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jeremybenn |
/* Decimal number arithmetic module for the decNumber C Library.
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Copyright (C) 2005, 2007, 2009 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 3, or (at your option) any later
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version.
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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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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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/* ------------------------------------------------------------------ */
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/* Decimal Number arithmetic module */
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/* ------------------------------------------------------------------ */
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/* This module comprises the routines for arbitrary-precision General */
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/* Decimal Arithmetic as defined in the specification which may be */
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/* found on the General Decimal Arithmetic 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) C99 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 or DECUSE64=1, the C99 64-bit int64_t and */
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/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
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/* and DECDPUN<=4 (see documentation). */
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/* */
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/* The code also conforms to C99 restrictions; in particular, */
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/* strict aliasing rules are observed. */
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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). Mathematical functions (for */
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/* example decNumberExp) as identified below are restricted more */
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/* tightly: digits, emax, and -emin in the context must be <= */
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/* DEC_MAX_MATH (999999), and their operand(s) must be within */
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/* these bounds. */
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/* */
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/* 3. Logical functions are further restricted; their operands must */
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/* be finite, positive, have an exponent of zero, and all digits */
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/* must be either 0 or 1. The result will only contain digits */
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/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
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/* */
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/* 4. 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 must not overlap. */
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/* */
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/* 5. 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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/* 6. 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 (packed or unpacked, or special length, 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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/* 7. 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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/* 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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/* (Except for SIGFPE, as and where documented.) */
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/* */
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/* 8. 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 to exit this. */
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/* Other routines can safely 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 does */
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/* not loop; it is for allocation 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 status is accumulated and is only applied just */
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/* before return by calling decContextSetStatus (via decStatus). */
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/* */
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/* Routines which allocate storage cannot, in general, 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. The multiply-by-reciprocal 'trick' is used 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 a floating-point or 64-bit multiply is */
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/* assumed to be available). */
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/* */
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/* 8. Unusual abbreviations that may be 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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/* msi -- most significant item (in an array) */
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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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/* ** -- raise to the power */
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/* ------------------------------------------------------------------ */
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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 "dconfig.h" /* for GCC definitions */
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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 lookup table used by the D2U macro */
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const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
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#define DECVERB 1 /* set to 1 for verbose DECCHECK */
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#define powers DECPOWERS /* old internal name */
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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 COMPTOTAL 0x04 /* .. */
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#define COMPNAN 0x05 /* .. [NaN processing] */
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#define COMPSIG 0x06 /* .. [signaling COMPARE] */
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#define COMPMAXMAG 0x07 /* .. */
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#define COMPMINMAG 0x08 /* .. */
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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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/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
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#define BIGEVEN (Int)0x80000002
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#define BIGODD (Int)0x80000003
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static Unit uarrone[1]={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 non-ANSI-89 64-bit types are needed. */
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#if !DECUSE64
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#error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
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#endif
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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 *, const decNumber *,
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decContext *, uByte, uInt *);
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static Flag decBiStr(const char *, const char *, const char *);
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static uInt decCheckMath(const decNumber *, decContext *, 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, Flag);
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static decNumber * decCompareOp(decNumber *, const decNumber *,
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const decNumber *, decContext *,
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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 * decDecap(decNumber *, Int);
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static decNumber * decDivideOp(decNumber *, const decNumber *,
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const decNumber *, decContext *, Flag, uInt *);
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static decNumber * decExpOp(decNumber *, const decNumber *,
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decContext *, uInt *);
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static void decFinalize(decNumber *, decContext *, Int *, uInt *);
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static Int decGetDigits(Unit *, Int);
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static Int decGetInt(const decNumber *);
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static decNumber * decLnOp(decNumber *, const decNumber *,
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decContext *, uInt *);
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static decNumber * decMultiplyOp(decNumber *, const decNumber *,
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const decNumber *, decContext *,
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uInt *);
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static decNumber * decNaNs(decNumber *, const decNumber *,
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const decNumber *, decContext *, uInt *);
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static decNumber * decQuantizeOp(decNumber *, const decNumber *,
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const decNumber *, decContext *, Flag,
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uInt *);
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static void decReverse(Unit *, Unit *);
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static void decSetCoeff(decNumber *, decContext *, const Unit *,
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Int, Int *, uInt *);
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static void decSetMaxValue(decNumber *, decContext *);
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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 void decToString(const decNumber *, char[], Flag);
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static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
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static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
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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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/* Local macros */
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/* masked special-values bits */
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#define SPECIALARG (rhs->bits & DECSPECIAL)
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#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
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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. */
|
| 302 |
|
|
/* To check for memory leaks, the decAllocBytes variable must be */
|
| 303 |
|
|
/* checked to be 0 at appropriate times (e.g., after the test */
|
| 304 |
|
|
/* harness completes a set of tests). This checking may be unreliable */
|
| 305 |
|
|
/* if the testing is done in a multi-thread environment. */
|
| 306 |
|
|
#endif
|
| 307 |
|
|
|
| 308 |
|
|
#if DECCHECK
|
| 309 |
|
|
/* Optional checking routines. Enabling these means that decNumber */
|
| 310 |
|
|
/* and decContext operands to operator routines are checked for */
|
| 311 |
|
|
/* correctness. This roughly doubles the execution time of the */
|
| 312 |
|
|
/* fastest routines (and adds 600+ bytes), so should not normally be */
|
| 313 |
|
|
/* used in 'production'. */
|
| 314 |
|
|
/* decCheckInexact is used to check that inexact results have a full */
|
| 315 |
|
|
/* complement of digits (where appropriate -- this is not the case */
|
| 316 |
|
|
/* for Quantize, for example) */
|
| 317 |
|
|
#define DECUNRESU ((decNumber *)(void *)0xffffffff)
|
| 318 |
|
|
#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
|
| 319 |
|
|
#define DECUNCONT ((decContext *)(void *)(0xffffffff))
|
| 320 |
|
|
static Flag decCheckOperands(decNumber *, const decNumber *,
|
| 321 |
|
|
const decNumber *, decContext *);
|
| 322 |
|
|
static Flag decCheckNumber(const decNumber *);
|
| 323 |
|
|
static void decCheckInexact(const decNumber *, decContext *);
|
| 324 |
|
|
#endif
|
| 325 |
|
|
|
| 326 |
|
|
#if DECTRACE || DECCHECK
|
| 327 |
|
|
/* Optional trace/debugging routines (may or may not be used) */
|
| 328 |
|
|
void decNumberShow(const decNumber *); /* displays the components of a number */
|
| 329 |
|
|
static void decDumpAr(char, const Unit *, Int);
|
| 330 |
|
|
#endif
|
| 331 |
|
|
|
| 332 |
|
|
/* ================================================================== */
|
| 333 |
|
|
/* Conversions */
|
| 334 |
|
|
/* ================================================================== */
|
| 335 |
|
|
|
| 336 |
|
|
/* ------------------------------------------------------------------ */
|
| 337 |
|
|
/* from-int32 -- conversion from Int or uInt */
|
| 338 |
|
|
/* */
|
| 339 |
|
|
/* dn is the decNumber to receive the integer */
|
| 340 |
|
|
/* in or uin is the integer to be converted */
|
| 341 |
|
|
/* returns dn */
|
| 342 |
|
|
/* */
|
| 343 |
|
|
/* No error is possible. */
|
| 344 |
|
|
/* ------------------------------------------------------------------ */
|
| 345 |
|
|
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
|
| 346 |
|
|
uInt unsig;
|
| 347 |
|
|
if (in>=0) unsig=in;
|
| 348 |
|
|
else { /* negative (possibly BADINT) */
|
| 349 |
|
|
if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
|
| 350 |
|
|
else unsig=-in; /* invert */
|
| 351 |
|
|
}
|
| 352 |
|
|
/* in is now positive */
|
| 353 |
|
|
decNumberFromUInt32(dn, unsig);
|
| 354 |
|
|
if (in<0) dn->bits=DECNEG; /* sign needed */
|
| 355 |
|
|
return dn;
|
| 356 |
|
|
} /* decNumberFromInt32 */
|
| 357 |
|
|
|
| 358 |
|
|
decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
|
| 359 |
|
|
Unit *up; /* work pointer */
|
| 360 |
|
|
decNumberZero(dn); /* clean */
|
| 361 |
|
|
if (uin==0) return dn; /* [or decGetDigits bad call] */
|
| 362 |
|
|
for (up=dn->lsu; uin>0; up++) {
|
| 363 |
|
|
*up=(Unit)(uin%(DECDPUNMAX+1));
|
| 364 |
|
|
uin=uin/(DECDPUNMAX+1);
|
| 365 |
|
|
}
|
| 366 |
|
|
dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
|
| 367 |
|
|
return dn;
|
| 368 |
|
|
} /* decNumberFromUInt32 */
|
| 369 |
|
|
|
| 370 |
|
|
/* ------------------------------------------------------------------ */
|
| 371 |
|
|
/* to-int32 -- conversion to Int or uInt */
|
| 372 |
|
|
/* */
|
| 373 |
|
|
/* dn is the decNumber to convert */
|
| 374 |
|
|
/* set is the context for reporting errors */
|
| 375 |
|
|
/* returns the converted decNumber, or 0 if Invalid is set */
|
| 376 |
|
|
/* */
|
| 377 |
|
|
/* Invalid is set if the decNumber does not have exponent==0 or if */
|
| 378 |
|
|
/* it is a NaN, Infinite, or out-of-range. */
|
| 379 |
|
|
/* ------------------------------------------------------------------ */
|
| 380 |
|
|
Int decNumberToInt32(const decNumber *dn, decContext *set) {
|
| 381 |
|
|
#if DECCHECK
|
| 382 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| 383 |
|
|
#endif
|
| 384 |
|
|
|
| 385 |
|
|
/* special or too many digits, or bad exponent */
|
| 386 |
|
|
if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
|
| 387 |
|
|
else { /* is a finite integer with 10 or fewer digits */
|
| 388 |
|
|
Int d; /* work */
|
| 389 |
|
|
const Unit *up; /* .. */
|
| 390 |
|
|
uInt hi=0, lo; /* .. */
|
| 391 |
|
|
up=dn->lsu; /* -> lsu */
|
| 392 |
|
|
lo=*up; /* get 1 to 9 digits */
|
| 393 |
|
|
#if DECDPUN>1 /* split to higher */
|
| 394 |
|
|
hi=lo/10;
|
| 395 |
|
|
lo=lo%10;
|
| 396 |
|
|
#endif
|
| 397 |
|
|
up++;
|
| 398 |
|
|
/* collect remaining Units, if any, into hi */
|
| 399 |
|
|
for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
|
| 400 |
|
|
/* now low has the lsd, hi the remainder */
|
| 401 |
|
|
if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
|
| 402 |
|
|
/* most-negative is a reprieve */
|
| 403 |
|
|
if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
|
| 404 |
|
|
/* bad -- drop through */
|
| 405 |
|
|
}
|
| 406 |
|
|
else { /* in-range always */
|
| 407 |
|
|
Int i=X10(hi)+lo;
|
| 408 |
|
|
if (dn->bits&DECNEG) return -i;
|
| 409 |
|
|
return i;
|
| 410 |
|
|
}
|
| 411 |
|
|
} /* integer */
|
| 412 |
|
|
decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
|
| 413 |
|
|
return 0;
|
| 414 |
|
|
} /* decNumberToInt32 */
|
| 415 |
|
|
|
| 416 |
|
|
uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
|
| 417 |
|
|
#if DECCHECK
|
| 418 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| 419 |
|
|
#endif
|
| 420 |
|
|
/* special or too many digits, or bad exponent, or negative (<0) */
|
| 421 |
|
|
if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
|
| 422 |
|
|
|| (dn->bits&DECNEG && !ISZERO(dn))); /* bad */
|
| 423 |
|
|
else { /* is a finite integer with 10 or fewer digits */
|
| 424 |
|
|
Int d; /* work */
|
| 425 |
|
|
const Unit *up; /* .. */
|
| 426 |
|
|
uInt hi=0, lo; /* .. */
|
| 427 |
|
|
up=dn->lsu; /* -> lsu */
|
| 428 |
|
|
lo=*up; /* get 1 to 9 digits */
|
| 429 |
|
|
#if DECDPUN>1 /* split to higher */
|
| 430 |
|
|
hi=lo/10;
|
| 431 |
|
|
lo=lo%10;
|
| 432 |
|
|
#endif
|
| 433 |
|
|
up++;
|
| 434 |
|
|
/* collect remaining Units, if any, into hi */
|
| 435 |
|
|
for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
|
| 436 |
|
|
|
| 437 |
|
|
/* now low has the lsd, hi the remainder */
|
| 438 |
|
|
if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
|
| 439 |
|
|
else return X10(hi)+lo;
|
| 440 |
|
|
} /* integer */
|
| 441 |
|
|
decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
|
| 442 |
|
|
return 0;
|
| 443 |
|
|
} /* decNumberToUInt32 */
|
| 444 |
|
|
|
| 445 |
|
|
/* ------------------------------------------------------------------ */
|
| 446 |
|
|
/* to-scientific-string -- conversion to numeric string */
|
| 447 |
|
|
/* to-engineering-string -- conversion to numeric string */
|
| 448 |
|
|
/* */
|
| 449 |
|
|
/* decNumberToString(dn, string); */
|
| 450 |
|
|
/* decNumberToEngString(dn, string); */
|
| 451 |
|
|
/* */
|
| 452 |
|
|
/* dn is the decNumber to convert */
|
| 453 |
|
|
/* string is the string where the result will be laid out */
|
| 454 |
|
|
/* */
|
| 455 |
|
|
/* string must be at least dn->digits+14 characters long */
|
| 456 |
|
|
/* */
|
| 457 |
|
|
/* No error is possible, and no status can be set. */
|
| 458 |
|
|
/* ------------------------------------------------------------------ */
|
| 459 |
|
|
char * decNumberToString(const decNumber *dn, char *string){
|
| 460 |
|
|
decToString(dn, string, 0);
|
| 461 |
|
|
return string;
|
| 462 |
|
|
} /* DecNumberToString */
|
| 463 |
|
|
|
| 464 |
|
|
char * decNumberToEngString(const decNumber *dn, char *string){
|
| 465 |
|
|
decToString(dn, string, 1);
|
| 466 |
|
|
return string;
|
| 467 |
|
|
} /* DecNumberToEngString */
|
| 468 |
|
|
|
| 469 |
|
|
/* ------------------------------------------------------------------ */
|
| 470 |
|
|
/* to-number -- conversion from numeric string */
|
| 471 |
|
|
/* */
|
| 472 |
|
|
/* decNumberFromString -- convert string to decNumber */
|
| 473 |
|
|
/* dn -- the number structure to fill */
|
| 474 |
|
|
/* chars[] -- the string to convert ('\0' terminated) */
|
| 475 |
|
|
/* set -- the context used for processing any error, */
|
| 476 |
|
|
/* determining the maximum precision available */
|
| 477 |
|
|
/* (set.digits), determining the maximum and minimum */
|
| 478 |
|
|
/* exponent (set.emax and set.emin), determining if */
|
| 479 |
|
|
/* extended values are allowed, and checking the */
|
| 480 |
|
|
/* rounding mode if overflow occurs or rounding is */
|
| 481 |
|
|
/* needed. */
|
| 482 |
|
|
/* */
|
| 483 |
|
|
/* The length of the coefficient and the size of the exponent are */
|
| 484 |
|
|
/* checked by this routine, so the correct error (Underflow or */
|
| 485 |
|
|
/* Overflow) can be reported or rounding applied, as necessary. */
|
| 486 |
|
|
/* */
|
| 487 |
|
|
/* If bad syntax is detected, the result will be a quiet NaN. */
|
| 488 |
|
|
/* ------------------------------------------------------------------ */
|
| 489 |
|
|
decNumber * decNumberFromString(decNumber *dn, const char chars[],
|
| 490 |
|
|
decContext *set) {
|
| 491 |
|
|
Int exponent=0; /* working exponent [assume 0] */
|
| 492 |
|
|
uByte bits=0; /* working flags [assume +ve] */
|
| 493 |
|
|
Unit *res; /* where result will be built */
|
| 494 |
|
|
Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
|
| 495 |
|
|
/* [+9 allows for ln() constants] */
|
| 496 |
|
|
Unit *allocres=NULL; /* -> allocated result, iff allocated */
|
| 497 |
|
|
Int d=0; /* count of digits found in decimal part */
|
| 498 |
|
|
const char *dotchar=NULL; /* where dot was found */
|
| 499 |
|
|
const char *cfirst=chars; /* -> first character of decimal part */
|
| 500 |
|
|
const char *last=NULL; /* -> last digit of decimal part */
|
| 501 |
|
|
const char *c; /* work */
|
| 502 |
|
|
Unit *up; /* .. */
|
| 503 |
|
|
#if DECDPUN>1
|
| 504 |
|
|
Int cut, out; /* .. */
|
| 505 |
|
|
#endif
|
| 506 |
|
|
Int residue; /* rounding residue */
|
| 507 |
|
|
uInt status=0; /* error code */
|
| 508 |
|
|
|
| 509 |
|
|
#if DECCHECK
|
| 510 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
|
| 511 |
|
|
return decNumberZero(dn);
|
| 512 |
|
|
#endif
|
| 513 |
|
|
|
| 514 |
|
|
do { /* status & malloc protection */
|
| 515 |
|
|
for (c=chars;; c++) { /* -> input character */
|
| 516 |
|
|
if (*c>='0' && *c<='9') { /* test for Arabic digit */
|
| 517 |
|
|
last=c;
|
| 518 |
|
|
d++; /* count of real digits */
|
| 519 |
|
|
continue; /* still in decimal part */
|
| 520 |
|
|
}
|
| 521 |
|
|
if (*c=='.' && dotchar==NULL) { /* first '.' */
|
| 522 |
|
|
dotchar=c; /* record offset into decimal part */
|
| 523 |
|
|
if (c==cfirst) cfirst++; /* first digit must follow */
|
| 524 |
|
|
continue;}
|
| 525 |
|
|
if (c==chars) { /* first in string... */
|
| 526 |
|
|
if (*c=='-') { /* valid - sign */
|
| 527 |
|
|
cfirst++;
|
| 528 |
|
|
bits=DECNEG;
|
| 529 |
|
|
continue;}
|
| 530 |
|
|
if (*c=='+') { /* valid + sign */
|
| 531 |
|
|
cfirst++;
|
| 532 |
|
|
continue;}
|
| 533 |
|
|
}
|
| 534 |
|
|
/* *c is not a digit, or a valid +, -, or '.' */
|
| 535 |
|
|
break;
|
| 536 |
|
|
} /* c */
|
| 537 |
|
|
|
| 538 |
|
|
if (last==NULL) { /* no digits yet */
|
| 539 |
|
|
status=DEC_Conversion_syntax;/* assume the worst */
|
| 540 |
|
|
if (*c=='\0') break; /* and no more to come... */
|
| 541 |
|
|
#if DECSUBSET
|
| 542 |
|
|
/* if subset then infinities and NaNs are not allowed */
|
| 543 |
|
|
if (!set->extended) break; /* hopeless */
|
| 544 |
|
|
#endif
|
| 545 |
|
|
/* Infinities and NaNs are possible, here */
|
| 546 |
|
|
if (dotchar!=NULL) break; /* .. unless had a dot */
|
| 547 |
|
|
decNumberZero(dn); /* be optimistic */
|
| 548 |
|
|
if (decBiStr(c, "infinity", "INFINITY")
|
| 549 |
|
|
|| decBiStr(c, "inf", "INF")) {
|
| 550 |
|
|
dn->bits=bits | DECINF;
|
| 551 |
|
|
status=0; /* is OK */
|
| 552 |
|
|
break; /* all done */
|
| 553 |
|
|
}
|
| 554 |
|
|
/* a NaN expected */
|
| 555 |
|
|
/* 2003.09.10 NaNs are now permitted to have a sign */
|
| 556 |
|
|
dn->bits=bits | DECNAN; /* assume simple NaN */
|
| 557 |
|
|
if (*c=='s' || *c=='S') { /* looks like an sNaN */
|
| 558 |
|
|
c++;
|
| 559 |
|
|
dn->bits=bits | DECSNAN;
|
| 560 |
|
|
}
|
| 561 |
|
|
if (*c!='n' && *c!='N') break; /* check caseless "NaN" */
|
| 562 |
|
|
c++;
|
| 563 |
|
|
if (*c!='a' && *c!='A') break; /* .. */
|
| 564 |
|
|
c++;
|
| 565 |
|
|
if (*c!='n' && *c!='N') break; /* .. */
|
| 566 |
|
|
c++;
|
| 567 |
|
|
/* now either nothing, or nnnn payload, expected */
|
| 568 |
|
|
/* -> start of integer and skip leading 0s [including plain 0] */
|
| 569 |
|
|
for (cfirst=c; *cfirst=='0';) cfirst++;
|
| 570 |
|
|
if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */
|
| 571 |
|
|
status=0; /* it's good */
|
| 572 |
|
|
break; /* .. */
|
| 573 |
|
|
}
|
| 574 |
|
|
/* something other than 0s; setup last and d as usual [no dots] */
|
| 575 |
|
|
for (c=cfirst;; c++, d++) {
|
| 576 |
|
|
if (*c<'0' || *c>'9') break; /* test for Arabic digit */
|
| 577 |
|
|
last=c;
|
| 578 |
|
|
}
|
| 579 |
|
|
if (*c!='\0') break; /* not all digits */
|
| 580 |
|
|
if (d>set->digits-1) {
|
| 581 |
|
|
/* [NB: payload in a decNumber can be full length unless */
|
| 582 |
|
|
/* clamped, in which case can only be digits-1] */
|
| 583 |
|
|
if (set->clamp) break;
|
| 584 |
|
|
if (d>set->digits) break;
|
| 585 |
|
|
} /* too many digits? */
|
| 586 |
|
|
/* good; drop through to convert the integer to coefficient */
|
| 587 |
|
|
status=0; /* syntax is OK */
|
| 588 |
|
|
bits=dn->bits; /* for copy-back */
|
| 589 |
|
|
} /* last==NULL */
|
| 590 |
|
|
|
| 591 |
|
|
else if (*c!='\0') { /* more to process... */
|
| 592 |
|
|
/* had some digits; exponent is only valid sequence now */
|
| 593 |
|
|
Flag nege; /* 1=negative exponent */
|
| 594 |
|
|
const char *firstexp; /* -> first significant exponent digit */
|
| 595 |
|
|
status=DEC_Conversion_syntax;/* assume the worst */
|
| 596 |
|
|
if (*c!='e' && *c!='E') break;
|
| 597 |
|
|
/* Found 'e' or 'E' -- now process explicit exponent */
|
| 598 |
|
|
/* 1998.07.11: sign no longer required */
|
| 599 |
|
|
nege=0;
|
| 600 |
|
|
c++; /* to (possible) sign */
|
| 601 |
|
|
if (*c=='-') {nege=1; c++;}
|
| 602 |
|
|
else if (*c=='+') c++;
|
| 603 |
|
|
if (*c=='\0') break;
|
| 604 |
|
|
|
| 605 |
|
|
for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */
|
| 606 |
|
|
firstexp=c; /* save exponent digit place */
|
| 607 |
|
|
for (; ;c++) {
|
| 608 |
|
|
if (*c<'0' || *c>'9') break; /* not a digit */
|
| 609 |
|
|
exponent=X10(exponent)+(Int)*c-(Int)'0';
|
| 610 |
|
|
} /* c */
|
| 611 |
|
|
/* if not now on a '\0', *c must not be a digit */
|
| 612 |
|
|
if (*c!='\0') break;
|
| 613 |
|
|
|
| 614 |
|
|
/* (this next test must be after the syntax checks) */
|
| 615 |
|
|
/* if it was too long the exponent may have wrapped, so check */
|
| 616 |
|
|
/* carefully and set it to a certain overflow if wrap possible */
|
| 617 |
|
|
if (c>=firstexp+9+1) {
|
| 618 |
|
|
if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
|
| 619 |
|
|
/* [up to 1999999999 is OK, for example 1E-1000000998] */
|
| 620 |
|
|
}
|
| 621 |
|
|
if (nege) exponent=-exponent; /* was negative */
|
| 622 |
|
|
status=0; /* is OK */
|
| 623 |
|
|
} /* stuff after digits */
|
| 624 |
|
|
|
| 625 |
|
|
/* Here when whole string has been inspected; syntax is good */
|
| 626 |
|
|
/* cfirst->first digit (never dot), last->last digit (ditto) */
|
| 627 |
|
|
|
| 628 |
|
|
/* strip leading zeros/dot [leave final 0 if all 0's] */
|
| 629 |
|
|
if (*cfirst=='0') { /* [cfirst has stepped over .] */
|
| 630 |
|
|
for (c=cfirst; c<last; c++, cfirst++) {
|
| 631 |
|
|
if (*c=='.') continue; /* ignore dots */
|
| 632 |
|
|
if (*c!='0') break; /* non-zero found */
|
| 633 |
|
|
d--; /* 0 stripped */
|
| 634 |
|
|
} /* c */
|
| 635 |
|
|
#if DECSUBSET
|
| 636 |
|
|
/* make a rapid exit for easy zeros if !extended */
|
| 637 |
|
|
if (*cfirst=='0' && !set->extended) {
|
| 638 |
|
|
decNumberZero(dn); /* clean result */
|
| 639 |
|
|
break; /* [could be return] */
|
| 640 |
|
|
}
|
| 641 |
|
|
#endif
|
| 642 |
|
|
} /* at least one leading 0 */
|
| 643 |
|
|
|
| 644 |
|
|
/* Handle decimal point... */
|
| 645 |
|
|
if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */
|
| 646 |
|
|
exponent-=(last-dotchar); /* adjust exponent */
|
| 647 |
|
|
/* [we can now ignore the .] */
|
| 648 |
|
|
|
| 649 |
|
|
/* OK, the digits string is good. Assemble in the decNumber, or in */
|
| 650 |
|
|
/* a temporary units array if rounding is needed */
|
| 651 |
|
|
if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */
|
| 652 |
|
|
else { /* rounding needed */
|
| 653 |
|
|
Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
|
| 654 |
|
|
res=resbuff; /* assume use local buffer */
|
| 655 |
|
|
if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
|
| 656 |
|
|
allocres=(Unit *)malloc(needbytes);
|
| 657 |
|
|
if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
|
| 658 |
|
|
res=allocres;
|
| 659 |
|
|
}
|
| 660 |
|
|
}
|
| 661 |
|
|
/* res now -> number lsu, buffer, or allocated storage for Unit array */
|
| 662 |
|
|
|
| 663 |
|
|
/* Place the coefficient into the selected Unit array */
|
| 664 |
|
|
/* [this is often 70% of the cost of this function when DECDPUN>1] */
|
| 665 |
|
|
#if DECDPUN>1
|
| 666 |
|
|
out=0; /* accumulator */
|
| 667 |
|
|
up=res+D2U(d)-1; /* -> msu */
|
| 668 |
|
|
cut=d-(up-res)*DECDPUN; /* digits in top unit */
|
| 669 |
|
|
for (c=cfirst;; c++) { /* along the digits */
|
| 670 |
|
|
if (*c=='.') continue; /* ignore '.' [don't decrement cut] */
|
| 671 |
|
|
out=X10(out)+(Int)*c-(Int)'0';
|
| 672 |
|
|
if (c==last) break; /* done [never get to trailing '.'] */
|
| 673 |
|
|
cut--;
|
| 674 |
|
|
if (cut>0) continue; /* more for this unit */
|
| 675 |
|
|
*up=(Unit)out; /* write unit */
|
| 676 |
|
|
up--; /* prepare for unit below.. */
|
| 677 |
|
|
cut=DECDPUN; /* .. */
|
| 678 |
|
|
out=0; /* .. */
|
| 679 |
|
|
} /* c */
|
| 680 |
|
|
*up=(Unit)out; /* write lsu */
|
| 681 |
|
|
|
| 682 |
|
|
#else
|
| 683 |
|
|
/* DECDPUN==1 */
|
| 684 |
|
|
up=res; /* -> lsu */
|
| 685 |
|
|
for (c=last; c>=cfirst; c--) { /* over each character, from least */
|
| 686 |
|
|
if (*c=='.') continue; /* ignore . [don't step up] */
|
| 687 |
|
|
*up=(Unit)((Int)*c-(Int)'0');
|
| 688 |
|
|
up++;
|
| 689 |
|
|
} /* c */
|
| 690 |
|
|
#endif
|
| 691 |
|
|
|
| 692 |
|
|
dn->bits=bits;
|
| 693 |
|
|
dn->exponent=exponent;
|
| 694 |
|
|
dn->digits=d;
|
| 695 |
|
|
|
| 696 |
|
|
/* if not in number (too long) shorten into the number */
|
| 697 |
|
|
if (d>set->digits) {
|
| 698 |
|
|
residue=0;
|
| 699 |
|
|
decSetCoeff(dn, set, res, d, &residue, &status);
|
| 700 |
|
|
/* always check for overflow or subnormal and round as needed */
|
| 701 |
|
|
decFinalize(dn, set, &residue, &status);
|
| 702 |
|
|
}
|
| 703 |
|
|
else { /* no rounding, but may still have overflow or subnormal */
|
| 704 |
|
|
/* [these tests are just for performance; finalize repeats them] */
|
| 705 |
|
|
if ((dn->exponent-1<set->emin-dn->digits)
|
| 706 |
|
|
|| (dn->exponent-1>set->emax-set->digits)) {
|
| 707 |
|
|
residue=0;
|
| 708 |
|
|
decFinalize(dn, set, &residue, &status);
|
| 709 |
|
|
}
|
| 710 |
|
|
}
|
| 711 |
|
|
/* decNumberShow(dn); */
|
| 712 |
|
|
} while(0); /* [for break] */
|
| 713 |
|
|
|
| 714 |
|
|
if (allocres!=NULL) free(allocres); /* drop any storage used */
|
| 715 |
|
|
if (status!=0) decStatus(dn, status, set);
|
| 716 |
|
|
return dn;
|
| 717 |
|
|
} /* decNumberFromString */
|
| 718 |
|
|
|
| 719 |
|
|
/* ================================================================== */
|
| 720 |
|
|
/* Operators */
|
| 721 |
|
|
/* ================================================================== */
|
| 722 |
|
|
|
| 723 |
|
|
/* ------------------------------------------------------------------ */
|
| 724 |
|
|
/* decNumberAbs -- absolute value operator */
|
| 725 |
|
|
/* */
|
| 726 |
|
|
/* This computes C = abs(A) */
|
| 727 |
|
|
/* */
|
| 728 |
|
|
/* res is C, the result. C may be A */
|
| 729 |
|
|
/* rhs is A */
|
| 730 |
|
|
/* set is the context */
|
| 731 |
|
|
/* */
|
| 732 |
|
|
/* See also decNumberCopyAbs for a quiet bitwise version of this. */
|
| 733 |
|
|
/* C must have space for set->digits digits. */
|
| 734 |
|
|
/* ------------------------------------------------------------------ */
|
| 735 |
|
|
/* This has the same effect as decNumberPlus unless A is negative, */
|
| 736 |
|
|
/* in which case it has the same effect as decNumberMinus. */
|
| 737 |
|
|
/* ------------------------------------------------------------------ */
|
| 738 |
|
|
decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
|
| 739 |
|
|
decContext *set) {
|
| 740 |
|
|
decNumber dzero; /* for 0 */
|
| 741 |
|
|
uInt status=0; /* accumulator */
|
| 742 |
|
|
|
| 743 |
|
|
#if DECCHECK
|
| 744 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 745 |
|
|
#endif
|
| 746 |
|
|
|
| 747 |
|
|
decNumberZero(&dzero); /* set 0 */
|
| 748 |
|
|
dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| 749 |
|
|
decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
|
| 750 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 751 |
|
|
#if DECCHECK
|
| 752 |
|
|
decCheckInexact(res, set);
|
| 753 |
|
|
#endif
|
| 754 |
|
|
return res;
|
| 755 |
|
|
} /* decNumberAbs */
|
| 756 |
|
|
|
| 757 |
|
|
/* ------------------------------------------------------------------ */
|
| 758 |
|
|
/* decNumberAdd -- add two Numbers */
|
| 759 |
|
|
/* */
|
| 760 |
|
|
/* This computes C = A + B */
|
| 761 |
|
|
/* */
|
| 762 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 763 |
|
|
/* lhs is A */
|
| 764 |
|
|
/* rhs is B */
|
| 765 |
|
|
/* set is the context */
|
| 766 |
|
|
/* */
|
| 767 |
|
|
/* C must have space for set->digits digits. */
|
| 768 |
|
|
/* ------------------------------------------------------------------ */
|
| 769 |
|
|
/* This just calls the routine shared with Subtract */
|
| 770 |
|
|
decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
|
| 771 |
|
|
const decNumber *rhs, decContext *set) {
|
| 772 |
|
|
uInt status=0; /* accumulator */
|
| 773 |
|
|
decAddOp(res, lhs, rhs, set, 0, &status);
|
| 774 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 775 |
|
|
#if DECCHECK
|
| 776 |
|
|
decCheckInexact(res, set);
|
| 777 |
|
|
#endif
|
| 778 |
|
|
return res;
|
| 779 |
|
|
} /* decNumberAdd */
|
| 780 |
|
|
|
| 781 |
|
|
/* ------------------------------------------------------------------ */
|
| 782 |
|
|
/* decNumberAnd -- AND two Numbers, digitwise */
|
| 783 |
|
|
/* */
|
| 784 |
|
|
/* This computes C = A & B */
|
| 785 |
|
|
/* */
|
| 786 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
|
| 787 |
|
|
/* lhs is A */
|
| 788 |
|
|
/* rhs is B */
|
| 789 |
|
|
/* set is the context (used for result length and error report) */
|
| 790 |
|
|
/* */
|
| 791 |
|
|
/* C must have space for set->digits digits. */
|
| 792 |
|
|
/* */
|
| 793 |
|
|
/* Logical function restrictions apply (see above); a NaN is */
|
| 794 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 795 |
|
|
/* ------------------------------------------------------------------ */
|
| 796 |
|
|
decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
|
| 797 |
|
|
const decNumber *rhs, decContext *set) {
|
| 798 |
|
|
