for an infinity.\n", dn->digits);
|
| 5837 |
|
|
#endif
|
| 5838 |
|
|
return 1;
|
| 5839 |
|
|
}
|
| 5840 |
|
|
if (*dn->lsu != 0)
|
| 5841 |
|
|
{
|
| 5842 |
|
|
#if DECTRACE
|
| 5843 |
|
|
printf ("LSU %d (not 0) for an infinity.\n", *dn->lsu);
|
| 5844 |
|
|
#endif
|
| 5845 |
|
|
return 1;
|
| 5846 |
|
|
}
|
| 5847 |
|
|
} /* Inf */
|
| 5848 |
|
|
/* 2002.12.26: negative NaNs can now appear through proposed IEEE */
|
| 5849 |
|
|
/* concrete formats (decimal64, etc.), though they are */
|
| 5850 |
|
|
/* never visible in strings. */
|
| 5851 |
|
|
return 0;
|
| 5852 |
|
|
|
| 5853 |
|
|
/* if ((dn->bits & DECINF) || (dn->bits & DECNEG)==0) return 0; */
|
| 5854 |
|
|
/* #if DECTRACE */
|
| 5855 |
|
|
/* printf("Negative NaN in number.\n"); */
|
| 5856 |
|
|
/* #endif */
|
| 5857 |
|
|
/* return 1; */
|
| 5858 |
|
|
}
|
| 5859 |
|
|
|
| 5860 |
|
|
/* check the coefficient */
|
| 5861 |
|
|
if (dn->digits < 1 || dn->digits > DECNUMMAXP)
|
| 5862 |
|
|
{
|
| 5863 |
|
|
#if DECTRACE
|
| 5864 |
|
|
printf ("Digits %d in number.\n", dn->digits);
|
| 5865 |
|
|
#endif
|
| 5866 |
|
|
return 1;
|
| 5867 |
|
|
}
|
| 5868 |
|
|
|
| 5869 |
|
|
d = dn->digits;
|
| 5870 |
|
|
|
| 5871 |
|
|
for (up = dn->lsu; d > 0; up++)
|
| 5872 |
|
|
{
|
| 5873 |
|
|
if (d > DECDPUN)
|
| 5874 |
|
|
maxuint = DECDPUNMAX;
|
| 5875 |
|
|
else
|
| 5876 |
|
|
{ /* we are at the msu */
|
| 5877 |
|
|
maxuint = powers[d] - 1;
|
| 5878 |
|
|
if (dn->digits > 1 && *up < powers[d - 1])
|
| 5879 |
|
|
{
|
| 5880 |
|
|
#if DECTRACE
|
| 5881 |
|
|
printf ("Leading 0 in number.\n");
|
| 5882 |
|
|
decNumberShow (dn);
|
| 5883 |
|
|
#endif
|
| 5884 |
|
|
return 1;
|
| 5885 |
|
|
}
|
| 5886 |
|
|
}
|
| 5887 |
|
|
if (*up > maxuint)
|
| 5888 |
|
|
{
|
| 5889 |
|
|
#if DECTRACE
|
| 5890 |
|
|
printf ("Bad Unit [%08x] in number at offset %d [maxuint %d].\n",
|
| 5891 |
|
|
*up, up - dn->lsu, maxuint);
|
| 5892 |
|
|
#endif
|
| 5893 |
|
|
return 1;
|
| 5894 |
|
|
}
|
| 5895 |
|
|
d -= DECDPUN;
|
| 5896 |
|
|
}
|
| 5897 |
|
|
|
| 5898 |
|
|
/* check the exponent. Note that input operands can have exponents */
|
| 5899 |
|
|
/* which are out of the set->emin/set->emax and set->digits range */
|
| 5900 |
|
|
/* (just as they can have more digits than set->digits). */
|
| 5901 |
|
|
ae = dn->exponent + dn->digits - 1; /* adjusted exponent */
|
| 5902 |
|
|
emax = DECNUMMAXE;
|
| 5903 |
|
|
emin = DECNUMMINE;
|
| 5904 |
|
|
digits = DECNUMMAXP;
|
| 5905 |
|
|
if (ae < emin - (digits - 1))
|
| 5906 |
|
|
{
|
| 5907 |
|
|
#if DECTRACE
|
| 5908 |
|
|
printf ("Adjusted exponent underflow [%d].\n", ae);
|
| 5909 |
|
|
decNumberShow (dn);
|
| 5910 |
|
|
#endif
|
| 5911 |
|
|
return 1;
|
| 5912 |
|
|
}
|
| 5913 |
|
|
if (ae > +emax)
|
| 5914 |
|
|
{
|
| 5915 |
|
|
#if DECTRACE
|
| 5916 |
|
|
printf ("Adjusted exponent overflow [%d].\n", ae);
|
| 5917 |
|
|
decNumberShow (dn);
|
| 5918 |
|
|
#endif
|
| 5919 |
|
|
return 1;
|
| 5920 |
|
|
}
|
| 5921 |
|
|
|
| 5922 |
|
|
return 0; /* it's OK */
|
| 5923 |
|
|
}
|
| 5924 |
|
|
#endif
|
| 5925 |
|
|
|
| 5926 |
|
|
#if DECALLOC
|
| 5927 |
|
|
#undef malloc
|
| 5928 |
|
|
#undef free
|
| 5929 |
|
|
/* ------------------------------------------------------------------ */
|
| 5930 |
|
|
/* decMalloc -- accountable allocation routine */
|
| 5931 |
|
|
/* n is the number of bytes to allocate */
|
| 5932 |
|
|
/* */
|
| 5933 |
|
|
/* Semantics is the same as the stdlib malloc routine, but bytes */
|
| 5934 |
|
|