const Unit *ua, *ub; /* -> operands */
|
| 799 |
|
|
const Unit *msua, *msub; /* -> operand msus */
|
| 800 |
|
|
Unit *uc, *msuc; /* -> result and its msu */
|
| 801 |
|
|
Int msudigs; /* digits in res msu */
|
| 802 |
|
|
#if DECCHECK
|
| 803 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 804 |
|
|
#endif
|
| 805 |
|
|
|
| 806 |
|
|
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| 807 |
|
|
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| 808 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 809 |
|
|
return res;
|
| 810 |
|
|
}
|
| 811 |
|
|
|
| 812 |
|
|
/* operands are valid */
|
| 813 |
|
|
ua=lhs->lsu; /* bottom-up */
|
| 814 |
|
|
ub=rhs->lsu; /* .. */
|
| 815 |
|
|
uc=res->lsu; /* .. */
|
| 816 |
|
|
msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| 817 |
|
|
msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| 818 |
|
|
msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| 819 |
|
|
msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| 820 |
|
|
for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| 821 |
|
|
Unit a, b; /* extract units */
|
| 822 |
|
|
if (ua>msua) a=0;
|
| 823 |
|
|
else a=*ua;
|
| 824 |
|
|
if (ub>msub) b=0;
|
| 825 |
|
|
else b=*ub;
|
| 826 |
|
|
*uc=0; /* can now write back */
|
| 827 |
|
|
if (a|b) { /* maybe 1 bits to examine */
|
| 828 |
|
|
Int i, j;
|
| 829 |
|
|
*uc=0; /* can now write back */
|
| 830 |
|
|
/* This loop could be unrolled and/or use BIN2BCD tables */
|
| 831 |
|
|
for (i=0; i<DECDPUN; i++) {
|
| 832 |
|
|
if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */
|
| 833 |
|
|
j=a%10;
|
| 834 |
|
|
a=a/10;
|
| 835 |
|
|
j|=b%10;
|
| 836 |
|
|
b=b/10;
|
| 837 |
|
|
if (j>1) {
|
| 838 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 839 |
|
|
return res;
|
| 840 |
|
|
}
|
| 841 |
|
|
if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| 842 |
|
|
} /* each digit */
|
| 843 |
|
|
} /* both OK */
|
| 844 |
|
|
} /* each unit */
|
| 845 |
|
|
/* [here uc-1 is the msu of the result] */
|
| 846 |
|
|
res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| 847 |
|
|
res->exponent=0; /* integer */
|
| 848 |
|
|
res->bits=0; /* sign=0 */
|
| 849 |
|
|
return res; /* [no status to set] */
|
| 850 |
|
|
} /* decNumberAnd */
|
| 851 |
|
|
|
| 852 |
|
|
/* ------------------------------------------------------------------ */
|
| 853 |
|
|
/* decNumberCompare -- compare two Numbers */
|
| 854 |
|
|
/* */
|
| 855 |
|
|
/* This computes C = A ? B */
|
| 856 |
|
|
/* */
|
| 857 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 858 |
|
|
/* lhs is A */
|
| 859 |
|
|
/* rhs is B */
|
| 860 |
|
|
/* set is the context */
|
| 861 |
|
|
/* */
|
| 862 |
|
|
/* C must have space for one digit (or NaN). */
|
| 863 |
|
|
/* ------------------------------------------------------------------ */
|
| 864 |
|
|
decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
|
| 865 |
|
|
const decNumber *rhs, decContext *set) {
|
| 866 |
|
|
uInt status=0; /* accumulator */
|
| 867 |
|
|
decCompareOp(res, lhs, rhs, set, COMPARE, &status);
|
| 868 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 869 |
|
|
return res;
|
| 870 |
|
|
} /* decNumberCompare */
|
| 871 |
|
|
|
| 872 |
|
|
/* ------------------------------------------------------------------ */
|
| 873 |
|
|
/* decNumberCompareSignal -- compare, signalling on all NaNs */
|
| 874 |
|
|
/* */
|
| 875 |
|
|
/* This computes C = A ? B */
|
| 876 |
|
|
/* */
|
| 877 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 878 |
|
|
/* lhs is A */
|
| 879 |
|
|
/* rhs is B */
|
| 880 |
|
|
/* set is the context */
|
| 881 |
|
|
/* */
|
| 882 |
|
|
/* C must have space for one digit (or NaN). */
|
| 883 |
|
|
/* ------------------------------------------------------------------ */
|
| 884 |
|
|
decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
|
| 885 |
|
|
const decNumber *rhs, decContext *set) {
|
| 886 |
|
|
uInt status=0; /* accumulator */
|
| 887 |
|
|
decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
|
| 888 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 889 |
|
|
return res;
|
| 890 |
|
|
} /* decNumberCompareSignal */
|
| 891 |
|
|
|
| 892 |
|
|
/* ------------------------------------------------------------------ */
|
| 893 |
|
|
/* decNumberCompareTotal -- compare two Numbers, using total ordering */
|
| 894 |
|
|
/* */
|
| 895 |
|
|
/* This computes C = A ? B, under total ordering */
|
| 896 |
|
|
/* */
|
| 897 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 898 |
|
|
/* lhs is A */
|
| 899 |
|
|
/* rhs is B */
|
| 900 |
|
|
/* set is the context */
|
| 901 |
|
|
/* */
|
| 902 |
|
|
/* C must have space for one digit; the result will always be one of */
|
| 903 |
|
|
/* -1, 0, or 1. */
|
| 904 |
|
|
/* ------------------------------------------------------------------ */
|
| 905 |
|
|
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
|
| 906 |
|
|
const decNumber *rhs, decContext *set) {
|
| 907 |
|
|
uInt status=0; /* accumulator */
|
| 908 |
|
|
decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
|
| 909 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 910 |
|
|
return res;
|
| 911 |
|
|
} /* decNumberCompareTotal */
|
| 912 |
|
|
|
| 913 |
|
|
/* ------------------------------------------------------------------ */
|
| 914 |
|
|
/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
|
| 915 |
|
|
/* */
|
| 916 |
|
|
/* This computes C = |A| ? |B|, under total ordering */
|
| 917 |
|
|
/* */
|
| 918 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 919 |
|
|
/* lhs is A */
|
| 920 |
|
|
/* rhs is B */
|
| 921 |
|
|
/* set is the context */
|
| 922 |
|
|
/* */
|
| 923 |
|
|
/* C must have space for one digit; the result will always be one of */
|
| 924 |
|
|
/* -1, 0, or 1. */
|
| 925 |
|
|
/* ------------------------------------------------------------------ */
|
| 926 |
|
|
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
|
| 927 |
|
|
const decNumber *rhs, decContext *set) {
|
| 928 |
|
|
uInt status=0; /* accumulator */
|
| 929 |
|
|
uInt needbytes; /* for space calculations */
|
| 930 |
|
|
decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
|
| 931 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 932 |
|
|
decNumber bufb[D2N(DECBUFFER+1)];
|
| 933 |
|
|
decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| 934 |
|
|
decNumber *a, *b; /* temporary pointers */
|
| 935 |
|
|
|
| 936 |
|
|
#if DECCHECK
|
| 937 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 938 |
|
|
#endif
|
| 939 |
|
|
|
| 940 |
|
|
do { /* protect allocated storage */
|
| 941 |
|
|
/* if either is negative, take a copy and absolute */
|
| 942 |
|
|
if (decNumberIsNegative(lhs)) { /* lhs<0 */
|
| 943 |
|
|
a=bufa;
|
| 944 |
|
|
needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
|
| 945 |
|
|
if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| 946 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 947 |
|
|
if (allocbufa==NULL) { /* hopeless -- abandon */
|
| 948 |
|
|
status|=DEC_Insufficient_storage;
|
| 949 |
|
|
break;}
|
| 950 |
|
|
a=allocbufa; /* use the allocated space */
|
| 951 |
|
|
}
|
| 952 |
|
|
decNumberCopy(a, lhs); /* copy content */
|
| 953 |
|
|
a->bits&=~DECNEG; /* .. and clear the sign */
|
| 954 |
|
|
lhs=a; /* use copy from here on */
|
| 955 |
|
|
}
|
| 956 |
|
|
if (decNumberIsNegative(rhs)) { /* rhs<0 */
|
| 957 |
|
|
b=bufb;
|
| 958 |
|
|
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| 959 |
|
|
if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| 960 |
|
|
allocbufb=(decNumber *)malloc(needbytes);
|
| 961 |
|
|
if (allocbufb==NULL) { /* hopeless -- abandon */
|
| 962 |
|
|
status|=DEC_Insufficient_storage;
|
| 963 |
|
|
break;}
|
| 964 |
|
|
b=allocbufb; /* use the allocated space */
|
| 965 |
|
|
}
|
| 966 |
|
|
decNumberCopy(b, rhs); /* copy content */
|
| 967 |
|
|
b->bits&=~DECNEG; /* .. and clear the sign */
|
| 968 |
|
|
rhs=b; /* use copy from here on */
|
| 969 |
|
|
}
|
| 970 |
|
|
decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
|
| 971 |
|
|
} while(0); /* end protected */
|
| 972 |
|
|
|
| 973 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| 974 |
|
|
if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| 975 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 976 |
|
|
return res;
|
| 977 |
|
|
} /* decNumberCompareTotalMag */
|
| 978 |
|
|
|
| 979 |
|
|
/* ------------------------------------------------------------------ */
|
| 980 |
|
|
/* decNumberDivide -- divide one number by another */
|
| 981 |
|
|
/* */
|
| 982 |
|
|
/* This computes C = A / B */
|
| 983 |
|
|
/* */
|
| 984 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| 985 |
|
|
/* lhs is A */
|
| 986 |
|
|
/* rhs is B */
|
| 987 |
|
|
/* set is the context */
|
| 988 |
|
|
/* */
|
| 989 |
|
|
/* C must have space for set->digits digits. */
|
| 990 |
|
|
/* ------------------------------------------------------------------ */
|
| 991 |
|
|
decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
|
| 992 |
|
|
const decNumber *rhs, decContext *set) {
|
| 993 |
|
|
uInt status=0; /* accumulator */
|
| 994 |
|
|
decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
|
| 995 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 996 |
|
|
#if DECCHECK
|
| 997 |
|
|
decCheckInexact(res, set);
|
| 998 |
|
|
#endif
|
| 999 |
|
|
return res;
|
| 1000 |
|
|
} /* decNumberDivide */
|
| 1001 |
|
|
|
| 1002 |
|
|
/* ------------------------------------------------------------------ */
|
| 1003 |
|
|
/* decNumberDivideInteger -- divide and return integer quotient */
|
| 1004 |
|
|
/* */
|
| 1005 |
|
|
/* This computes C = A # B, where # is the integer divide operator */
|
| 1006 |
|
|
/* */
|
| 1007 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
|
| 1008 |
|
|
/* lhs is A */
|
| 1009 |
|
|
/* rhs is B */
|
| 1010 |
|
|
/* set is the context */
|
| 1011 |
|
|
/* */
|
| 1012 |
|
|
/* C must have space for set->digits digits. */
|
| 1013 |
|
|
/* ------------------------------------------------------------------ */
|
| 1014 |
|
|
decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
|
| 1015 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1016 |
|
|
uInt status=0; /* accumulator */
|
| 1017 |
|
|
decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
|
| 1018 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1019 |
|
|
return res;
|
| 1020 |
|
|
} /* decNumberDivideInteger */
|
| 1021 |
|
|
|
| 1022 |
|
|
/* ------------------------------------------------------------------ */
|
| 1023 |
|
|
/* decNumberExp -- exponentiation */
|
| 1024 |
|
|
/* */
|
| 1025 |
|
|
/* This computes C = exp(A) */
|
| 1026 |
|
|
/* */
|
| 1027 |
|
|
/* res is C, the result. C may be A */
|
| 1028 |
|
|
/* rhs is A */
|
| 1029 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 1030 |
|
|
/* */
|
| 1031 |
|
|
/* C must have space for set->digits digits. */
|
| 1032 |
|
|
/* */
|
| 1033 |
|
|
/* Mathematical function restrictions apply (see above); a NaN is */
|
| 1034 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1035 |
|
|
/* */
|
| 1036 |
|
|
/* Finite results will always be full precision and Inexact, except */
|
| 1037 |
|
|
/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
|
| 1038 |
|
|
/* */
|
| 1039 |
|
|
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| 1040 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 1041 |
|
|
/* error in rare cases. */
|
| 1042 |
|
|
/* ------------------------------------------------------------------ */
|
| 1043 |
|
|
/* This is a wrapper for decExpOp which can handle the slightly wider */
|
| 1044 |
|
|
/* (double) range needed by Ln (which has to be able to calculate */
|
| 1045 |
|
|
/* exp(-a) where a can be the tiniest number (Ntiny). */
|
| 1046 |
|
|
/* ------------------------------------------------------------------ */
|
| 1047 |
|
|
decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
|
| 1048 |
|
|
decContext *set) {
|
| 1049 |
|
|
uInt status=0; /* accumulator */
|
| 1050 |
|
|
#if DECSUBSET
|
| 1051 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| 1052 |
|
|
#endif
|
| 1053 |
|
|
|
| 1054 |
|
|
#if DECCHECK
|
| 1055 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1056 |
|
|
#endif
|
| 1057 |
|
|
|
| 1058 |
|
|
/* Check restrictions; these restrictions ensure that if h=8 (see */
|
| 1059 |
|
|
/* decExpOp) then the result will either overflow or underflow to 0. */
|
| 1060 |
|
|
/* Other math functions restrict the input range, too, for inverses. */
|
| 1061 |
|
|
/* If not violated then carry out the operation. */
|
| 1062 |
|
|
if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
|
| 1063 |
|
|
#if DECSUBSET
|
| 1064 |
|
|
if (!set->extended) {
|
| 1065 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 1066 |
|
|
if (rhs->digits>set->digits) {
|
| 1067 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 1068 |
|
|
if (allocrhs==NULL) break;
|
| 1069 |
|
|
rhs=allocrhs;
|
| 1070 |
|
|
}
|
| 1071 |
|
|
}
|
| 1072 |
|
|
#endif
|
| 1073 |
|
|
decExpOp(res, rhs, set, &status);
|
| 1074 |
|
|
} while(0); /* end protected */
|
| 1075 |
|
|
|
| 1076 |
|
|
#if DECSUBSET
|
| 1077 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| 1078 |
|
|
#endif
|
| 1079 |
|
|
/* apply significant status */
|
| 1080 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1081 |
|
|
#if DECCHECK
|
| 1082 |
|
|
decCheckInexact(res, set);
|
| 1083 |
|
|
#endif
|
| 1084 |
|
|
return res;
|
| 1085 |
|
|
} /* decNumberExp */
|
| 1086 |
|
|
|
| 1087 |
|
|
/* ------------------------------------------------------------------ */
|
| 1088 |
|
|
/* decNumberFMA -- fused multiply add */
|
| 1089 |
|
|
/* */
|
| 1090 |
|
|
/* This computes D = (A * B) + C with only one rounding */
|
| 1091 |
|
|
/* */
|
| 1092 |
|
|
/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
|
| 1093 |
|
|
/* lhs is A */
|
| 1094 |
|
|
/* rhs is B */
|
| 1095 |
|
|
/* fhs is C [far hand side] */
|
| 1096 |
|
|
/* set is the context */
|
| 1097 |
|
|
/* */
|
| 1098 |
|
|
/* Mathematical function restrictions apply (see above); a NaN is */
|
| 1099 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1100 |
|
|
/* */
|
| 1101 |
|
|
/* C must have space for set->digits digits. */
|
| 1102 |
|
|
/* ------------------------------------------------------------------ */
|
| 1103 |
|
|
decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
|
| 1104 |
|
|
const decNumber *rhs, const decNumber *fhs,
|
| 1105 |
|
|
decContext *set) {
|
| 1106 |
|
|
uInt status=0; /* accumulator */
|
| 1107 |
|
|
decContext dcmul; /* context for the multiplication */
|
| 1108 |
|
|
uInt needbytes; /* for space calculations */
|
| 1109 |
|
|
decNumber bufa[D2N(DECBUFFER*2+1)];
|
| 1110 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 1111 |
|
|
decNumber *acc; /* accumulator pointer */
|
| 1112 |
|
|
decNumber dzero; /* work */
|
| 1113 |
|
|
|
| 1114 |
|
|
#if DECCHECK
|
| 1115 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 1116 |
|
|
if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
|
| 1117 |
|
|
#endif
|
| 1118 |
|
|
|
| 1119 |
|
|
do { /* protect allocated storage */
|
| 1120 |
|
|
#if DECSUBSET
|
| 1121 |
|
|
if (!set->extended) { /* [undefined if subset] */
|
| 1122 |
|
|
status|=DEC_Invalid_operation;
|
| 1123 |
|
|
break;}
|
| 1124 |
|
|
#endif
|
| 1125 |
|
|
/* Check math restrictions [these ensure no overflow or underflow] */
|
| 1126 |
|
|
if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
|
| 1127 |
|
|
|| (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
|
| 1128 |
|
|
|| (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
|
| 1129 |
|
|
/* set up context for multiply */
|
| 1130 |
|
|
dcmul=*set;
|
| 1131 |
|
|
dcmul.digits=lhs->digits+rhs->digits; /* just enough */
|
| 1132 |
|
|
/* [The above may be an over-estimate for subset arithmetic, but that's OK] */
|
| 1133 |
|
|
dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */
|
| 1134 |
|
|
dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */
|
| 1135 |
|
|
/* set up decNumber space to receive the result of the multiply */
|
| 1136 |
|
|
acc=bufa; /* may fit */
|
| 1137 |
|
|
needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
|
| 1138 |
|
|
if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| 1139 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 1140 |
|
|
if (allocbufa==NULL) { /* hopeless -- abandon */
|
| 1141 |
|
|
status|=DEC_Insufficient_storage;
|
| 1142 |
|
|
break;}
|
| 1143 |
|
|
acc=allocbufa; /* use the allocated space */
|
| 1144 |
|
|
}
|
| 1145 |
|
|
/* multiply with extended range and necessary precision */
|
| 1146 |
|
|
/*printf("emin=%ld\n", dcmul.emin); */
|
| 1147 |
|
|
decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
|
| 1148 |
|
|
/* Only Invalid operation (from sNaN or Inf * 0) is possible in */
|
| 1149 |
|
|
/* status; if either is seen than ignore fhs (in case it is */
|
| 1150 |
|
|
/* another sNaN) and set acc to NaN unless we had an sNaN */
|
| 1151 |
|
|
/* [decMultiplyOp leaves that to caller] */
|
| 1152 |
|
|
/* Note sNaN has to go through addOp to shorten payload if */
|
| 1153 |
|
|
/* necessary */
|
| 1154 |
|
|
if ((status&DEC_Invalid_operation)!=0) {
|
| 1155 |
|
|
if (!(status&DEC_sNaN)) { /* but be true invalid */
|
| 1156 |
|
|
decNumberZero(res); /* acc not yet set */
|
| 1157 |
|
|
res->bits=DECNAN;
|
| 1158 |
|
|
break;
|
| 1159 |
|
|
}
|
| 1160 |
|
|
decNumberZero(&dzero); /* make 0 (any non-NaN would do) */
|
| 1161 |
|
|
fhs=&dzero; /* use that */
|
| 1162 |
|
|
}
|
| 1163 |
|
|
#if DECCHECK
|
| 1164 |
|
|
else { /* multiply was OK */
|
| 1165 |
|
|
if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
|
| 1166 |
|
|
}
|
| 1167 |
|
|
#endif
|
| 1168 |
|
|
/* add the third operand and result -> res, and all is done */
|
| 1169 |
|
|
decAddOp(res, acc, fhs, set, 0, &status);
|
| 1170 |
|
|
} while(0); /* end protected */
|
| 1171 |
|
|
|
| 1172 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| 1173 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1174 |
|
|
#if DECCHECK
|
| 1175 |
|
|
decCheckInexact(res, set);
|
| 1176 |
|
|
#endif
|
| 1177 |
|
|
return res;
|
| 1178 |
|
|
} /* decNumberFMA */
|
| 1179 |
|
|
|
| 1180 |
|
|
/* ------------------------------------------------------------------ */
|
| 1181 |
|
|
/* decNumberInvert -- invert a Number, digitwise */
|
| 1182 |
|
|
/* */
|
| 1183 |
|
|
/* This computes C = ~A */
|
| 1184 |
|
|
/* */
|
| 1185 |
|
|
/* res is C, the result. C may be A (e.g., X=~X) */
|
| 1186 |
|
|
/* rhs is A */
|
| 1187 |
|
|
/* set is the context (used for result length and error report) */
|
| 1188 |
|
|
/* */
|
| 1189 |
|
|
/* C must have space for set->digits digits. */
|
| 1190 |
|
|
/* */
|
| 1191 |
|
|
/* Logical function restrictions apply (see above); a NaN is */
|
| 1192 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1193 |
|
|
/* ------------------------------------------------------------------ */
|
| 1194 |
|
|
decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
|
| 1195 |
|
|
decContext *set) {
|
| 1196 |
|
|
const Unit *ua, *msua; /* -> operand and its msu */
|
| 1197 |
|
|
Unit *uc, *msuc; /* -> result and its msu */
|
| 1198 |
|
|
Int msudigs; /* digits in res msu */
|
| 1199 |
|
|
#if DECCHECK
|
| 1200 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1201 |
|
|
#endif
|
| 1202 |
|
|
|
| 1203 |
|
|
if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| 1204 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 1205 |
|
|
return res;
|
| 1206 |
|
|
}
|
| 1207 |
|
|
/* operand is valid */
|
| 1208 |
|
|
ua=rhs->lsu; /* bottom-up */
|
| 1209 |
|
|
uc=res->lsu; /* .. */
|
| 1210 |
|
|
msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| 1211 |
|
|
msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| 1212 |
|
|
msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| 1213 |
|
|
for (; uc<=msuc; ua++, uc++) { /* Unit loop */
|
| 1214 |
|
|
Unit a; /* extract unit */
|
| 1215 |
|
|
Int i, j; /* work */
|
| 1216 |
|
|
if (ua>msua) a=0;
|
| 1217 |
|
|
else a=*ua;
|
| 1218 |
|
|
*uc=0; /* can now write back */
|
| 1219 |
|
|
/* always need to examine all bits in rhs */
|
| 1220 |
|
|
/* This loop could be unrolled and/or use BIN2BCD tables */
|
| 1221 |
|
|
for (i=0; i<DECDPUN; i++) {
|
| 1222 |
|
|
if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */
|
| 1223 |
|
|
j=a%10;
|
| 1224 |
|
|
a=a/10;
|
| 1225 |
|
|
if (j>1) {
|
| 1226 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 1227 |
|
|
return res;
|
| 1228 |
|
|
}
|
| 1229 |
|
|
if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| 1230 |
|
|
} /* each digit */
|
| 1231 |
|
|
} /* each unit */
|
| 1232 |
|
|
/* [here uc-1 is the msu of the result] */
|
| 1233 |
|
|
res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| 1234 |
|
|
res->exponent=0; /* integer */
|
| 1235 |
|
|
res->bits=0; /* sign=0 */
|
| 1236 |
|
|
return res; /* [no status to set] */
|
| 1237 |
|
|
} /* decNumberInvert */
|
| 1238 |
|
|
|
| 1239 |
|
|
/* ------------------------------------------------------------------ */
|
| 1240 |
|
|
/* decNumberLn -- natural logarithm */
|
| 1241 |
|
|
/* */
|
| 1242 |
|
|
/* This computes C = ln(A) */
|
| 1243 |
|
|
/* */
|
| 1244 |
|
|
/* res is C, the result. C may be A */
|
| 1245 |
|
|
/* rhs is A */
|
| 1246 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 1247 |
|
|
/* */
|
| 1248 |
|
|
/* C must have space for set->digits digits. */
|
| 1249 |
|
|
/* */
|
| 1250 |
|
|
/* Notable cases: */
|
| 1251 |
|
|
/* A<0 -> Invalid */
|
| 1252 |
|
|
/* A=0 -> -Infinity (Exact) */
|
| 1253 |
|
|
/* A=+Infinity -> +Infinity (Exact) */
|
| 1254 |
|
|
/* A=1 exactly -> 0 (Exact) */
|
| 1255 |
|
|
/* */
|
| 1256 |
|
|
/* Mathematical function restrictions apply (see above); a NaN is */
|
| 1257 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1258 |
|
|
/* */
|
| 1259 |
|
|
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| 1260 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 1261 |
|
|
/* error in rare cases. */
|
| 1262 |
|
|
/* ------------------------------------------------------------------ */
|
| 1263 |
|
|
/* This is a wrapper for decLnOp which can handle the slightly wider */
|
| 1264 |
|
|
/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
|
| 1265 |
|
|
/* to calculate at p+e+2). */
|
| 1266 |
|
|
/* ------------------------------------------------------------------ */
|
| 1267 |
|
|
decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
|
| 1268 |
|
|
decContext *set) {
|
| 1269 |
|
|
uInt status=0; /* accumulator */
|
| 1270 |
|
|
#if DECSUBSET
|
| 1271 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| 1272 |
|
|
#endif
|
| 1273 |
|
|
|
| 1274 |
|
|
#if DECCHECK
|
| 1275 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1276 |
|
|
#endif
|
| 1277 |
|
|
|
| 1278 |
|
|
/* Check restrictions; this is a math function; if not violated */
|
| 1279 |
|
|
/* then carry out the operation. */
|
| 1280 |
|
|
if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
|
| 1281 |
|
|
#if DECSUBSET
|
| 1282 |
|
|
if (!set->extended) {
|
| 1283 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 1284 |
|
|
if (rhs->digits>set->digits) {
|
| 1285 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 1286 |
|
|
if (allocrhs==NULL) break;
|
| 1287 |
|
|
rhs=allocrhs;
|
| 1288 |
|
|
}
|
| 1289 |
|
|
/* special check in subset for rhs=0 */
|
| 1290 |
|
|
if (ISZERO(rhs)) { /* +/- zeros -> error */
|
| 1291 |
|
|
status|=DEC_Invalid_operation;
|
| 1292 |
|
|
break;}
|
| 1293 |
|
|
} /* extended=0 */
|
| 1294 |
|
|
#endif
|
| 1295 |
|
|
decLnOp(res, rhs, set, &status);
|
| 1296 |
|
|
} while(0); /* end protected */
|
| 1297 |
|
|
|
| 1298 |
|
|
#if DECSUBSET
|
| 1299 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| 1300 |
|
|
#endif
|
| 1301 |
|
|
/* apply significant status */
|
| 1302 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1303 |
|
|
#if DECCHECK
|
| 1304 |
|
|
decCheckInexact(res, set);
|
| 1305 |
|
|
#endif
|
| 1306 |
|
|
return res;
|
| 1307 |
|
|
} /* decNumberLn */
|
| 1308 |
|
|
|
| 1309 |
|
|
/* ------------------------------------------------------------------ */
|
| 1310 |
|
|
/* decNumberLogB - get adjusted exponent, by 754 rules */
|
| 1311 |
|
|
/* */
|
| 1312 |
|
|
/* This computes C = adjustedexponent(A) */
|
| 1313 |
|
|
/* */
|
| 1314 |
|
|
/* res is C, the result. C may be A */
|
| 1315 |
|
|
/* rhs is A */
|
| 1316 |
|
|
/* set is the context, used only for digits and status */
|
| 1317 |
|
|
/* */
|
| 1318 |
|
|
/* C must have space for 10 digits (A might have 10**9 digits and */
|
| 1319 |
|
|
/* an exponent of +999999999, or one digit and an exponent of */
|
| 1320 |
|
|
/* -1999999999). */
|
| 1321 |
|
|
/* */
|
| 1322 |
|
|
/* This returns the adjusted exponent of A after (in theory) padding */
|
| 1323 |
|
|
/* with zeros on the right to set->digits digits while keeping the */
|
| 1324 |
|
|
/* same value. The exponent is not limited by emin/emax. */
|
| 1325 |
|
|
/* */
|
| 1326 |
|
|
/* Notable cases: */
|
| 1327 |
|
|
/* A<0 -> Use |A| */
|
| 1328 |
|
|
/* A=0 -> -Infinity (Division by zero) */
|
| 1329 |
|
|
/* A=Infinite -> +Infinity (Exact) */
|
| 1330 |
|
|
/* A=1 exactly -> 0 (Exact) */
|
| 1331 |
|
|
/* NaNs are propagated as usual */
|
| 1332 |
|
|
/* ------------------------------------------------------------------ */
|
| 1333 |
|
|
decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
|
| 1334 |
|
|
decContext *set) {
|
| 1335 |
|
|
uInt status=0; /* accumulator */
|
| 1336 |
|
|
|
| 1337 |
|
|
#if DECCHECK
|
| 1338 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1339 |
|
|
#endif
|
| 1340 |
|
|
|
| 1341 |
|
|
/* NaNs as usual; Infinities return +Infinity; 0->oops */
|
| 1342 |
|
|
if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
|
| 1343 |
|
|
else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
|
| 1344 |
|
|
else if (decNumberIsZero(rhs)) {
|
| 1345 |
|
|
decNumberZero(res); /* prepare for Infinity */
|
| 1346 |
|
|
res->bits=DECNEG|DECINF; /* -Infinity */
|
| 1347 |
|
|
status|=DEC_Division_by_zero; /* as per 754 */
|
| 1348 |
|
|
}
|
| 1349 |
|
|
else { /* finite non-zero */
|
| 1350 |
|
|
Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
|
| 1351 |
|
|
decNumberFromInt32(res, ae); /* lay it out */
|
| 1352 |
|
|
}
|
| 1353 |
|
|
|
| 1354 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1355 |
|
|
return res;
|
| 1356 |
|
|
} /* decNumberLogB */
|
| 1357 |
|
|
|
| 1358 |
|
|
/* ------------------------------------------------------------------ */
|
| 1359 |
|
|
/* decNumberLog10 -- logarithm in base 10 */
|
| 1360 |
|
|
/* */
|
| 1361 |
|
|
/* This computes C = log10(A) */
|
| 1362 |
|
|
/* */
|
| 1363 |
|
|
/* res is C, the result. C may be A */
|
| 1364 |
|
|
/* rhs is A */
|
| 1365 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 1366 |
|
|
/* */
|
| 1367 |
|
|
/* C must have space for set->digits digits. */
|
| 1368 |
|
|
/* */
|
| 1369 |
|
|
/* Notable cases: */
|
| 1370 |
|
|
/* A<0 -> Invalid */
|
| 1371 |
|
|
/* A=0 -> -Infinity (Exact) */
|
| 1372 |
|
|
/* A=+Infinity -> +Infinity (Exact) */
|
| 1373 |
|
|
/* A=10**n (if n is an integer) -> n (Exact) */
|
| 1374 |
|
|
/* */
|
| 1375 |
|
|
/* Mathematical function restrictions apply (see above); a NaN is */
|
| 1376 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1377 |
|
|
/* */
|
| 1378 |
|
|
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| 1379 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 1380 |
|
|
/* error in rare cases. */
|
| 1381 |
|
|
/* ------------------------------------------------------------------ */
|
| 1382 |
|
|
/* This calculates ln(A)/ln(10) using appropriate precision. For */
|
| 1383 |
|
|
/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
|
| 1384 |
|
|
/* requested digits and t is the number of digits in the exponent */
|
| 1385 |
|
|
/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
|
| 1386 |
|
|
/* fastpath in decLnOp. The final division is done to the requested */
|
| 1387 |
|
|
/* precision. */
|
| 1388 |
|
|
/* ------------------------------------------------------------------ */
|
| 1389 |
|
|
decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
|
| 1390 |
|
|
decContext *set) {
|
| 1391 |
|
|
uInt status=0, ignore=0; /* status accumulators */
|
| 1392 |
|
|
uInt needbytes; /* for space calculations */
|
| 1393 |
|
|
Int p; /* working precision */
|
| 1394 |
|
|
Int t; /* digits in exponent of A */
|
| 1395 |
|
|
|
| 1396 |
|
|
/* buffers for a and b working decimals */
|
| 1397 |
|
|
/* (adjustment calculator, same size) */
|
| 1398 |
|
|
decNumber bufa[D2N(DECBUFFER+2)];
|
| 1399 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 1400 |
|
|
decNumber *a=bufa; /* temporary a */
|
| 1401 |
|
|
decNumber bufb[D2N(DECBUFFER+2)];
|
| 1402 |
|
|
decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| 1403 |
|
|
decNumber *b=bufb; /* temporary b */
|
| 1404 |
|
|
decNumber bufw[D2N(10)]; /* working 2-10 digit number */
|
| 1405 |
|
|
decNumber *w=bufw; /* .. */
|
| 1406 |
|
|
#if DECSUBSET
|
| 1407 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| 1408 |
|
|
#endif
|
| 1409 |
|
|
|
| 1410 |
|
|
decContext aset; /* working context */
|
| 1411 |
|
|
|
| 1412 |
|
|
#if DECCHECK
|
| 1413 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1414 |
|
|
#endif
|
| 1415 |
|
|
|
| 1416 |
|
|
/* Check restrictions; this is a math function; if not violated */
|
| 1417 |
|
|
/* then carry out the operation. */
|
| 1418 |
|
|
if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
|
| 1419 |
|
|
#if DECSUBSET
|
| 1420 |
|
|
if (!set->extended) {
|
| 1421 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 1422 |
|
|
if (rhs->digits>set->digits) {
|
| 1423 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 1424 |
|
|
if (allocrhs==NULL) break;
|
| 1425 |
|
|
rhs=allocrhs;
|
| 1426 |
|
|
}
|
| 1427 |
|
|
/* special check in subset for rhs=0 */
|
| 1428 |
|
|
if (ISZERO(rhs)) { /* +/- zeros -> error */
|
| 1429 |
|
|
status|=DEC_Invalid_operation;
|
| 1430 |
|
|
break;}
|
| 1431 |
|
|
} /* extended=0 */
|
| 1432 |
|
|
#endif
|
| 1433 |
|
|
|
| 1434 |
|
|
decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
|
| 1435 |
|
|
|
| 1436 |
|
|
/* handle exact powers of 10; only check if +ve finite */
|
| 1437 |
|
|
if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
|
| 1438 |
|
|
Int residue=0; /* (no residue) */
|
| 1439 |
|
|
uInt copystat=0; /* clean status */
|
| 1440 |
|
|
|
| 1441 |
|
|
/* round to a single digit... */
|
| 1442 |
|
|
aset.digits=1;
|
| 1443 |
|
|
decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */
|
| 1444 |
|
|
/* if exact and the digit is 1, rhs is a power of 10 */
|
| 1445 |
|
|
if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
|
| 1446 |
|
|
/* the exponent, conveniently, is the power of 10; making */
|
| 1447 |
|
|
/* this the result needs a little care as it might not fit, */
|
| 1448 |
|
|
/* so first convert it into the working number, and then move */
|
| 1449 |
|
|
/* to res */
|
| 1450 |
|
|
decNumberFromInt32(w, w->exponent);
|
| 1451 |
|
|
residue=0;
|
| 1452 |
|
|
decCopyFit(res, w, set, &residue, &status); /* copy & round */
|
| 1453 |
|
|
decFinish(res, set, &residue, &status); /* cleanup/set flags */
|
| 1454 |
|
|
break;
|
| 1455 |
|
|
} /* not a power of 10 */
|
| 1456 |
|
|
} /* not a candidate for exact */
|
| 1457 |
|
|
|
| 1458 |
|
|
/* simplify the information-content calculation to use 'total */
|
| 1459 |
|
|
/* number of digits in a, including exponent' as compared to the */
|
| 1460 |
|
|
/* requested digits, as increasing this will only rarely cost an */
|
| 1461 |
|
|
/* iteration in ln(a) anyway */
|
| 1462 |
|
|
t=6; /* it can never be >6 */
|
| 1463 |
|
|
|
| 1464 |
|
|
/* allocate space when needed... */
|
| 1465 |
|
|
p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
|
| 1466 |
|
|
needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
|
| 1467 |
|
|
if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| 1468 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 1469 |
|
|
if (allocbufa==NULL) { /* hopeless -- abandon */
|
| 1470 |
|
|
status|=DEC_Insufficient_storage;
|
| 1471 |
|
|
break;}
|
| 1472 |
|
|
a=allocbufa; /* use the allocated space */
|
| 1473 |
|
|
}
|
| 1474 |
|
|
aset.digits=p; /* as calculated */
|
| 1475 |
|
|
aset.emax=DEC_MAX_MATH; /* usual bounds */
|
| 1476 |
|
|
aset.emin=-DEC_MAX_MATH; /* .. */
|
| 1477 |
|
|
aset.clamp=0; /* and no concrete format */
|
| 1478 |
|
|
decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */
|
| 1479 |
|
|
|
| 1480 |
|
|
/* skip the division if the result so far is infinite, NaN, or */
|
| 1481 |
|
|
/* zero, or there was an error; note NaN from sNaN needs copy */
|
| 1482 |
|
|
if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
|
| 1483 |
|
|
if (a->bits&DECSPECIAL || ISZERO(a)) {
|
| 1484 |
|
|
decNumberCopy(res, a); /* [will fit] */
|
| 1485 |
|
|
break;}
|
| 1486 |
|
|
|
| 1487 |
|
|
/* for ln(10) an extra 3 digits of precision are needed */
|
| 1488 |
|
|
p=set->digits+3;
|
| 1489 |
|
|
needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
|
| 1490 |
|
|
if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| 1491 |
|
|
allocbufb=(decNumber *)malloc(needbytes);
|
| 1492 |
|
|
if (allocbufb==NULL) { /* hopeless -- abandon */
|
| 1493 |
|
|
status|=DEC_Insufficient_storage;
|
| 1494 |
|
|
break;}
|
| 1495 |
|
|
b=allocbufb; /* use the allocated space */
|
| 1496 |
|
|
}
|
| 1497 |
|
|
decNumberZero(w); /* set up 10... */
|
| 1498 |
|
|
#if DECDPUN==1
|
| 1499 |
|
|
w->lsu[1]=1; w->lsu[0]=0; /* .. */
|
| 1500 |
|
|
#else
|
| 1501 |
|
|
w->lsu[0]=10; /* .. */
|
| 1502 |
|
|
#endif
|
| 1503 |
|
|
w->digits=2; /* .. */
|
| 1504 |
|
|
|
| 1505 |
|
|
aset.digits=p;
|
| 1506 |
|
|
decLnOp(b, w, &aset, &ignore); /* b=ln(10) */
|
| 1507 |
|
|
|
| 1508 |
|
|
aset.digits=set->digits; /* for final divide */
|
| 1509 |
|
|
decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
|
| 1510 |
|
|
} while(0); /* [for break] */
|
| 1511 |
|
|
|
| 1512 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| 1513 |
|
|
if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| 1514 |
|
|
#if DECSUBSET
|
| 1515 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| 1516 |
|
|
#endif
|
| 1517 |
|
|
/* apply significant status */
|
| 1518 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1519 |
|
|
#if DECCHECK
|
| 1520 |
|
|
decCheckInexact(res, set);
|
| 1521 |
|
|
#endif
|
| 1522 |
|
|
return res;
|
| 1523 |
|
|
} /* decNumberLog10 */
|
| 1524 |
|
|
|
| 1525 |
|
|
/* ------------------------------------------------------------------ */
|
| 1526 |
|
|
/* decNumberMax -- compare two Numbers and return the maximum */
|
| 1527 |
|
|
/* */
|
| 1528 |
|
|
/* This computes C = A ? B, returning the maximum by 754 rules */
|
| 1529 |
|
|
/* */
|
| 1530 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 1531 |
|
|
/* lhs is A */
|
| 1532 |
|
|
/* rhs is B */
|
| 1533 |
|
|
/* set is the context */
|
| 1534 |
|
|
/* */
|
| 1535 |
|
|
/* C must have space for set->digits digits. */
|
| 1536 |
|
|
/* ------------------------------------------------------------------ */
|
| 1537 |
|
|
decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
|
| 1538 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1539 |
|
|
uInt status=0; /* accumulator */
|
| 1540 |
|
|
decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
|
| 1541 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1542 |
|
|
#if DECCHECK
|
| 1543 |
|
|
decCheckInexact(res, set);
|
| 1544 |
|
|
#endif
|
| 1545 |
|
|
return res;
|
| 1546 |
|
|
} /* decNumberMax */
|
| 1547 |
|
|
|
| 1548 |
|
|
/* ------------------------------------------------------------------ */
|
| 1549 |
|
|
/* decNumberMaxMag -- compare and return the maximum by magnitude */
|
| 1550 |
|
|
/* */
|
| 1551 |
|
|
/* This computes C = A ? B, returning the maximum by 754 rules */
|
| 1552 |
|
|
/* */
|
| 1553 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 1554 |
|
|
/* lhs is A */
|
| 1555 |
|
|
/* rhs is B */
|
| 1556 |
|
|
/* set is the context */
|
| 1557 |
|
|
/* */
|
| 1558 |
|
|
/* C must have space for set->digits digits. */
|
| 1559 |
|
|
/* ------------------------------------------------------------------ */
|
| 1560 |
|
|
decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
|
| 1561 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1562 |
|
|
uInt status=0; /* accumulator */
|
| 1563 |
|
|
decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
|
| 1564 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1565 |
|
|
#if DECCHECK
|
| 1566 |
|
|
decCheckInexact(res, set);
|
| 1567 |
|
|
#endif
|
| 1568 |
|
|
return res;
|
| 1569 |
|
|
} /* decNumberMaxMag */
|
| 1570 |
|
|
|
| 1571 |
|
|
/* ------------------------------------------------------------------ */
|
| 1572 |
|
|
/* decNumberMin -- compare two Numbers and return the minimum */
|
| 1573 |
|
|
/* */
|
| 1574 |
|
|
/* This computes C = A ? B, returning the minimum by 754 rules */
|
| 1575 |
|
|
/* */
|
| 1576 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 1577 |
|
|
/* lhs is A */
|
| 1578 |
|
|
/* rhs is B */
|
| 1579 |
|
|
/* set is the context */
|
| 1580 |
|
|
/* */
|
| 1581 |
|
|
/* C must have space for set->digits digits. */
|
| 1582 |
|
|
/* ------------------------------------------------------------------ */
|
| 1583 |
|
|
decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
|
| 1584 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1585 |
|
|
uInt status=0; /* accumulator */
|
| 1586 |
|
|
decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
|
| 1587 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1588 |
|
|
#if DECCHECK
|
| 1589 |
|
|
decCheckInexact(res, set);
|
| 1590 |
|
|
#endif
|
| 1591 |
|
|
return res;
|
| 1592 |
|
|
} /* decNumberMin */
|
| 1593 |
|
|
|
| 1594 |
|
|
/* ------------------------------------------------------------------ */
|
| 1595 |
|
|
/* decNumberMinMag -- compare and return the minimum by magnitude */
|
| 1596 |
|
|
/* */
|
| 1597 |
|
|
/* This computes C = A ? B, returning the minimum by 754 rules */
|
| 1598 |
|
|
/* */
|
| 1599 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 1600 |
|
|
/* lhs is A */
|
| 1601 |
|
|
/* rhs is B */
|
| 1602 |
|
|
/* set is the context */
|
| 1603 |
|
|
/* */
|
| 1604 |
|
|
/* C must have space for set->digits digits. */
|
| 1605 |
|
|
/* ------------------------------------------------------------------ */
|
| 1606 |
|
|
decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
|
| 1607 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1608 |
|
|
uInt status=0; /* accumulator */
|
| 1609 |
|
|
decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
|
| 1610 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1611 |
|
|
#if DECCHECK
|
| 1612 |
|
|
decCheckInexact(res, set);
|
| 1613 |
|
|
#endif
|
| 1614 |
|
|
return res;
|
| 1615 |
|
|
} /* decNumberMinMag */
|
| 1616 |
|
|
|
| 1617 |
|
|
/* ------------------------------------------------------------------ */
|
| 1618 |
|
|
/* decNumberMinus -- prefix minus operator */
|
| 1619 |
|
|
/* */
|
| 1620 |
|
|
/* This computes C = 0 - A */
|
| 1621 |
|
|
/* */
|
| 1622 |
|
|
/* res is C, the result. C may be A */
|
| 1623 |
|
|
/* rhs is A */
|
| 1624 |
|
|
/* set is the context */
|
| 1625 |
|
|
/* */
|
| 1626 |
|
|
/* See also decNumberCopyNegate for a quiet bitwise version of this. */
|
| 1627 |
|
|
/* C must have space for set->digits digits. */
|
| 1628 |
|
|
/* ------------------------------------------------------------------ */
|
| 1629 |
|
|
/* Simply use AddOp for the subtract, which will do the necessary. */
|
| 1630 |
|
|
/* ------------------------------------------------------------------ */
|
| 1631 |
|
|
decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
|
| 1632 |
|
|
decContext *set) {
|
| 1633 |
|
|
decNumber dzero;
|
| 1634 |
|
|
uInt status=0; /* accumulator */
|
| 1635 |
|
|
|
| 1636 |
|
|
#if DECCHECK
|
| 1637 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1638 |
|
|
#endif
|
| 1639 |
|
|
|
| 1640 |
|
|
decNumberZero(&dzero); /* make 0 */
|
| 1641 |
|
|
dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| 1642 |
|
|
decAddOp(res, &dzero, rhs, set, DECNEG, &status);
|
| 1643 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1644 |
|
|
#if DECCHECK
|
| 1645 |
|
|
decCheckInexact(res, set);
|
| 1646 |
|
|
#endif
|
| 1647 |
|
|
return res;
|
| 1648 |
|
|
} /* decNumberMinus */
|
| 1649 |
|
|
|
| 1650 |
|
|
/* ------------------------------------------------------------------ */
|
| 1651 |
|
|
/* decNumberNextMinus -- next towards -Infinity */
|
| 1652 |
|
|
/* */
|
| 1653 |
|
|
/* This computes C = A - infinitesimal, rounded towards -Infinity */
|
| 1654 |
|
|
/* */
|
| 1655 |
|
|
/* res is C, the result. C may be A */
|
| 1656 |
|
|
/* rhs is A */
|
| 1657 |
|
|
/* set is the context */
|
| 1658 |
|
|
/* */
|
| 1659 |
|
|
/* This is a generalization of 754 NextDown. */
|
| 1660 |
|
|
/* ------------------------------------------------------------------ */
|
| 1661 |
|
|
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
|
| 1662 |
|
|
decContext *set) {
|
| 1663 |
|
|
decNumber dtiny; /* constant */
|
| 1664 |
|
|
decContext workset=*set; /* work */
|
| 1665 |
|
|
uInt status=0; /* accumulator */
|
| 1666 |
|
|
#if DECCHECK
|
| 1667 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1668 |
|
|
#endif
|
| 1669 |
|
|
|
| 1670 |
|
|
/* +Infinity is the special case */
|
| 1671 |
|
|
if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
|
| 1672 |
|
|
decSetMaxValue(res, set); /* is +ve */
|
| 1673 |
|
|
/* there is no status to set */
|
| 1674 |
|
|
return res;
|
| 1675 |
|
|
}
|
| 1676 |
|
|
decNumberZero(&dtiny); /* start with 0 */
|
| 1677 |
|
|
dtiny.lsu[0]=1; /* make number that is .. */
|
| 1678 |
|
|
dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| 1679 |
|
|
workset.round=DEC_ROUND_FLOOR;
|
| 1680 |
|
|
decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
|
| 1681 |
|
|
status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
|
| 1682 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1683 |
|
|
return res;
|
| 1684 |
|
|
} /* decNumberNextMinus */
|
| 1685 |
|
|
|
| 1686 |
|
|
/* ------------------------------------------------------------------ */
|
| 1687 |
|
|
/* decNumberNextPlus -- next towards +Infinity */
|
| 1688 |
|
|
/* */
|
| 1689 |
|
|
/* This computes C = A + infinitesimal, rounded towards +Infinity */
|
| 1690 |
|
|
/* */
|
| 1691 |
|
|
/* res is C, the result. C may be A */
|
| 1692 |
|
|
/* rhs is A */
|
| 1693 |
|
|
/* set is the context */
|
| 1694 |
|
|
/* */
|
| 1695 |
|
|
/* This is a generalization of 754 NextUp. */
|
| 1696 |
|
|
/* ------------------------------------------------------------------ */
|
| 1697 |
|
|
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
|
| 1698 |
|
|
decContext *set) {
|
| 1699 |
|
|
decNumber dtiny; /* constant */
|
| 1700 |
|
|
decContext workset=*set; /* work */
|
| 1701 |
|
|
uInt status=0; /* accumulator */
|
| 1702 |
|
|
#if DECCHECK
|
| 1703 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1704 |
|
|
#endif
|
| 1705 |
|
|
|
| 1706 |
|
|
/* -Infinity is the special case */
|
| 1707 |
|
|
if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
|
| 1708 |
|
|
decSetMaxValue(res, set);
|
| 1709 |
|
|
res->bits=DECNEG; /* negative */
|
| 1710 |
|
|
/* there is no status to set */
|
| 1711 |
|
|
return res;
|
| 1712 |
|
|
}
|
| 1713 |
|
|
decNumberZero(&dtiny); /* start with 0 */
|
| 1714 |
|
|
dtiny.lsu[0]=1; /* make number that is .. */
|
| 1715 |
|
|
dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| 1716 |
|
|
workset.round=DEC_ROUND_CEILING;
|
| 1717 |
|
|
decAddOp(res, rhs, &dtiny, &workset, 0, &status);
|
| 1718 |
|
|
status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
|
| 1719 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1720 |
|
|
return res;
|
| 1721 |
|
|
} /* decNumberNextPlus */
|
| 1722 |
|
|
|
| 1723 |
|
|
/* ------------------------------------------------------------------ */
|
| 1724 |
|
|
/* decNumberNextToward -- next towards rhs */
|
| 1725 |
|
|
/* */
|
| 1726 |
|
|
/* This computes C = A +/- infinitesimal, rounded towards */
|
| 1727 |
|
|
/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
|
| 1728 |
|
|
/* modified during revision but dropped from 754-2008. */
|
| 1729 |
|
|
/* */
|
| 1730 |
|
|
/* res is C, the result. C may be A or B. */
|
| 1731 |
|
|
/* lhs is A */
|
| 1732 |
|
|
/* rhs is B */
|
| 1733 |
|
|
/* set is the context */
|
| 1734 |
|
|
/* */
|
| 1735 |
|
|
/* This is a generalization of 754-1985 NextAfter. */
|
| 1736 |
|
|
/* ------------------------------------------------------------------ */
|
| 1737 |
|
|
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
|
| 1738 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1739 |
|
|
decNumber dtiny; /* constant */
|
| 1740 |
|
|
decContext workset=*set; /* work */
|
| 1741 |
|
|
Int result; /* .. */
|
| 1742 |
|
|
uInt status=0; /* accumulator */
|
| 1743 |
|
|
#if DECCHECK
|
| 1744 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 1745 |
|
|
#endif
|
| 1746 |
|
|
|
| 1747 |
|
|
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
|
| 1748 |
|
|
decNaNs(res, lhs, rhs, set, &status);
|
| 1749 |
|
|
}
|
| 1750 |
|
|
else { /* Is numeric, so no chance of sNaN Invalid, etc. */
|
| 1751 |
|
|
result=decCompare(lhs, rhs, 0); /* sign matters */
|
| 1752 |
|
|
if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
|
| 1753 |
|
|
else { /* valid compare */
|
| 1754 |
|
|
if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */
|
| 1755 |
|
|
else { /* differ: need NextPlus or NextMinus */
|
| 1756 |
|
|
uByte sub; /* add or subtract */
|
| 1757 |
|
|
if (result<0) { /* lhs<rhs, do nextplus */
|
| 1758 |
|
|
/* -Infinity is the special case */
|
| 1759 |
|
|
if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
|
| 1760 |
|
|
decSetMaxValue(res, set);
|
| 1761 |
|
|
res->bits=DECNEG; /* negative */
|
| 1762 |
|
|
return res; /* there is no status to set */
|
| 1763 |
|
|
}
|
| 1764 |
|
|
workset.round=DEC_ROUND_CEILING;
|
| 1765 |
|
|
sub=0; /* add, please */
|
| 1766 |
|
|
} /* plus */
|
| 1767 |
|
|
else { /* lhs>rhs, do nextminus */
|
| 1768 |
|
|
/* +Infinity is the special case */
|
| 1769 |
|
|
if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
|
| 1770 |
|
|
decSetMaxValue(res, set);
|
| 1771 |
|
|
return res; /* there is no status to set */
|
| 1772 |
|
|
}
|
| 1773 |
|
|
workset.round=DEC_ROUND_FLOOR;
|
| 1774 |
|
|
sub=DECNEG; /* subtract, please */
|
| 1775 |
|
|
} /* minus */
|
| 1776 |
|
|
decNumberZero(&dtiny); /* start with 0 */
|
| 1777 |
|
|
dtiny.lsu[0]=1; /* make number that is .. */
|
| 1778 |
|
|
dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| 1779 |
|
|
decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
|
| 1780 |
|
|
/* turn off exceptions if the result is a normal number */
|
| 1781 |
|
|
/* (including Nmin), otherwise let all status through */
|
| 1782 |
|
|
if (decNumberIsNormal(res, set)) status=0;
|
| 1783 |
|
|
} /* unequal */
|
| 1784 |
|
|
} /* compare OK */
|
| 1785 |
|
|
} /* numeric */
|
| 1786 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1787 |
|
|
return res;
|
| 1788 |
|
|
} /* decNumberNextToward */
|
| 1789 |
|
|
|
| 1790 |
|
|
/* ------------------------------------------------------------------ */
|
| 1791 |
|
|
/* decNumberOr -- OR two Numbers, digitwise */
|
| 1792 |
|
|
/* */
|
| 1793 |
|
|
/* This computes C = A | B */
|
| 1794 |
|
|
/* */
|
| 1795 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
|
| 1796 |
|
|
/* lhs is A */
|
| 1797 |
|
|
/* rhs is B */
|
| 1798 |
|
|
/* set is the context (used for result length and error report) */
|
| 1799 |
|
|
/* */
|
| 1800 |
|
|
/* C must have space for set->digits digits. */
|
| 1801 |
|
|
/* */
|
| 1802 |
|
|
/* Logical function restrictions apply (see above); a NaN is */
|
| 1803 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1804 |
|
|
/* ------------------------------------------------------------------ */
|
| 1805 |
|
|
decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
|
| 1806 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1807 |
|
|
const Unit *ua, *ub; /* -> operands */
|
| 1808 |
|
|
const Unit *msua, *msub; /* -> operand msus */
|
| 1809 |
|
|
Unit *uc, *msuc; /* -> result and its msu */
|
| 1810 |
|
|
Int msudigs; /* digits in res msu */
|
| 1811 |
|
|
#if DECCHECK
|
| 1812 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 1813 |
|
|
#endif
|
| 1814 |
|
|
|
| 1815 |
|
|
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| 1816 |
|
|
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| 1817 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 1818 |
|
|
return res;
|
| 1819 |
|
|
}
|
| 1820 |
|
|
/* operands are valid */
|
| 1821 |
|
|
ua=lhs->lsu; /* bottom-up */
|
| 1822 |
|
|
ub=rhs->lsu; /* .. */
|
| 1823 |
|
|
uc=res->lsu; /* .. */
|
| 1824 |
|
|
msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| 1825 |
|
|
msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| 1826 |
|
|
msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| 1827 |
|
|
msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| 1828 |
|
|
for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| 1829 |
|
|
Unit a, b; /* extract units */
|
| 1830 |
|
|
if (ua>msua) a=0;
|
| 1831 |
|
|
else a=*ua;
|
| 1832 |
|
|
if (ub>msub) b=0;
|
| 1833 |
|
|
else b=*ub;
|
| 1834 |
|
|
*uc=0; /* can now write back */
|
| 1835 |
|
|
if (a|b) { /* maybe 1 bits to examine */
|
| 1836 |
|
|
Int i, j;
|
| 1837 |
|
|
/* This loop could be unrolled and/or use BIN2BCD tables */
|
| 1838 |
|
|
for (i=0; i<DECDPUN; i++) {
|
| 1839 |
|
|
if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */
|
| 1840 |
|
|
j=a%10;
|
| 1841 |
|
|
a=a/10;
|
| 1842 |
|
|
j|=b%10;
|
| 1843 |
|
|
b=b/10;
|
| 1844 |
|
|
if (j>1) {
|
| 1845 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 1846 |
|
|
return res;
|
| 1847 |
|
|
}
|
| 1848 |
|
|
if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| 1849 |
|
|
} /* each digit */
|
| 1850 |
|
|
} /* non-zero */
|
| 1851 |
|
|
} /* each unit */
|
| 1852 |
|
|
/* [here uc-1 is the msu of the result] */
|
| 1853 |
|
|
res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| 1854 |
|
|
res->exponent=0; /* integer */
|
| 1855 |
|
|
res->bits=0; /* sign=0 */
|
| 1856 |
|
|
return res; /* [no status to set] */
|
| 1857 |
|
|
} /* decNumberOr */
|
| 1858 |
|
|
|
| 1859 |
|
|
/* ------------------------------------------------------------------ */
|
| 1860 |
|
|
/* decNumberPlus -- prefix plus operator */
|
| 1861 |
|
|
/* */
|
| 1862 |
|
|
/* This computes C = 0 + A */
|
| 1863 |
|
|
/* */
|
| 1864 |
|
|
/* res is C, the result. C may be A */
|
| 1865 |
|
|
/* rhs is A */
|
| 1866 |
|
|
/* set is the context */
|
| 1867 |
|
|
/* */
|
| 1868 |
|
|
/* See also decNumberCopy for a quiet bitwise version of this. */
|
| 1869 |
|
|
/* C must have space for set->digits digits. */
|
| 1870 |
|
|
/* ------------------------------------------------------------------ */
|
| 1871 |
|
|
/* This simply uses AddOp; Add will take fast path after preparing A. */
|
| 1872 |
|
|
/* Performance is a concern here, as this routine is often used to */
|
| 1873 |
|
|
/* check operands and apply rounding and overflow/underflow testing. */
|
| 1874 |
|
|
/* ------------------------------------------------------------------ */
|
| 1875 |
|
|
decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
|
| 1876 |
|
|
decContext *set) {
|
| 1877 |
|
|
decNumber dzero;
|
| 1878 |
|
|
uInt status=0; /* accumulator */
|
| 1879 |
|
|
#if DECCHECK
|
| 1880 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 1881 |
|
|
#endif
|
| 1882 |
|
|
|
| 1883 |
|
|
decNumberZero(&dzero); /* make 0 */
|
| 1884 |
|
|
dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| 1885 |
|
|
decAddOp(res, &dzero, rhs, set, 0, &status);
|
| 1886 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1887 |
|
|
#if DECCHECK
|
| 1888 |
|
|
decCheckInexact(res, set);
|
| 1889 |
|
|
#endif
|
| 1890 |
|
|
return res;
|
| 1891 |
|
|
} /* decNumberPlus */
|
| 1892 |
|
|
|
| 1893 |
|
|
/* ------------------------------------------------------------------ */
|
| 1894 |
|
|
/* decNumberMultiply -- multiply two Numbers */
|
| 1895 |
|
|
/* */
|
| 1896 |
|
|
/* This computes C = A x B */
|
| 1897 |
|
|
/* */
|
| 1898 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 1899 |
|
|
/* lhs is A */
|
| 1900 |
|
|
/* rhs is B */
|
| 1901 |
|
|
/* set is the context */
|
| 1902 |
|
|
/* */
|
| 1903 |
|
|
/* C must have space for set->digits digits. */
|
| 1904 |
|
|
/* ------------------------------------------------------------------ */
|
| 1905 |
|
|
decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
|
| 1906 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1907 |
|
|
uInt status=0; /* accumulator */
|
| 1908 |
|
|
decMultiplyOp(res, lhs, rhs, set, &status);
|
| 1909 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 1910 |
|
|
#if DECCHECK
|
| 1911 |
|
|
decCheckInexact(res, set);
|
| 1912 |
|
|
#endif
|
| 1913 |
|
|
return res;
|
| 1914 |
|
|
} /* decNumberMultiply */
|
| 1915 |
|
|
|
| 1916 |
|
|
/* ------------------------------------------------------------------ */
|
| 1917 |
|
|
/* decNumberPower -- raise a number to a power */
|
| 1918 |
|
|
/* */
|
| 1919 |
|
|
/* This computes C = A ** B */
|
| 1920 |
|
|
/* */
|
| 1921 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
|
| 1922 |
|
|
/* lhs is A */
|
| 1923 |
|
|
/* rhs is B */
|
| 1924 |
|
|
/* set is the context */
|
| 1925 |
|
|
/* */
|
| 1926 |
|
|
/* C must have space for set->digits digits. */
|
| 1927 |
|
|
/* */
|
| 1928 |
|
|
/* Mathematical function restrictions apply (see above); a NaN is */
|
| 1929 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 1930 |
|
|
/* */
|
| 1931 |
|
|
/* However, if 1999999997<=B<=999999999 and B is an integer then the */
|
| 1932 |
|
|
/* restrictions on A and the context are relaxed to the usual bounds, */
|
| 1933 |
|
|
/* for compatibility with the earlier (integer power only) version */
|
| 1934 |
|
|
/* of this function. */
|
| 1935 |
|
|
/* */
|
| 1936 |
|
|
/* When B is an integer, the result may be exact, even if rounded. */
|
| 1937 |
|
|
/* */
|
| 1938 |
|
|
/* The final result is rounded according to the context; it will */
|
| 1939 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 1940 |
|
|
/* error in rare cases. */
|
| 1941 |
|
|
/* ------------------------------------------------------------------ */
|
| 1942 |
|
|
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
|
| 1943 |
|
|
const decNumber *rhs, decContext *set) {
|
| 1944 |
|
|
#if DECSUBSET
|
| 1945 |
|
|
decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| 1946 |
|
|
decNumber *allocrhs=NULL; /* .., rhs */
|
| 1947 |
|
|
#endif
|
| 1948 |
|
|
decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */
|
| 1949 |
|
|
decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */
|
| 1950 |
|
|
Int reqdigits=set->digits; /* requested DIGITS */
|
| 1951 |
|
|
Int n; /* rhs in binary */
|
| 1952 |
|
|
Flag rhsint=0; /* 1 if rhs is an integer */
|
| 1953 |
|
|
Flag useint=0; /* 1 if can use integer calculation */
|
| 1954 |
|
|
Flag isoddint=0; /* 1 if rhs is an integer and odd */
|
| 1955 |
|
|
Int i; /* work */
|
| 1956 |
|
|
#if DECSUBSET
|
| 1957 |
|
|
Int dropped; /* .. */
|
| 1958 |
|
|
#endif
|
| 1959 |
|
|
uInt needbytes; /* buffer size needed */
|
| 1960 |
|
|
Flag seenbit; /* seen a bit while powering */
|
| 1961 |
|
|
Int residue=0; /* rounding residue */
|
| 1962 |
|
|
uInt status=0; /* accumulators */
|
| 1963 |
|
|
uByte bits=0; /* result sign if errors */
|
| 1964 |
|
|
decContext aset; /* working context */
|
| 1965 |
|
|
decNumber dnOne; /* work value 1... */
|
| 1966 |
|
|
/* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
|
| 1967 |
|
|
decNumber dacbuff[D2N(DECBUFFER+9)];
|
| 1968 |
|
|
decNumber *dac=dacbuff; /* -> result accumulator */
|
| 1969 |
|
|
/* same again for possible 1/lhs calculation */
|
| 1970 |
|
|
decNumber invbuff[D2N(DECBUFFER+9)];
|
| 1971 |
|
|
|
| 1972 |
|
|
#if DECCHECK
|
| 1973 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 1974 |
|
|
#endif
|
| 1975 |
|
|
|
| 1976 |
|
|
do { /* protect allocated storage */
|
| 1977 |
|
|
#if DECSUBSET
|
| 1978 |
|
|
if (!set->extended) { /* reduce operands and set status, as needed */
|
| 1979 |
|
|
if (lhs->digits>reqdigits) {
|
| 1980 |
|
|
alloclhs=decRoundOperand(lhs, set, &status);
|
| 1981 |
|
|
if (alloclhs==NULL) break;
|
| 1982 |
|
|
lhs=alloclhs;
|
| 1983 |
|
|
}
|
| 1984 |
|
|
if (rhs->digits>reqdigits) {
|
| 1985 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 1986 |
|
|
if (allocrhs==NULL) break;
|
| 1987 |
|
|
rhs=allocrhs;
|
| 1988 |
|
|
}
|
| 1989 |
|
|
}
|
| 1990 |
|
|
#endif
|
| 1991 |
|
|
/* [following code does not require input rounding] */
|
| 1992 |
|
|
|
| 1993 |
|
|
/* handle NaNs and rhs Infinity (lhs infinity is harder) */
|
| 1994 |
|
|
if (SPECIALARGS) {
|
| 1995 |
|
|
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
|
| 1996 |
|
|
decNaNs(res, lhs, rhs, set, &status);
|
| 1997 |
|
|
break;}
|
| 1998 |
|
|
if (decNumberIsInfinite(rhs)) { /* rhs Infinity */
|
| 1999 |
|
|
Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */
|
| 2000 |
|
|
if (decNumberIsNegative(lhs) /* lhs<0 */
|
| 2001 |
|
|
&& !decNumberIsZero(lhs)) /* .. */
|
| 2002 |
|
|
status|=DEC_Invalid_operation;
|
| 2003 |
|
|
else { /* lhs >=0 */
|
| 2004 |
|
|
decNumberZero(&dnOne); /* set up 1 */
|
| 2005 |
|
|
dnOne.lsu[0]=1;
|
| 2006 |
|
|
decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
|
| 2007 |
|
|
decNumberZero(res); /* prepare for 0/1/Infinity */
|
| 2008 |
|
|
if (decNumberIsNegative(dac)) { /* lhs<1 */
|
| 2009 |
|
|
if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
|
| 2010 |
|
|
}
|
| 2011 |
|
|
else if (dac->lsu[0]==0) { /* lhs=1 */
|
| 2012 |
|
|
/* 1**Infinity is inexact, so return fully-padded 1.0000 */
|
| 2013 |
|
|
Int shift=set->digits-1;
|
| 2014 |
|
|
*res->lsu=1; /* was 0, make int 1 */
|
| 2015 |
|
|
res->digits=decShiftToMost(res->lsu, 1, shift);
|
| 2016 |
|
|
res->exponent=-shift; /* make 1.0000... */
|
| 2017 |
|
|
status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
|
| 2018 |
|
|
}
|
| 2019 |
|
|
else { /* lhs>1 */
|
| 2020 |
|
|
if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
|
| 2021 |
|
|
}
|
| 2022 |
|
|
} /* lhs>=0 */
|
| 2023 |
|
|
break;}
|
| 2024 |
|
|
/* [lhs infinity drops through] */
|
| 2025 |
|
|
} /* specials */
|
| 2026 |
|
|
|
| 2027 |
|
|
/* Original rhs may be an integer that fits and is in range */
|
| 2028 |
|
|
n=decGetInt(rhs);
|
| 2029 |
|
|
if (n!=BADINT) { /* it is an integer */
|
| 2030 |
|
|
rhsint=1; /* record the fact for 1**n */
|
| 2031 |
|
|
isoddint=(Flag)n&1; /* [works even if big] */
|
| 2032 |
|
|
if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */
|
| 2033 |
|
|
useint=1; /* looks good */
|
| 2034 |
|
|
}
|
| 2035 |
|
|
|
| 2036 |
|
|
if (decNumberIsNegative(lhs) /* -x .. */
|
| 2037 |
|
|
&& isoddint) bits=DECNEG; /* .. to an odd power */
|
| 2038 |
|
|
|
| 2039 |
|
|
/* handle LHS infinity */
|
| 2040 |
|
|
if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
|
| 2041 |
|
|
uByte rbits=rhs->bits; /* save */
|
| 2042 |
|
|
decNumberZero(res); /* prepare */
|
| 2043 |
|
|
if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */
|
| 2044 |
|
|
else {
|
| 2045 |
|
|
/* -Inf**nonint -> error */
|
| 2046 |
|
|
if (!rhsint && decNumberIsNegative(lhs)) {
|
| 2047 |
|
|
status|=DEC_Invalid_operation; /* -Inf**nonint is error */
|
| 2048 |
|
|
break;}
|
| 2049 |
|
|
if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
|
| 2050 |
|
|
/* [otherwise will be 0 or -0] */
|
| 2051 |
|
|
res->bits=bits;
|
| 2052 |
|
|
}
|
| 2053 |
|
|
break;}
|
| 2054 |
|
|
|
| 2055 |
|
|
/* similarly handle LHS zero */
|
| 2056 |
|
|
if (decNumberIsZero(lhs)) {
|
| 2057 |
|
|
if (n==0) { /* 0**0 => Error */
|
| 2058 |
|
|
#if DECSUBSET
|
| 2059 |
|
|
if (!set->extended) { /* [unless subset] */
|
| 2060 |
|
|
decNumberZero(res);
|
| 2061 |
|
|
*res->lsu=1; /* return 1 */
|
| 2062 |
|
|
break;}
|
| 2063 |
|
|
#endif
|
| 2064 |
|
|
status|=DEC_Invalid_operation;
|
| 2065 |
|
|
}
|
| 2066 |
|
|
else { /* 0**x */
|
| 2067 |
|
|
uByte rbits=rhs->bits; /* save */
|
| 2068 |
|
|
if (rbits & DECNEG) { /* was a 0**(-n) */
|
| 2069 |
|
|
#if DECSUBSET
|
| 2070 |
|
|
if (!set->extended) { /* [bad if subset] */
|
| 2071 |
|
|
status|=DEC_Invalid_operation;
|
| 2072 |
|
|
break;}
|
| 2073 |
|
|
#endif
|
| 2074 |
|
|
bits|=DECINF;
|
| 2075 |
|
|
}
|
| 2076 |
|
|
decNumberZero(res); /* prepare */
|
| 2077 |
|
|
/* [otherwise will be 0 or -0] */
|
| 2078 |
|
|
res->bits=bits;
|
| 2079 |
|
|
}
|
| 2080 |
|
|
break;}
|
| 2081 |
|
|
|
| 2082 |
|
|
/* here both lhs and rhs are finite; rhs==0 is handled in the */
|
| 2083 |
|
|
/* integer path. Next handle the non-integer cases */
|
| 2084 |
|
|
if (!useint) { /* non-integral rhs */
|
| 2085 |
|
|
/* any -ve lhs is bad, as is either operand or context out of */
|
| 2086 |
|
|
/* bounds */
|
| 2087 |
|
|
if (decNumberIsNegative(lhs)) {
|
| 2088 |
|
|
status|=DEC_Invalid_operation;
|
| 2089 |
|
|
break;}
|
| 2090 |
|
|
if (decCheckMath(lhs, set, &status)
|
| 2091 |
|
|
|| decCheckMath(rhs, set, &status)) break; /* variable status */
|
| 2092 |
|
|
|
| 2093 |
|
|
decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
|
| 2094 |
|
|
aset.emax=DEC_MAX_MATH; /* usual bounds */
|
| 2095 |
|
|
aset.emin=-DEC_MAX_MATH; /* .. */
|
| 2096 |
|
|
aset.clamp=0; /* and no concrete format */
|
| 2097 |
|
|
|
| 2098 |
|
|
/* calculate the result using exp(ln(lhs)*rhs), which can */
|
| 2099 |
|
|
/* all be done into the accumulator, dac. The precision needed */
|
| 2100 |
|
|
/* is enough to contain the full information in the lhs (which */
|
| 2101 |
|
|
/* is the total digits, including exponent), or the requested */
|
| 2102 |
|
|
/* precision, if larger, + 4; 6 is used for the exponent */
|
| 2103 |
|
|
/* maximum length, and this is also used when it is shorter */
|
| 2104 |
|
|
/* than the requested digits as it greatly reduces the >0.5 ulp */
|
| 2105 |
|
|
/* cases at little cost (because Ln doubles digits each */
|
| 2106 |
|
|
/* iteration so a few extra digits rarely causes an extra */
|
| 2107 |
|
|
/* iteration) */
|
| 2108 |
|
|
aset.digits=MAXI(lhs->digits, set->digits)+6+4;
|
| 2109 |
|
|
} /* non-integer rhs */
|
| 2110 |
|
|
|
| 2111 |
|
|
else { /* rhs is in-range integer */
|
| 2112 |
|
|
if (n==0) { /* x**0 = 1 */
|
| 2113 |
|
|
/* (0**0 was handled above) */
|
| 2114 |
|
|
decNumberZero(res); /* result=1 */
|
| 2115 |
|
|
*res->lsu=1; /* .. */
|
| 2116 |
|
|
break;}
|
| 2117 |
|
|
/* rhs is a non-zero integer */
|
| 2118 |
|
|
if (n<0) n=-n; /* use abs(n) */
|
| 2119 |
|
|
|
| 2120 |
|
|
aset=*set; /* clone the context */
|
| 2121 |
|
|
aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */
|
| 2122 |
|
|
/* calculate the working DIGITS */
|
| 2123 |
|
|
aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
|
| 2124 |
|
|
#if DECSUBSET
|
| 2125 |
|
|
if (!set->extended) aset.digits--; /* use classic precision */
|
| 2126 |
|
|
#endif
|
| 2127 |
|
|
/* it's an error if this is more than can be handled */
|
| 2128 |
|
|
if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
|
| 2129 |
|
|
} /* integer path */
|
| 2130 |
|
|
|
| 2131 |
|
|
/* aset.digits is the count of digits for the accumulator needed */
|
| 2132 |
|
|
/* if accumulator is too long for local storage, then allocate */
|
| 2133 |
|
|
needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
|
| 2134 |
|
|
/* [needbytes also used below if 1/lhs needed] */
|
| 2135 |
|
|
if (needbytes>sizeof(dacbuff)) {
|
| 2136 |
|
|
allocdac=(decNumber *)malloc(needbytes);
|
| 2137 |
|
|
if (allocdac==NULL) { /* hopeless -- abandon */
|
| 2138 |
|
|
status|=DEC_Insufficient_storage;
|
| 2139 |
|
|
break;}
|
| 2140 |
|
|
dac=allocdac; /* use the allocated space */
|
| 2141 |
|
|
}
|
| 2142 |
|
|
/* here, aset is set up and accumulator is ready for use */
|
| 2143 |
|
|
|
| 2144 |
|
|
if (!useint) { /* non-integral rhs */
|
| 2145 |
|
|
/* x ** y; special-case x=1 here as it will otherwise always */
|
| 2146 |
|
|
/* reduce to integer 1; decLnOp has a fastpath which detects */
|
| 2147 |
|
|
/* the case of x=1 */
|
| 2148 |
|
|
decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */
|
| 2149 |
|
|
/* [no error possible, as lhs 0 already handled] */
|
| 2150 |
|
|
if (ISZERO(dac)) { /* x==1, 1.0, etc. */
|
| 2151 |
|
|
/* need to return fully-padded 1.0000 etc., but rhsint->1 */
|
| 2152 |
|
|
*dac->lsu=1; /* was 0, make int 1 */
|
| 2153 |
|
|
if (!rhsint) { /* add padding */
|
| 2154 |
|
|
Int shift=set->digits-1;
|
| 2155 |
|
|
dac->digits=decShiftToMost(dac->lsu, 1, shift);
|
| 2156 |
|
|
dac->exponent=-shift; /* make 1.0000... */
|
| 2157 |
|
|
status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
|
| 2158 |
|
|
}
|
| 2159 |
|
|
}
|
| 2160 |
|
|
else {
|
| 2161 |
|
|
decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */
|
| 2162 |
|
|
decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */
|
| 2163 |
|
|
}
|
| 2164 |
|
|
/* and drop through for final rounding */
|
| 2165 |
|
|
} /* non-integer rhs */
|
| 2166 |
|
|
|
| 2167 |
|
|
else { /* carry on with integer */
|
| 2168 |
|
|
decNumberZero(dac); /* acc=1 */
|
| 2169 |
|
|
*dac->lsu=1; /* .. */
|
| 2170 |
|
|
|
| 2171 |
|
|
/* if a negative power the constant 1 is needed, and if not subset */
|
| 2172 |
|
|
/* invert the lhs now rather than inverting the result later */
|
| 2173 |
|
|
if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
|
| 2174 |
|
|
decNumber *inv=invbuff; /* asssume use fixed buffer */
|
| 2175 |
|
|
decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */
|
| 2176 |
|
|
#if DECSUBSET
|
| 2177 |
|
|
if (set->extended) { /* need to calculate 1/lhs */
|
| 2178 |
|
|
#endif
|
| 2179 |
|
|
/* divide lhs into 1, putting result in dac [dac=1/dac] */
|
| 2180 |
|
|
decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
|
| 2181 |
|
|
/* now locate or allocate space for the inverted lhs */
|
| 2182 |
|
|
if (needbytes>sizeof(invbuff)) {
|
| 2183 |
|
|
allocinv=(decNumber *)malloc(needbytes);
|
| 2184 |
|
|
if (allocinv==NULL) { /* hopeless -- abandon */
|
| 2185 |
|
|
status|=DEC_Insufficient_storage;
|
| 2186 |
|
|
break;}
|
| 2187 |
|
|
inv=allocinv; /* use the allocated space */
|
| 2188 |
|
|
}
|
| 2189 |
|
|
/* [inv now points to big-enough buffer or allocated storage] */
|
| 2190 |
|
|
decNumberCopy(inv, dac); /* copy the 1/lhs */
|
| 2191 |
|
|
decNumberCopy(dac, &dnOne); /* restore acc=1 */
|
| 2192 |
|
|
lhs=inv; /* .. and go forward with new lhs */
|
| 2193 |
|
|
#if DECSUBSET
|
| 2194 |
|
|
}
|
| 2195 |
|
|
#endif
|
| 2196 |
|
|
}
|
| 2197 |
|
|
|
| 2198 |
|
|
/* Raise-to-the-power loop... */
|
| 2199 |
|
|
seenbit=0; /* set once a 1-bit is encountered */
|
| 2200 |
|
|
for (i=1;;i++){ /* for each bit [top bit ignored] */
|
| 2201 |
|
|
/* abandon if had overflow or terminal underflow */
|
| 2202 |
|
|
if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
|
| 2203 |
|
|
if (status&DEC_Overflow || ISZERO(dac)) break;
|
| 2204 |
|
|
}
|
| 2205 |
|
|
/* [the following two lines revealed an optimizer bug in a C++ */
|
| 2206 |
|
|
/* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
|
| 2207 |
|
|
n=n<<1; /* move next bit to testable position */
|
| 2208 |
|
|
if (n<0) { /* top bit is set */
|
| 2209 |
|
|
seenbit=1; /* OK, significant bit seen */
|
| 2210 |
|
|
decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
|
| 2211 |
|
|
}
|
| 2212 |
|
|
if (i==31) break; /* that was the last bit */
|
| 2213 |
|
|
if (!seenbit) continue; /* no need to square 1 */
|
| 2214 |
|
|
decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
|
| 2215 |
|
|
} /*i*/ /* 32 bits */
|
| 2216 |
|
|
|
| 2217 |
|
|
/* complete internal overflow or underflow processing */
|
| 2218 |
|
|
if (status & (DEC_Overflow|DEC_Underflow)) {
|
| 2219 |
|
|
#if DECSUBSET
|
| 2220 |
|
|
/* If subset, and power was negative, reverse the kind of -erflow */
|
| 2221 |
|
|
/* [1/x not yet done] */
|
| 2222 |
|
|
if (!set->extended && decNumberIsNegative(rhs)) {
|
| 2223 |
|
|
if (status & DEC_Overflow)
|
| 2224 |
|
|
status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
|
| 2225 |
|
|
else { /* trickier -- Underflow may or may not be set */
|
| 2226 |
|
|
status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
|
| 2227 |
|
|
status|=DEC_Overflow;
|
| 2228 |
|
|
}
|
| 2229 |
|
|
}
|
| 2230 |
|
|
#endif
|
| 2231 |
|
|
dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
|
| 2232 |
|
|
/* round subnormals [to set.digits rather than aset.digits] */
|
| 2233 |
|
|
/* or set overflow result similarly as required */
|
| 2234 |
|
|
decFinalize(dac, set, &residue, &status);
|
| 2235 |
|
|
decNumberCopy(res, dac); /* copy to result (is now OK length) */
|
| 2236 |
|
|
break;
|
| 2237 |
|
|
}
|
| 2238 |
|
|
|
| 2239 |
|
|
#if DECSUBSET
|
| 2240 |
|
|
if (!set->extended && /* subset math */
|
| 2241 |
|
|
decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
|
| 2242 |
|
|
/* so divide result into 1 [dac=1/dac] */
|
| 2243 |
|
|
decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
|
| 2244 |
|
|
}
|
| 2245 |
|
|
#endif
|
| 2246 |
|
|
} /* rhs integer path */
|
| 2247 |
|
|
|
| 2248 |
|
|
/* reduce result to the requested length and copy to result */
|
| 2249 |
|
|
decCopyFit(res, dac, set, &residue, &status);
|
| 2250 |
|
|
decFinish(res, set, &residue, &status); /* final cleanup */
|
| 2251 |
|
|
#if DECSUBSET
|
| 2252 |
|
|
if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
|
| 2253 |
|
|
#endif
|
| 2254 |
|
|
} while(0); /* end protected */
|
| 2255 |
|
|
|
| 2256 |
|
|
if (allocdac!=NULL) free(allocdac); /* drop any storage used */
|
| 2257 |
|
|
if (allocinv!=NULL) free(allocinv); /* .. */
|
| 2258 |
|
|
#if DECSUBSET
|
| 2259 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 2260 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| 2261 |
|
|
#endif
|
| 2262 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2263 |