/* allocated are accounted for globally, and corruption fences are */
|
| 5935 |
|
|
/* added before and after the 'actual' storage. */
|
| 5936 |
|
|
/* ------------------------------------------------------------------ */
|
| 5937 |
|
|
/* This routine allocates storage with an extra twelve bytes; 8 are */
|
| 5938 |
|
|
/* at the start and hold: */
|
| 5939 |
|
|
/* 0-3 the original length requested */
|
| 5940 |
|
|
/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
|
| 5941 |
|
|
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
|
| 5942 |
|
|
/* ------------------------------------------------------------------ */
|
| 5943 |
|
|
static void *
|
| 5944 |
|
|
decMalloc (uInt n)
|
| 5945 |
|
|
{
|
| 5946 |
|
|
uInt size = n + 12; /* true size */
|
| 5947 |
|
|
void *alloc; /* -> allocated storage */
|
| 5948 |
|
|
uInt *j; /* work */
|
| 5949 |
|
|
uByte *b, *b0; /* .. */
|
| 5950 |
|
|
|
| 5951 |
|
|
alloc = malloc (size); /* -> allocated storage */
|
| 5952 |
|
|
if (alloc == NULL)
|
| 5953 |
|
|
return NULL; /* out of strorage */
|
| 5954 |
|
|
b0 = (uByte *) alloc; /* as bytes */
|
| 5955 |
|
|
decAllocBytes += n; /* account for storage */
|
| 5956 |
|
|
j = (uInt *) alloc; /* -> first four bytes */
|
| 5957 |
|
|
*j = n; /* save n */
|
| 5958 |
|
|
/* printf("++ alloc(%d)\n", n); */
|
| 5959 |
|
|
for (b = b0 + 4; b < b0 + 8; b++)
|
| 5960 |
|
|
*b = DECFENCE;
|
| 5961 |
|
|
for (b = b0 + n + 8; b < b0 + n + 12; b++)
|
| 5962 |
|
|
*b = DECFENCE;
|
| 5963 |
|
|
return b0 + 8; /* -> play area */
|
| 5964 |
|
|
}
|
| 5965 |
|
|
|
| 5966 |
|
|
/* ------------------------------------------------------------------ */
|
| 5967 |
|
|
/* decFree -- accountable free routine */
|
| 5968 |
|
|
/* alloc is the storage to free */
|
| 5969 |
|
|
/* */
|
| 5970 |
|
|
/* Semantics is the same as the stdlib malloc routine, except that */
|
| 5971 |
|
|
/* the global storage accounting is updated and the fences are */
|
| 5972 |
|
|
/* checked to ensure that no routine has written 'out of bounds'. */
|
| 5973 |
|
|
/* ------------------------------------------------------------------ */
|
| 5974 |
|
|
/* This routine first checks that the fences have not been corrupted. */
|
| 5975 |
|
|
/* It then frees the storage using the 'truw' storage address (that */
|
| 5976 |
|
|
/* is, offset by 8). */
|
| 5977 |
|
|
/* ------------------------------------------------------------------ */
|
| 5978 |
|
|
static void
|
| 5979 |
|
|
decFree (void *alloc)
|
| 5980 |
|
|
{
|
| 5981 |
|
|
uInt *j, n; /* pointer, original length */
|
| 5982 |
|
|
uByte *b, *b0; /* work */
|
| 5983 |
|
|
|
| 5984 |
|
|
if (alloc == NULL)
|
| 5985 |
|
|
return; /* allowed; it's a nop */
|
| 5986 |
|
|
b0 = (uByte *) alloc; /* as bytes */
|
| 5987 |
|
|
b0 -= 8; /* -> true start of storage */
|
| 5988 |
|
|
j = (uInt *) b0; /* -> first four bytes */
|
| 5989 |
|
|
n = *j; /* lift */
|
| 5990 |
|
|
for (b = b0 + 4; b < b0 + 8; b++)
|
| 5991 |
|
|
if (*b != DECFENCE)
|
| 5992 |
|
|
printf ("=== Corrupt byte [%02x] at offset %d from %d ===\n", *b,
|
| 5993 |
|
|
b - b0 - 8, (Int) b0);
|
| 5994 |
|
|
for (b = b0 + n + 8; b < b0 + n + 12; b++)
|
| 5995 |
|
|
if (*b != DECFENCE)
|
| 5996 |
|
|
printf ("=== Corrupt byte [%02x] at offset +%d from %d, n=%d ===\n", *b,
|
| 5997 |
|
|
b - b0 - 8, (Int) b0, n);
|
| 5998 |
|
|
free (b0); /* drop the storage */
|
| 5999 |
|
|
decAllocBytes -= n; /* account for storage */
|
| 6000 |
|
|
}
|
| 6001 |
|
|
#endif
|