|
|
#if DECCHECK
|
| 2264 |
|
|
decCheckInexact(res, set);
|
| 2265 |
|
|
#endif
|
| 2266 |
|
|
return res;
|
| 2267 |
|
|
} /* decNumberPower */
|
| 2268 |
|
|
|
| 2269 |
|
|
/* ------------------------------------------------------------------ */
|
| 2270 |
|
|
/* decNumberQuantize -- force exponent to requested value */
|
| 2271 |
|
|
/* */
|
| 2272 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 2273 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 2274 |
|
|
/* of C has exponent of B. The numerical value of C will equal A, */
|
| 2275 |
|
|
/* except for the effects of any rounding that occurred. */
|
| 2276 |
|
|
/* */
|
| 2277 |
|
|
/* res is C, the result. C may be A or B */
|
| 2278 |
|
|
/* lhs is A, the number to adjust */
|
| 2279 |
|
|
/* rhs is B, the number with exponent to match */
|
| 2280 |
|
|
/* set is the context */
|
| 2281 |
|
|
/* */
|
| 2282 |
|
|
/* C must have space for set->digits digits. */
|
| 2283 |
|
|
/* */
|
| 2284 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 2285 |
|
|
/* after the operation is guaranteed to be equal to that of B. */
|
| 2286 |
|
|
/* ------------------------------------------------------------------ */
|
| 2287 |
|
|
decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
|
| 2288 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2289 |
|
|
uInt status=0; /* accumulator */
|
| 2290 |
|
|
decQuantizeOp(res, lhs, rhs, set, 1, &status);
|
| 2291 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2292 |
|
|
return res;
|
| 2293 |
|
|
} /* decNumberQuantize */
|
| 2294 |
|
|
|
| 2295 |
|
|
/* ------------------------------------------------------------------ */
|
| 2296 |
|
|
/* decNumberReduce -- remove trailing zeros */
|
| 2297 |
|
|
/* */
|
| 2298 |
|
|
/* This computes C = 0 + A, and normalizes the result */
|
| 2299 |
|
|
/* */
|
| 2300 |
|
|
/* res is C, the result. C may be A */
|
| 2301 |
|
|
/* rhs is A */
|
| 2302 |
|
|
/* set is the context */
|
| 2303 |
|
|
/* */
|
| 2304 |
|
|
/* C must have space for set->digits digits. */
|
| 2305 |
|
|
/* ------------------------------------------------------------------ */
|
| 2306 |
|
|
/* Previously known as Normalize */
|
| 2307 |
|
|
decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
|
| 2308 |
|
|
decContext *set) {
|
| 2309 |
|
|
return decNumberReduce(res, rhs, set);
|
| 2310 |
|
|
} /* decNumberNormalize */
|
| 2311 |
|
|
|
| 2312 |
|
|
decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
|
| 2313 |
|
|
decContext *set) {
|
| 2314 |
|
|
#if DECSUBSET
|
| 2315 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| 2316 |
|
|
#endif
|
| 2317 |
|
|
uInt status=0; /* as usual */
|
| 2318 |
|
|
Int residue=0; /* as usual */
|
| 2319 |
|
|
Int dropped; /* work */
|
| 2320 |
|
|
|
| 2321 |
|
|
#if DECCHECK
|
| 2322 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 2323 |
|
|
#endif
|
| 2324 |
|
|
|
| 2325 |
|
|
do { /* protect allocated storage */
|
| 2326 |
|
|
#if DECSUBSET
|
| 2327 |
|
|
if (!set->extended) {
|
| 2328 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 2329 |
|
|
if (rhs->digits>set->digits) {
|
| 2330 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 2331 |
|
|
if (allocrhs==NULL) break;
|
| 2332 |
|
|
rhs=allocrhs;
|
| 2333 |
|
|
}
|
| 2334 |
|
|
}
|
| 2335 |
|
|
#endif
|
| 2336 |
|
|
/* [following code does not require input rounding] */
|
| 2337 |
|
|
|
| 2338 |
|
|
/* Infinities copy through; NaNs need usual treatment */
|
| 2339 |
|
|
if (decNumberIsNaN(rhs)) {
|
| 2340 |
|
|
decNaNs(res, rhs, NULL, set, &status);
|
| 2341 |
|
|
break;
|
| 2342 |
|
|
}
|
| 2343 |
|
|
|
| 2344 |
|
|
/* reduce result to the requested length and copy to result */
|
| 2345 |
|
|
decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
|
| 2346 |
|
|
decFinish(res, set, &residue, &status); /* cleanup/set flags */
|
| 2347 |
|
|
decTrim(res, set, 1, 0, &dropped); /* normalize in place */
|
| 2348 |
|
|
/* [may clamp] */
|
| 2349 |
|
|
} while(0); /* end protected */
|
| 2350 |
|
|
|
| 2351 |
|
|
#if DECSUBSET
|
| 2352 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| 2353 |
|
|
#endif
|
| 2354 |
|
|
if (status!=0) decStatus(res, status, set);/* then report status */
|
| 2355 |
|
|
return res;
|
| 2356 |
|
|
} /* decNumberReduce */
|
| 2357 |
|
|
|
| 2358 |
|
|
/* ------------------------------------------------------------------ */
|
| 2359 |
|
|
/* decNumberRescale -- force exponent to requested value */
|
| 2360 |
|
|
/* */
|
| 2361 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 2362 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 2363 |
|
|
/* of C has the value B. The numerical value of C will equal A, */
|
| 2364 |
|
|
/* except for the effects of any rounding that occurred. */
|
| 2365 |
|
|
/* */
|
| 2366 |
|
|
/* res is C, the result. C may be A or B */
|
| 2367 |
|
|
/* lhs is A, the number to adjust */
|
| 2368 |
|
|
/* rhs is B, the requested exponent */
|
| 2369 |
|
|
/* set is the context */
|
| 2370 |
|
|
/* */
|
| 2371 |
|
|
/* C must have space for set->digits digits. */
|
| 2372 |
|
|
/* */
|
| 2373 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 2374 |
|
|
/* after the operation is guaranteed to be equal to B. */
|
| 2375 |
|
|
/* ------------------------------------------------------------------ */
|
| 2376 |
|
|
decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
|
| 2377 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2378 |
|
|
uInt status=0; /* accumulator */
|
| 2379 |
|
|
decQuantizeOp(res, lhs, rhs, set, 0, &status);
|
| 2380 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2381 |
|
|
return res;
|
| 2382 |
|
|
} /* decNumberRescale */
|
| 2383 |
|
|
|
| 2384 |
|
|
/* ------------------------------------------------------------------ */
|
| 2385 |
|
|
/* decNumberRemainder -- divide and return remainder */
|
| 2386 |
|
|
/* */
|
| 2387 |
|
|
/* This computes C = A % B */
|
| 2388 |
|
|
/* */
|
| 2389 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| 2390 |
|
|
/* lhs is A */
|
| 2391 |
|
|
/* rhs is B */
|
| 2392 |
|
|
/* set is the context */
|
| 2393 |
|
|
/* */
|
| 2394 |
|
|
/* C must have space for set->digits digits. */
|
| 2395 |
|
|
/* ------------------------------------------------------------------ */
|
| 2396 |
|
|
decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
|
| 2397 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2398 |
|
|
uInt status=0; /* accumulator */
|
| 2399 |
|
|
decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
|
| 2400 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2401 |
|
|
#if DECCHECK
|
| 2402 |
|
|
decCheckInexact(res, set);
|
| 2403 |
|
|
#endif
|
| 2404 |
|
|
return res;
|
| 2405 |
|
|
} /* decNumberRemainder */
|
| 2406 |
|
|
|
| 2407 |
|
|
/* ------------------------------------------------------------------ */
|
| 2408 |
|
|
/* decNumberRemainderNear -- divide and return remainder from nearest */
|
| 2409 |
|
|
/* */
|
| 2410 |
|
|
/* This computes C = A % B, where % is the IEEE remainder operator */
|
| 2411 |
|
|
/* */
|
| 2412 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| 2413 |
|
|
/* lhs is A */
|
| 2414 |
|
|
/* rhs is B */
|
| 2415 |
|
|
/* set is the context */
|
| 2416 |
|
|
/* */
|
| 2417 |
|
|
/* C must have space for set->digits digits. */
|
| 2418 |
|
|
/* ------------------------------------------------------------------ */
|
| 2419 |
|
|
decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
|
| 2420 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2421 |
|
|
uInt status=0; /* accumulator */
|
| 2422 |
|
|
decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
|
| 2423 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2424 |
|
|
#if DECCHECK
|
| 2425 |
|
|
decCheckInexact(res, set);
|
| 2426 |
|
|
#endif
|
| 2427 |
|
|
return res;
|
| 2428 |
|
|
} /* decNumberRemainderNear */
|
| 2429 |
|
|
|
| 2430 |
|
|
/* ------------------------------------------------------------------ */
|
| 2431 |
|
|
/* decNumberRotate -- rotate the coefficient of a Number left/right */
|
| 2432 |
|
|
/* */
|
| 2433 |
|
|
/* This computes C = A rot B (in base ten and rotating set->digits */
|
| 2434 |
|
|
/* digits). */
|
| 2435 |
|
|
/* */
|
| 2436 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
|
| 2437 |
|
|
/* lhs is A */
|
| 2438 |
|
|
/* rhs is B, the number of digits to rotate (-ve to right) */
|
| 2439 |
|
|
/* set is the context */
|
| 2440 |
|
|
/* */
|
| 2441 |
|
|
/* The digits of the coefficient of A are rotated to the left (if B */
|
| 2442 |
|
|
/* is positive) or to the right (if B is negative) without adjusting */
|
| 2443 |
|
|
/* the exponent or the sign of A. If lhs->digits is less than */
|
| 2444 |
|
|
/* set->digits the coefficient is padded with zeros on the left */
|
| 2445 |
|
|
/* before the rotate. Any leading zeros in the result are removed */
|
| 2446 |
|
|
/* as usual. */
|
| 2447 |
|
|
/* */
|
| 2448 |
|
|
/* B must be an integer (q=0) and in the range -set->digits through */
|
| 2449 |
|
|
/* +set->digits. */
|
| 2450 |
|
|
/* C must have space for set->digits digits. */
|
| 2451 |
|
|
/* NaNs are propagated as usual. Infinities are unaffected (but */
|
| 2452 |
|
|
/* B must be valid). No status is set unless B is invalid or an */
|
| 2453 |
|
|
/* operand is an sNaN. */
|
| 2454 |
|
|
/* ------------------------------------------------------------------ */
|
| 2455 |
|
|
decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
|
| 2456 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2457 |
|
|
uInt status=0; /* accumulator */
|
| 2458 |
|
|
Int rotate; /* rhs as an Int */
|
| 2459 |
|
|
|
| 2460 |
|
|
#if DECCHECK
|
| 2461 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 2462 |
|
|
#endif
|
| 2463 |
|
|
|
| 2464 |
|
|
/* NaNs propagate as normal */
|
| 2465 |
|
|
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| 2466 |
|
|
decNaNs(res, lhs, rhs, set, &status);
|
| 2467 |
|
|
/* rhs must be an integer */
|
| 2468 |
|
|
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| 2469 |
|
|
status=DEC_Invalid_operation;
|
| 2470 |
|
|
else { /* both numeric, rhs is an integer */
|
| 2471 |
|
|
rotate=decGetInt(rhs); /* [cannot fail] */
|
| 2472 |
|
|
if (rotate==BADINT /* something bad .. */
|
| 2473 |
|
|
|| rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */
|
| 2474 |
|
|
|| abs(rotate)>set->digits) /* .. or out of range */
|
| 2475 |
|
|
status=DEC_Invalid_operation;
|
| 2476 |
|
|
else { /* rhs is OK */
|
| 2477 |
|
|
decNumberCopy(res, lhs);
|
| 2478 |
|
|
/* convert -ve rotate to equivalent positive rotation */
|
| 2479 |
|
|
if (rotate<0) rotate=set->digits+rotate;
|
| 2480 |
|
|
if (rotate!=0 && rotate!=set->digits /* zero or full rotation */
|
| 2481 |
|
|
&& !decNumberIsInfinite(res)) { /* lhs was infinite */
|
| 2482 |
|
|
/* left-rotate to do; 0 < rotate < set->digits */
|
| 2483 |
|
|
uInt units, shift; /* work */
|
| 2484 |
|
|
uInt msudigits; /* digits in result msu */
|
| 2485 |
|
|
Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */
|
| 2486 |
|
|
Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
|
| 2487 |
|
|
for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */
|
| 2488 |
|
|
res->digits=set->digits; /* now full-length */
|
| 2489 |
|
|
msudigits=MSUDIGITS(res->digits); /* actual digits in msu */
|
| 2490 |
|
|
|
| 2491 |
|
|
/* rotation here is done in-place, in three steps */
|
| 2492 |
|
|
/* 1. shift all to least up to one unit to unit-align final */
|
| 2493 |
|
|
/* lsd [any digits shifted out are rotated to the left, */
|
| 2494 |
|
|
/* abutted to the original msd (which may require split)] */
|
| 2495 |
|
|
/* */
|
| 2496 |
|
|
/* [if there are no whole units left to rotate, the */
|
| 2497 |
|
|
/* rotation is now complete] */
|
| 2498 |
|
|
/* */
|
| 2499 |
|
|
/* 2. shift to least, from below the split point only, so that */
|
| 2500 |
|
|
/* the final msd is in the right place in its Unit [any */
|
| 2501 |
|
|
/* digits shifted out will fit exactly in the current msu, */
|
| 2502 |
|
|
/* left aligned, no split required] */
|
| 2503 |
|
|
/* */
|
| 2504 |
|
|
/* 3. rotate all the units by reversing left part, right */
|
| 2505 |
|
|
/* part, and then whole */
|
| 2506 |
|
|
/* */
|
| 2507 |
|
|
/* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
|
| 2508 |
|
|
/* */
|
| 2509 |
|
|
/* start: 00a bcd efg hij klm npq */
|
| 2510 |
|
|
/* */
|
| 2511 |
|
|
/* 1a 000 0ab cde fgh|ijk lmn [pq saved] */
|
| 2512 |
|
|
/* 1b 00p qab cde fgh|ijk lmn */
|
| 2513 |
|
|
/* */
|
| 2514 |
|
|
/* 2a 00p qab cde fgh|00i jkl [mn saved] */
|
| 2515 |
|
|
/* 2b mnp qab cde fgh|00i jkl */
|
| 2516 |
|
|
/* */
|
| 2517 |
|
|
/* 3a fgh cde qab mnp|00i jkl */
|
| 2518 |
|
|
/* 3b fgh cde qab mnp|jkl 00i */
|
| 2519 |
|
|
/* 3c 00i jkl mnp qab cde fgh */
|
| 2520 |
|
|
|
| 2521 |
|
|
/* Step 1: amount to shift is the partial right-rotate count */
|
| 2522 |
|
|
rotate=set->digits-rotate; /* make it right-rotate */
|
| 2523 |
|
|
units=rotate/DECDPUN; /* whole units to rotate */
|
| 2524 |
|
|
shift=rotate%DECDPUN; /* left-over digits count */
|
| 2525 |
|
|
if (shift>0) { /* not an exact number of units */
|
| 2526 |
|
|
uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
|
| 2527 |
|
|
decShiftToLeast(res->lsu, D2U(res->digits), shift);
|
| 2528 |
|
|
if (shift>msudigits) { /* msumax-1 needs >0 digits */
|
| 2529 |
|
|
uInt rem=save%powers[shift-msudigits];/* split save */
|
| 2530 |
|
|
*msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
|
| 2531 |
|
|
*(msumax-1)=*(msumax-1)
|
| 2532 |
|
|
+(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
|
| 2533 |
|
|
}
|
| 2534 |
|
|
else { /* all fits in msumax */
|
| 2535 |
|
|
*msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
|
| 2536 |
|
|
}
|
| 2537 |
|
|
} /* digits shift needed */
|
| 2538 |
|
|
|
| 2539 |
|
|
/* If whole units to rotate... */
|
| 2540 |
|
|
if (units>0) { /* some to do */
|
| 2541 |
|
|
/* Step 2: the units to touch are the whole ones in rotate, */
|
| 2542 |
|
|
/* if any, and the shift is DECDPUN-msudigits (which may be */
|
| 2543 |
|
|
/* 0, again) */
|
| 2544 |
|
|
shift=DECDPUN-msudigits;
|
| 2545 |
|
|
if (shift>0) { /* not an exact number of units */
|
| 2546 |
|
|
uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
|
| 2547 |
|
|
decShiftToLeast(res->lsu, units, shift);
|
| 2548 |
|
|
*msumax=*msumax+(Unit)(save*powers[msudigits]);
|
| 2549 |
|
|
} /* partial shift needed */
|
| 2550 |
|
|
|
| 2551 |
|
|
/* Step 3: rotate the units array using triple reverse */
|
| 2552 |
|
|
/* (reversing is easy and fast) */
|
| 2553 |
|
|
decReverse(res->lsu+units, msumax); /* left part */
|
| 2554 |
|
|
decReverse(res->lsu, res->lsu+units-1); /* right part */
|
| 2555 |
|
|
decReverse(res->lsu, msumax); /* whole */
|
| 2556 |
|
|
} /* whole units to rotate */
|
| 2557 |
|
|
/* the rotation may have left an undetermined number of zeros */
|
| 2558 |
|
|
/* on the left, so true length needs to be calculated */
|
| 2559 |
|
|
res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
|
| 2560 |
|
|
} /* rotate needed */
|
| 2561 |
|
|
} /* rhs OK */
|
| 2562 |
|
|
} /* numerics */
|
| 2563 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2564 |
|
|
return res;
|
| 2565 |
|
|
} /* decNumberRotate */
|
| 2566 |
|
|
|
| 2567 |
|
|
/* ------------------------------------------------------------------ */
|
| 2568 |
|
|
/* decNumberSameQuantum -- test for equal exponents */
|
| 2569 |
|
|
/* */
|
| 2570 |
|
|
/* res is the result number, which will contain either 0 or 1 */
|
| 2571 |
|
|
/* lhs is a number to test */
|
| 2572 |
|
|
/* rhs is the second (usually a pattern) */
|
| 2573 |
|
|
/* */
|
| 2574 |
|
|
/* No errors are possible and no context is needed. */
|
| 2575 |
|
|
/* ------------------------------------------------------------------ */
|
| 2576 |
|
|
decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
|
| 2577 |
|
|
const decNumber *rhs) {
|
| 2578 |
|
|
Unit ret=0; /* return value */
|
| 2579 |
|
|
|
| 2580 |
|
|
#if DECCHECK
|
| 2581 |
|
|
if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
|
| 2582 |
|
|
#endif
|
| 2583 |
|
|
|
| 2584 |
|
|
if (SPECIALARGS) {
|
| 2585 |
|
|
if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
|
| 2586 |
|
|
else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
|
| 2587 |
|
|
/* [anything else with a special gives 0] */
|
| 2588 |
|
|
}
|
| 2589 |
|
|
else if (lhs->exponent==rhs->exponent) ret=1;
|
| 2590 |
|
|
|
| 2591 |
|
|
decNumberZero(res); /* OK to overwrite an operand now */
|
| 2592 |
|
|
*res->lsu=ret;
|
| 2593 |
|
|
return res;
|
| 2594 |
|
|
} /* decNumberSameQuantum */
|
| 2595 |
|
|
|
| 2596 |
|
|
/* ------------------------------------------------------------------ */
|
| 2597 |
|
|
/* decNumberScaleB -- multiply by a power of 10 */
|
| 2598 |
|
|
/* */
|
| 2599 |
|
|
/* This computes C = A x 10**B where B is an integer (q=0) with */
|
| 2600 |
|
|
/* maximum magnitude 2*(emax+digits) */
|
| 2601 |
|
|
/* */
|
| 2602 |
|
|
/* res is C, the result. C may be A or B */
|
| 2603 |
|
|
/* lhs is A, the number to adjust */
|
| 2604 |
|
|
/* rhs is B, the requested power of ten to use */
|
| 2605 |
|
|
/* set is the context */
|
| 2606 |
|
|
/* */
|
| 2607 |
|
|
/* C must have space for set->digits digits. */
|
| 2608 |
|
|
/* */
|
| 2609 |
|
|
/* The result may underflow or overflow. */
|
| 2610 |
|
|
/* ------------------------------------------------------------------ */
|
| 2611 |
|
|
decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
|
| 2612 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2613 |
|
|
Int reqexp; /* requested exponent change [B] */
|
| 2614 |
|
|
uInt status=0; /* accumulator */
|
| 2615 |
|
|
Int residue; /* work */
|
| 2616 |
|
|
|
| 2617 |
|
|
#if DECCHECK
|
| 2618 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 2619 |
|
|
#endif
|
| 2620 |
|
|
|
| 2621 |
|
|
/* Handle special values except lhs infinite */
|
| 2622 |
|
|
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| 2623 |
|
|
decNaNs(res, lhs, rhs, set, &status);
|
| 2624 |
|
|
/* rhs must be an integer */
|
| 2625 |
|
|
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| 2626 |
|
|
status=DEC_Invalid_operation;
|
| 2627 |
|
|
else {
|
| 2628 |
|
|
/* lhs is a number; rhs is a finite with q==0 */
|
| 2629 |
|
|
reqexp=decGetInt(rhs); /* [cannot fail] */
|
| 2630 |
|
|
if (reqexp==BADINT /* something bad .. */
|
| 2631 |
|
|
|| reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */
|
| 2632 |
|
|
|| abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
|
| 2633 |
|
|
status=DEC_Invalid_operation;
|
| 2634 |
|
|
else { /* rhs is OK */
|
| 2635 |
|
|
decNumberCopy(res, lhs); /* all done if infinite lhs */
|
| 2636 |
|
|
if (!decNumberIsInfinite(res)) { /* prepare to scale */
|
| 2637 |
|
|
res->exponent+=reqexp; /* adjust the exponent */
|
| 2638 |
|
|
residue=0;
|
| 2639 |
|
|
decFinalize(res, set, &residue, &status); /* .. and check */
|
| 2640 |
|
|
} /* finite LHS */
|
| 2641 |
|
|
} /* rhs OK */
|
| 2642 |
|
|
} /* rhs finite */
|
| 2643 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2644 |
|
|
return res;
|
| 2645 |
|
|
} /* decNumberScaleB */
|
| 2646 |
|
|
|
| 2647 |
|
|
/* ------------------------------------------------------------------ */
|
| 2648 |
|
|
/* decNumberShift -- shift the coefficient of a Number left or right */
|
| 2649 |
|
|
/* */
|
| 2650 |
|
|
/* This computes C = A << B or C = A >> -B (in base ten). */
|
| 2651 |
|
|
/* */
|
| 2652 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
|
| 2653 |
|
|
/* lhs is A */
|
| 2654 |
|
|
/* rhs is B, the number of digits to shift (-ve to right) */
|
| 2655 |
|
|
/* set is the context */
|
| 2656 |
|
|
/* */
|
| 2657 |
|
|
/* The digits of the coefficient of A are shifted to the left (if B */
|
| 2658 |
|
|
/* is positive) or to the right (if B is negative) without adjusting */
|
| 2659 |
|
|
/* the exponent or the sign of A. */
|
| 2660 |
|
|
/* */
|
| 2661 |
|
|
/* B must be an integer (q=0) and in the range -set->digits through */
|
| 2662 |
|
|
/* +set->digits. */
|
| 2663 |
|
|
/* C must have space for set->digits digits. */
|
| 2664 |
|
|
/* NaNs are propagated as usual. Infinities are unaffected (but */
|
| 2665 |
|
|
/* B must be valid). No status is set unless B is invalid or an */
|
| 2666 |
|
|
/* operand is an sNaN. */
|
| 2667 |
|
|
/* ------------------------------------------------------------------ */
|
| 2668 |
|
|
decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
|
| 2669 |
|
|
const decNumber *rhs, decContext *set) {
|
| 2670 |
|
|
uInt status=0; /* accumulator */
|
| 2671 |
|
|
Int shift; /* rhs as an Int */
|
| 2672 |
|
|
|
| 2673 |
|
|
#if DECCHECK
|
| 2674 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 2675 |
|
|
#endif
|
| 2676 |
|
|
|
| 2677 |
|
|
/* NaNs propagate as normal */
|
| 2678 |
|
|
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| 2679 |
|
|
decNaNs(res, lhs, rhs, set, &status);
|
| 2680 |
|
|
/* rhs must be an integer */
|
| 2681 |
|
|
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| 2682 |
|
|
status=DEC_Invalid_operation;
|
| 2683 |
|
|
else { /* both numeric, rhs is an integer */
|
| 2684 |
|
|
shift=decGetInt(rhs); /* [cannot fail] */
|
| 2685 |
|
|
if (shift==BADINT /* something bad .. */
|
| 2686 |
|
|
|| shift==BIGODD || shift==BIGEVEN /* .. very big .. */
|
| 2687 |
|
|
|| abs(shift)>set->digits) /* .. or out of range */
|
| 2688 |
|
|
status=DEC_Invalid_operation;
|
| 2689 |
|
|
else { /* rhs is OK */
|
| 2690 |
|
|
decNumberCopy(res, lhs);
|
| 2691 |
|
|
if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
|
| 2692 |
|
|
if (shift>0) { /* to left */
|
| 2693 |
|
|
if (shift==set->digits) { /* removing all */
|
| 2694 |
|
|
*res->lsu=0; /* so place 0 */
|
| 2695 |
|
|
res->digits=1; /* .. */
|
| 2696 |
|
|
}
|
| 2697 |
|
|
else { /* */
|
| 2698 |
|
|
/* first remove leading digits if necessary */
|
| 2699 |
|
|
if (res->digits+shift>set->digits) {
|
| 2700 |
|
|
decDecap(res, res->digits+shift-set->digits);
|
| 2701 |
|
|
/* that updated res->digits; may have gone to 1 (for a */
|
| 2702 |
|
|
/* single digit or for zero */
|
| 2703 |
|
|
}
|
| 2704 |
|
|
if (res->digits>1 || *res->lsu) /* if non-zero.. */
|
| 2705 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, shift);
|
| 2706 |
|
|
} /* partial left */
|
| 2707 |
|
|
} /* left */
|
| 2708 |
|
|
else { /* to right */
|
| 2709 |
|
|
if (-shift>=res->digits) { /* discarding all */
|
| 2710 |
|
|
*res->lsu=0; /* so place 0 */
|
| 2711 |
|
|
res->digits=1; /* .. */
|
| 2712 |
|
|
}
|
| 2713 |
|
|
else {
|
| 2714 |
|
|
decShiftToLeast(res->lsu, D2U(res->digits), -shift);
|
| 2715 |
|
|
res->digits-=(-shift);
|
| 2716 |
|
|
}
|
| 2717 |
|
|
} /* to right */
|
| 2718 |
|
|
} /* non-0 non-Inf shift */
|
| 2719 |
|
|
} /* rhs OK */
|
| 2720 |
|
|
} /* numerics */
|
| 2721 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 2722 |
|
|
return res;
|
| 2723 |
|
|
} /* decNumberShift */
|
| 2724 |
|
|
|
| 2725 |
|
|
/* ------------------------------------------------------------------ */
|
| 2726 |
|
|
/* decNumberSquareRoot -- square root operator */
|
| 2727 |
|
|
/* */
|
| 2728 |
|
|
/* This computes C = squareroot(A) */
|
| 2729 |
|
|
/* */
|
| 2730 |
|
|
/* res is C, the result. C may be A */
|
| 2731 |
|
|
/* rhs is A */
|
| 2732 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 2733 |
|
|
/* */
|
| 2734 |
|
|
/* C must have space for set->digits digits. */
|
| 2735 |
|
|
/* ------------------------------------------------------------------ */
|
| 2736 |
|
|
/* This uses the following varying-precision algorithm in: */
|
| 2737 |
|
|
/* */
|
| 2738 |
|
|
/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
|
| 2739 |
|
|
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
|
| 2740 |
|
|
/* pp229-237, ACM, September 1985. */
|
| 2741 |
|
|
/* */
|
| 2742 |
|
|
/* The square-root is calculated using Newton's method, after which */
|
| 2743 |
|
|
/* a check is made to ensure the result is correctly rounded. */
|
| 2744 |
|
|
/* */
|
| 2745 |
|
|
/* % [Reformatted original Numerical Turing source code follows.] */
|
| 2746 |
|
|
/* function sqrt(x : real) : real */
|
| 2747 |
|
|
/* % sqrt(x) returns the properly rounded approximation to the square */
|
| 2748 |
|
|
/* % root of x, in the precision of the calling environment, or it */
|
| 2749 |
|
|
/* % fails if x < 0. */
|
| 2750 |
|
|
/* % t e hull and a abrham, august, 1984 */
|
| 2751 |
|
|
/* if x <= 0 then */
|
| 2752 |
|
|
/* if x < 0 then */
|
| 2753 |
|
|
/* assert false */
|
| 2754 |
|
|
/* else */
|
| 2755 |
|
|
/* result 0 */
|
| 2756 |
|
|
/* end if */
|
| 2757 |
|
|
/* end if */
|
| 2758 |
|
|
/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
|
| 2759 |
|
|
/* var e := getexp(x) % exponent part of x */
|
| 2760 |
|
|
/* var approx : real */
|
| 2761 |
|
|
/* if e mod 2 = 0 then */
|
| 2762 |
|
|
/* approx := .259 + .819 * f % approx to root of f */
|
| 2763 |
|
|
/* else */
|
| 2764 |
|
|
/* f := f/l0 % adjustments */
|
| 2765 |
|
|
/* e := e + 1 % for odd */
|
| 2766 |
|
|
/* approx := .0819 + 2.59 * f % exponent */
|
| 2767 |
|
|
/* end if */
|
| 2768 |
|
|
/* */
|
| 2769 |
|
|
/* var p:= 3 */
|
| 2770 |
|
|
/* const maxp := currentprecision + 2 */
|
| 2771 |
|
|
/* loop */
|
| 2772 |
|
|
/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
|
| 2773 |
|
|
/* precision p */
|
| 2774 |
|
|
/* approx := .5 * (approx + f/approx) */
|
| 2775 |
|
|
/* exit when p = maxp */
|
| 2776 |
|
|
/* end loop */
|
| 2777 |
|
|
/* */
|
| 2778 |
|
|
/* % approx is now within 1 ulp of the properly rounded square root */
|
| 2779 |
|
|
/* % of f; to ensure proper rounding, compare squares of (approx - */
|
| 2780 |
|
|
/* % l/2 ulp) and (approx + l/2 ulp) with f. */
|
| 2781 |
|
|
/* p := currentprecision */
|
| 2782 |
|
|
/* begin */
|
| 2783 |
|
|
/* precision p + 2 */
|
| 2784 |
|
|
/* const approxsubhalf := approx - setexp(.5, -p) */
|
| 2785 |
|
|
/* if mulru(approxsubhalf, approxsubhalf) > f then */
|
| 2786 |
|
|
/* approx := approx - setexp(.l, -p + 1) */
|
| 2787 |
|
|
/* else */
|
| 2788 |
|
|
/* const approxaddhalf := approx + setexp(.5, -p) */
|
| 2789 |
|
|
/* if mulrd(approxaddhalf, approxaddhalf) < f then */
|
| 2790 |
|
|
/* approx := approx + setexp(.l, -p + 1) */
|
| 2791 |
|
|
/* end if */
|
| 2792 |
|
|
/* end if */
|
| 2793 |
|
|
/* end */
|
| 2794 |
|
|
/* result setexp(approx, e div 2) % fix exponent */
|
| 2795 |
|
|
/* end sqrt */
|
| 2796 |
|
|
/* ------------------------------------------------------------------ */
|
| 2797 |
|
|
decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
|
| 2798 |
|
|
decContext *set) {
|
| 2799 |
|
|
decContext workset, approxset; /* work contexts */
|
| 2800 |
|
|
decNumber dzero; /* used for constant zero */
|
| 2801 |
|
|
Int maxp; /* largest working precision */
|
| 2802 |
|
|
Int workp; /* working precision */
|
| 2803 |
|
|
Int residue=0; /* rounding residue */
|
| 2804 |
|
|
uInt status=0, ignore=0; /* status accumulators */
|
| 2805 |
|
|
uInt rstatus; /* .. */
|
| 2806 |
|
|
Int exp; /* working exponent */
|
| 2807 |
|
|
Int ideal; /* ideal (preferred) exponent */
|
| 2808 |
|
|
Int needbytes; /* work */
|
| 2809 |
|
|
Int dropped; /* .. */
|
| 2810 |
|
|
|
| 2811 |
|
|
#if DECSUBSET
|
| 2812 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| 2813 |
|
|
#endif
|
| 2814 |
|
|
/* buffer for f [needs +1 in case DECBUFFER 0] */
|
| 2815 |
|
|
decNumber buff[D2N(DECBUFFER+1)];
|
| 2816 |
|
|
/* buffer for a [needs +2 to match likely maxp] */
|
| 2817 |
|
|
decNumber bufa[D2N(DECBUFFER+2)];
|
| 2818 |
|
|
/* buffer for temporary, b [must be same size as a] */
|
| 2819 |
|
|
decNumber bufb[D2N(DECBUFFER+2)];
|
| 2820 |
|
|
decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */
|
| 2821 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 2822 |
|
|
decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| 2823 |
|
|
decNumber *f=buff; /* reduced fraction */
|
| 2824 |
|
|
decNumber *a=bufa; /* approximation to result */
|
| 2825 |
|
|
decNumber *b=bufb; /* intermediate result */
|
| 2826 |
|
|
/* buffer for temporary variable, up to 3 digits */
|
| 2827 |
|
|
decNumber buft[D2N(3)];
|
| 2828 |
|
|
decNumber *t=buft; /* up-to-3-digit constant or work */
|
| 2829 |
|
|
|
| 2830 |
|
|
#if DECCHECK
|
| 2831 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 2832 |
|
|
#endif
|
| 2833 |
|
|
|
| 2834 |
|
|
do { /* protect allocated storage */
|
| 2835 |
|
|
#if DECSUBSET
|
| 2836 |
|
|
if (!set->extended) {
|
| 2837 |
|
|
/* reduce operand and set lostDigits status, as needed */
|
| 2838 |
|
|
if (rhs->digits>set->digits) {
|
| 2839 |
|
|
allocrhs=decRoundOperand(rhs, set, &status);
|
| 2840 |
|
|
if (allocrhs==NULL) break;
|
| 2841 |
|
|
/* [Note: 'f' allocation below could reuse this buffer if */
|
| 2842 |
|
|
/* used, but as this is rare they are kept separate for clarity.] */
|
| 2843 |
|
|
rhs=allocrhs;
|
| 2844 |
|
|
}
|
| 2845 |
|
|
}
|
| 2846 |
|
|
#endif
|
| 2847 |
|
|
/* [following code does not require input rounding] */
|
| 2848 |
|
|
|
| 2849 |
|
|
/* handle infinities and NaNs */
|
| 2850 |
|
|
if (SPECIALARG) {
|
| 2851 |
|
|
if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| 2852 |
|
|
if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
|
| 2853 |
|
|
else decNumberCopy(res, rhs); /* +Infinity */
|
| 2854 |
|
|
}
|
| 2855 |
|
|
else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
|
| 2856 |
|
|
break;
|
| 2857 |
|
|
}
|
| 2858 |
|
|
|
| 2859 |
|
|
/* calculate the ideal (preferred) exponent [floor(exp/2)] */
|
| 2860 |
|
|
/* [It would be nicer to write: ideal=rhs->exponent>>1, but this */
|
| 2861 |
|
|
/* generates a compiler warning. Generated code is the same.] */
|
| 2862 |
|
|
ideal=(rhs->exponent&~1)/2; /* target */
|
| 2863 |
|
|
|
| 2864 |
|
|
/* handle zeros */
|
| 2865 |
|
|
if (ISZERO(rhs)) {
|
| 2866 |
|
|
decNumberCopy(res, rhs); /* could be 0 or -0 */
|
| 2867 |
|
|
res->exponent=ideal; /* use the ideal [safe] */
|
| 2868 |
|
|
/* use decFinish to clamp any out-of-range exponent, etc. */
|
| 2869 |
|
|
decFinish(res, set, &residue, &status);
|
| 2870 |
|
|
break;
|
| 2871 |
|
|
}
|
| 2872 |
|
|
|
| 2873 |
|
|
/* any other -x is an oops */
|
| 2874 |
|
|
if (decNumberIsNegative(rhs)) {
|
| 2875 |
|
|
status|=DEC_Invalid_operation;
|
| 2876 |
|
|
break;
|
| 2877 |
|
|
}
|
| 2878 |
|
|
|
| 2879 |
|
|
/* space is needed for three working variables */
|
| 2880 |
|
|
/* f -- the same precision as the RHS, reduced to 0.01->0.99... */
|
| 2881 |
|
|
/* a -- Hull's approximation -- precision, when assigned, is */
|
| 2882 |
|
|
/* currentprecision+1 or the input argument precision, */
|
| 2883 |
|
|
/* whichever is larger (+2 for use as temporary) */
|
| 2884 |
|
|
/* b -- intermediate temporary result (same size as a) */
|
| 2885 |
|
|
/* if any is too long for local storage, then allocate */
|
| 2886 |
|
|
workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */
|
| 2887 |
|
|
workp=MAXI(workp, 7); /* at least 7 for low cases */
|
| 2888 |
|
|
maxp=workp+2; /* largest working precision */
|
| 2889 |
|
|
|
| 2890 |
|
|
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| 2891 |
|
|
if (needbytes>(Int)sizeof(buff)) {
|
| 2892 |
|
|
allocbuff=(decNumber *)malloc(needbytes);
|
| 2893 |
|
|
if (allocbuff==NULL) { /* hopeless -- abandon */
|
| 2894 |
|
|
status|=DEC_Insufficient_storage;
|
| 2895 |
|
|
break;}
|
| 2896 |
|
|
f=allocbuff; /* use the allocated space */
|
| 2897 |
|
|
}
|
| 2898 |
|
|
/* a and b both need to be able to hold a maxp-length number */
|
| 2899 |
|
|
needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
|
| 2900 |
|
|
if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */
|
| 2901 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 2902 |
|
|
allocbufb=(decNumber *)malloc(needbytes);
|
| 2903 |
|
|
if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
|
| 2904 |
|
|
status|=DEC_Insufficient_storage;
|
| 2905 |
|
|
break;}
|
| 2906 |
|
|
a=allocbufa; /* use the allocated spaces */
|
| 2907 |
|
|
b=allocbufb; /* .. */
|
| 2908 |
|
|
}
|
| 2909 |
|
|
|
| 2910 |
|
|
/* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
|
| 2911 |
|
|
decNumberCopy(f, rhs);
|
| 2912 |
|
|
exp=f->exponent+f->digits; /* adjusted to Hull rules */
|
| 2913 |
|
|
f->exponent=-(f->digits); /* to range */
|
| 2914 |
|
|
|
| 2915 |
|
|
/* set up working context */
|
| 2916 |
|
|
decContextDefault(&workset, DEC_INIT_DECIMAL64);
|
| 2917 |
|
|
workset.emax=DEC_MAX_EMAX;
|
| 2918 |
|
|
workset.emin=DEC_MIN_EMIN;
|
| 2919 |
|
|
|
| 2920 |
|
|
/* [Until further notice, no error is possible and status bits */
|
| 2921 |
|
|
/* (Rounded, etc.) should be ignored, not accumulated.] */
|
| 2922 |
|
|
|
| 2923 |
|
|
/* Calculate initial approximation, and allow for odd exponent */
|
| 2924 |
|
|
workset.digits=workp; /* p for initial calculation */
|
| 2925 |
|
|
t->bits=0; t->digits=3;
|
| 2926 |
|
|
a->bits=0; a->digits=3;
|
| 2927 |
|
|
if ((exp & 1)==0) { /* even exponent */
|
| 2928 |
|
|
/* Set t=0.259, a=0.819 */
|
| 2929 |
|
|
t->exponent=-3;
|
| 2930 |
|
|
a->exponent=-3;
|
| 2931 |
|
|
#if DECDPUN>=3
|
| 2932 |
|
|
t->lsu[0]=259;
|
| 2933 |
|
|
a->lsu[0]=819;
|
| 2934 |
|
|
#elif DECDPUN==2
|
| 2935 |
|
|
t->lsu[0]=59; t->lsu[1]=2;
|
| 2936 |
|
|
a->lsu[0]=19; a->lsu[1]=8;
|
| 2937 |
|
|
#else
|
| 2938 |
|
|
t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
|
| 2939 |
|
|
a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
|
| 2940 |
|
|
#endif
|
| 2941 |
|
|
}
|
| 2942 |
|
|
else { /* odd exponent */
|
| 2943 |
|
|
/* Set t=0.0819, a=2.59 */
|
| 2944 |
|
|
f->exponent--; /* f=f/10 */
|
| 2945 |
|
|
exp++; /* e=e+1 */
|
| 2946 |
|
|
t->exponent=-4;
|
| 2947 |
|
|
a->exponent=-2;
|
| 2948 |
|
|
#if DECDPUN>=3
|
| 2949 |
|
|
t->lsu[0]=819;
|
| 2950 |
|
|
a->lsu[0]=259;
|
| 2951 |
|
|
#elif DECDPUN==2
|
| 2952 |
|
|
t->lsu[0]=19; t->lsu[1]=8;
|
| 2953 |
|
|
a->lsu[0]=59; a->lsu[1]=2;
|
| 2954 |
|
|
#else
|
| 2955 |
|
|
t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
|
| 2956 |
|
|
a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
|
| 2957 |
|
|
#endif
|
| 2958 |
|
|
}
|
| 2959 |
|
|
|
| 2960 |
|
|
decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */
|
| 2961 |
|
|
decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */
|
| 2962 |
|
|
/* [a is now the initial approximation for sqrt(f), calculated with */
|
| 2963 |
|
|
/* currentprecision, which is also a's precision.] */
|
| 2964 |
|
|
|
| 2965 |
|
|
/* the main calculation loop */
|
| 2966 |
|
|
decNumberZero(&dzero); /* make 0 */
|
| 2967 |
|
|
decNumberZero(t); /* set t = 0.5 */
|
| 2968 |
|
|
t->lsu[0]=5; /* .. */
|
| 2969 |
|
|
t->exponent=-1; /* .. */
|
| 2970 |
|
|
workset.digits=3; /* initial p */
|
| 2971 |
|
|
for (; workset.digits<maxp;) {
|
| 2972 |
|
|
/* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
|
| 2973 |
|
|
workset.digits=MINI(workset.digits*2-2, maxp);
|
| 2974 |
|
|
/* a = 0.5 * (a + f/a) */
|
| 2975 |
|
|
/* [calculated at p then rounded to currentprecision] */
|
| 2976 |
|
|
decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
|
| 2977 |
|
|
decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */
|
| 2978 |
|
|
decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */
|
| 2979 |
|
|
} /* loop */
|
| 2980 |
|
|
|
| 2981 |
|
|
/* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
|
| 2982 |
|
|
/* now reduce to length, etc.; this needs to be done with a */
|
| 2983 |
|
|
/* having the correct exponent so as to handle subnormals */
|
| 2984 |
|
|
/* correctly */
|
| 2985 |
|
|
approxset=*set; /* get emin, emax, etc. */
|
| 2986 |
|
|
approxset.round=DEC_ROUND_HALF_EVEN;
|
| 2987 |
|
|
a->exponent+=exp/2; /* set correct exponent */
|
| 2988 |
|
|
rstatus=0; /* clear status */
|
| 2989 |
|
|
residue=0; /* .. and accumulator */
|
| 2990 |
|
|
decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */
|
| 2991 |
|
|
decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */
|
| 2992 |
|
|
|
| 2993 |
|
|
/* Overflow was possible if the input exponent was out-of-range, */
|
| 2994 |
|
|
/* in which case quit */
|
| 2995 |
|
|
if (rstatus&DEC_Overflow) {
|
| 2996 |
|
|
status=rstatus; /* use the status as-is */
|
| 2997 |
|
|
decNumberCopy(res, a); /* copy to result */
|
| 2998 |
|
|
break;
|
| 2999 |
|
|
}
|
| 3000 |
|
|
|
| 3001 |
|
|
/* Preserve status except Inexact/Rounded */
|
| 3002 |
|
|
status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
|
| 3003 |
|
|
|
| 3004 |
|
|
/* Carry out the Hull correction */
|
| 3005 |
|
|
a->exponent-=exp/2; /* back to 0.1->1 */
|
| 3006 |
|
|
|
| 3007 |
|
|
/* a is now at final precision and within 1 ulp of the properly */
|
| 3008 |
|
|
/* rounded square root of f; to ensure proper rounding, compare */
|
| 3009 |
|
|
/* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
|
| 3010 |
|
|
/* Here workset.digits=maxp and t=0.5, and a->digits determines */
|
| 3011 |
|
|
/* the ulp */
|
| 3012 |
|
|
workset.digits--; /* maxp-1 is OK now */
|
| 3013 |
|
|
t->exponent=-a->digits-1; /* make 0.5 ulp */
|
| 3014 |
|
|
decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
|
| 3015 |
|
|
workset.round=DEC_ROUND_UP;
|
| 3016 |
|
|
decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */
|
| 3017 |
|
|
decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
|
| 3018 |
|
|
if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */
|
| 3019 |
|
|
/* this is the more common adjustment, though both are rare */
|
| 3020 |
|
|
t->exponent++; /* make 1.0 ulp */
|
| 3021 |
|
|
t->lsu[0]=1; /* .. */
|
| 3022 |
|
|
decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
|
| 3023 |
|
|
/* assign to approx [round to length] */
|
| 3024 |
|
|
approxset.emin-=exp/2; /* adjust to match a */
|
| 3025 |
|
|
approxset.emax-=exp/2;
|
| 3026 |
|
|
decAddOp(a, &dzero, a, &approxset, 0, &ignore);
|
| 3027 |
|
|
}
|
| 3028 |
|
|
else {
|
| 3029 |
|
|
decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
|
| 3030 |
|
|
workset.round=DEC_ROUND_DOWN;
|
| 3031 |
|
|
decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
|
| 3032 |
|
|
decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */
|
| 3033 |
|
|
if (decNumberIsNegative(b)) { /* b < f */
|
| 3034 |
|
|
t->exponent++; /* make 1.0 ulp */
|
| 3035 |
|
|
t->lsu[0]=1; /* .. */
|
| 3036 |
|
|
decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
|
| 3037 |
|
|
/* assign to approx [round to length] */
|
| 3038 |
|
|
approxset.emin-=exp/2; /* adjust to match a */
|
| 3039 |
|
|
approxset.emax-=exp/2;
|
| 3040 |
|
|
decAddOp(a, &dzero, a, &approxset, 0, &ignore);
|
| 3041 |
|
|
}
|
| 3042 |
|
|
}
|
| 3043 |
|
|
/* [no errors are possible in the above, and rounding/inexact during */
|
| 3044 |
|
|
/* estimation are irrelevant, so status was not accumulated] */
|
| 3045 |
|
|
|
| 3046 |
|
|
/* Here, 0.1 <= a < 1 (still), so adjust back */
|
| 3047 |
|
|
a->exponent+=exp/2; /* set correct exponent */
|
| 3048 |
|
|
|
| 3049 |
|
|
/* count droppable zeros [after any subnormal rounding] by */
|
| 3050 |
|
|
/* trimming a copy */
|
| 3051 |
|
|
decNumberCopy(b, a);
|
| 3052 |
|
|
decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */
|
| 3053 |
|
|
|
| 3054 |
|
|
/* Set Inexact and Rounded. The answer can only be exact if */
|
| 3055 |
|
|
/* it is short enough so that squaring it could fit in workp */
|
| 3056 |
|
|
/* digits, so this is the only (relatively rare) condition that */
|
| 3057 |
|
|
/* a careful check is needed */
|
| 3058 |
|
|
if (b->digits*2-1 > workp) { /* cannot fit */
|
| 3059 |
|
|
status|=DEC_Inexact|DEC_Rounded;
|
| 3060 |
|
|
}
|
| 3061 |
|
|
else { /* could be exact/unrounded */
|
| 3062 |
|
|
uInt mstatus=0; /* local status */
|
| 3063 |
|
|
decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
|
| 3064 |
|
|
if (mstatus&DEC_Overflow) { /* result just won't fit */
|
| 3065 |
|
|
status|=DEC_Inexact|DEC_Rounded;
|
| 3066 |
|
|
}
|
| 3067 |
|
|
else { /* plausible */
|
| 3068 |
|
|
decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
|
| 3069 |
|
|
if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
|
| 3070 |
|
|
else { /* is Exact */
|
| 3071 |
|
|
/* here, dropped is the count of trailing zeros in 'a' */
|
| 3072 |
|
|
/* use closest exponent to ideal... */
|
| 3073 |
|
|
Int todrop=ideal-a->exponent; /* most that can be dropped */
|
| 3074 |
|
|
if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
|
| 3075 |
|
|
else { /* unrounded */
|
| 3076 |
|
|
/* there are some to drop, but emax may not allow all */
|
| 3077 |
|
|
Int maxexp=set->emax-set->digits+1;
|
| 3078 |
|
|
Int maxdrop=maxexp-a->exponent;
|
| 3079 |
|
|
if (todrop>maxdrop && set->clamp) { /* apply clamping */
|
| 3080 |
|
|
todrop=maxdrop;
|
| 3081 |
|
|
status|=DEC_Clamped;
|
| 3082 |
|
|
}
|
| 3083 |
|
|
if (dropped<todrop) { /* clamp to those available */
|
| 3084 |
|
|
todrop=dropped;
|
| 3085 |
|
|
status|=DEC_Clamped;
|
| 3086 |
|
|
}
|
| 3087 |
|
|
if (todrop>0) { /* have some to drop */
|
| 3088 |
|
|
decShiftToLeast(a->lsu, D2U(a->digits), todrop);
|
| 3089 |
|
|
a->exponent+=todrop; /* maintain numerical value */
|
| 3090 |
|
|
a->digits-=todrop; /* new length */
|
| 3091 |
|
|
}
|
| 3092 |
|
|
}
|
| 3093 |
|
|
}
|
| 3094 |
|
|
}
|
| 3095 |
|
|
}
|
| 3096 |
|
|
|
| 3097 |
|
|
/* double-check Underflow, as perhaps the result could not have */
|
| 3098 |
|
|
/* been subnormal (initial argument too big), or it is now Exact */
|
| 3099 |
|
|
if (status&DEC_Underflow) {
|
| 3100 |
|
|
Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
|
| 3101 |
|
|
/* check if truly subnormal */
|
| 3102 |
|
|
#if DECEXTFLAG /* DEC_Subnormal too */
|
| 3103 |
|
|
if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
|
| 3104 |
|
|
#else
|
| 3105 |
|
|
if (ae>=set->emin*2) status&=~DEC_Underflow;
|
| 3106 |
|
|
#endif
|
| 3107 |
|
|
/* check if truly inexact */
|
| 3108 |
|
|
if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
|
| 3109 |
|
|
}
|
| 3110 |
|
|
|
| 3111 |
|
|
decNumberCopy(res, a); /* a is now the result */
|
| 3112 |
|
|
} while(0); /* end protected */
|
| 3113 |
|
|
|
| 3114 |
|
|
if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */
|
| 3115 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* .. */
|
| 3116 |
|
|
if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| 3117 |
|
|
#if DECSUBSET
|
| 3118 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| 3119 |
|
|
#endif
|
| 3120 |
|
|
if (status!=0) decStatus(res, status, set);/* then report status */
|
| 3121 |
|
|
#if DECCHECK
|
| 3122 |
|
|
decCheckInexact(res, set);
|
| 3123 |
|
|
#endif
|
| 3124 |
|
|
return res;
|
| 3125 |
|
|
} /* decNumberSquareRoot */
|
| 3126 |
|
|
|
| 3127 |
|
|
/* ------------------------------------------------------------------ */
|
| 3128 |
|
|
/* decNumberSubtract -- subtract two Numbers */
|
| 3129 |
|
|
/* */
|
| 3130 |
|
|
/* This computes C = A - B */
|
| 3131 |
|
|
/* */
|
| 3132 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
|
| 3133 |
|
|
/* lhs is A */
|
| 3134 |
|
|
/* rhs is B */
|
| 3135 |
|
|
/* set is the context */
|
| 3136 |
|
|
/* */
|
| 3137 |
|
|
/* C must have space for set->digits digits. */
|
| 3138 |
|
|
/* ------------------------------------------------------------------ */
|
| 3139 |
|
|
decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
|
| 3140 |
|
|
const decNumber *rhs, decContext *set) {
|
| 3141 |
|
|
uInt status=0; /* accumulator */
|
| 3142 |
|
|
|
| 3143 |
|
|
decAddOp(res, lhs, rhs, set, DECNEG, &status);
|
| 3144 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 3145 |
|
|
#if DECCHECK
|
| 3146 |
|
|
decCheckInexact(res, set);
|
| 3147 |
|
|
#endif
|
| 3148 |
|
|
return res;
|
| 3149 |
|
|
} /* decNumberSubtract */
|
| 3150 |
|
|
|
| 3151 |
|
|
/* ------------------------------------------------------------------ */
|
| 3152 |
|
|
/* decNumberToIntegralExact -- round-to-integral-value with InExact */
|
| 3153 |
|
|
/* decNumberToIntegralValue -- round-to-integral-value */
|
| 3154 |
|
|
/* */
|
| 3155 |
|
|
/* res is the result */
|
| 3156 |
|
|
/* rhs is input number */
|
| 3157 |
|
|
/* set is the context */
|
| 3158 |
|
|
/* */
|
| 3159 |
|
|
/* res must have space for any value of rhs. */
|
| 3160 |
|
|
/* */
|
| 3161 |
|
|
/* This implements the IEEE special operators and therefore treats */
|
| 3162 |
|
|
/* special values as valid. For finite numbers it returns */
|
| 3163 |
|
|
/* rescale(rhs, 0) if rhs->exponent is <0. */
|
| 3164 |
|
|
/* Otherwise the result is rhs (so no error is possible, except for */
|
| 3165 |
|
|
/* sNaN). */
|
| 3166 |
|
|
/* */
|
| 3167 |
|
|
/* The context is used for rounding mode and status after sNaN, but */
|
| 3168 |
|
|
/* the digits setting is ignored. The Exact version will signal */
|
| 3169 |
|
|
/* Inexact if the result differs numerically from rhs; the other */
|
| 3170 |
|
|
/* never signals Inexact. */
|
| 3171 |
|
|
/* ------------------------------------------------------------------ */
|
| 3172 |
|
|
decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
|
| 3173 |
|
|
decContext *set) {
|
| 3174 |
|
|
decNumber dn;
|
| 3175 |
|
|
decContext workset; /* working context */
|
| 3176 |
|
|
uInt status=0; /* accumulator */
|
| 3177 |
|
|
|
| 3178 |
|
|
#if DECCHECK
|
| 3179 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 3180 |
|
|
#endif
|
| 3181 |
|
|
|
| 3182 |
|
|
/* handle infinities and NaNs */
|
| 3183 |
|
|
if (SPECIALARG) {
|
| 3184 |
|
|
if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */
|
| 3185 |
|
|
else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
|
| 3186 |
|
|
}
|
| 3187 |
|
|
else { /* finite */
|
| 3188 |
|
|
/* have a finite number; no error possible (res must be big enough) */
|
| 3189 |
|
|
if (rhs->exponent>=0) return decNumberCopy(res, rhs);
|
| 3190 |
|
|
/* that was easy, but if negative exponent there is work to do... */
|
| 3191 |
|
|
workset=*set; /* clone rounding, etc. */
|
| 3192 |
|
|
workset.digits=rhs->digits; /* no length rounding */
|
| 3193 |
|
|
workset.traps=0; /* no traps */
|
| 3194 |
|
|
decNumberZero(&dn); /* make a number with exponent 0 */
|
| 3195 |
|
|
decNumberQuantize(res, rhs, &dn, &workset);
|
| 3196 |
|
|
status|=workset.status;
|
| 3197 |
|
|
}
|
| 3198 |
|
|
if (status!=0) decStatus(res, status, set);
|
| 3199 |
|
|
return res;
|
| 3200 |
|
|
} /* decNumberToIntegralExact */
|
| 3201 |
|
|
|
| 3202 |
|
|
decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
|
| 3203 |
|
|
decContext *set) {
|
| 3204 |
|
|
decContext workset=*set; /* working context */
|
| 3205 |
|
|
workset.traps=0; /* no traps */
|
| 3206 |
|
|
decNumberToIntegralExact(res, rhs, &workset);
|
| 3207 |
|
|
/* this never affects set, except for sNaNs; NaN will have been set */
|
| 3208 |
|
|
/* or propagated already, so no need to call decStatus */
|
| 3209 |
|
|
set->status|=workset.status&DEC_Invalid_operation;
|
| 3210 |
|
|
return res;
|
| 3211 |
|
|
} /* decNumberToIntegralValue */
|
| 3212 |
|
|
|
| 3213 |
|
|
/* ------------------------------------------------------------------ */
|
| 3214 |
|
|
/* decNumberXor -- XOR two Numbers, digitwise */
|
| 3215 |
|
|
/* */
|
| 3216 |
|
|
/* This computes C = A ^ B */
|
| 3217 |
|
|
/* */
|
| 3218 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
|
| 3219 |
|
|
/* lhs is A */
|
| 3220 |
|
|
/* rhs is B */
|
| 3221 |
|
|
/* set is the context (used for result length and error report) */
|
| 3222 |
|
|
/* */
|
| 3223 |
|
|
/* C must have space for set->digits digits. */
|
| 3224 |
|
|
/* */
|
| 3225 |
|
|
/* Logical function restrictions apply (see above); a NaN is */
|
| 3226 |
|
|
/* returned with Invalid_operation if a restriction is violated. */
|
| 3227 |
|
|
/* ------------------------------------------------------------------ */
|
| 3228 |
|
|
decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
|
| 3229 |
|
|
const decNumber *rhs, decContext *set) {
|
| 3230 |
|
|
const Unit *ua, *ub; /* -> operands */
|
| 3231 |
|
|
const Unit *msua, *msub; /* -> operand msus */
|
| 3232 |
|
|
Unit *uc, *msuc; /* -> result and its msu */
|
| 3233 |
|
|
Int msudigs; /* digits in res msu */
|
| 3234 |
|
|
#if DECCHECK
|
| 3235 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 3236 |
|
|
#endif
|
| 3237 |
|
|
|
| 3238 |
|
|
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| 3239 |
|
|
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| 3240 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 3241 |
|
|
return res;
|
| 3242 |
|
|
}
|
| 3243 |
|
|
/* operands are valid */
|
| 3244 |
|
|
ua=lhs->lsu; /* bottom-up */
|
| 3245 |
|
|
ub=rhs->lsu; /* .. */
|
| 3246 |
|
|
uc=res->lsu; /* .. */
|
| 3247 |
|
|
msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| 3248 |
|
|
msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| 3249 |
|
|
msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| 3250 |
|
|
msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| 3251 |
|
|
for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| 3252 |
|
|
Unit a, b; /* extract units */
|
| 3253 |
|
|
if (ua>msua) a=0;
|
| 3254 |
|
|
else a=*ua;
|
| 3255 |
|
|
if (ub>msub) b=0;
|
| 3256 |
|
|
else b=*ub;
|
| 3257 |
|
|
*uc=0; /* can now write back */
|
| 3258 |
|
|
if (a|b) { /* maybe 1 bits to examine */
|
| 3259 |
|
|
Int i, j;
|
| 3260 |
|
|
/* This loop could be unrolled and/or use BIN2BCD tables */
|
| 3261 |
|
|
for (i=0; i<DECDPUN; i++) {
|
| 3262 |
|
|
if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */
|
| 3263 |
|
|
j=a%10;
|
| 3264 |
|
|
a=a/10;
|
| 3265 |
|
|
j|=b%10;
|
| 3266 |
|
|
b=b/10;
|
| 3267 |
|
|
if (j>1) {
|
| 3268 |
|
|
decStatus(res, DEC_Invalid_operation, set);
|
| 3269 |
|
|
return res;
|
| 3270 |
|
|
}
|
| 3271 |
|
|
if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| 3272 |
|
|
} /* each digit */
|
| 3273 |
|
|
} /* non-zero */
|
| 3274 |
|
|
} /* each unit */
|
| 3275 |
|
|
/* [here uc-1 is the msu of the result] */
|
| 3276 |
|
|
res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| 3277 |
|
|
res->exponent=0; /* integer */
|
| 3278 |
|
|
res->bits=0; /* sign=0 */
|
| 3279 |
|
|
return res; /* [no status to set] */
|
| 3280 |
|
|
} /* decNumberXor */
|
| 3281 |
|
|
|
| 3282 |
|
|
|
| 3283 |
|
|
/* ================================================================== */
|
| 3284 |
|
|
/* Utility routines */
|
| 3285 |
|
|
/* ================================================================== */
|
| 3286 |
|
|
|
| 3287 |
|
|
/* ------------------------------------------------------------------ */
|
| 3288 |
|
|
/* decNumberClass -- return the decClass of a decNumber */
|
| 3289 |
|
|
/* dn -- the decNumber to test */
|
| 3290 |
|
|
/* set -- the context to use for Emin */
|
| 3291 |
|
|
/* returns the decClass enum */
|
| 3292 |
|
|
/* ------------------------------------------------------------------ */
|
| 3293 |
|
|
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
|
| 3294 |
|
|
if (decNumberIsSpecial(dn)) {
|
| 3295 |
|
|
if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
|
| 3296 |
|
|
if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
|
| 3297 |
|
|
/* must be an infinity */
|
| 3298 |
|
|
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
|
| 3299 |
|
|
return DEC_CLASS_POS_INF;
|
| 3300 |
|
|
}
|
| 3301 |
|
|
/* is finite */
|
| 3302 |
|
|
if (decNumberIsNormal(dn, set)) { /* most common */
|
| 3303 |
|
|
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
|
| 3304 |
|
|
return DEC_CLASS_POS_NORMAL;
|
| 3305 |
|
|
}
|
| 3306 |
|
|
/* is subnormal or zero */
|
| 3307 |
|
|
if (decNumberIsZero(dn)) { /* most common */
|
| 3308 |
|
|
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
|
| 3309 |
|
|
return DEC_CLASS_POS_ZERO;
|
| 3310 |
|
|
}
|
| 3311 |
|
|
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
|
| 3312 |
|
|
return DEC_CLASS_POS_SUBNORMAL;
|
| 3313 |
|
|
} /* decNumberClass */
|
| 3314 |
|
|
|
| 3315 |
|
|
/* ------------------------------------------------------------------ */
|
| 3316 |
|
|
/* decNumberClassToString -- convert decClass to a string */
|
| 3317 |
|
|
/* */
|
| 3318 |
|
|
/* eclass is a valid decClass */
|
| 3319 |
|
|
/* returns a constant string describing the class (max 13+1 chars) */
|
| 3320 |
|
|
/* ------------------------------------------------------------------ */
|
| 3321 |
|
|
const char *decNumberClassToString(enum decClass eclass) {
|
| 3322 |
|
|
if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
|
| 3323 |
|
|
if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
|
| 3324 |
|
|
if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
|
| 3325 |
|
|
if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
|
| 3326 |
|
|
if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
|
| 3327 |
|
|
if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
|
| 3328 |
|
|
if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
|
| 3329 |
|
|
if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
|
| 3330 |
|
|
if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
|
| 3331 |
|
|
if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
|
| 3332 |
|
|
return DEC_ClassString_UN; /* Unknown */
|
| 3333 |
|
|
} /* decNumberClassToString */
|
| 3334 |
|
|
|
| 3335 |
|
|
/* ------------------------------------------------------------------ */
|
| 3336 |
|
|
/* decNumberCopy -- copy a number */
|
| 3337 |
|
|
/* */
|
| 3338 |
|
|
/* dest is the target decNumber */
|
| 3339 |
|
|
/* src is the source decNumber */
|
| 3340 |
|
|
/* returns dest */
|
| 3341 |
|
|
/* */
|
| 3342 |
|
|
/* (dest==src is allowed and is a no-op) */
|
| 3343 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 3344 |
|
|
/* so special values are unchanged and no error is possible. */
|
| 3345 |
|
|
/* ------------------------------------------------------------------ */
|
| 3346 |
|
|
decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
|
| 3347 |
|
|
|
| 3348 |
|
|
#if DECCHECK
|
| 3349 |
|
|
if (src==NULL) return decNumberZero(dest);
|
| 3350 |
|
|
#endif
|
| 3351 |
|
|
|
| 3352 |
|
|
if (dest==src) return dest; /* no copy required */
|
| 3353 |
|
|
|
| 3354 |
|
|
/* Use explicit assignments here as structure assignment could copy */
|
| 3355 |
|
|
/* more than just the lsu (for small DECDPUN). This would not affect */
|
| 3356 |
|
|
/* the value of the results, but could disturb test harness spill */
|
| 3357 |
|
|
/* checking. */
|
| 3358 |
|
|
dest->bits=src->bits;
|
| 3359 |
|
|
dest->exponent=src->exponent;
|
| 3360 |
|
|
dest->digits=src->digits;
|
| 3361 |
|
|
dest->lsu[0]=src->lsu[0];
|
| 3362 |
|
|
if (src->digits>DECDPUN) { /* more Units to come */
|
| 3363 |
|
|
const Unit *smsup, *s; /* work */
|
| 3364 |
|
|
Unit *d; /* .. */
|
| 3365 |
|
|
/* memcpy for the remaining Units would be safe as they cannot */
|
| 3366 |
|
|
/* overlap. However, this explicit loop is faster in short cases. */
|
| 3367 |
|
|
d=dest->lsu+1; /* -> first destination */
|
| 3368 |
|
|
smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */
|
| 3369 |
|
|
for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
|
| 3370 |
|
|
}
|
| 3371 |
|
|
return dest;
|
| 3372 |
|
|
} /* decNumberCopy */
|
| 3373 |
|
|
|
| 3374 |
|
|
/* ------------------------------------------------------------------ */
|
| 3375 |
|
|
/* decNumberCopyAbs -- quiet absolute value operator */
|
| 3376 |
|
|
/* */
|
| 3377 |
|
|
/* This sets C = abs(A) */
|
| 3378 |
|
|
/* */
|
| 3379 |
|
|
/* res is C, the result. C may be A */
|
| 3380 |
|
|
/* rhs is A */
|
| 3381 |
|
|
/* */
|
| 3382 |
|
|
/* C must have space for set->digits digits. */
|
| 3383 |
|
|
/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| 3384 |
|
|
/* See also decNumberAbs for a checking version of this. */
|
| 3385 |
|
|
/* ------------------------------------------------------------------ */
|
| 3386 |
|
|
decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
|
| 3387 |
|
|
#if DECCHECK
|
| 3388 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| 3389 |
|
|
#endif
|
| 3390 |
|
|
decNumberCopy(res, rhs);
|
| 3391 |
|
|
res->bits&=~DECNEG; /* turn off sign */
|
| 3392 |
|
|
return res;
|
| 3393 |
|
|
} /* decNumberCopyAbs */
|
| 3394 |
|
|
|
| 3395 |
|
|
/* ------------------------------------------------------------------ */
|
| 3396 |
|
|
/* decNumberCopyNegate -- quiet negate value operator */
|
| 3397 |
|
|
/* */
|
| 3398 |
|
|
/* This sets C = negate(A) */
|
| 3399 |
|
|
/* */
|
| 3400 |
|
|
/* res is C, the result. C may be A */
|
| 3401 |
|
|
/* rhs is A */
|
| 3402 |
|
|
/* */
|
| 3403 |
|
|
/* C must have space for set->digits digits. */
|
| 3404 |
|
|
/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| 3405 |
|
|
/* See also decNumberMinus for a checking version of this. */
|
| 3406 |
|
|
/* ------------------------------------------------------------------ */
|
| 3407 |
|
|
decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
|
| 3408 |
|
|
#if DECCHECK
|
| 3409 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| 3410 |
|
|
#endif
|
| 3411 |
|
|
decNumberCopy(res, rhs);
|
| 3412 |
|
|
res->bits^=DECNEG; /* invert the sign */
|
| 3413 |
|
|
return res;
|
| 3414 |
|
|
} /* decNumberCopyNegate */
|
| 3415 |
|
|
|
| 3416 |
|
|
/* ------------------------------------------------------------------ */
|
| 3417 |
|
|
/* decNumberCopySign -- quiet copy and set sign operator */
|
| 3418 |
|
|
/* */
|
| 3419 |
|
|
/* This sets C = A with the sign of B */
|
| 3420 |
|
|
/* */
|
| 3421 |
|
|
/* res is C, the result. C may be A */
|
| 3422 |
|
|
/* lhs is A */
|
| 3423 |
|
|
/* rhs is B */
|
| 3424 |
|
|
/* */
|
| 3425 |
|
|
/* C must have space for set->digits digits. */
|
| 3426 |
|
|
/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| 3427 |
|
|
/* ------------------------------------------------------------------ */
|
| 3428 |
|
|
decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
|
| 3429 |
|
|
const decNumber *rhs) {
|
| 3430 |
|
|
uByte sign; /* rhs sign */
|
| 3431 |
|
|
#if DECCHECK
|
| 3432 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| 3433 |
|
|
#endif
|
| 3434 |
|
|
sign=rhs->bits & DECNEG; /* save sign bit */
|
| 3435 |
|
|
decNumberCopy(res, lhs);
|
| 3436 |
|
|
res->bits&=~DECNEG; /* clear the sign */
|
| 3437 |
|
|
res->bits|=sign; /* set from rhs */
|
| 3438 |
|
|
return res;
|
| 3439 |
|
|
} /* decNumberCopySign */
|
| 3440 |
|
|
|
| 3441 |
|
|
/* ------------------------------------------------------------------ */
|
| 3442 |
|
|
/* decNumberGetBCD -- get the coefficient in BCD8 */
|
| 3443 |
|
|
/* dn is the source decNumber */
|
| 3444 |
|
|
/* bcd is the uInt array that will receive dn->digits BCD bytes, */
|
| 3445 |
|
|
/* most-significant at offset 0 */
|
| 3446 |
|
|
/* returns bcd */
|
| 3447 |
|
|
/* */
|
| 3448 |
|
|
/* bcd must have at least dn->digits bytes. No error is possible; if */
|
| 3449 |
|
|
/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
|
| 3450 |
|
|
/* ------------------------------------------------------------------ */
|
| 3451 |
|
|
uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
|
| 3452 |
|
|
uByte *ub=bcd+dn->digits-1; /* -> lsd */
|
| 3453 |
|
|
const Unit *up=dn->lsu; /* Unit pointer, -> lsu */
|
| 3454 |
|
|
|
| 3455 |
|
|
#if DECDPUN==1 /* trivial simple copy */
|
| 3456 |
|
|
for (; ub>=bcd; ub--, up++) *ub=*up;
|
| 3457 |
|
|
#else /* chopping needed */
|
| 3458 |
|
|
uInt u=*up; /* work */
|
| 3459 |
|
|
uInt cut=DECDPUN; /* downcounter through unit */
|
| 3460 |
|
|
for (; ub>=bcd; ub--) {
|
| 3461 |
|
|
*ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */
|
| 3462 |
|
|
u=u/10;
|
| 3463 |
|
|
cut--;
|
| 3464 |
|
|
if (cut>0) continue; /* more in this unit */
|
| 3465 |
|
|
up++;
|
| 3466 |
|
|
u=*up;
|
| 3467 |
|
|
cut=DECDPUN;
|
| 3468 |
|
|
}
|
| 3469 |
|
|
#endif
|
| 3470 |
|
|
return bcd;
|
| 3471 |
|
|
} /* decNumberGetBCD */
|
| 3472 |
|
|
|
| 3473 |
|
|
/* ------------------------------------------------------------------ */
|
| 3474 |
|
|
/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
|
| 3475 |
|
|
/* dn is the target decNumber */
|
| 3476 |
|
|
/* bcd is the uInt array that will source n BCD bytes, most- */
|
| 3477 |
|
|
/* significant at offset 0 */
|
| 3478 |
|
|
/* n is the number of digits in the source BCD array (bcd) */
|
| 3479 |
|
|
/* returns dn */
|
| 3480 |
|
|
/* */
|
| 3481 |
|
|
/* dn must have space for at least n digits. No error is possible; */
|
| 3482 |
|
|
/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
|
| 3483 |
|
|
/* and bcd[0] zero. */
|
| 3484 |
|
|
/* ------------------------------------------------------------------ */
|
| 3485 |
|
|
decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
|
| 3486 |
|
|
Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */
|
| 3487 |
|
|
const uByte *ub=bcd; /* -> source msd */
|
| 3488 |
|
|
|
| 3489 |
|
|
#if DECDPUN==1 /* trivial simple copy */
|
| 3490 |
|
|
for (; ub<bcd+n; ub++, up--) *up=*ub;
|
| 3491 |
|
|
#else /* some assembly needed */
|
| 3492 |
|
|
/* calculate how many digits in msu, and hence first cut */
|
| 3493 |
|
|
Int cut=MSUDIGITS(n); /* [faster than remainder] */
|
| 3494 |
|
|
for (;up>=dn->lsu; up--) { /* each Unit from msu */
|
| 3495 |
|
|
*up=0; /* will take <=DECDPUN digits */
|
| 3496 |
|
|
for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
|
| 3497 |
|
|
cut=DECDPUN; /* next Unit has all digits */
|
| 3498 |
|
|
}
|
| 3499 |
|
|
#endif
|
| 3500 |
|
|
dn->digits=n; /* set digit count */
|
| 3501 |
|
|
return dn;
|
| 3502 |
|
|
} /* decNumberSetBCD */
|
| 3503 |
|
|
|
| 3504 |
|
|
/* ------------------------------------------------------------------ */
|
| 3505 |
|
|
/* decNumberIsNormal -- test normality of a decNumber */
|
| 3506 |
|
|
/* dn is the decNumber to test */
|
| 3507 |
|
|
/* set is the context to use for Emin */
|
| 3508 |
|
|
/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
|
| 3509 |
|
|
/* ------------------------------------------------------------------ */
|
| 3510 |
|
|
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
|
| 3511 |
|
|
Int ae; /* adjusted exponent */
|
| 3512 |
|
|
#if DECCHECK
|
| 3513 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| 3514 |
|
|
#endif
|
| 3515 |
|
|
|
| 3516 |
|
|
if (decNumberIsSpecial(dn)) return 0; /* not finite */
|
| 3517 |
|
|
if (decNumberIsZero(dn)) return 0; /* not non-zero */
|
| 3518 |
|
|
|
| 3519 |
|
|
ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| 3520 |
|
|
if (ae<set->emin) return 0; /* is subnormal */
|
| 3521 |
|
|
return 1;
|
| 3522 |
|
|
} /* decNumberIsNormal */
|
| 3523 |
|
|
|
| 3524 |
|
|
/* ------------------------------------------------------------------ */
|
| 3525 |
|
|
/* decNumberIsSubnormal -- test subnormality of a decNumber */
|
| 3526 |
|
|
/* dn is the decNumber to test */
|
| 3527 |
|
|
/* set is the context to use for Emin */
|
| 3528 |
|
|
/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
|
| 3529 |
|
|
/* ------------------------------------------------------------------ */
|
| 3530 |
|
|
Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
|
| 3531 |
|
|
Int ae; /* adjusted exponent */
|
| 3532 |
|
|
#if DECCHECK
|
| 3533 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| 3534 |
|
|
#endif
|
| 3535 |
|
|
|
| 3536 |
|
|
if (decNumberIsSpecial(dn)) return 0; /* not finite */
|
| 3537 |
|
|
if (decNumberIsZero(dn)) return 0; /* not non-zero */
|
| 3538 |
|
|
|
| 3539 |
|
|
ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| 3540 |
|
|
if (ae<set->emin) return 1; /* is subnormal */
|
| 3541 |
|
|
return 0;
|
| 3542 |
|
|
} /* decNumberIsSubnormal */
|
| 3543 |
|
|
|
| 3544 |
|
|
/* ------------------------------------------------------------------ */
|
| 3545 |
|
|
/* decNumberTrim -- remove insignificant zeros */
|
| 3546 |
|
|
/* */
|
| 3547 |
|
|
/* dn is the number to trim */
|
| 3548 |
|
|
/* returns dn */
|
| 3549 |
|
|
/* */
|
| 3550 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 3551 |
|
|
/* so special values are unchanged and no error is possible. The */
|
| 3552 |
|
|
/* zeros are removed unconditionally. */
|
| 3553 |
|
|
/* ------------------------------------------------------------------ */
|
| 3554 |
|
|
decNumber * decNumberTrim(decNumber *dn) {
|
| 3555 |
|
|
Int dropped; /* work */
|
| 3556 |
|
|
decContext set; /* .. */
|
| 3557 |
|
|
#if DECCHECK
|
| 3558 |
|
|
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
|
| 3559 |
|
|
#endif
|
| 3560 |
|
|
decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */
|
| 3561 |
|
|
return decTrim(dn, &set, 0, 1, &dropped);
|
| 3562 |
|
|
} /* decNumberTrim */
|
| 3563 |
|
|
|
| 3564 |
|
|
/* ------------------------------------------------------------------ */
|
| 3565 |
|
|
/* decNumberVersion -- return the name and version of this module */
|
| 3566 |
|
|
/* */
|
| 3567 |
|
|
/* No error is possible. */
|
| 3568 |
|
|
/* ------------------------------------------------------------------ */
|
| 3569 |
|
|
const char * decNumberVersion(void) {
|
| 3570 |
|
|
return DECVERSION;
|
| 3571 |
|
|
} /* decNumberVersion */
|
| 3572 |
|
|
|
| 3573 |
|
|
/* ------------------------------------------------------------------ */
|
| 3574 |
|
|
/* decNumberZero -- set a number to 0 */
|
| 3575 |
|
|
/* */
|
| 3576 |
|
|
/* dn is the number to set, with space for one digit */
|
| 3577 |
|
|
/* returns dn */
|
| 3578 |
|
|
/* */
|
| 3579 |
|
|
/* No error is possible. */
|
| 3580 |
|
|
/* ------------------------------------------------------------------ */
|
| 3581 |
|
|
/* Memset is not used as it is much slower in some environments. */
|
| 3582 |
|
|
decNumber * decNumberZero(decNumber *dn) {
|
| 3583 |
|
|
|
| 3584 |
|
|
#if DECCHECK
|
| 3585 |
|
|
if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
|
| 3586 |
|
|
#endif
|
| 3587 |
|
|
|
| 3588 |
|
|
dn->bits=0;
|
| 3589 |
|
|
dn->exponent=0;
|
| 3590 |
|
|
dn->digits=1;
|
| 3591 |
|
|
dn->lsu[0]=0;
|
| 3592 |
|
|
return dn;
|
| 3593 |
|
|
} /* decNumberZero */
|
| 3594 |
|
|
|
| 3595 |
|
|
/* ================================================================== */
|
| 3596 |
|
|
/* Local routines */
|
| 3597 |
|
|
/* ================================================================== */
|
| 3598 |
|
|
|
| 3599 |
|
|
/* ------------------------------------------------------------------ */
|
| 3600 |
|
|
/* decToString -- lay out a number into a string */
|
| 3601 |
|
|
/* */
|
| 3602 |
|
|
/* dn is the number to lay out */
|
| 3603 |
|
|
/* string is where to lay out the number */
|
| 3604 |
|
|
/* eng is 1 if Engineering, 0 if Scientific */
|
| 3605 |
|
|
/* */
|
| 3606 |
|
|
/* string must be at least dn->digits+14 characters long */
|
| 3607 |
|
|
/* No error is possible. */
|
| 3608 |
|
|
/* */
|
| 3609 |
|
|
/* Note that this routine can generate a -0 or 0.000. These are */
|
| 3610 |
|
|
/* never generated in subset to-number or arithmetic, but can occur */
|
| 3611 |
|
|
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
|
| 3612 |
|
|
/* ------------------------------------------------------------------ */
|
| 3613 |
|
|
/* If DECCHECK is enabled the string "?" is returned if a number is */
|
| 3614 |
|
|
/* invalid. */
|
| 3615 |
|
|
static void decToString(const decNumber *dn, char *string, Flag eng) {
|
| 3616 |
|
|
Int exp=dn->exponent; /* local copy */
|
| 3617 |
|
|
Int e; /* E-part value */
|
| 3618 |
|
|
Int pre; /* digits before the '.' */
|
| 3619 |
|
|
Int cut; /* for counting digits in a Unit */
|
| 3620 |
|
|
char *c=string; /* work [output pointer] */
|
| 3621 |
|
|
const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
|
| 3622 |
|
|
uInt u, pow; /* work */
|
| 3623 |
|
|
|
| 3624 |
|
|
#if DECCHECK
|
| 3625 |
|
|
if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
|
| 3626 |
|
|
strcpy(string, "?");
|
| 3627 |
|
|
return;}
|
| 3628 |
|
|
#endif
|
| 3629 |
|
|
|
| 3630 |
|
|
if (decNumberIsNegative(dn)) { /* Negatives get a minus */
|
| 3631 |
|
|
*c='-';
|
| 3632 |
|
|
c++;
|
| 3633 |
|
|
}
|
| 3634 |
|
|
if (dn->bits&DECSPECIAL) { /* Is a special value */
|
| 3635 |
|
|
if (decNumberIsInfinite(dn)) {
|
| 3636 |
|
|
strcpy(c, "Inf");
|
| 3637 |
|
|
strcpy(c+3, "inity");
|
| 3638 |
|
|
return;}
|
| 3639 |
|
|
/* a NaN */
|
| 3640 |
|
|
if (dn->bits&DECSNAN) { /* signalling NaN */
|
| 3641 |
|
|
*c='s';
|
| 3642 |
|
|
c++;
|
| 3643 |
|
|
}
|
| 3644 |
|
|
strcpy(c, "NaN");
|
| 3645 |
|
|
c+=3; /* step past */
|
| 3646 |
|
|
/* if not a clean non-zero coefficient, that's all there is in a */
|
| 3647 |
|
|
/* NaN string */
|
| 3648 |
|
|
if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
|
| 3649 |
|
|
/* [drop through to add integer] */
|
| 3650 |
|
|
}
|
| 3651 |
|
|
|
| 3652 |
|
|
/* calculate how many digits in msu, and hence first cut */
|
| 3653 |
|
|
cut=MSUDIGITS(dn->digits); /* [faster than remainder] */
|
| 3654 |
|
|
cut--; /* power of ten for digit */
|
| 3655 |
|
|
|
| 3656 |
|
|
if (exp==0) { /* simple integer [common fastpath] */
|
| 3657 |
|
|
for (;up>=dn->lsu; up--) { /* each Unit from msu */
|
| 3658 |
|
|
u=*up; /* contains DECDPUN digits to lay out */
|
| 3659 |
|
|
for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
|
| 3660 |
|
|
cut=DECDPUN-1; /* next Unit has all digits */
|
| 3661 |
|
|
}
|
| 3662 |
|
|
*c='\0'; /* terminate the string */
|
| 3663 |
|
|
return;}
|
| 3664 |
|
|
|
| 3665 |
|
|
/* non-0 exponent -- assume plain form */
|
| 3666 |
|
|
pre=dn->digits+exp; /* digits before '.' */
|
| 3667 |
|
|
e=0; /* no E */
|
| 3668 |
|
|
if ((exp>0) || (pre<-5)) { /* need exponential form */
|
| 3669 |
|
|
e=exp+dn->digits-1; /* calculate E value */
|
| 3670 |
|
|
pre=1; /* assume one digit before '.' */
|
| 3671 |
|
|
if (eng && (e!=0)) { /* engineering: may need to adjust */
|
| 3672 |
|
|
Int adj; /* adjustment */
|
| 3673 |
|
|
/* The C remainder operator is undefined for negative numbers, so */
|
| 3674 |
|
|
/* a positive remainder calculation must be used here */
|
| 3675 |
|
|
if (e<0) {
|
| 3676 |
|
|
adj=(-e)%3;
|
| 3677 |
|
|
if (adj!=0) adj=3-adj;
|
| 3678 |
|
|
}
|
| 3679 |
|
|
else { /* e>0 */
|
| 3680 |
|
|
adj=e%3;
|
| 3681 |
|
|
}
|
| 3682 |
|
|
e=e-adj;
|
| 3683 |
|
|
/* if dealing with zero still produce an exponent which is a */
|
| 3684 |
|
|
/* multiple of three, as expected, but there will only be the */
|
| 3685 |
|
|
/* one zero before the E, still. Otherwise note the padding. */
|
| 3686 |
|
|
if (!ISZERO(dn)) pre+=adj;
|
| 3687 |
|
|
else { /* is zero */
|
| 3688 |
|
|
if (adj!=0) { /* 0.00Esnn needed */
|
| 3689 |
|
|
e=e+3;
|
| 3690 |
|
|
pre=-(2-adj);
|
| 3691 |
|
|
}
|
| 3692 |
|
|
} /* zero */
|
| 3693 |
|
|
} /* eng */
|
| 3694 |
|
|
} /* need exponent */
|
| 3695 |
|
|
|
| 3696 |
|
|
/* lay out the digits of the coefficient, adding 0s and . as needed */
|
| 3697 |
|
|
u=*up;
|
| 3698 |
|
|
if (pre>0) { /* xxx.xxx or xx00 (engineering) form */
|
| 3699 |
|
|
Int n=pre;
|
| 3700 |
|
|
for (; pre>0; pre--, c++, cut--) {
|
| 3701 |
|
|
if (cut<0) { /* need new Unit */
|
| 3702 |
|
|
if (up==dn->lsu) break; /* out of input digits (pre>digits) */
|
| 3703 |
|
|
up--;
|
| 3704 |
|
|
cut=DECDPUN-1;
|
| 3705 |
|
|
u=*up;
|
| 3706 |
|
|
}
|
| 3707 |
|
|
TODIGIT(u, cut, c, pow);
|
| 3708 |
|
|
}
|
| 3709 |
|
|
if (n<dn->digits) { /* more to come, after '.' */
|
| 3710 |
|
|
*c='.'; c++;
|
| 3711 |
|
|
for (;; c++, cut--) {
|
| 3712 |
|
|
if (cut<0) { /* need new Unit */
|
| 3713 |
|
|
if (up==dn->lsu) break; /* out of input digits */
|
| 3714 |
|
|
up--;
|
| 3715 |
|
|
cut=DECDPUN-1;
|
| 3716 |
|
|
u=*up;
|
| 3717 |
|
|
}
|
| 3718 |
|
|
TODIGIT(u, cut, c, pow);
|
| 3719 |
|
|
}
|
| 3720 |
|
|
}
|
| 3721 |
|
|
else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
|
| 3722 |
|
|
}
|
| 3723 |
|
|
else { /* 0.xxx or 0.000xxx form */
|
| 3724 |
|
|
*c='0'; c++;
|
| 3725 |
|
|
*c='.'; c++;
|
| 3726 |
|
|
for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */
|
| 3727 |
|
|
for (; ; c++, cut--) {
|
| 3728 |
|
|
if (cut<0) { /* need new Unit */
|
| 3729 |
|
|
if (up==dn->lsu) break; /* out of input digits */
|
| 3730 |
|
|
up--;
|
| 3731 |
|
|
cut=DECDPUN-1;
|
| 3732 |
|
|
u=*up;
|
| 3733 |
|
|
}
|
| 3734 |
|
|
TODIGIT(u, cut, c, pow);
|
| 3735 |
|
|
}
|
| 3736 |
|
|
}
|
| 3737 |
|
|
|
| 3738 |
|
|
/* Finally add the E-part, if needed. It will never be 0, has a
|
| 3739 |
|
|
base maximum and minimum of +999999999 through -999999999, but
|
| 3740 |
|
|
could range down to -1999999998 for anormal numbers */
|
| 3741 |
|
|
if (e!=0) {
|
| 3742 |
|
|
Flag had=0; /* 1=had non-zero */
|
| 3743 |
|
|
*c='E'; c++;
|
| 3744 |
|
|
*c='+'; c++; /* assume positive */
|
| 3745 |
|
|
u=e; /* .. */
|
| 3746 |
|
|
if (e<0) {
|
| 3747 |
|
|
*(c-1)='-'; /* oops, need - */
|
| 3748 |
|
|
u=-e; /* uInt, please */
|
| 3749 |
|
|
}
|
| 3750 |
|
|
/* lay out the exponent [_itoa or equivalent is not ANSI C] */
|
| 3751 |
|
|
for (cut=9; cut>=0; cut--) {
|
| 3752 |
|
|
TODIGIT(u, cut, c, pow);
|
| 3753 |
|
|
if (*c=='0' && !had) continue; /* skip leading zeros */
|
| 3754 |
|
|
had=1; /* had non-0 */
|
| 3755 |
|
|
c++; /* step for next */
|
| 3756 |
|
|
} /* cut */
|
| 3757 |
|
|
}
|
| 3758 |
|
|
*c='\0'; /* terminate the string (all paths) */
|
| 3759 |
|
|
return;
|
| 3760 |
|
|
} /* decToString */
|
| 3761 |
|
|
|
| 3762 |
|
|
/* ------------------------------------------------------------------ */
|
| 3763 |
|
|
/* decAddOp -- add/subtract operation */
|
| 3764 |
|
|
/* */
|
| 3765 |
|
|
/* This computes C = A + B */
|
| 3766 |
|
|
/* */
|
| 3767 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| 3768 |
|
|
/* lhs is A */
|
| 3769 |
|
|
/* rhs is B */
|
| 3770 |
|
|
/* set is the context */
|
| 3771 |
|
|
/* negate is DECNEG if rhs should be negated, or 0 otherwise */
|
| 3772 |
|
|
/* status accumulates status for the caller */
|
| 3773 |
|
|
/* */
|
| 3774 |
|
|
/* C must have space for set->digits digits. */
|
| 3775 |
|
|
/* Inexact in status must be 0 for correct Exact zero sign in result */
|
| 3776 |
|
|
/* ------------------------------------------------------------------ */
|
| 3777 |
|
|
/* If possible, the coefficient is calculated directly into C. */
|
| 3778 |
|
|
/* However, if: */
|
| 3779 |
|
|
/* -- a digits+1 calculation is needed because the numbers are */
|
| 3780 |
|
|
/* unaligned and span more than set->digits digits */
|
| 3781 |
|
|
/* -- a carry to digits+1 digits looks possible */
|
| 3782 |
|
|
/* -- C is the same as A or B, and the result would destructively */
|
| 3783 |
|
|
/* overlap the A or B coefficient */
|
| 3784 |
|
|
/* then the result must be calculated into a temporary buffer. In */
|
| 3785 |
|
|
/* this case a local (stack) buffer is used if possible, and only if */
|
| 3786 |
|
|
/* too long for that does malloc become the final resort. */
|
| 3787 |
|
|
/* */
|
| 3788 |
|
|
/* Misalignment is handled as follows: */
|
| 3789 |
|
|
/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
|
| 3790 |
|
|
/* BPad: Apply the padding by a combination of shifting (whole */
|
| 3791 |
|
|
/* units) and multiplication (part units). */
|
| 3792 |
|
|
/* */
|
| 3793 |
|
|
/* Addition, especially x=x+1, is speed-critical. */
|
| 3794 |
|
|
/* The static buffer is larger than might be expected to allow for */
|
| 3795 |
|
|
/* calls from higher-level funtions (notable exp). */
|
| 3796 |
|
|
/* ------------------------------------------------------------------ */
|
| 3797 |
|
|
static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
|
| 3798 |
|
|
const decNumber *rhs, decContext *set,
|
| 3799 |
|
|
uByte negate, uInt *status) {
|
| 3800 |
|
|
#if DECSUBSET
|
| 3801 |
|
|
decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| 3802 |
|
|
decNumber *allocrhs=NULL; /* .., rhs */
|
| 3803 |
|
|
#endif
|
| 3804 |
|
|
Int rhsshift; /* working shift (in Units) */
|
| 3805 |
|
|
Int maxdigits; /* longest logical length */
|
| 3806 |
|
|
Int mult; /* multiplier */
|
| 3807 |
|
|
Int residue; /* rounding accumulator */
|
| 3808 |
|
|
uByte bits; /* result bits */
|
| 3809 |
|
|
Flag diffsign; /* non-0 if arguments have different sign */
|
| 3810 |
|
|
Unit *acc; /* accumulator for result */
|
| 3811 |
|
|
Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
|
| 3812 |
|
|
/* allocations when called from */
|
| 3813 |
|
|
/* other operations, notable exp] */
|
| 3814 |
|
|
Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
|
| 3815 |
|
|
Int reqdigits=set->digits; /* local copy; requested DIGITS */
|
| 3816 |
|
|
Int padding; /* work */
|
| 3817 |
|
|
|
| 3818 |
|
|
#if DECCHECK
|
| 3819 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 3820 |
|
|
#endif
|
| 3821 |
|
|
|
| 3822 |
|
|
do { /* protect allocated storage */
|
| 3823 |
|
|
#if DECSUBSET
|
| 3824 |
|
|
if (!set->extended) {
|
| 3825 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 3826 |
|
|
if (lhs->digits>reqdigits) {
|
| 3827 |
|
|
alloclhs=decRoundOperand(lhs, set, status);
|
| 3828 |
|
|
if (alloclhs==NULL) break;
|
| 3829 |
|
|
lhs=alloclhs;
|
| 3830 |
|
|
}
|
| 3831 |
|
|
if (rhs->digits>reqdigits) {
|
| 3832 |
|
|
allocrhs=decRoundOperand(rhs, set, status);
|
| 3833 |
|
|
if (allocrhs==NULL) break;
|
| 3834 |
|
|
rhs=allocrhs;
|
| 3835 |
|
|
}
|
| 3836 |
|
|
}
|
| 3837 |
|
|
#endif
|
| 3838 |
|
|
/* [following code does not require input rounding] */
|
| 3839 |
|
|
|
| 3840 |
|
|
/* note whether signs differ [used all paths] */
|
| 3841 |
|
|
diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
|
| 3842 |
|
|
|
| 3843 |
|
|
/* handle infinities and NaNs */
|
| 3844 |
|
|
if (SPECIALARGS) { /* a special bit set */
|
| 3845 |
|
|
if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */
|
| 3846 |
|
|
decNaNs(res, lhs, rhs, set, status);
|
| 3847 |
|
|
else { /* one or two infinities */
|
| 3848 |
|
|
if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
|
| 3849 |
|
|
/* two infinities with different signs is invalid */
|
| 3850 |
|
|
if (decNumberIsInfinite(rhs) && diffsign) {
|
| 3851 |
|
|
*status|=DEC_Invalid_operation;
|
| 3852 |
|
|
break;
|
| 3853 |
|
|
}
|
| 3854 |
|
|
bits=lhs->bits & DECNEG; /* get sign from LHS */
|
| 3855 |
|
|
}
|
| 3856 |
|
|
else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
|
| 3857 |
|
|
bits|=DECINF;
|
| 3858 |
|
|
decNumberZero(res);
|
| 3859 |
|
|
res->bits=bits; /* set +/- infinity */
|
| 3860 |
|
|
} /* an infinity */
|
| 3861 |
|
|
break;
|
| 3862 |
|
|
}
|
| 3863 |
|
|
|
| 3864 |
|
|
/* Quick exit for add 0s; return the non-0, modified as need be */
|
| 3865 |
|
|
if (ISZERO(lhs)) {
|
| 3866 |
|
|
Int adjust; /* work */
|
| 3867 |
|
|
Int lexp=lhs->exponent; /* save in case LHS==RES */
|
| 3868 |
|
|
bits=lhs->bits; /* .. */
|
| 3869 |
|
|
residue=0; /* clear accumulator */
|
| 3870 |
|
|
decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
|
| 3871 |
|
|
res->bits^=negate; /* flip if rhs was negated */
|
| 3872 |
|
|
#if DECSUBSET
|
| 3873 |
|
|
if (set->extended) { /* exponents on zeros count */
|
| 3874 |
|
|
#endif
|
| 3875 |
|
|
/* exponent will be the lower of the two */
|
| 3876 |
|
|
adjust=lexp-res->exponent; /* adjustment needed [if -ve] */
|
| 3877 |
|
|
if (ISZERO(res)) { /* both 0: special IEEE 754 rules */
|
| 3878 |
|
|
if (adjust<0) res->exponent=lexp; /* set exponent */
|
| 3879 |
|
|
/* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
|
| 3880 |
|
|
if (diffsign) {
|
| 3881 |
|
|
if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
|
| 3882 |
|
|
else res->bits=DECNEG; /* preserve 0 sign */
|
| 3883 |
|
|
}
|
| 3884 |
|
|
}
|
| 3885 |
|
|
else { /* non-0 res */
|
| 3886 |
|
|
if (adjust<0) { /* 0-padding needed */
|
| 3887 |
|
|
if ((res->digits-adjust)>set->digits) {
|
| 3888 |
|
|
adjust=res->digits-set->digits; /* to fit exactly */
|
| 3889 |
|
|
*status|=DEC_Rounded; /* [but exact] */
|
| 3890 |
|
|
}
|
| 3891 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| 3892 |
|
|
res->exponent+=adjust; /* set the exponent. */
|
| 3893 |
|
|
}
|
| 3894 |
|
|
} /* non-0 res */
|
| 3895 |
|
|
#if DECSUBSET
|
| 3896 |
|
|
} /* extended */
|
| 3897 |
|
|
#endif
|
| 3898 |
|
|
decFinish(res, set, &residue, status); /* clean and finalize */
|
| 3899 |
|
|
break;}
|
| 3900 |
|
|
|
| 3901 |
|
|
if (ISZERO(rhs)) { /* [lhs is non-zero] */
|
| 3902 |
|
|
Int adjust; /* work */
|
| 3903 |
|
|
Int rexp=rhs->exponent; /* save in case RHS==RES */
|
| 3904 |
|
|
bits=rhs->bits; /* be clean */
|
| 3905 |
|
|
residue=0; /* clear accumulator */
|
| 3906 |
|
|
decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
|
| 3907 |
|
|
#if DECSUBSET
|
| 3908 |
|
|
if (set->extended) { /* exponents on zeros count */
|
| 3909 |
|
|
#endif
|
| 3910 |
|
|
/* exponent will be the lower of the two */
|
| 3911 |
|
|
/* [0-0 case handled above] */
|
| 3912 |
|
|
adjust=rexp-res->exponent; /* adjustment needed [if -ve] */
|
| 3913 |
|
|
if (adjust<0) { /* 0-padding needed */
|
| 3914 |
|
|
if ((res->digits-adjust)>set->digits) {
|
| 3915 |
|
|
adjust=res->digits-set->digits; /* to fit exactly */
|
| 3916 |
|
|
*status|=DEC_Rounded; /* [but exact] */
|
| 3917 |
|
|
}
|
| 3918 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| 3919 |
|
|
res->exponent+=adjust; /* set the exponent. */
|
| 3920 |
|
|
}
|
| 3921 |
|
|
#if DECSUBSET
|
| 3922 |
|
|
} /* extended */
|
| 3923 |
|
|
#endif
|
| 3924 |
|
|
decFinish(res, set, &residue, status); /* clean and finalize */
|
| 3925 |
|
|
break;}
|
| 3926 |
|
|
|
| 3927 |
|
|
/* [NB: both fastpath and mainpath code below assume these cases */
|
| 3928 |
|
|
/* (notably 0-0) have already been handled] */
|
| 3929 |
|
|
|
| 3930 |
|
|
/* calculate the padding needed to align the operands */
|
| 3931 |
|
|
padding=rhs->exponent-lhs->exponent;
|
| 3932 |
|
|
|
| 3933 |
|
|
/* Fastpath cases where the numbers are aligned and normal, the RHS */
|
| 3934 |
|
|
/* is all in one unit, no operand rounding is needed, and no carry, */
|
| 3935 |
|
|
/* lengthening, or borrow is needed */
|
| 3936 |
|
|
if (padding==0
|
| 3937 |
|
|
&& rhs->digits<=DECDPUN
|
| 3938 |
|
|
&& rhs->exponent>=set->emin /* [some normals drop through] */
|
| 3939 |
|
|
&& rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
|
| 3940 |
|
|
&& rhs->digits<=reqdigits
|
| 3941 |
|
|
&& lhs->digits<=reqdigits) {
|
| 3942 |
|
|
Int partial=*lhs->lsu;
|
| 3943 |
|
|
if (!diffsign) { /* adding */
|
| 3944 |
|
|
partial+=*rhs->lsu;
|
| 3945 |
|
|
if ((partial<=DECDPUNMAX) /* result fits in unit */
|
| 3946 |
|
|
&& (lhs->digits>=DECDPUN || /* .. and no digits-count change */
|
| 3947 |
|
|
partial<(Int)powers[lhs->digits])) { /* .. */
|
| 3948 |
|
|
if (res!=lhs) decNumberCopy(res, lhs); /* not in place */
|
| 3949 |
|
|
*res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */
|
| 3950 |
|
|
break;
|
| 3951 |
|
|
}
|
| 3952 |
|
|
/* else drop out for careful add */
|
| 3953 |
|
|
}
|
| 3954 |
|
|
else { /* signs differ */
|
| 3955 |
|
|
partial-=*rhs->lsu;
|
| 3956 |
|
|
if (partial>0) { /* no borrow needed, and non-0 result */
|
| 3957 |
|
|
if (res!=lhs) decNumberCopy(res, lhs); /* not in place */
|
| 3958 |
|
|
*res->lsu=(Unit)partial;
|
| 3959 |
|
|
/* this could have reduced digits [but result>0] */
|
| 3960 |
|
|
res->digits=decGetDigits(res->lsu, D2U(res->digits));
|
| 3961 |
|
|
break;
|
| 3962 |
|
|
}
|
| 3963 |
|
|
/* else drop out for careful subtract */
|
| 3964 |
|
|
}
|
| 3965 |
|
|
}
|
| 3966 |
|
|
|
| 3967 |
|
|
/* Now align (pad) the lhs or rhs so they can be added or */
|
| 3968 |
|
|
/* subtracted, as necessary. If one number is much larger than */
|
| 3969 |
|
|
/* the other (that is, if in plain form there is a least one */
|
| 3970 |
|
|
/* digit between the lowest digit of one and the highest of the */
|
| 3971 |
|
|
/* other) padding with up to DIGITS-1 trailing zeros may be */
|
| 3972 |
|
|
/* needed; then apply rounding (as exotic rounding modes may be */
|
| 3973 |
|
|
/* affected by the residue). */
|
| 3974 |
|
|
rhsshift=0; /* rhs shift to left (padding) in Units */
|
| 3975 |
|
|
bits=lhs->bits; /* assume sign is that of LHS */
|
| 3976 |
|
|
mult=1; /* likely multiplier */
|
| 3977 |
|
|
|
| 3978 |
|
|
/* [if padding==0 the operands are aligned; no padding is needed] */
|
| 3979 |
|
|
if (padding!=0) {
|
| 3980 |
|
|
/* some padding needed; always pad the RHS, as any required */
|
| 3981 |
|
|
/* padding can then be effected by a simple combination of */
|
| 3982 |
|
|
/* shifts and a multiply */
|
| 3983 |
|
|
Flag swapped=0;
|
| 3984 |
|
|
if (padding<0) { /* LHS needs the padding */
|
| 3985 |
|
|
const decNumber *t;
|
| 3986 |
|
|
padding=-padding; /* will be +ve */
|
| 3987 |
|
|
bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
|
| 3988 |
|
|
t=lhs; lhs=rhs; rhs=t;
|
| 3989 |
|
|
swapped=1;
|
| 3990 |
|
|
}
|
| 3991 |
|
|
|
| 3992 |
|
|
/* If, after pad, rhs would be longer than lhs by digits+1 or */
|
| 3993 |
|
|
/* more then lhs cannot affect the answer, except as a residue, */
|
| 3994 |
|
|
/* so only need to pad up to a length of DIGITS+1. */
|
| 3995 |
|
|
if (rhs->digits+padding > lhs->digits+reqdigits+1) {
|
| 3996 |
|
|
/* The RHS is sufficient */
|
| 3997 |
|
|
/* for residue use the relative sign indication... */
|
| 3998 |
|
|
Int shift=reqdigits-rhs->digits; /* left shift needed */
|
| 3999 |
|
|
residue=1; /* residue for rounding */
|
| 4000 |
|
|
if (diffsign) residue=-residue; /* signs differ */
|
| 4001 |
|
|
/* copy, shortening if necessary */
|
| 4002 |
|
|
decCopyFit(res, rhs, set, &residue, status);
|
| 4003 |
|
|
/* if it was already shorter, then need to pad with zeros */
|
| 4004 |
|
|
if (shift>0) {
|
| 4005 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, shift);
|
| 4006 |
|
|
res->exponent-=shift; /* adjust the exponent. */
|
| 4007 |
|
|
}
|
| 4008 |
|
|
/* flip the result sign if unswapped and rhs was negated */
|
| 4009 |
|
|
if (!swapped) res->bits^=negate;
|
| 4010 |
|
|
decFinish(res, set, &residue, status); /* done */
|
| 4011 |
|
|
break;}
|
| 4012 |
|
|
|
| 4013 |
|
|
/* LHS digits may affect result */
|
| 4014 |
|
|
rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */
|
| 4015 |
|
|
mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
|
| 4016 |
|
|
} /* padding needed */
|
| 4017 |
|
|
|
| 4018 |
|
|
if (diffsign) mult=-mult; /* signs differ */
|
| 4019 |
|
|
|
| 4020 |
|
|
/* determine the longer operand */
|
| 4021 |
|
|
maxdigits=rhs->digits+padding; /* virtual length of RHS */
|
| 4022 |
|
|
if (lhs->digits>maxdigits) maxdigits=lhs->digits;
|
| 4023 |
|
|
|
| 4024 |
|
|
/* Decide on the result buffer to use; if possible place directly */
|
| 4025 |
|
|
/* into result. */
|
| 4026 |
|
|
acc=res->lsu; /* assume add direct to result */
|
| 4027 |
|
|
/* If destructive overlap, or the number is too long, or a carry or */
|
| 4028 |
|
|
/* borrow to DIGITS+1 might be possible, a buffer must be used. */
|
| 4029 |
|
|
/* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
|
| 4030 |
|
|
if ((maxdigits>=reqdigits) /* is, or could be, too large */
|
| 4031 |
|
|
|| (res==rhs && rhsshift>0)) { /* destructive overlap */
|
| 4032 |
|
|
/* buffer needed, choose it; units for maxdigits digits will be */
|
| 4033 |
|
|
/* needed, +1 Unit for carry or borrow */
|
| 4034 |
|
|
Int need=D2U(maxdigits)+1;
|
| 4035 |
|
|
acc=accbuff; /* assume use local buffer */
|
| 4036 |
|
|
if (need*sizeof(Unit)>sizeof(accbuff)) {
|
| 4037 |
|
|
/* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
|
| 4038 |
|
|
allocacc=(Unit *)malloc(need*sizeof(Unit));
|
| 4039 |
|
|
if (allocacc==NULL) { /* hopeless -- abandon */
|
| 4040 |
|
|
*status|=DEC_Insufficient_storage;
|
| 4041 |
|
|
break;}
|
| 4042 |
|
|
acc=allocacc;
|
| 4043 |
|
|
}
|
| 4044 |
|
|
}
|
| 4045 |
|
|
|
| 4046 |
|
|
res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */
|
| 4047 |
|
|
res->exponent=lhs->exponent; /* .. operands (even if aliased) */
|
| 4048 |
|
|
|
| 4049 |
|
|
#if DECTRACE
|
| 4050 |
|
|
decDumpAr('A', lhs->lsu, D2U(lhs->digits));
|
| 4051 |
|
|
decDumpAr('B', rhs->lsu, D2U(rhs->digits));
|
| 4052 |
|
|
printf(" :h: %ld %ld\n", rhsshift, mult);
|
| 4053 |
|
|
#endif
|
| 4054 |
|
|
|
| 4055 |
|
|
/* add [A+B*m] or subtract [A+B*(-m)] */
|
| 4056 |
|
|
res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
|
| 4057 |
|
|
rhs->lsu, D2U(rhs->digits),
|
| 4058 |
|
|
rhsshift, acc, mult)
|
| 4059 |
|
|
*DECDPUN; /* [units -> digits] */
|
| 4060 |
|
|
if (res->digits<0) { /* borrowed... */
|
| 4061 |
|
|
res->digits=-res->digits;
|
| 4062 |
|
|
res->bits^=DECNEG; /* flip the sign */
|
| 4063 |
|
|
}
|
| 4064 |
|
|
#if DECTRACE
|
| 4065 |
|
|
decDumpAr('+', acc, D2U(res->digits));
|
| 4066 |
|
|
#endif
|
| 4067 |
|
|
|
| 4068 |
|
|
/* If a buffer was used the result must be copied back, possibly */
|
| 4069 |
|
|
/* shortening. (If no buffer was used then the result must have */
|
| 4070 |
|
|
/* fit, so can't need rounding and residue must be 0.) */
|
| 4071 |
|
|
residue=0; /* clear accumulator */
|
| 4072 |
|
|
if (acc!=res->lsu) {
|
| 4073 |
|
|
#if DECSUBSET
|
| 4074 |
|
|
if (set->extended) { /* round from first significant digit */
|
| 4075 |
|
|
#endif
|
| 4076 |
|
|
/* remove leading zeros that were added due to rounding up to */
|
| 4077 |
|
|
/* integral Units -- before the test for rounding. */
|
| 4078 |
|
|
if (res->digits>reqdigits)
|
| 4079 |
|
|
res->digits=decGetDigits(acc, D2U(res->digits));
|
| 4080 |
|
|
decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| 4081 |
|
|
#if DECSUBSET
|
| 4082 |
|
|
}
|
| 4083 |
|
|
else { /* subset arithmetic rounds from original significant digit */
|
| 4084 |
|
|
/* May have an underestimate. This only occurs when both */
|
| 4085 |
|
|
/* numbers fit in DECDPUN digits and are padding with a */
|
| 4086 |
|
|
/* negative multiple (-10, -100...) and the top digit(s) become */
|
| 4087 |
|
|
/* 0. (This only matters when using X3.274 rules where the */
|
| 4088 |
|
|
/* leading zero could be included in the rounding.) */
|
| 4089 |
|
|
if (res->digits<maxdigits) {
|
| 4090 |
|
|
*(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
|
| 4091 |
|
|
res->digits=maxdigits;
|
| 4092 |
|
|
}
|
| 4093 |
|
|
else {
|
| 4094 |
|
|
/* remove leading zeros that added due to rounding up to */
|
| 4095 |
|
|
/* integral Units (but only those in excess of the original */
|
| 4096 |
|
|
/* maxdigits length, unless extended) before test for rounding. */
|
| 4097 |
|
|
if (res->digits>reqdigits) {
|
| 4098 |
|
|
res->digits=decGetDigits(acc, D2U(res->digits));
|
| 4099 |
|
|
if (res->digits<maxdigits) res->digits=maxdigits;
|
| 4100 |
|
|
}
|
| 4101 |
|
|
}
|
| 4102 |
|
|
decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| 4103 |
|
|
/* Now apply rounding if needed before removing leading zeros. */
|
| 4104 |
|
|
/* This is safe because subnormals are not a possibility */
|
| 4105 |
|
|
if (residue!=0) {
|
| 4106 |
|
|
decApplyRound(res, set, residue, status);
|
| 4107 |
|
|
residue=0; /* did what needed to be done */
|
| 4108 |
|
|
}
|
| 4109 |
|
|
} /* subset */
|
| 4110 |
|
|
#endif
|
| 4111 |
|
|
} /* used buffer */
|
| 4112 |
|
|
|
| 4113 |
|
|
/* strip leading zeros [these were left on in case of subset subtract] */
|
| 4114 |
|
|
res->digits=decGetDigits(res->lsu, D2U(res->digits));
|
| 4115 |
|
|
|
| 4116 |
|
|
/* apply checks and rounding */
|
| 4117 |
|
|
decFinish(res, set, &residue, status);
|
| 4118 |
|
|
|
| 4119 |
|
|
/* "When the sum of two operands with opposite signs is exactly */
|
| 4120 |
|
|
/* zero, the sign of that sum shall be '+' in all rounding modes */
|
| 4121 |
|
|
/* except round toward -Infinity, in which mode that sign shall be */
|
| 4122 |
|
|
/* '-'." [Subset zeros also never have '-', set by decFinish.] */
|
| 4123 |
|
|
if (ISZERO(res) && diffsign
|
| 4124 |
|
|
#if DECSUBSET
|
| 4125 |
|
|
&& set->extended
|
| 4126 |
|
|
#endif
|
| 4127 |
|
|
&& (*status&DEC_Inexact)==0) {
|
| 4128 |
|
|
if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */
|
| 4129 |
|
|
else res->bits&=~DECNEG; /* sign + */
|
| 4130 |
|
|
}
|
| 4131 |
|
|
} while(0); /* end protected */
|
| 4132 |
|
|
|
| 4133 |
|
|
if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| 4134 |
|
|
#if DECSUBSET
|
| 4135 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| 4136 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 4137 |
|
|
#endif
|
| 4138 |
|
|
return res;
|
| 4139 |
|
|
} /* decAddOp */
|
| 4140 |
|
|
|
| 4141 |
|
|
/* ------------------------------------------------------------------ */
|
| 4142 |
|
|
/* decDivideOp -- division operation */
|
| 4143 |
|
|
/* */
|
| 4144 |
|
|
/* This routine performs the calculations for all four division */
|
| 4145 |
|
|
/* operators (divide, divideInteger, remainder, remainderNear). */
|
| 4146 |
|
|
/* */
|
| 4147 |
|
|
/* C=A op B */
|
| 4148 |
|
|
/* */
|
| 4149 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| 4150 |
|
|
/* lhs is A */
|
| 4151 |
|
|
/* rhs is B */
|
| 4152 |
|
|
/* set is the context */
|
| 4153 |
|
|
/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
|
| 4154 |
|
|
/* status is the usual accumulator */
|
| 4155 |
|
|
/* */
|
| 4156 |
|
|
/* C must have space for set->digits digits. */
|
| 4157 |
|
|
/* */
|
| 4158 |
|
|
/* ------------------------------------------------------------------ */
|
| 4159 |
|
|
/* The underlying algorithm of this routine is the same as in the */
|
| 4160 |
|
|
/* 1981 S/370 implementation, that is, non-restoring long division */
|
| 4161 |
|
|
/* with bi-unit (rather than bi-digit) estimation for each unit */
|
| 4162 |
|
|
/* multiplier. In this pseudocode overview, complications for the */
|
| 4163 |
|
|
/* Remainder operators and division residues for exact rounding are */
|
| 4164 |
|
|
/* omitted for clarity. */
|
| 4165 |
|
|
/* */
|
| 4166 |
|
|
/* Prepare operands and handle special values */
|
| 4167 |
|
|
/* Test for x/0 and then 0/x */
|
| 4168 |
|
|
/* Exp =Exp1 - Exp2 */
|
| 4169 |
|
|
/* Exp =Exp +len(var1) -len(var2) */
|
| 4170 |
|
|
/* Sign=Sign1 * Sign2 */
|
| 4171 |
|
|
/* Pad accumulator (Var1) to double-length with 0's (pad1) */
|
| 4172 |
|
|
/* Pad Var2 to same length as Var1 */
|
| 4173 |
|
|
/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
|
| 4174 |
|
|
/* have=0 */
|
| 4175 |
|
|
/* Do until (have=digits+1 OR residue=0) */
|
| 4176 |
|
|
/* if exp<0 then if integer divide/residue then leave */
|
| 4177 |
|
|
/* this_unit=0 */
|
| 4178 |
|
|
/* Do forever */
|
| 4179 |
|
|
/* compare numbers */
|
| 4180 |
|
|
/* if <0 then leave inner_loop */
|
| 4181 |
|
|
/* if =0 then (* quick exit without subtract *) do */
|
| 4182 |
|
|
/* this_unit=this_unit+1; output this_unit */
|
| 4183 |
|
|
/* leave outer_loop; end */
|
| 4184 |
|
|
/* Compare lengths of numbers (mantissae): */
|
| 4185 |
|
|
/* If same then tops2=msu2pair -- {units 1&2 of var2} */
|
| 4186 |
|
|
/* else tops2=msu2plus -- {0, unit 1 of var2} */
|
| 4187 |
|
|
/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
|
| 4188 |
|
|
/* mult=tops1/tops2 -- Good and safe guess at divisor */
|
| 4189 |
|
|
/* if mult=0 then mult=1 */
|
| 4190 |
|
|
/* this_unit=this_unit+mult */
|
| 4191 |
|
|
/* subtract */
|
| 4192 |
|
|
/* end inner_loop */
|
| 4193 |
|
|
/* if have\=0 | this_unit\=0 then do */
|
| 4194 |
|
|
/* output this_unit */
|
| 4195 |
|
|
/* have=have+1; end */
|
| 4196 |
|
|
/* var2=var2/10 */
|
| 4197 |
|
|
/* exp=exp-1 */
|
| 4198 |
|
|
/* end outer_loop */
|
| 4199 |
|
|
/* exp=exp+1 -- set the proper exponent */
|
| 4200 |
|
|
/* if have=0 then generate answer=0 */
|
| 4201 |
|
|
/* Return (Result is defined by Var1) */
|
| 4202 |
|
|
/* */
|
| 4203 |
|
|
/* ------------------------------------------------------------------ */
|
| 4204 |
|
|
/* Two working buffers are needed during the division; one (digits+ */
|
| 4205 |
|
|
/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
|
| 4206 |
|
|
/* long subtractions. These are acc and var1 respectively. */
|
| 4207 |
|
|
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
|
| 4208 |
|
|
/* The static buffers may be larger than might be expected to allow */
|
| 4209 |
|
|
/* for calls from higher-level funtions (notable exp). */
|
| 4210 |
|
|
/* ------------------------------------------------------------------ */
|
| 4211 |
|
|
static decNumber * decDivideOp(decNumber *res,
|
| 4212 |
|
|
const decNumber *lhs, const decNumber *rhs,
|
| 4213 |
|
|
decContext *set, Flag op, uInt *status) {
|
| 4214 |
|
|
#if DECSUBSET
|
| 4215 |
|
|
decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| 4216 |
|
|
decNumber *allocrhs=NULL; /* .., rhs */
|
| 4217 |
|
|
#endif
|
| 4218 |
|
|
Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
|
| 4219 |
|
|
Unit *acc=accbuff; /* -> accumulator array for result */
|
| 4220 |
|
|
Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */
|
| 4221 |
|
|
Unit *accnext; /* -> where next digit will go */
|
| 4222 |
|
|
Int acclength; /* length of acc needed [Units] */
|
| 4223 |
|
|
Int accunits; /* count of units accumulated */
|
| 4224 |
|
|
Int accdigits; /* count of digits accumulated */
|
| 4225 |
|
|
|
| 4226 |
|
|
Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */
|
| 4227 |
|
|
Unit *var1=varbuff; /* -> var1 array for long subtraction */
|
| 4228 |
|
|
Unit *varalloc=NULL; /* -> allocated buffer, iff used */
|
| 4229 |
|
|
Unit *msu1; /* -> msu of var1 */
|
| 4230 |
|
|
|
| 4231 |
|
|
const Unit *var2; /* -> var2 array */
|
| 4232 |
|
|
const Unit *msu2; /* -> msu of var2 */
|
| 4233 |
|
|
Int msu2plus; /* msu2 plus one [does not vary] */
|
| 4234 |
|
|
eInt msu2pair; /* msu2 pair plus one [does not vary] */
|
| 4235 |
|
|
|
| 4236 |
|
|
Int var1units, var2units; /* actual lengths */
|
| 4237 |
|
|
Int var2ulen; /* logical length (units) */
|
| 4238 |
|
|
Int var1initpad=0; /* var1 initial padding (digits) */
|
| 4239 |
|
|
Int maxdigits; /* longest LHS or required acc length */
|
| 4240 |
|
|
Int mult; /* multiplier for subtraction */
|
| 4241 |
|
|
Unit thisunit; /* current unit being accumulated */
|
| 4242 |
|
|
Int residue; /* for rounding */
|
| 4243 |
|
|
Int reqdigits=set->digits; /* requested DIGITS */
|
| 4244 |
|
|
Int exponent; /* working exponent */
|
| 4245 |
|
|
Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */
|
| 4246 |
|
|
uByte bits; /* working sign */
|
| 4247 |
|
|
Unit *target; /* work */
|
| 4248 |
|
|
const Unit *source; /* .. */
|
| 4249 |
|
|
uInt const *pow; /* .. */
|
| 4250 |
|
|
Int shift, cut; /* .. */
|
| 4251 |
|
|
#if DECSUBSET
|
| 4252 |
|
|
Int dropped; /* work */
|
| 4253 |
|
|
#endif
|
| 4254 |
|
|
|
| 4255 |
|
|
#if DECCHECK
|
| 4256 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 4257 |
|
|
#endif
|
| 4258 |
|
|
|
| 4259 |
|
|
do { /* protect allocated storage */
|
| 4260 |
|
|
#if DECSUBSET
|
| 4261 |
|
|
if (!set->extended) {
|
| 4262 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 4263 |
|
|
if (lhs->digits>reqdigits) {
|
| 4264 |
|
|
alloclhs=decRoundOperand(lhs, set, status);
|
| 4265 |
|
|
if (alloclhs==NULL) break;
|
| 4266 |
|
|
lhs=alloclhs;
|
| 4267 |
|
|
}
|
| 4268 |
|
|
if (rhs->digits>reqdigits) {
|
| 4269 |
|
|
allocrhs=decRoundOperand(rhs, set, status);
|
| 4270 |
|
|
if (allocrhs==NULL) break;
|
| 4271 |
|
|
rhs=allocrhs;
|
| 4272 |
|
|
}
|
| 4273 |
|
|
}
|
| 4274 |
|
|
#endif
|
| 4275 |
|
|
/* [following code does not require input rounding] */
|
| 4276 |
|
|
|
| 4277 |
|
|
bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */
|
| 4278 |
|
|
|
| 4279 |
|
|
/* handle infinities and NaNs */
|
| 4280 |
|
|
if (SPECIALARGS) { /* a special bit set */
|
| 4281 |
|
|
if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
|
| 4282 |
|
|
decNaNs(res, lhs, rhs, set, status);
|
| 4283 |
|
|
break;
|
| 4284 |
|
|
}
|
| 4285 |
|
|
/* one or two infinities */
|
| 4286 |
|
|
if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */
|
| 4287 |
|
|
if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
|
| 4288 |
|
|
op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
|
| 4289 |
|
|
*status|=DEC_Invalid_operation;
|
| 4290 |
|
|
break;
|
| 4291 |
|
|
}
|
| 4292 |
|
|
/* [Note that infinity/0 raises no exceptions] */
|
| 4293 |
|
|
decNumberZero(res);
|
| 4294 |
|
|
res->bits=bits|DECINF; /* set +/- infinity */
|
| 4295 |
|
|
break;
|
| 4296 |
|
|
}
|
| 4297 |
|
|
else { /* RHS (divisor) is infinite */
|
| 4298 |
|
|
residue=0;
|
| 4299 |
|
|
if (op&(REMAINDER|REMNEAR)) {
|
| 4300 |
|
|
/* result is [finished clone of] lhs */
|
| 4301 |
|
|
decCopyFit(res, lhs, set, &residue, status);
|
| 4302 |
|
|
}
|
| 4303 |
|
|
else { /* a division */
|
| 4304 |
|
|
decNumberZero(res);
|
| 4305 |
|
|
res->bits=bits; /* set +/- zero */
|
| 4306 |
|
|
/* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
|
| 4307 |
|
|
/* is a 0 with infinitely negative exponent, clamped to minimum */
|
| 4308 |
|
|
if (op&DIVIDE) {
|
| 4309 |
|
|
res->exponent=set->emin-set->digits+1;
|
| 4310 |
|
|
*status|=DEC_Clamped;
|
| 4311 |
|
|
}
|
| 4312 |
|
|
}
|
| 4313 |
|
|
decFinish(res, set, &residue, status);
|
| 4314 |
|
|
break;
|
| 4315 |
|
|
}
|
| 4316 |
|
|
}
|
| 4317 |
|
|
|
| 4318 |
|
|
/* handle 0 rhs (x/0) */
|
| 4319 |
|
|
if (ISZERO(rhs)) { /* x/0 is always exceptional */
|
| 4320 |
|
|
if (ISZERO(lhs)) {
|
| 4321 |
|
|
decNumberZero(res); /* [after lhs test] */
|
| 4322 |
|
|
*status|=DEC_Division_undefined;/* 0/0 will become NaN */
|
| 4323 |
|
|
}
|
| 4324 |
|
|
else {
|
| 4325 |
|
|
decNumberZero(res);
|
| 4326 |
|
|
if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
|
| 4327 |
|
|
else {
|
| 4328 |
|
|
*status|=DEC_Division_by_zero; /* x/0 */
|
| 4329 |
|
|
res->bits=bits|DECINF; /* .. is +/- Infinity */
|
| 4330 |
|
|
}
|
| 4331 |
|
|
}
|
| 4332 |
|
|
break;}
|
| 4333 |
|
|
|
| 4334 |
|
|
/* handle 0 lhs (0/x) */
|
| 4335 |
|
|
if (ISZERO(lhs)) { /* 0/x [x!=0] */
|
| 4336 |
|
|
#if DECSUBSET
|
| 4337 |
|
|
if (!set->extended) decNumberZero(res);
|
| 4338 |
|
|
else {
|
| 4339 |
|
|
#endif
|
| 4340 |
|
|
if (op&DIVIDE) {
|
| 4341 |
|
|
residue=0;
|
| 4342 |
|
|
exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
|
| 4343 |
|
|
decNumberCopy(res, lhs); /* [zeros always fit] */
|
| 4344 |
|
|
res->bits=bits; /* sign as computed */
|
| 4345 |
|
|
res->exponent=exponent; /* exponent, too */
|
| 4346 |
|
|
decFinalize(res, set, &residue, status); /* check exponent */
|
| 4347 |
|
|
}
|
| 4348 |
|
|
else if (op&DIVIDEINT) {
|
| 4349 |
|
|
decNumberZero(res); /* integer 0 */
|
| 4350 |
|
|
res->bits=bits; /* sign as computed */
|
| 4351 |
|
|
}
|
| 4352 |
|
|
else { /* a remainder */
|
| 4353 |
|
|
exponent=rhs->exponent; /* [save in case overwrite] */
|
| 4354 |
|
|
decNumberCopy(res, lhs); /* [zeros always fit] */
|
| 4355 |
|
|
if (exponent<res->exponent) res->exponent=exponent; /* use lower */
|
| 4356 |
|
|
}
|
| 4357 |
|
|
#if DECSUBSET
|
| 4358 |
|
|
}
|
| 4359 |
|
|
#endif
|
| 4360 |
|
|
break;}
|
| 4361 |
|
|
|
| 4362 |
|
|
/* Precalculate exponent. This starts off adjusted (and hence fits */
|
| 4363 |
|
|
/* in 31 bits) and becomes the usual unadjusted exponent as the */
|
| 4364 |
|
|
/* division proceeds. The order of evaluation is important, here, */
|
| 4365 |
|
|
/* to avoid wrap. */
|
| 4366 |
|
|
exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
|
| 4367 |
|
|
|
| 4368 |
|
|
/* If the working exponent is -ve, then some quick exits are */
|
| 4369 |
|
|
/* possible because the quotient is known to be <1 */
|
| 4370 |
|
|
/* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
|
| 4371 |
|
|
if (exponent<0 && !(op==DIVIDE)) {
|
| 4372 |
|
|
if (op&DIVIDEINT) {
|
| 4373 |
|
|
decNumberZero(res); /* integer part is 0 */
|
| 4374 |
|
|
#if DECSUBSET
|
| 4375 |
|
|
if (set->extended)
|
| 4376 |
|
|
#endif
|
| 4377 |
|
|
res->bits=bits; /* set +/- zero */
|
| 4378 |
|
|
break;}
|
| 4379 |
|
|
/* fastpath remainders so long as the lhs has the smaller */
|
| 4380 |
|
|
/* (or equal) exponent */
|
| 4381 |
|
|
if (lhs->exponent<=rhs->exponent) {
|
| 4382 |
|
|
if (op&REMAINDER || exponent<-1) {
|
| 4383 |
|
|
/* It is REMAINDER or safe REMNEAR; result is [finished */
|
| 4384 |
|
|
/* clone of] lhs (r = x - 0*y) */
|
| 4385 |
|
|
residue=0;
|
| 4386 |
|
|
decCopyFit(res, lhs, set, &residue, status);
|
| 4387 |
|
|
decFinish(res, set, &residue, status);
|
| 4388 |
|
|
break;
|
| 4389 |
|
|
}
|
| 4390 |
|
|
/* [unsafe REMNEAR drops through] */
|
| 4391 |
|
|
}
|
| 4392 |
|
|
} /* fastpaths */
|
| 4393 |
|
|
|
| 4394 |
|
|
/* Long (slow) division is needed; roll up the sleeves... */
|
| 4395 |
|
|
|
| 4396 |
|
|
/* The accumulator will hold the quotient of the division. */
|
| 4397 |
|
|
/* If it needs to be too long for stack storage, then allocate. */
|
| 4398 |
|
|
acclength=D2U(reqdigits+DECDPUN); /* in Units */
|
| 4399 |
|
|
if (acclength*sizeof(Unit)>sizeof(accbuff)) {
|
| 4400 |
|
|
/* printf("malloc dvacc %ld units\n", acclength); */
|
| 4401 |
|
|
allocacc=(Unit *)malloc(acclength*sizeof(Unit));
|
| 4402 |
|
|
if (allocacc==NULL) { /* hopeless -- abandon */
|
| 4403 |
|
|
*status|=DEC_Insufficient_storage;
|
| 4404 |
|
|
break;}
|
| 4405 |
|
|
acc=allocacc; /* use the allocated space */
|
| 4406 |
|
|
}
|
| 4407 |
|
|
|
| 4408 |
|
|
/* var1 is the padded LHS ready for subtractions. */
|
| 4409 |
|
|
/* If it needs to be too long for stack storage, then allocate. */
|
| 4410 |
|
|
/* The maximum units needed for var1 (long subtraction) is: */
|
| 4411 |
|
|
/* Enough for */
|
| 4412 |
|
|
/* (rhs->digits+reqdigits-1) -- to allow full slide to right */
|
| 4413 |
|
|
/* or (lhs->digits) -- to allow for long lhs */
|
| 4414 |
|
|
/* whichever is larger */
|
| 4415 |
|
|
/* +1 -- for rounding of slide to right */
|
| 4416 |
|
|
/* +1 -- for leading 0s */
|
| 4417 |
|
|
/* +1 -- for pre-adjust if a remainder or DIVIDEINT */
|
| 4418 |
|
|
/* [Note: unused units do not participate in decUnitAddSub data] */
|
| 4419 |
|
|
maxdigits=rhs->digits+reqdigits-1;
|
| 4420 |
|
|
if (lhs->digits>maxdigits) maxdigits=lhs->digits;
|
| 4421 |
|
|
var1units=D2U(maxdigits)+2;
|
| 4422 |
|
|
/* allocate a guard unit above msu1 for REMAINDERNEAR */
|
| 4423 |
|
|
if (!(op&DIVIDE)) var1units++;
|
| 4424 |
|
|
if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
|
| 4425 |
|
|
/* printf("malloc dvvar %ld units\n", var1units+1); */
|
| 4426 |
|
|
varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
|
| 4427 |
|
|
if (varalloc==NULL) { /* hopeless -- abandon */
|
| 4428 |
|
|
*status|=DEC_Insufficient_storage;
|
| 4429 |
|
|
break;}
|
| 4430 |
|
|
var1=varalloc; /* use the allocated space */
|
| 4431 |
|
|
}
|
| 4432 |
|
|
|
| 4433 |
|
|
/* Extend the lhs and rhs to full long subtraction length. The lhs */
|
| 4434 |
|
|
/* is truly extended into the var1 buffer, with 0 padding, so a */
|
| 4435 |
|
|
/* subtract in place is always possible. The rhs (var2) has */
|
| 4436 |
|
|
/* virtual padding (implemented by decUnitAddSub). */
|
| 4437 |
|
|
/* One guard unit was allocated above msu1 for rem=rem+rem in */
|
| 4438 |
|
|
/* REMAINDERNEAR. */
|
| 4439 |
|
|
msu1=var1+var1units-1; /* msu of var1 */
|
| 4440 |
|
|
source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
|
| 4441 |
|
|
for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
|
| 4442 |
|
|
for (; target>=var1; target--) *target=0;
|
| 4443 |
|
|
|
| 4444 |
|
|
/* rhs (var2) is left-aligned with var1 at the start */
|
| 4445 |
|
|
var2ulen=var1units; /* rhs logical length (units) */
|
| 4446 |
|
|
var2units=D2U(rhs->digits); /* rhs actual length (units) */
|
| 4447 |
|
|
var2=rhs->lsu; /* -> rhs array */
|
| 4448 |
|
|
msu2=var2+var2units-1; /* -> msu of var2 [never changes] */
|
| 4449 |
|
|
/* now set up the variables which will be used for estimating the */
|
| 4450 |
|
|
/* multiplication factor. If these variables are not exact, add */
|
| 4451 |
|
|
/* 1 to make sure that the multiplier is never overestimated. */
|
| 4452 |
|
|
msu2plus=*msu2; /* it's value .. */
|
| 4453 |
|
|
if (var2units>1) msu2plus++; /* .. +1 if any more */
|
| 4454 |
|
|
msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
|
| 4455 |
|
|
if (var2units>1) { /* .. [else treat 2nd as 0] */
|
| 4456 |
|
|
msu2pair+=*(msu2-1); /* .. */
|
| 4457 |
|
|
if (var2units>2) msu2pair++; /* .. +1 if any more */
|
| 4458 |
|
|
}
|
| 4459 |
|
|
|
| 4460 |
|
|
/* The calculation is working in units, which may have leading zeros, */
|
| 4461 |
|
|
/* but the exponent was calculated on the assumption that they are */
|
| 4462 |
|
|
/* both left-aligned. Adjust the exponent to compensate: add the */
|
| 4463 |
|
|
/* number of leading zeros in var1 msu and subtract those in var2 msu. */
|
| 4464 |
|
|
/* [This is actually done by counting the digits and negating, as */
|
| 4465 |
|
|
/* lead1=DECDPUN-digits1, and similarly for lead2.] */
|
| 4466 |
|
|
for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
|
| 4467 |
|
|
for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
|
| 4468 |
|
|
|
| 4469 |
|
|
/* Now, if doing an integer divide or remainder, ensure that */
|
| 4470 |
|
|
/* the result will be Unit-aligned. To do this, shift the var1 */
|
| 4471 |
|
|
/* accumulator towards least if need be. (It's much easier to */
|
| 4472 |
|
|
/* do this now than to reassemble the residue afterwards, if */
|
| 4473 |
|
|
/* doing a remainder.) Also ensure the exponent is not negative. */
|
| 4474 |
|
|
if (!(op&DIVIDE)) {
|
| 4475 |
|
|
Unit *u; /* work */
|
| 4476 |
|
|
/* save the initial 'false' padding of var1, in digits */
|
| 4477 |
|
|
var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
|
| 4478 |
|
|
/* Determine the shift to do. */
|
| 4479 |
|
|
if (exponent<0) cut=-exponent;
|
| 4480 |
|
|
else cut=DECDPUN-exponent%DECDPUN;
|
| 4481 |
|
|
decShiftToLeast(var1, var1units, cut);
|
| 4482 |
|
|
exponent+=cut; /* maintain numerical value */
|
| 4483 |
|
|
var1initpad-=cut; /* .. and reduce padding */
|
| 4484 |
|
|
/* clean any most-significant units which were just emptied */
|
| 4485 |
|
|
for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
|
| 4486 |
|
|
} /* align */
|
| 4487 |
|
|
else { /* is DIVIDE */
|
| 4488 |
|
|
maxexponent=lhs->exponent-rhs->exponent; /* save */
|
| 4489 |
|
|
/* optimization: if the first iteration will just produce 0, */
|
| 4490 |
|
|
/* preadjust to skip it [valid for DIVIDE only] */
|
| 4491 |
|
|
if (*msu1<*msu2) {
|
| 4492 |
|
|
var2ulen--; /* shift down */
|
| 4493 |
|
|
exponent-=DECDPUN; /* update the exponent */
|
| 4494 |
|
|
}
|
| 4495 |
|
|
}
|
| 4496 |
|
|
|
| 4497 |
|
|
/* ---- start the long-division loops ------------------------------ */
|
| 4498 |
|
|
accunits=0; /* no units accumulated yet */
|
| 4499 |
|
|
accdigits=0; /* .. or digits */
|
| 4500 |
|
|
accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */
|
| 4501 |
|
|
for (;;) { /* outer forever loop */
|
| 4502 |
|
|
thisunit=0; /* current unit assumed 0 */
|
| 4503 |
|
|
/* find the next unit */
|
| 4504 |
|
|
for (;;) { /* inner forever loop */
|
| 4505 |
|
|
/* strip leading zero units [from either pre-adjust or from */
|
| 4506 |
|
|
/* subtract last time around]. Leave at least one unit. */
|
| 4507 |
|
|
for (; *msu1==0 && msu1>var1; msu1--) var1units--;
|
| 4508 |
|
|
|
| 4509 |
|
|
if (var1units<var2ulen) break; /* var1 too low for subtract */
|
| 4510 |
|
|
if (var1units==var2ulen) { /* unit-by-unit compare needed */
|
| 4511 |
|
|
/* compare the two numbers, from msu */
|
| 4512 |
|
|
const Unit *pv1, *pv2;
|
| 4513 |
|
|
Unit v2; /* units to compare */
|
| 4514 |
|
|
pv2=msu2; /* -> msu */
|
| 4515 |
|
|
for (pv1=msu1; ; pv1--, pv2--) {
|
| 4516 |
|
|
/* v1=*pv1 -- always OK */
|
| 4517 |
|
|
v2=0; /* assume in padding */
|
| 4518 |
|
|
if (pv2>=var2) v2=*pv2; /* in range */
|
| 4519 |
|
|
if (*pv1!=v2) break; /* no longer the same */
|
| 4520 |
|
|
if (pv1==var1) break; /* done; leave pv1 as is */
|
| 4521 |
|
|
}
|
| 4522 |
|
|
/* here when all inspected or a difference seen */
|
| 4523 |
|
|
if (*pv1<v2) break; /* var1 too low to subtract */
|
| 4524 |
|
|
if (*pv1==v2) { /* var1 == var2 */
|
| 4525 |
|
|
/* reach here if var1 and var2 are identical; subtraction */
|
| 4526 |
|
|
/* would increase digit by one, and the residue will be 0 so */
|
| 4527 |
|
|
/* the calculation is done; leave the loop with residue=0. */
|
| 4528 |
|
|
thisunit++; /* as though subtracted */
|
| 4529 |
|
|
*var1=0; /* set var1 to 0 */
|
| 4530 |
|
|
var1units=1; /* .. */
|
| 4531 |
|
|
break; /* from inner */
|
| 4532 |
|
|
} /* var1 == var2 */
|
| 4533 |
|
|
/* *pv1>v2. Prepare for real subtraction; the lengths are equal */
|
| 4534 |
|
|
/* Estimate the multiplier (there's always a msu1-1)... */
|
| 4535 |
|
|
/* Bring in two units of var2 to provide a good estimate. */
|
| 4536 |
|
|
mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
|
| 4537 |
|
|
} /* lengths the same */
|
| 4538 |
|
|
else { /* var1units > var2ulen, so subtraction is safe */
|
| 4539 |
|
|
/* The var2 msu is one unit towards the lsu of the var1 msu, */
|
| 4540 |
|
|
/* so only one unit for var2 can be used. */
|
| 4541 |
|
|
mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
|
| 4542 |
|
|
}
|
| 4543 |
|
|
if (mult==0) mult=1; /* must always be at least 1 */
|
| 4544 |
|
|
/* subtraction needed; var1 is > var2 */
|
| 4545 |
|
|
thisunit=(Unit)(thisunit+mult); /* accumulate */
|
| 4546 |
|
|
/* subtract var1-var2, into var1; only the overlap needs */
|
| 4547 |
|
|
/* processing, as this is an in-place calculation */
|
| 4548 |
|
|
shift=var2ulen-var2units;
|
| 4549 |
|
|
#if DECTRACE
|
| 4550 |
|
|
decDumpAr('1', &var1[shift], var1units-shift);
|
| 4551 |
|
|
decDumpAr('2', var2, var2units);
|
| 4552 |
|
|
printf("m=%ld\n", -mult);
|
| 4553 |
|
|
#endif
|
| 4554 |
|
|
decUnitAddSub(&var1[shift], var1units-shift,
|
| 4555 |
|
|
var2, var2units, 0,
|
| 4556 |
|
|
&var1[shift], -mult);
|
| 4557 |
|
|
#if DECTRACE
|
| 4558 |
|
|
decDumpAr('#', &var1[shift], var1units-shift);
|
| 4559 |
|
|
#endif
|
| 4560 |
|
|
/* var1 now probably has leading zeros; these are removed at the */
|
| 4561 |
|
|
/* top of the inner loop. */
|
| 4562 |
|
|
} /* inner loop */
|
| 4563 |
|
|
|
| 4564 |
|
|
/* The next unit has been calculated in full; unless it's a */
|
| 4565 |
|
|
/* leading zero, add to acc */
|
| 4566 |
|
|
if (accunits!=0 || thisunit!=0) { /* is first or non-zero */
|
| 4567 |
|
|
*accnext=thisunit; /* store in accumulator */
|
| 4568 |
|
|
/* account exactly for the new digits */
|
| 4569 |
|
|
if (accunits==0) {
|
| 4570 |
|
|
accdigits++; /* at least one */
|
| 4571 |
|
|
for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
|
| 4572 |
|
|
}
|
| 4573 |
|
|
else accdigits+=DECDPUN;
|
| 4574 |
|
|
accunits++; /* update count */
|
| 4575 |
|
|
accnext--; /* ready for next */
|
| 4576 |
|
|
if (accdigits>reqdigits) break; /* have enough digits */
|
| 4577 |
|
|
}
|
| 4578 |
|
|
|
| 4579 |
|
|
/* if the residue is zero, the operation is done (unless divide */
|
| 4580 |
|
|
/* or divideInteger and still not enough digits yet) */
|
| 4581 |
|
|
if (*var1==0 && var1units==1) { /* residue is 0 */
|
| 4582 |
|
|
if (op&(REMAINDER|REMNEAR)) break;
|
| 4583 |
|
|
if ((op&DIVIDE) && (exponent<=maxexponent)) break;
|
| 4584 |
|
|
/* [drop through if divideInteger] */
|
| 4585 |
|
|
}
|
| 4586 |
|
|
/* also done enough if calculating remainder or integer */
|
| 4587 |
|
|
/* divide and just did the last ('units') unit */
|
| 4588 |
|
|
if (exponent==0 && !(op&DIVIDE)) break;
|
| 4589 |
|
|
|
| 4590 |
|
|
/* to get here, var1 is less than var2, so divide var2 by the per- */
|
| 4591 |
|
|
/* Unit power of ten and go for the next digit */
|
| 4592 |
|
|
var2ulen--; /* shift down */
|
| 4593 |
|
|
exponent-=DECDPUN; /* update the exponent */
|
| 4594 |
|
|
} /* outer loop */
|
| 4595 |
|
|
|
| 4596 |
|
|
/* ---- division is complete --------------------------------------- */
|
| 4597 |
|
|
/* here: acc has at least reqdigits+1 of good results (or fewer */
|
| 4598 |
|
|
/* if early stop), starting at accnext+1 (its lsu) */
|
| 4599 |
|
|
/* var1 has any residue at the stopping point */
|
| 4600 |
|
|
/* accunits is the number of digits collected in acc */
|
| 4601 |
|
|
if (accunits==0) { /* acc is 0 */
|
| 4602 |
|
|
accunits=1; /* show have a unit .. */
|
| 4603 |
|
|
accdigits=1; /* .. */
|
| 4604 |
|
|
*accnext=0; /* .. whose value is 0 */
|
| 4605 |
|
|
}
|
| 4606 |
|
|
else accnext++; /* back to last placed */
|
| 4607 |
|
|
/* accnext now -> lowest unit of result */
|
| 4608 |
|
|
|
| 4609 |
|
|
residue=0; /* assume no residue */
|
| 4610 |
|
|
if (op&DIVIDE) {
|
| 4611 |
|
|
/* record the presence of any residue, for rounding */
|
| 4612 |
|
|
if (*var1!=0 || var1units>1) residue=1;
|
| 4613 |
|
|
else { /* no residue */
|
| 4614 |
|
|
/* Had an exact division; clean up spurious trailing 0s. */
|
| 4615 |
|
|
/* There will be at most DECDPUN-1, from the final multiply, */
|
| 4616 |
|
|
/* and then only if the result is non-0 (and even) and the */
|
| 4617 |
|
|
/* exponent is 'loose'. */
|
| 4618 |
|
|
#if DECDPUN>1
|
| 4619 |
|
|
Unit lsu=*accnext;
|
| 4620 |
|
|
if (!(lsu&0x01) && (lsu!=0)) {
|
| 4621 |
|
|
/* count the trailing zeros */
|
| 4622 |
|
|
Int drop=0;
|
| 4623 |
|
|
for (;; drop++) { /* [will terminate because lsu!=0] */
|
| 4624 |
|
|
if (exponent>=maxexponent) break; /* don't chop real 0s */
|
| 4625 |
|
|
#if DECDPUN<=4
|
| 4626 |
|
|
if ((lsu-QUOT10(lsu, drop+1)
|
| 4627 |
|
|
*powers[drop+1])!=0) break; /* found non-0 digit */
|
| 4628 |
|
|
#else
|
| 4629 |
|
|
if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */
|
| 4630 |
|
|
#endif
|
| 4631 |
|
|
exponent++;
|
| 4632 |
|
|
}
|
| 4633 |
|
|
if (drop>0) {
|
| 4634 |
|
|
accunits=decShiftToLeast(accnext, accunits, drop);
|
| 4635 |
|
|
accdigits=decGetDigits(accnext, accunits);
|
| 4636 |
|
|
accunits=D2U(accdigits);
|
| 4637 |
|
|
/* [exponent was adjusted in the loop] */
|
| 4638 |
|
|
}
|
| 4639 |
|
|
} /* neither odd nor 0 */
|
| 4640 |
|
|
#endif
|
| 4641 |
|
|
} /* exact divide */
|
| 4642 |
|
|
} /* divide */
|
| 4643 |
|
|
else /* op!=DIVIDE */ {
|
| 4644 |
|
|
/* check for coefficient overflow */
|
| 4645 |
|
|
if (accdigits+exponent>reqdigits) {
|
| 4646 |
|
|
*status|=DEC_Division_impossible;
|
| 4647 |
|
|
break;
|
| 4648 |
|
|
}
|
| 4649 |
|
|
if (op & (REMAINDER|REMNEAR)) {
|
| 4650 |
|
|
/* [Here, the exponent will be 0, because var1 was adjusted */
|
| 4651 |
|
|
/* appropriately.] */
|
| 4652 |
|
|
Int postshift; /* work */
|
| 4653 |
|
|
Flag wasodd=0; /* integer was odd */
|
| 4654 |
|
|
Unit *quotlsu; /* for save */
|
| 4655 |
|
|
Int quotdigits; /* .. */
|
| 4656 |
|
|
|
| 4657 |
|
|
bits=lhs->bits; /* remainder sign is always as lhs */
|
| 4658 |
|
|
|
| 4659 |
|
|
/* Fastpath when residue is truly 0 is worthwhile [and */
|
| 4660 |
|
|
/* simplifies the code below] */
|
| 4661 |
|
|
if (*var1==0 && var1units==1) { /* residue is 0 */
|
| 4662 |
|
|
Int exp=lhs->exponent; /* save min(exponents) */
|
| 4663 |
|
|
if (rhs->exponent<exp) exp=rhs->exponent;
|
| 4664 |
|
|
decNumberZero(res); /* 0 coefficient */
|
| 4665 |
|
|
#if DECSUBSET
|
| 4666 |
|
|
if (set->extended)
|
| 4667 |
|
|
#endif
|
| 4668 |
|
|
res->exponent=exp; /* .. with proper exponent */
|
| 4669 |
|
|
res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
|
| 4670 |
|
|
decFinish(res, set, &residue, status); /* might clamp */
|
| 4671 |
|
|
break;
|
| 4672 |
|
|
}
|
| 4673 |
|
|
/* note if the quotient was odd */
|
| 4674 |
|
|
if (*accnext & 0x01) wasodd=1; /* acc is odd */
|
| 4675 |
|
|
quotlsu=accnext; /* save in case need to reinspect */
|
| 4676 |
|
|
quotdigits=accdigits; /* .. */
|
| 4677 |
|
|
|
| 4678 |
|
|
/* treat the residue, in var1, as the value to return, via acc */
|
| 4679 |
|
|
/* calculate the unused zero digits. This is the smaller of: */
|
| 4680 |
|
|
/* var1 initial padding (saved above) */
|
| 4681 |
|
|
/* var2 residual padding, which happens to be given by: */
|
| 4682 |
|
|
postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
|
| 4683 |
|
|
/* [the 'exponent' term accounts for the shifts during divide] */
|
| 4684 |
|
|
if (var1initpad<postshift) postshift=var1initpad;
|
| 4685 |
|
|
|
| 4686 |
|
|
/* shift var1 the requested amount, and adjust its digits */
|
| 4687 |
|
|
var1units=decShiftToLeast(var1, var1units, postshift);
|
| 4688 |
|
|
accnext=var1;
|
| 4689 |
|
|
accdigits=decGetDigits(var1, var1units);
|
| 4690 |
|
|
accunits=D2U(accdigits);
|
| 4691 |
|
|
|
| 4692 |
|
|
exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */
|
| 4693 |
|
|
if (rhs->exponent<exponent) exponent=rhs->exponent;
|
| 4694 |
|
|
|
| 4695 |
|
|
/* Now correct the result if doing remainderNear; if it */
|
| 4696 |
|
|
/* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
|
| 4697 |
|
|
/* the integer was odd then the result should be rem-rhs. */
|
| 4698 |
|
|
if (op&REMNEAR) {
|
| 4699 |
|
|
Int compare, tarunits; /* work */
|
| 4700 |
|
|
Unit *up; /* .. */
|
| 4701 |
|
|
/* calculate remainder*2 into the var1 buffer (which has */
|
| 4702 |
|
|
/* 'headroom' of an extra unit and hence enough space) */
|
| 4703 |
|
|
/* [a dedicated 'double' loop would be faster, here] */
|
| 4704 |
|
|
tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
|
| 4705 |
|
|
0, accnext, 1);
|
| 4706 |
|
|
/* decDumpAr('r', accnext, tarunits); */
|
| 4707 |
|
|
|
| 4708 |
|
|
/* Here, accnext (var1) holds tarunits Units with twice the */
|
| 4709 |
|
|
/* remainder's coefficient, which must now be compared to the */
|
| 4710 |
|
|
/* RHS. The remainder's exponent may be smaller than the RHS's. */
|
| 4711 |
|
|
compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
|
| 4712 |
|
|
rhs->exponent-exponent);
|
| 4713 |
|
|
if (compare==BADINT) { /* deep trouble */
|
| 4714 |
|
|
*status|=DEC_Insufficient_storage;
|
| 4715 |
|
|
break;}
|
| 4716 |
|
|
|
| 4717 |
|
|
/* now restore the remainder by dividing by two; the lsu */
|
| 4718 |
|
|
/* is known to be even. */
|
| 4719 |
|
|
for (up=accnext; up<accnext+tarunits; up++) {
|
| 4720 |
|
|
Int half; /* half to add to lower unit */
|
| 4721 |
|
|
half=*up & 0x01;
|
| 4722 |
|
|
*up/=2; /* [shift] */
|
| 4723 |
|
|
if (!half) continue;
|
| 4724 |
|
|
*(up-1)+=(DECDPUNMAX+1)/2;
|
| 4725 |
|
|
}
|
| 4726 |
|
|
/* [accunits still describes the original remainder length] */
|
| 4727 |
|
|
|
| 4728 |
|
|
if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
|
| 4729 |
|
|
Int exp, expunits, exprem; /* work */
|
| 4730 |
|
|
/* This is effectively causing round-up of the quotient, */
|
| 4731 |
|
|
/* so if it was the rare case where it was full and all */
|
| 4732 |
|
|
/* nines, it would overflow and hence division-impossible */
|
| 4733 |
|
|
/* should be raised */
|
| 4734 |
|
|
Flag allnines=0; /* 1 if quotient all nines */
|
| 4735 |
|
|
if (quotdigits==reqdigits) { /* could be borderline */
|
| 4736 |
|
|
for (up=quotlsu; ; up++) {
|
| 4737 |
|
|
if (quotdigits>DECDPUN) {
|
| 4738 |
|
|
if (*up!=DECDPUNMAX) break;/* non-nines */
|
| 4739 |
|
|
}
|
| 4740 |
|
|
else { /* this is the last Unit */
|
| 4741 |
|
|
if (*up==powers[quotdigits]-1) allnines=1;
|
| 4742 |
|
|
break;
|
| 4743 |
|
|
}
|
| 4744 |
|
|
quotdigits-=DECDPUN; /* checked those digits */
|
| 4745 |
|
|
} /* up */
|
| 4746 |
|
|
} /* borderline check */
|
| 4747 |
|
|
if (allnines) {
|
| 4748 |
|
|
*status|=DEC_Division_impossible;
|
| 4749 |
|
|
break;}
|
| 4750 |
|
|
|
| 4751 |
|
|
/* rem-rhs is needed; the sign will invert. Again, var1 */
|
| 4752 |
|
|
/* can safely be used for the working Units array. */
|
| 4753 |
|
|
exp=rhs->exponent-exponent; /* RHS padding needed */
|
| 4754 |
|
|
/* Calculate units and remainder from exponent. */
|
| 4755 |
|
|
expunits=exp/DECDPUN;
|
| 4756 |
|
|
exprem=exp%DECDPUN;
|
| 4757 |
|
|
/* subtract [A+B*(-m)]; the result will always be negative */
|
| 4758 |
|
|
accunits=-decUnitAddSub(accnext, accunits,
|
| 4759 |
|
|
rhs->lsu, D2U(rhs->digits),
|
| 4760 |
|
|
expunits, accnext, -(Int)powers[exprem]);
|
| 4761 |
|
|
accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
|
| 4762 |
|
|
accunits=D2U(accdigits); /* and recalculate the units for copy */
|
| 4763 |
|
|
/* [exponent is as for original remainder] */
|
| 4764 |
|
|
bits^=DECNEG; /* flip the sign */
|
| 4765 |
|
|
}
|
| 4766 |
|
|
} /* REMNEAR */
|
| 4767 |
|
|
} /* REMAINDER or REMNEAR */
|
| 4768 |
|
|
} /* not DIVIDE */
|
| 4769 |
|
|
|
| 4770 |
|
|
/* Set exponent and bits */
|
| 4771 |
|
|
res->exponent=exponent;
|
| 4772 |
|
|
res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
|
| 4773 |
|
|
|
| 4774 |
|
|
/* Now the coefficient. */
|
| 4775 |
|
|
decSetCoeff(res, set, accnext, accdigits, &residue, status);
|
| 4776 |
|
|
|
| 4777 |
|
|
decFinish(res, set, &residue, status); /* final cleanup */
|
| 4778 |
|
|
|
| 4779 |
|
|
#if DECSUBSET
|
| 4780 |
|
|
/* If a divide then strip trailing zeros if subset [after round] */
|
| 4781 |
|
|
if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
|
| 4782 |
|
|
#endif
|
| 4783 |
|
|
} while(0); /* end protected */
|
| 4784 |
|
|
|
| 4785 |
|
|
if (varalloc!=NULL) free(varalloc); /* drop any storage used */
|
| 4786 |
|
|
if (allocacc!=NULL) free(allocacc); /* .. */
|
| 4787 |
|
|
#if DECSUBSET
|
| 4788 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| 4789 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 4790 |
|
|
#endif
|
| 4791 |
|
|
return res;
|
| 4792 |
|
|
} /* decDivideOp */
|
| 4793 |
|
|
|
| 4794 |
|
|
/* ------------------------------------------------------------------ */
|
| 4795 |
|
|
/* decMultiplyOp -- multiplication operation */
|
| 4796 |
|
|
/* */
|
| 4797 |
|
|
/* This routine performs the multiplication C=A x B. */
|
| 4798 |
|
|
/* */
|
| 4799 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
|
| 4800 |
|
|
/* lhs is A */
|
| 4801 |
|
|
/* rhs is B */
|
| 4802 |
|
|
/* set is the context */
|
| 4803 |
|
|
/* status is the usual accumulator */
|
| 4804 |
|
|
/* */
|
| 4805 |
|
|
/* C must have space for set->digits digits. */
|
| 4806 |
|
|
/* */
|
| 4807 |
|
|
/* ------------------------------------------------------------------ */
|
| 4808 |
|
|
/* 'Classic' multiplication is used rather than Karatsuba, as the */
|
| 4809 |
|
|
/* latter would give only a minor improvement for the short numbers */
|
| 4810 |
|
|
/* expected to be handled most (and uses much more memory). */
|
| 4811 |
|
|
/* */
|
| 4812 |
|
|
/* There are two major paths here: the general-purpose ('old code') */
|
| 4813 |
|
|
/* path which handles all DECDPUN values, and a fastpath version */
|
| 4814 |
|
|
/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
|
| 4815 |
|
|
/* than two calls to decUnitAddSub would be made. */
|
| 4816 |
|
|
/* */
|
| 4817 |
|
|
/* The fastpath version lumps units together into 8-digit or 9-digit */
|
| 4818 |
|
|
/* chunks, and also uses a lazy carry strategy to minimise expensive */
|
| 4819 |
|
|
/* 64-bit divisions. The chunks are then broken apart again into */
|
| 4820 |
|
|
/* units for continuing processing. Despite this overhead, the */
|
| 4821 |
|
|
/* fastpath can speed up some 16-digit operations by 10x (and much */
|
| 4822 |
|
|
/* more for higher-precision calculations). */
|
| 4823 |
|
|
/* */
|
| 4824 |
|
|
/* A buffer always has to be used for the accumulator; in the */
|
| 4825 |
|
|
/* fastpath, buffers are also always needed for the chunked copies of */
|
| 4826 |
|
|
/* of the operand coefficients. */
|
| 4827 |
|
|
/* Static buffers are larger than needed just for multiply, to allow */
|
| 4828 |
|
|
/* for calls from other operations (notably exp). */
|
| 4829 |
|
|
/* ------------------------------------------------------------------ */
|
| 4830 |
|
|
#define FASTMUL (DECUSE64 && DECDPUN<5)
|
| 4831 |
|
|
static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
|
| 4832 |
|
|
const decNumber *rhs, decContext *set,
|
| 4833 |
|
|
uInt *status) {
|
| 4834 |
|
|
Int accunits; /* Units of accumulator in use */
|
| 4835 |
|
|
Int exponent; /* work */
|
| 4836 |
|
|
Int residue=0; /* rounding residue */
|
| 4837 |
|
|
uByte bits; /* result sign */
|
| 4838 |
|
|
Unit *acc; /* -> accumulator Unit array */
|
| 4839 |
|
|
Int needbytes; /* size calculator */
|
| 4840 |
|
|
void *allocacc=NULL; /* -> allocated accumulator, iff allocated */
|
| 4841 |
|
|
Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
|
| 4842 |
|
|
/* *4 for calls from other operations) */
|
| 4843 |
|
|
const Unit *mer, *mermsup; /* work */
|
| 4844 |
|
|
Int madlength; /* Units in multiplicand */
|
| 4845 |
|
|
Int shift; /* Units to shift multiplicand by */
|
| 4846 |
|
|
|
| 4847 |
|
|
#if FASTMUL
|
| 4848 |
|
|
/* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
|
| 4849 |
|
|
/* (DECDPUN is 2 or 4) then work in base 10**8 */
|
| 4850 |
|
|
#if DECDPUN & 1 /* odd */
|
| 4851 |
|
|
#define FASTBASE 1000000000 /* base */
|
| 4852 |
|
|
#define FASTDIGS 9 /* digits in base */
|
| 4853 |
|
|
#define FASTLAZY 18 /* carry resolution point [1->18] */
|
| 4854 |
|
|
#else
|
| 4855 |
|
|
#define FASTBASE 100000000
|
| 4856 |
|
|
#define FASTDIGS 8
|
| 4857 |
|
|
#define FASTLAZY 1844 /* carry resolution point [1->1844] */
|
| 4858 |
|
|
#endif
|
| 4859 |
|
|
/* three buffers are used, two for chunked copies of the operands */
|
| 4860 |
|
|
/* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
|
| 4861 |
|
|
/* lazy carry evaluation */
|
| 4862 |
|
|
uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
|
| 4863 |
|
|
uInt *zlhi=zlhibuff; /* -> lhs array */
|
| 4864 |
|
|
uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */
|
| 4865 |
|
|
uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
|
| 4866 |
|
|
uInt *zrhi=zrhibuff; /* -> rhs array */
|
| 4867 |
|
|
uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */
|
| 4868 |
|
|
uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
|
| 4869 |
|
|
/* [allocacc is shared for both paths, as only one will run] */
|
| 4870 |
|
|
uLong *zacc=zaccbuff; /* -> accumulator array for exact result */
|
| 4871 |
|
|
#if DECDPUN==1
|
| 4872 |
|
|
Int zoff; /* accumulator offset */
|
| 4873 |
|
|
#endif
|
| 4874 |
|
|
uInt *lip, *rip; /* item pointers */
|
| 4875 |
|
|
uInt *lmsi, *rmsi; /* most significant items */
|
| 4876 |
|
|
Int ilhs, irhs, iacc; /* item counts in the arrays */
|
| 4877 |
|
|
Int lazy; /* lazy carry counter */
|
| 4878 |
|
|
uLong lcarry; /* uLong carry */
|
| 4879 |
|
|
uInt carry; /* carry (NB not uLong) */
|
| 4880 |
|
|
Int count; /* work */
|
| 4881 |
|
|
const Unit *cup; /* .. */
|
| 4882 |
|
|
Unit *up; /* .. */
|
| 4883 |
|
|
uLong *lp; /* .. */
|
| 4884 |
|
|
Int p; /* .. */
|
| 4885 |
|
|
#endif
|
| 4886 |
|
|
|
| 4887 |
|
|
#if DECSUBSET
|
| 4888 |
|
|
decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */
|
| 4889 |
|
|
decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */
|
| 4890 |
|
|
#endif
|
| 4891 |
|
|
|
| 4892 |
|
|
#if DECCHECK
|
| 4893 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 4894 |
|
|
#endif
|
| 4895 |
|
|
|
| 4896 |
|
|
/* precalculate result sign */
|
| 4897 |
|
|
bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
|
| 4898 |
|
|
|
| 4899 |
|
|
/* handle infinities and NaNs */
|
| 4900 |
|
|
if (SPECIALARGS) { /* a special bit set */
|
| 4901 |
|
|
if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
|
| 4902 |
|
|
decNaNs(res, lhs, rhs, set, status);
|
| 4903 |
|
|
return res;}
|
| 4904 |
|
|
/* one or two infinities; Infinity * 0 is invalid */
|
| 4905 |
|
|
if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
|
| 4906 |
|
|
||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
|
| 4907 |
|
|
*status|=DEC_Invalid_operation;
|
| 4908 |
|
|
return res;}
|
| 4909 |
|
|
decNumberZero(res);
|
| 4910 |
|
|
res->bits=bits|DECINF; /* infinity */
|
| 4911 |
|
|
return res;}
|
| 4912 |
|
|
|
| 4913 |
|
|
/* For best speed, as in DMSRCN [the original Rexx numerics */
|
| 4914 |
|
|
/* module], use the shorter number as the multiplier (rhs) and */
|
| 4915 |
|
|
/* the longer as the multiplicand (lhs) to minimise the number of */
|
| 4916 |
|
|
/* adds (partial products) */
|
| 4917 |
|
|
if (lhs->digits<rhs->digits) { /* swap... */
|
| 4918 |
|
|
const decNumber *hold=lhs;
|
| 4919 |
|
|
lhs=rhs;
|
| 4920 |
|
|
rhs=hold;
|
| 4921 |
|
|
}
|
| 4922 |
|
|
|
| 4923 |
|
|
do { /* protect allocated storage */
|
| 4924 |
|
|
#if DECSUBSET
|
| 4925 |
|
|
if (!set->extended) {
|
| 4926 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 4927 |
|
|
if (lhs->digits>set->digits) {
|
| 4928 |
|
|
alloclhs=decRoundOperand(lhs, set, status);
|
| 4929 |
|
|
if (alloclhs==NULL) break;
|
| 4930 |
|
|
lhs=alloclhs;
|
| 4931 |
|
|
}
|
| 4932 |
|
|
if (rhs->digits>set->digits) {
|
| 4933 |
|
|
allocrhs=decRoundOperand(rhs, set, status);
|
| 4934 |
|
|
if (allocrhs==NULL) break;
|
| 4935 |
|
|
rhs=allocrhs;
|
| 4936 |
|
|
}
|
| 4937 |
|
|
}
|
| 4938 |
|
|
#endif
|
| 4939 |
|
|
/* [following code does not require input rounding] */
|
| 4940 |
|
|
|
| 4941 |
|
|
#if FASTMUL /* fastpath can be used */
|
| 4942 |
|
|
/* use the fast path if there are enough digits in the shorter */
|
| 4943 |
|
|
/* operand to make the setup and takedown worthwhile */
|
| 4944 |
|
|
#define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */
|
| 4945 |
|
|
if (rhs->digits>NEEDTWO) { /* use fastpath... */
|
| 4946 |
|
|
/* calculate the number of elements in each array */
|
| 4947 |
|
|
ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
|
| 4948 |
|
|
irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
|
| 4949 |
|
|
iacc=ilhs+irhs;
|
| 4950 |
|
|
|
| 4951 |
|
|
/* allocate buffers if required, as usual */
|
| 4952 |
|
|
needbytes=ilhs*sizeof(uInt);
|
| 4953 |
|
|
if (needbytes>(Int)sizeof(zlhibuff)) {
|
| 4954 |
|
|
alloclhi=(uInt *)malloc(needbytes);
|
| 4955 |
|
|
zlhi=alloclhi;}
|
| 4956 |
|
|
needbytes=irhs*sizeof(uInt);
|
| 4957 |
|
|
if (needbytes>(Int)sizeof(zrhibuff)) {
|
| 4958 |
|
|
allocrhi=(uInt *)malloc(needbytes);
|
| 4959 |
|
|
zrhi=allocrhi;}
|
| 4960 |
|
|
|
| 4961 |
|
|
/* Allocating the accumulator space needs a special case when */
|
| 4962 |
|
|
/* DECDPUN=1 because when converting the accumulator to Units */
|
| 4963 |
|
|
/* after the multiplication each 8-byte item becomes 9 1-byte */
|
| 4964 |
|
|
/* units. Therefore iacc extra bytes are needed at the front */
|
| 4965 |
|
|
/* (rounded up to a multiple of 8 bytes), and the uLong */
|
| 4966 |
|
|
/* accumulator starts offset the appropriate number of units */
|
| 4967 |
|
|
/* to the right to avoid overwrite during the unchunking. */
|
| 4968 |
|
|
needbytes=iacc*sizeof(uLong);
|
| 4969 |
|
|
#if DECDPUN==1
|
| 4970 |
|
|
zoff=(iacc+7)/8; /* items to offset by */
|
| 4971 |
|
|
needbytes+=zoff*8;
|
| 4972 |
|
|
#endif
|
| 4973 |
|
|
if (needbytes>(Int)sizeof(zaccbuff)) {
|
| 4974 |
|
|
allocacc=(uLong *)malloc(needbytes);
|
| 4975 |
|
|
zacc=(uLong *)allocacc;}
|
| 4976 |
|
|
if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
|
| 4977 |
|
|
*status|=DEC_Insufficient_storage;
|
| 4978 |
|
|
break;}
|
| 4979 |
|
|
|
| 4980 |
|
|
acc=(Unit *)zacc; /* -> target Unit array */
|
| 4981 |
|
|
#if DECDPUN==1
|
| 4982 |
|
|
zacc+=zoff; /* start uLong accumulator to right */
|
| 4983 |
|
|
#endif
|
| 4984 |
|
|
|
| 4985 |
|
|
/* assemble the chunked copies of the left and right sides */
|
| 4986 |
|
|
for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
|
| 4987 |
|
|
for (p=0, *lip=0; p<FASTDIGS && count>0;
|
| 4988 |
|
|
p+=DECDPUN, cup++, count-=DECDPUN)
|
| 4989 |
|
|
*lip+=*cup*powers[p];
|
| 4990 |
|
|
lmsi=lip-1; /* save -> msi */
|
| 4991 |
|
|
for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
|
| 4992 |
|
|
for (p=0, *rip=0; p<FASTDIGS && count>0;
|
| 4993 |
|
|
p+=DECDPUN, cup++, count-=DECDPUN)
|
| 4994 |
|
|
*rip+=*cup*powers[p];
|
| 4995 |
|
|
rmsi=rip-1; /* save -> msi */
|
| 4996 |
|
|
|
| 4997 |
|
|
/* zero the accumulator */
|
| 4998 |
|
|
for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
|
| 4999 |
|
|
|
| 5000 |
|
|
/* Start the multiplication */
|
| 5001 |
|
|
/* Resolving carries can dominate the cost of accumulating the */
|
| 5002 |
|
|
/* partial products, so this is only done when necessary. */
|
| 5003 |
|
|
/* Each uLong item in the accumulator can hold values up to */
|
| 5004 |
|
|
/* 2**64-1, and each partial product can be as large as */
|
| 5005 |
|
|
/* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */
|
| 5006 |
|
|
/* itself 18.4 times in a uLong without overflowing, so during */
|
| 5007 |
|
|
/* the main calculation resolution is carried out every 18th */
|
| 5008 |
|
|
/* add -- every 162 digits. Similarly, when FASTDIGS=8, the */
|
| 5009 |
|
|
/* partial products can be added to themselves 1844.6 times in */
|
| 5010 |
|
|
/* a uLong without overflowing, so intermediate carry */
|
| 5011 |
|
|
/* resolution occurs only every 14752 digits. Hence for common */
|
| 5012 |
|
|
/* short numbers usually only the one final carry resolution */
|
| 5013 |
|
|
/* occurs. */
|
| 5014 |
|
|
/* (The count is set via FASTLAZY to simplify experiments to */
|
| 5015 |
|
|
/* measure the value of this approach: a 35% improvement on a */
|
| 5016 |
|
|
/* [34x34] multiply.) */
|
| 5017 |
|
|
lazy=FASTLAZY; /* carry delay count */
|
| 5018 |
|
|
for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */
|
| 5019 |
|
|
lp=zacc+(rip-zrhi); /* where to add the lhs */
|
| 5020 |
|
|
for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
|
| 5021 |
|
|
*lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */
|
| 5022 |
|
|
} /* lip loop */
|
| 5023 |
|
|
lazy--;
|
| 5024 |
|
|
if (lazy>0 && rip!=rmsi) continue;
|
| 5025 |
|
|
lazy=FASTLAZY; /* reset delay count */
|
| 5026 |
|
|
/* spin up the accumulator resolving overflows */
|
| 5027 |
|
|
for (lp=zacc; lp<zacc+iacc; lp++) {
|
| 5028 |
|
|
if (*lp<FASTBASE) continue; /* it fits */
|
| 5029 |
|
|
lcarry=*lp/FASTBASE; /* top part [slow divide] */
|
| 5030 |
|
|
/* lcarry can exceed 2**32-1, so check again; this check */
|
| 5031 |
|
|
/* and occasional extra divide (slow) is well worth it, as */
|
| 5032 |
|
|
/* it allows FASTLAZY to be increased to 18 rather than 4 */
|
| 5033 |
|
|
/* in the FASTDIGS=9 case */
|
| 5034 |
|
|
if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */
|
| 5035 |
|
|
else { /* two-place carry [fairly rare] */
|
| 5036 |
|
|
uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */
|
| 5037 |
|
|
*(lp+2)+=carry2; /* add to item+2 */
|
| 5038 |
|
|
*lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
|
| 5039 |
|
|
carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
|
| 5040 |
|
|
}
|
| 5041 |
|
|
*(lp+1)+=carry; /* add to item above [inline] */
|
| 5042 |
|
|
*lp-=((uLong)FASTBASE*carry); /* [inline] */
|
| 5043 |
|
|
} /* carry resolution */
|
| 5044 |
|
|
} /* rip loop */
|
| 5045 |
|
|
|
| 5046 |
|
|
/* The multiplication is complete; time to convert back into */
|
| 5047 |
|
|
/* units. This can be done in-place in the accumulator and in */
|
| 5048 |
|
|
/* 32-bit operations, because carries were resolved after the */
|
| 5049 |
|
|
/* final add. This needs N-1 divides and multiplies for */
|
| 5050 |
|
|
/* each item in the accumulator (which will become up to N */
|
| 5051 |
|
|
/* units, where 2<=N<=9). */
|
| 5052 |
|
|
for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
|
| 5053 |
|
|
uInt item=(uInt)*lp; /* decapitate to uInt */
|
| 5054 |
|
|
for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
|
| 5055 |
|
|
uInt part=item/(DECDPUNMAX+1);
|
| 5056 |
|
|
*up=(Unit)(item-(part*(DECDPUNMAX+1)));
|
| 5057 |
|
|
item=part;
|
| 5058 |
|
|
} /* p */
|
| 5059 |
|
|
*up=(Unit)item; up++; /* [final needs no division] */
|
| 5060 |
|
|
} /* lp */
|
| 5061 |
|
|
accunits=up-acc; /* count of units */
|
| 5062 |
|
|
}
|
| 5063 |
|
|
else { /* here to use units directly, without chunking ['old code'] */
|
| 5064 |
|
|
#endif
|
| 5065 |
|
|
|
| 5066 |
|
|
/* if accumulator will be too long for local storage, then allocate */
|
| 5067 |
|
|
acc=accbuff; /* -> assume buffer for accumulator */
|
| 5068 |
|
|
needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
|
| 5069 |
|
|
if (needbytes>(Int)sizeof(accbuff)) {
|
| 5070 |
|
|
allocacc=(Unit *)malloc(needbytes);
|
| 5071 |
|
|
if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
|
| 5072 |
|
|
acc=(Unit *)allocacc; /* use the allocated space */
|
| 5073 |
|
|
}
|
| 5074 |
|
|
|
| 5075 |
|
|
/* Now the main long multiplication loop */
|
| 5076 |
|
|
/* Unlike the equivalent in the IBM Java implementation, there */
|
| 5077 |
|
|
/* is no advantage in calculating from msu to lsu. So, do it */
|
| 5078 |
|
|
/* by the book, as it were. */
|
| 5079 |
|
|
/* Each iteration calculates ACC=ACC+MULTAND*MULT */
|
| 5080 |
|
|
accunits=1; /* accumulator starts at '0' */
|
| 5081 |
|
|
*acc=0; /* .. (lsu=0) */
|
| 5082 |
|
|
shift=0; /* no multiplicand shift at first */
|
| 5083 |
|
|
madlength=D2U(lhs->digits); /* this won't change */
|
| 5084 |
|
|
mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */
|
| 5085 |
|
|
|
| 5086 |
|
|
for (mer=rhs->lsu; mer<mermsup; mer++) {
|
| 5087 |
|
|
/* Here, *mer is the next Unit in the multiplier to use */
|
| 5088 |
|
|
/* If non-zero [optimization] add it... */
|
| 5089 |
|
|
if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
|
| 5090 |
|
|
lhs->lsu, madlength, 0,
|
| 5091 |
|
|
&acc[shift], *mer)
|
| 5092 |
|
|
+ shift;
|
| 5093 |
|
|
else { /* extend acc with a 0; it will be used shortly */
|
| 5094 |
|
|
*(acc+accunits)=0; /* [this avoids length of <=0 later] */
|
| 5095 |
|
|
accunits++;
|
| 5096 |
|
|
}
|
| 5097 |
|
|
/* multiply multiplicand by 10**DECDPUN for next Unit to left */
|
| 5098 |
|
|
shift++; /* add this for 'logical length' */
|
| 5099 |
|
|
} /* n */
|
| 5100 |
|
|
#if FASTMUL
|
| 5101 |
|
|
} /* unchunked units */
|
| 5102 |
|
|
#endif
|
| 5103 |
|
|
/* common end-path */
|
| 5104 |
|
|
#if DECTRACE
|
| 5105 |
|
|
decDumpAr('*', acc, accunits); /* Show exact result */
|
| 5106 |
|
|
#endif
|
| 5107 |
|
|
|
| 5108 |
|
|
/* acc now contains the exact result of the multiplication, */
|
| 5109 |
|
|
/* possibly with a leading zero unit; build the decNumber from */
|
| 5110 |
|
|
/* it, noting if any residue */
|
| 5111 |
|
|
res->bits=bits; /* set sign */
|
| 5112 |
|
|
res->digits=decGetDigits(acc, accunits); /* count digits exactly */
|
| 5113 |
|
|
|
| 5114 |
|
|
/* There can be a 31-bit wrap in calculating the exponent. */
|
| 5115 |
|
|
/* This can only happen if both input exponents are negative and */
|
| 5116 |
|
|
/* both their magnitudes are large. If there was a wrap, set a */
|
| 5117 |
|
|
/* safe very negative exponent, from which decFinalize() will */
|
| 5118 |
|
|
/* raise a hard underflow shortly. */
|
| 5119 |
|
|
exponent=lhs->exponent+rhs->exponent; /* calculate exponent */
|
| 5120 |
|
|
if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
|
| 5121 |
|
|
exponent=-2*DECNUMMAXE; /* force underflow */
|
| 5122 |
|
|
res->exponent=exponent; /* OK to overwrite now */
|
| 5123 |
|
|
|
| 5124 |
|
|
|
| 5125 |
|
|
/* Set the coefficient. If any rounding, residue records */
|
| 5126 |
|
|
decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| 5127 |
|
|
decFinish(res, set, &residue, status); /* final cleanup */
|
| 5128 |
|
|
} while(0); /* end protected */
|
| 5129 |
|
|
|
| 5130 |
|
|
if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| 5131 |
|
|
#if DECSUBSET
|
| 5132 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| 5133 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 5134 |
|
|
#endif
|
| 5135 |
|
|
#if FASTMUL
|
| 5136 |
|
|
if (allocrhi!=NULL) free(allocrhi); /* .. */
|
| 5137 |
|
|
if (alloclhi!=NULL) free(alloclhi); /* .. */
|
| 5138 |
|
|
#endif
|
| 5139 |
|
|
return res;
|
| 5140 |
|
|
} /* decMultiplyOp */
|
| 5141 |
|
|
|
| 5142 |
|
|
/* ------------------------------------------------------------------ */
|
| 5143 |
|
|
/* decExpOp -- effect exponentiation */
|
| 5144 |
|
|
/* */
|
| 5145 |
|
|
/* This computes C = exp(A) */
|
| 5146 |
|
|
/* */
|
| 5147 |
|
|
/* res is C, the result. C may be A */
|
| 5148 |
|
|
/* rhs is A */
|
| 5149 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 5150 |
|
|
/* */
|
| 5151 |
|
|
/* C must have space for set->digits digits. status is updated but */
|
| 5152 |
|
|
/* not set. */
|
| 5153 |
|
|
/* */
|
| 5154 |
|
|
/* Restrictions: */
|
| 5155 |
|
|
/* */
|
| 5156 |
|
|
/* digits, emax, and -emin in the context must be less than */
|
| 5157 |
|
|
/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
|
| 5158 |
|
|
/* bounds or a zero. This is an internal routine, so these */
|
| 5159 |
|
|
/* restrictions are contractual and not enforced. */
|
| 5160 |
|
|
/* */
|
| 5161 |
|
|
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| 5162 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 5163 |
|
|
/* error in rare cases. */
|
| 5164 |
|
|
/* */
|
| 5165 |
|
|
/* Finite results will always be full precision and Inexact, except */
|
| 5166 |
|
|
/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
|
| 5167 |
|
|
/* ------------------------------------------------------------------ */
|
| 5168 |
|
|
/* This approach used here is similar to the algorithm described in */
|
| 5169 |
|
|
/* */
|
| 5170 |
|
|
/* Variable Precision Exponential Function, T. E. Hull and */
|
| 5171 |
|
|
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
|
| 5172 |
|
|
/* pp79-91, ACM, June 1986. */
|
| 5173 |
|
|
/* */
|
| 5174 |
|
|
/* with the main difference being that the iterations in the series */
|
| 5175 |
|
|
/* evaluation are terminated dynamically (which does not require the */
|
| 5176 |
|
|
/* extra variable-precision variables which are expensive in this */
|
| 5177 |
|
|
/* context). */
|
| 5178 |
|
|
/* */
|
| 5179 |
|
|
/* The error analysis in Hull & Abrham's paper applies except for the */
|
| 5180 |
|
|
/* round-off error accumulation during the series evaluation. This */
|
| 5181 |
|
|
/* code does not precalculate the number of iterations and so cannot */
|
| 5182 |
|
|
/* use Horner's scheme. Instead, the accumulation is done at double- */
|
| 5183 |
|
|
/* precision, which ensures that the additions of the terms are exact */
|
| 5184 |
|
|
/* and do not accumulate round-off (and any round-off errors in the */
|
| 5185 |
|
|
/* terms themselves move 'to the right' faster than they can */
|
| 5186 |
|
|
/* accumulate). This code also extends the calculation by allowing, */
|
| 5187 |
|
|
/* in the spirit of other decNumber operators, the input to be more */
|
| 5188 |
|
|
/* precise than the result (the precision used is based on the more */
|
| 5189 |
|
|
/* precise of the input or requested result). */
|
| 5190 |
|
|
/* */
|
| 5191 |
|
|
/* Implementation notes: */
|
| 5192 |
|
|
/* */
|
| 5193 |
|
|
/* 1. This is separated out as decExpOp so it can be called from */
|
| 5194 |
|
|
/* other Mathematical functions (notably Ln) with a wider range */
|
| 5195 |
|
|
/* than normal. In particular, it can handle the slightly wider */
|
| 5196 |
|
|
/* (double) range needed by Ln (which has to be able to calculate */
|
| 5197 |
|
|
/* exp(-x) where x can be the tiniest number (Ntiny). */
|
| 5198 |
|
|
/* */
|
| 5199 |
|
|
/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
|
| 5200 |
|
|
/* iterations by appoximately a third with additional (although */
|
| 5201 |
|
|
/* diminishing) returns as the range is reduced to even smaller */
|
| 5202 |
|
|
/* fractions. However, h (the power of 10 used to correct the */
|
| 5203 |
|
|
/* result at the end, see below) must be kept <=8 as otherwise */
|
| 5204 |
|
|
/* the final result cannot be computed. Hence the leverage is a */
|
| 5205 |
|
|
/* sliding value (8-h), where potentially the range is reduced */
|
| 5206 |
|
|
/* more for smaller values. */
|
| 5207 |
|
|
/* */
|
| 5208 |
|
|
/* The leverage that can be applied in this way is severely */
|
| 5209 |
|
|
/* limited by the cost of the raise-to-the power at the end, */
|
| 5210 |
|
|
/* which dominates when the number of iterations is small (less */
|
| 5211 |
|
|
/* than ten) or when rhs is short. As an example, the adjustment */
|
| 5212 |
|
|
/* x**10,000,000 needs 31 multiplications, all but one full-width. */
|
| 5213 |
|
|
/* */
|
| 5214 |
|
|
/* 3. The restrictions (especially precision) could be raised with */
|
| 5215 |
|
|
/* care, but the full decNumber range seems very hard within the */
|
| 5216 |
|
|
/* 32-bit limits. */
|
| 5217 |
|
|
/* */
|
| 5218 |
|
|
/* 4. The working precisions for the static buffers are twice the */
|
| 5219 |
|
|
/* obvious size to allow for calls from decNumberPower. */
|
| 5220 |
|
|
/* ------------------------------------------------------------------ */
|
| 5221 |
|
|
decNumber * decExpOp(decNumber *res, const decNumber *rhs,
|
| 5222 |
|
|
decContext *set, uInt *status) {
|
| 5223 |
|
|
uInt ignore=0; /* working status */
|
| 5224 |
|
|
Int h; /* adjusted exponent for 0.xxxx */
|
| 5225 |
|
|
Int p; /* working precision */
|
| 5226 |
|
|
Int residue; /* rounding residue */
|
| 5227 |
|
|
uInt needbytes; /* for space calculations */
|
| 5228 |
|
|
const decNumber *x=rhs; /* (may point to safe copy later) */
|
| 5229 |
|
|
decContext aset, tset, dset; /* working contexts */
|
| 5230 |
|
|
Int comp; /* work */
|
| 5231 |
|
|
|
| 5232 |
|
|
/* the argument is often copied to normalize it, so (unusually) it */
|
| 5233 |
|
|
/* is treated like other buffers, using DECBUFFER, +1 in case */
|
| 5234 |
|
|
/* DECBUFFER is 0 */
|
| 5235 |
|
|
decNumber bufr[D2N(DECBUFFER*2+1)];
|
| 5236 |
|
|
decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */
|
| 5237 |
|
|
|
| 5238 |
|
|
/* the working precision will be no more than set->digits+8+1 */
|
| 5239 |
|
|
/* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
|
| 5240 |
|
|
/* is 0 (and twice that for the accumulator) */
|
| 5241 |
|
|
|
| 5242 |
|
|
/* buffer for t, term (working precision plus) */
|
| 5243 |
|
|
decNumber buft[D2N(DECBUFFER*2+9+1)];
|
| 5244 |
|
|
decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */
|
| 5245 |
|
|
decNumber *t=buft; /* term */
|
| 5246 |
|
|
/* buffer for a, accumulator (working precision * 2), at least 9 */
|
| 5247 |
|
|
decNumber bufa[D2N(DECBUFFER*4+18+1)];
|
| 5248 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 5249 |
|
|
decNumber *a=bufa; /* accumulator */
|
| 5250 |
|
|
/* decNumber for the divisor term; this needs at most 9 digits */
|
| 5251 |
|
|
/* and so can be fixed size [16 so can use standard context] */
|
| 5252 |
|
|
decNumber bufd[D2N(16)];
|
| 5253 |
|
|
decNumber *d=bufd; /* divisor */
|
| 5254 |
|
|
decNumber numone; /* constant 1 */
|
| 5255 |
|
|
|
| 5256 |
|
|
#if DECCHECK
|
| 5257 |
|
|
Int iterations=0; /* for later sanity check */
|
| 5258 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 5259 |
|
|
#endif
|
| 5260 |
|
|
|
| 5261 |
|
|
do { /* protect allocated storage */
|
| 5262 |
|
|
if (SPECIALARG) { /* handle infinities and NaNs */
|
| 5263 |
|
|
if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| 5264 |
|
|
if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */
|
| 5265 |
|
|
decNumberZero(res);
|
| 5266 |
|
|
else decNumberCopy(res, rhs); /* +Infinity -> self */
|
| 5267 |
|
|
}
|
| 5268 |
|
|
else decNaNs(res, rhs, NULL, set, status); /* a NaN */
|
| 5269 |
|
|
break;}
|
| 5270 |
|
|
|
| 5271 |
|
|
if (ISZERO(rhs)) { /* zeros -> exact 1 */
|
| 5272 |
|
|
decNumberZero(res); /* make clean 1 */
|
| 5273 |
|
|
*res->lsu=1; /* .. */
|
| 5274 |
|
|
break;} /* [no status to set] */
|
| 5275 |
|
|
|
| 5276 |
|
|
/* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
|
| 5277 |
|
|
/* positive and negative tiny cases which will result in inexact */
|
| 5278 |
|
|
/* 1. This also allows the later add-accumulate to always be */
|
| 5279 |
|
|
/* exact (because its length will never be more than twice the */
|
| 5280 |
|
|
/* working precision). */
|
| 5281 |
|
|
/* The comparator (tiny) needs just one digit, so use the */
|
| 5282 |
|
|
/* decNumber d for it (reused as the divisor, etc., below); its */
|
| 5283 |
|
|
/* exponent is such that if x is positive it will have */
|
| 5284 |
|
|
/* set->digits-1 zeros between the decimal point and the digit, */
|
| 5285 |
|
|
/* which is 4, and if x is negative one more zero there as the */
|
| 5286 |
|
|
/* more precise result will be of the form 0.9999999 rather than */
|
| 5287 |
|
|
/* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */
|
| 5288 |
|
|
/* or 0.00000004 if digits=7 and x<0. If RHS not larger than */
|
| 5289 |
|
|
/* this then the result will be 1.000000 */
|
| 5290 |
|
|
decNumberZero(d); /* clean */
|
| 5291 |
|
|
*d->lsu=4; /* set 4 .. */
|
| 5292 |
|
|
d->exponent=-set->digits; /* * 10**(-d) */
|
| 5293 |
|
|
if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */
|
| 5294 |
|
|
comp=decCompare(d, rhs, 1); /* signless compare */
|
| 5295 |
|
|
if (comp==BADINT) {
|
| 5296 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5297 |
|
|
break;}
|
| 5298 |
|
|
if (comp>=0) { /* rhs < d */
|
| 5299 |
|
|
Int shift=set->digits-1;
|
| 5300 |
|
|
decNumberZero(res); /* set 1 */
|
| 5301 |
|
|
*res->lsu=1; /* .. */
|
| 5302 |
|
|
res->digits=decShiftToMost(res->lsu, 1, shift);
|
| 5303 |
|
|
res->exponent=-shift; /* make 1.0000... */
|
| 5304 |
|
|
*status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */
|
| 5305 |
|
|
break;} /* tiny */
|
| 5306 |
|
|
|
| 5307 |
|
|
/* set up the context to be used for calculating a, as this is */
|
| 5308 |
|
|
/* used on both paths below */
|
| 5309 |
|
|
decContextDefault(&aset, DEC_INIT_DECIMAL64);
|
| 5310 |
|
|
/* accumulator bounds are as requested (could underflow) */
|
| 5311 |
|
|
aset.emax=set->emax; /* usual bounds */
|
| 5312 |
|
|
aset.emin=set->emin; /* .. */
|
| 5313 |
|
|
aset.clamp=0; /* and no concrete format */
|
| 5314 |
|
|
|
| 5315 |
|
|
/* calculate the adjusted (Hull & Abrham) exponent (where the */
|
| 5316 |
|
|
/* decimal point is just to the left of the coefficient msd) */
|
| 5317 |
|
|
h=rhs->exponent+rhs->digits;
|
| 5318 |
|
|
/* if h>8 then 10**h cannot be calculated safely; however, when */
|
| 5319 |
|
|
/* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
|
| 5320 |
|
|
/* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
|
| 5321 |
|
|
/* overflow (or underflow to 0) is guaranteed -- so this case can */
|
| 5322 |
|
|
/* be handled by simply forcing the appropriate excess */
|
| 5323 |
|
|
if (h>8) { /* overflow/underflow */
|
| 5324 |
|
|
/* set up here so Power call below will over or underflow to */
|
| 5325 |
|
|
/* zero; set accumulator to either 2 or 0.02 */
|
| 5326 |
|
|
/* [stack buffer for a is always big enough for this] */
|
| 5327 |
|
|
decNumberZero(a);
|
| 5328 |
|
|
*a->lsu=2; /* not 1 but < exp(1) */
|
| 5329 |
|
|
if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
|
| 5330 |
|
|
h=8; /* clamp so 10**h computable */
|
| 5331 |
|
|
p=9; /* set a working precision */
|
| 5332 |
|
|
}
|
| 5333 |
|
|
else { /* h<=8 */
|
| 5334 |
|
|
Int maxlever=(rhs->digits>8?1:0);
|
| 5335 |
|
|
/* [could/should increase this for precisions >40 or so, too] */
|
| 5336 |
|
|
|
| 5337 |
|
|
/* if h is 8, cannot normalize to a lower upper limit because */
|
| 5338 |
|
|
/* the final result will not be computable (see notes above), */
|
| 5339 |
|
|
/* but leverage can be applied whenever h is less than 8. */
|
| 5340 |
|
|
/* Apply as much as possible, up to a MAXLEVER digits, which */
|
| 5341 |
|
|
/* sets the tradeoff against the cost of the later a**(10**h). */
|
| 5342 |
|
|
/* As h is increased, the working precision below also */
|
| 5343 |
|
|
/* increases to compensate for the "constant digits at the */
|
| 5344 |
|
|
/* front" effect. */
|
| 5345 |
|
|
Int lever=MINI(8-h, maxlever); /* leverage attainable */
|
| 5346 |
|
|
Int use=-rhs->digits-lever; /* exponent to use for RHS */
|
| 5347 |
|
|
h+=lever; /* apply leverage selected */
|
| 5348 |
|
|
if (h<0) { /* clamp */
|
| 5349 |
|
|
use+=h; /* [may end up subnormal] */
|
| 5350 |
|
|
h=0;
|
| 5351 |
|
|
}
|
| 5352 |
|
|
/* Take a copy of RHS if it needs normalization (true whenever x>=1) */
|
| 5353 |
|
|
if (rhs->exponent!=use) {
|
| 5354 |
|
|
decNumber *newrhs=bufr; /* assume will fit on stack */
|
| 5355 |
|
|
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| 5356 |
|
|
if (needbytes>sizeof(bufr)) { /* need malloc space */
|
| 5357 |
|
|
allocrhs=(decNumber *)malloc(needbytes);
|
| 5358 |
|
|
if (allocrhs==NULL) { /* hopeless -- abandon */
|
| 5359 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5360 |
|
|
break;}
|
| 5361 |
|
|
newrhs=allocrhs; /* use the allocated space */
|
| 5362 |
|
|
}
|
| 5363 |
|
|
decNumberCopy(newrhs, rhs); /* copy to safe space */
|
| 5364 |
|
|
newrhs->exponent=use; /* normalize; now <1 */
|
| 5365 |
|
|
x=newrhs; /* ready for use */
|
| 5366 |
|
|
/* decNumberShow(x); */
|
| 5367 |
|
|
}
|
| 5368 |
|
|
|
| 5369 |
|
|
/* Now use the usual power series to evaluate exp(x). The */
|
| 5370 |
|
|
/* series starts as 1 + x + x^2/2 ... so prime ready for the */
|
| 5371 |
|
|
/* third term by setting the term variable t=x, the accumulator */
|
| 5372 |
|
|
/* a=1, and the divisor d=2. */
|
| 5373 |
|
|
|
| 5374 |
|
|
/* First determine the working precision. From Hull & Abrham */
|
| 5375 |
|
|
/* this is set->digits+h+2. However, if x is 'over-precise' we */
|
| 5376 |
|
|
/* need to allow for all its digits to potentially participate */
|
| 5377 |
|
|
/* (consider an x where all the excess digits are 9s) so in */
|
| 5378 |
|
|
/* this case use x->digits+h+2 */
|
| 5379 |
|
|
p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */
|
| 5380 |
|
|
|
| 5381 |
|
|
/* a and t are variable precision, and depend on p, so space */
|
| 5382 |
|
|
/* must be allocated for them if necessary */
|
| 5383 |
|
|
|
| 5384 |
|
|
/* the accumulator needs to be able to hold 2p digits so that */
|
| 5385 |
|
|
/* the additions on the second and subsequent iterations are */
|
| 5386 |
|
|
/* sufficiently exact. */
|
| 5387 |
|
|
needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
|
| 5388 |
|
|
if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| 5389 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 5390 |
|
|
if (allocbufa==NULL) { /* hopeless -- abandon */
|
| 5391 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5392 |
|
|
break;}
|
| 5393 |
|
|
a=allocbufa; /* use the allocated space */
|
| 5394 |
|
|
}
|
| 5395 |
|
|
/* the term needs to be able to hold p digits (which is */
|
| 5396 |
|
|
/* guaranteed to be larger than x->digits, so the initial copy */
|
| 5397 |
|
|
/* is safe); it may also be used for the raise-to-power */
|
| 5398 |
|
|
/* calculation below, which needs an extra two digits */
|
| 5399 |
|
|
needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
|
| 5400 |
|
|
if (needbytes>sizeof(buft)) { /* need malloc space */
|
| 5401 |
|
|
allocbuft=(decNumber *)malloc(needbytes);
|
| 5402 |
|
|
if (allocbuft==NULL) { /* hopeless -- abandon */
|
| 5403 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5404 |
|
|
break;}
|
| 5405 |
|
|
t=allocbuft; /* use the allocated space */
|
| 5406 |
|
|
}
|
| 5407 |
|
|
|
| 5408 |
|
|
decNumberCopy(t, x); /* term=x */
|
| 5409 |
|
|
decNumberZero(a); *a->lsu=1; /* accumulator=1 */
|
| 5410 |
|
|
decNumberZero(d); *d->lsu=2; /* divisor=2 */
|
| 5411 |
|
|
decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */
|
| 5412 |
|
|
|
| 5413 |
|
|
/* set up the contexts for calculating a, t, and d */
|
| 5414 |
|
|
decContextDefault(&tset, DEC_INIT_DECIMAL64);
|
| 5415 |
|
|
dset=tset;
|
| 5416 |
|
|
/* accumulator bounds are set above, set precision now */
|
| 5417 |
|
|
aset.digits=p*2; /* double */
|
| 5418 |
|
|
/* term bounds avoid any underflow or overflow */
|
| 5419 |
|
|
tset.digits=p;
|
| 5420 |
|
|
tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */
|
| 5421 |
|
|
/* [dset.digits=16, etc., are sufficient] */
|
| 5422 |
|
|
|
| 5423 |
|
|
/* finally ready to roll */
|
| 5424 |
|
|
for (;;) {
|
| 5425 |
|
|
#if DECCHECK
|
| 5426 |
|
|
iterations++;
|
| 5427 |
|
|
#endif
|
| 5428 |
|
|
/* only the status from the accumulation is interesting */
|
| 5429 |
|
|
/* [but it should remain unchanged after first add] */
|
| 5430 |
|
|
decAddOp(a, a, t, &aset, 0, status); /* a=a+t */
|
| 5431 |
|
|
decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */
|
| 5432 |
|
|
decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */
|
| 5433 |
|
|
/* the iteration ends when the term cannot affect the result, */
|
| 5434 |
|
|
/* if rounded to p digits, which is when its value is smaller */
|
| 5435 |
|
|
/* than the accumulator by p+1 digits. There must also be */
|
| 5436 |
|
|
/* full precision in a. */
|
| 5437 |
|
|
if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
|
| 5438 |
|
|
&& (a->digits>=p)) break;
|
| 5439 |
|
|
decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */
|
| 5440 |
|
|
} /* iterate */
|
| 5441 |
|
|
|
| 5442 |
|
|
#if DECCHECK
|
| 5443 |
|
|
/* just a sanity check; comment out test to show always */
|
| 5444 |
|
|
if (iterations>p+3)
|
| 5445 |
|
|
printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
|
| 5446 |
|
|
(LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
|
| 5447 |
|
|
#endif
|
| 5448 |
|
|
} /* h<=8 */
|
| 5449 |
|
|
|
| 5450 |
|
|
/* apply postconditioning: a=a**(10**h) -- this is calculated */
|
| 5451 |
|
|
/* at a slightly higher precision than Hull & Abrham suggest */
|
| 5452 |
|
|
if (h>0) {
|
| 5453 |
|
|
Int seenbit=0; /* set once a 1-bit is seen */
|
| 5454 |
|
|
Int i; /* counter */
|
| 5455 |
|
|
Int n=powers[h]; /* always positive */
|
| 5456 |
|
|
aset.digits=p+2; /* sufficient precision */
|
| 5457 |
|
|
/* avoid the overhead and many extra digits of decNumberPower */
|
| 5458 |
|
|
/* as all that is needed is the short 'multipliers' loop; here */
|
| 5459 |
|
|
/* accumulate the answer into t */
|
| 5460 |
|
|
decNumberZero(t); *t->lsu=1; /* acc=1 */
|
| 5461 |
|
|
for (i=1;;i++){ /* for each bit [top bit ignored] */
|
| 5462 |
|
|
/* abandon if have had overflow or terminal underflow */
|
| 5463 |
|
|
if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
|
| 5464 |
|
|
if (*status&DEC_Overflow || ISZERO(t)) break;}
|
| 5465 |
|
|
n=n<<1; /* move next bit to testable position */
|
| 5466 |
|
|
if (n<0) { /* top bit is set */
|
| 5467 |
|
|
seenbit=1; /* OK, have a significant bit */
|
| 5468 |
|
|
decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
|
| 5469 |
|
|
}
|
| 5470 |
|
|
if (i==31) break; /* that was the last bit */
|
| 5471 |
|
|
if (!seenbit) continue; /* no need to square 1 */
|
| 5472 |
|
|
decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
|
| 5473 |
|
|
} /*i*/ /* 32 bits */
|
| 5474 |
|
|
/* decNumberShow(t); */
|
| 5475 |
|
|
a=t; /* and carry on using t instead of a */
|
| 5476 |
|
|
}
|
| 5477 |
|
|
|
| 5478 |
|
|
/* Copy and round the result to res */
|
| 5479 |
|
|
residue=1; /* indicate dirt to right .. */
|
| 5480 |
|
|
if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
|
| 5481 |
|
|
aset.digits=set->digits; /* [use default rounding] */
|
| 5482 |
|
|
decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
|
| 5483 |
|
|
decFinish(res, set, &residue, status); /* cleanup/set flags */
|
| 5484 |
|
|
} while(0); /* end protected */
|
| 5485 |
|
|
|
| 5486 |
|
|
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| 5487 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* .. */
|
| 5488 |
|
|
if (allocbuft!=NULL) free(allocbuft); /* .. */
|
| 5489 |
|
|
/* [status is handled by caller] */
|
| 5490 |
|
|
return res;
|
| 5491 |
|
|
} /* decExpOp */
|
| 5492 |
|
|
|
| 5493 |
|
|
/* ------------------------------------------------------------------ */
|
| 5494 |
|
|
/* Initial-estimate natural logarithm table */
|
| 5495 |
|
|
/* */
|
| 5496 |
|
|
/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
|
| 5497 |
|
|
/* The result is a 4-digit encode of the coefficient (c=the */
|
| 5498 |
|
|
/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
|
| 5499 |
|
|
/* exponent (e=the bottom 2 bits encoding 0-3) */
|
| 5500 |
|
|
/* */
|
| 5501 |
|
|
/* The resulting value is given by: */
|
| 5502 |
|
|
/* */
|
| 5503 |
|
|
/* v = -c * 10**(-e-3) */
|
| 5504 |
|
|
/* */
|
| 5505 |
|
|
/* where e and c are extracted from entry k = LNnn[x-10] */
|
| 5506 |
|
|
/* where x is truncated (NB) into the range 10 through 99, */
|
| 5507 |
|
|
/* and then c = k>>2 and e = k&3. */
|
| 5508 |
|
|
/* ------------------------------------------------------------------ */
|
| 5509 |
|
|
const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
|
| 5510 |
|
|
6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
|
| 5511 |
|
|
5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
|
| 5512 |
|
|
39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
|
| 5513 |
|
|
29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
|
| 5514 |
|
|
22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
|
| 5515 |
|
|
15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
|
| 5516 |
|
|
10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
|
| 5517 |
|
|
5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
|
| 5518 |
|
|
10130, 6046, 20055};
|
| 5519 |
|
|
|
| 5520 |
|
|
/* ------------------------------------------------------------------ */
|
| 5521 |
|
|
/* decLnOp -- effect natural logarithm */
|
| 5522 |
|
|
/* */
|
| 5523 |
|
|
/* This computes C = ln(A) */
|
| 5524 |
|
|
/* */
|
| 5525 |
|
|
/* res is C, the result. C may be A */
|
| 5526 |
|
|
/* rhs is A */
|
| 5527 |
|
|
/* set is the context; note that rounding mode has no effect */
|
| 5528 |
|
|
/* */
|
| 5529 |
|
|
/* C must have space for set->digits digits. */
|
| 5530 |
|
|
/* */
|
| 5531 |
|
|
/* Notable cases: */
|
| 5532 |
|
|
/* A<0 -> Invalid */
|
| 5533 |
|
|
/* A=0 -> -Infinity (Exact) */
|
| 5534 |
|
|
/* A=+Infinity -> +Infinity (Exact) */
|
| 5535 |
|
|
/* A=1 exactly -> 0 (Exact) */
|
| 5536 |
|
|
/* */
|
| 5537 |
|
|
/* Restrictions (as for Exp): */
|
| 5538 |
|
|
/* */
|
| 5539 |
|
|
/* digits, emax, and -emin in the context must be less than */
|
| 5540 |
|
|
/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
|
| 5541 |
|
|
/* bounds or a zero. This is an internal routine, so these */
|
| 5542 |
|
|
/* restrictions are contractual and not enforced. */
|
| 5543 |
|
|
/* */
|
| 5544 |
|
|
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| 5545 |
|
|
/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| 5546 |
|
|
/* error in rare cases. */
|
| 5547 |
|
|
/* ------------------------------------------------------------------ */
|
| 5548 |
|
|
/* The result is calculated using Newton's method, with each */
|
| 5549 |
|
|
/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
|
| 5550 |
|
|
/* Epperson 1989. */
|
| 5551 |
|
|
/* */
|
| 5552 |
|
|
/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
|
| 5553 |
|
|
/* This has to be calculated at the sum of the precision of x and the */
|
| 5554 |
|
|
/* working precision. */
|
| 5555 |
|
|
/* */
|
| 5556 |
|
|
/* Implementation notes: */
|
| 5557 |
|
|
/* */
|
| 5558 |
|
|
/* 1. This is separated out as decLnOp so it can be called from */
|
| 5559 |
|
|
/* other Mathematical functions (e.g., Log 10) with a wider range */
|
| 5560 |
|
|
/* than normal. In particular, it can handle the slightly wider */
|
| 5561 |
|
|
/* (+9+2) range needed by a power function. */
|
| 5562 |
|
|
/* */
|
| 5563 |
|
|
/* 2. The speed of this function is about 10x slower than exp, as */
|
| 5564 |
|
|
/* it typically needs 4-6 iterations for short numbers, and the */
|
| 5565 |
|
|
/* extra precision needed adds a squaring effect, twice. */
|
| 5566 |
|
|
/* */
|
| 5567 |
|
|
/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
|
| 5568 |
|
|
/* as these are common requests. ln(10) is used by log10(x). */
|
| 5569 |
|
|
/* */
|
| 5570 |
|
|
/* 4. An iteration might be saved by widening the LNnn table, and */
|
| 5571 |
|
|
/* would certainly save at least one if it were made ten times */
|
| 5572 |
|
|
/* bigger, too (for truncated fractions 0.100 through 0.999). */
|
| 5573 |
|
|
/* However, for most practical evaluations, at least four or five */
|
| 5574 |
|
|
/* iterations will be neede -- so this would only speed up by */
|
| 5575 |
|
|
/* 20-25% and that probably does not justify increasing the table */
|
| 5576 |
|
|
/* size. */
|
| 5577 |
|
|
/* */
|
| 5578 |
|
|
/* 5. The static buffers are larger than might be expected to allow */
|
| 5579 |
|
|
/* for calls from decNumberPower. */
|
| 5580 |
|
|
/* ------------------------------------------------------------------ */
|
| 5581 |
|
|
decNumber * decLnOp(decNumber *res, const decNumber *rhs,
|
| 5582 |
|
|
decContext *set, uInt *status) {
|
| 5583 |
|
|
uInt ignore=0; /* working status accumulator */
|
| 5584 |
|
|
uInt needbytes; /* for space calculations */
|
| 5585 |
|
|
Int residue; /* rounding residue */
|
| 5586 |
|
|
Int r; /* rhs=f*10**r [see below] */
|
| 5587 |
|
|
Int p; /* working precision */
|
| 5588 |
|
|
Int pp; /* precision for iteration */
|
| 5589 |
|
|
Int t; /* work */
|
| 5590 |
|
|
|
| 5591 |
|
|
/* buffers for a (accumulator, typically precision+2) and b */
|
| 5592 |
|
|
/* (adjustment calculator, same size) */
|
| 5593 |
|
|
decNumber bufa[D2N(DECBUFFER+12)];
|
| 5594 |
|
|
decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| 5595 |
|
|
decNumber *a=bufa; /* accumulator/work */
|
| 5596 |
|
|
decNumber bufb[D2N(DECBUFFER*2+2)];
|
| 5597 |
|
|
decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */
|
| 5598 |
|
|
decNumber *b=bufb; /* adjustment/work */
|
| 5599 |
|
|
|
| 5600 |
|
|
decNumber numone; /* constant 1 */
|
| 5601 |
|
|
decNumber cmp; /* work */
|
| 5602 |
|
|
decContext aset, bset; /* working contexts */
|
| 5603 |
|
|
|
| 5604 |
|
|
#if DECCHECK
|
| 5605 |
|
|
Int iterations=0; /* for later sanity check */
|
| 5606 |
|
|
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| 5607 |
|
|
#endif
|
| 5608 |
|
|
|
| 5609 |
|
|
do { /* protect allocated storage */
|
| 5610 |
|
|
if (SPECIALARG) { /* handle infinities and NaNs */
|
| 5611 |
|
|
if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| 5612 |
|
|
if (decNumberIsNegative(rhs)) /* -Infinity -> error */
|
| 5613 |
|
|
*status|=DEC_Invalid_operation;
|
| 5614 |
|
|
else decNumberCopy(res, rhs); /* +Infinity -> self */
|
| 5615 |
|
|
}
|
| 5616 |
|
|
else decNaNs(res, rhs, NULL, set, status); /* a NaN */
|
| 5617 |
|
|
break;}
|
| 5618 |
|
|
|
| 5619 |
|
|
if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */
|
| 5620 |
|
|
decNumberZero(res); /* make clean */
|
| 5621 |
|
|
res->bits=DECINF|DECNEG; /* set - infinity */
|
| 5622 |
|
|
break;} /* [no status to set] */
|
| 5623 |
|
|
|
| 5624 |
|
|
/* Non-zero negatives are bad... */
|
| 5625 |
|
|
if (decNumberIsNegative(rhs)) { /* -x -> error */
|
| 5626 |
|
|
*status|=DEC_Invalid_operation;
|
| 5627 |
|
|
break;}
|
| 5628 |
|
|
|
| 5629 |
|
|
/* Here, rhs is positive, finite, and in range */
|
| 5630 |
|
|
|
| 5631 |
|
|
/* lookaside fastpath code for ln(2) and ln(10) at common lengths */
|
| 5632 |
|
|
if (rhs->exponent==0 && set->digits<=40) {
|
| 5633 |
|
|
#if DECDPUN==1
|
| 5634 |
|
|
if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
|
| 5635 |
|
|
#else
|
| 5636 |
|
|
if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */
|
| 5637 |
|
|
#endif
|
| 5638 |
|
|
aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
|
| 5639 |
|
|
#define LN10 "2.302585092994045684017991454684364207601"
|
| 5640 |
|
|
decNumberFromString(res, LN10, &aset);
|
| 5641 |
|
|
*status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
|
| 5642 |
|
|
break;}
|
| 5643 |
|
|
if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
|
| 5644 |
|
|
aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
|
| 5645 |
|
|
#define LN2 "0.6931471805599453094172321214581765680755"
|
| 5646 |
|
|
decNumberFromString(res, LN2, &aset);
|
| 5647 |
|
|
*status|=(DEC_Inexact | DEC_Rounded);
|
| 5648 |
|
|
break;}
|
| 5649 |
|
|
} /* integer and short */
|
| 5650 |
|
|
|
| 5651 |
|
|
/* Determine the working precision. This is normally the */
|
| 5652 |
|
|
/* requested precision + 2, with a minimum of 9. However, if */
|
| 5653 |
|
|
/* the rhs is 'over-precise' then allow for all its digits to */
|
| 5654 |
|
|
/* potentially participate (consider an rhs where all the excess */
|
| 5655 |
|
|
/* digits are 9s) so in this case use rhs->digits+2. */
|
| 5656 |
|
|
p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
|
| 5657 |
|
|
|
| 5658 |
|
|
/* Allocate space for the accumulator and the high-precision */
|
| 5659 |
|
|
/* adjustment calculator, if necessary. The accumulator must */
|
| 5660 |
|
|
/* be able to hold p digits, and the adjustment up to */
|
| 5661 |
|
|
/* rhs->digits+p digits. They are also made big enough for 16 */
|
| 5662 |
|
|
/* digits so that they can be used for calculating the initial */
|
| 5663 |
|
|
/* estimate. */
|
| 5664 |
|
|
needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
|
| 5665 |
|
|
if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| 5666 |
|
|
allocbufa=(decNumber *)malloc(needbytes);
|
| 5667 |
|
|
if (allocbufa==NULL) { /* hopeless -- abandon */
|
| 5668 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5669 |
|
|
break;}
|
| 5670 |
|
|
a=allocbufa; /* use the allocated space */
|
| 5671 |
|
|
}
|
| 5672 |
|
|
pp=p+rhs->digits;
|
| 5673 |
|
|
needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
|
| 5674 |
|
|
if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| 5675 |
|
|
allocbufb=(decNumber *)malloc(needbytes);
|
| 5676 |
|
|
if (allocbufb==NULL) { /* hopeless -- abandon */
|
| 5677 |
|
|
*status|=DEC_Insufficient_storage;
|
| 5678 |
|
|
break;}
|
| 5679 |
|
|
b=allocbufb; /* use the allocated space */
|
| 5680 |
|
|
}
|
| 5681 |
|
|
|
| 5682 |
|
|
/* Prepare an initial estimate in acc. Calculate this by */
|
| 5683 |
|
|
/* considering the coefficient of x to be a normalized fraction, */
|
| 5684 |
|
|
/* f, with the decimal point at far left and multiplied by */
|
| 5685 |
|
|
/* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */
|
| 5686 |
|
|
/* ln(x) = ln(f) + ln(10)*r */
|
| 5687 |
|
|
/* Get the initial estimate for ln(f) from a small lookup */
|
| 5688 |
|
|
/* table (see above) indexed by the first two digits of f, */
|
| 5689 |
|
|
/* truncated. */
|
| 5690 |
|
|
|
| 5691 |
|
|
decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
|
| 5692 |
|
|
r=rhs->exponent+rhs->digits; /* 'normalised' exponent */
|
| 5693 |
|
|
decNumberFromInt32(a, r); /* a=r */
|
| 5694 |
|
|
decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */
|
| 5695 |
|
|
b->exponent=-6; /* .. */
|
| 5696 |
|
|
decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */
|
| 5697 |
|
|
/* now get top two digits of rhs into b by simple truncate and */
|
| 5698 |
|
|
/* force to integer */
|
| 5699 |
|
|
residue=0; /* (no residue) */
|
| 5700 |
|
|
aset.digits=2; aset.round=DEC_ROUND_DOWN;
|
| 5701 |
|
|
decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
|
| 5702 |
|
|
b->exponent=0; /* make integer */
|
| 5703 |
|
|
t=decGetInt(b); /* [cannot fail] */
|
| 5704 |
|
|
if (t<10) t=X10(t); /* adjust single-digit b */
|
| 5705 |
|
|
t=LNnn[t-10]; /* look up ln(b) */
|
| 5706 |
|
|
decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */
|
| 5707 |
|
|
b->exponent=-(t&3)-3; /* set exponent */
|
| 5708 |
|
|
b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */
|
| 5709 |
|
|
aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
|
| 5710 |
|
|
decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
|
| 5711 |
|
|
/* the initial estimate is now in a, with up to 4 digits correct. */
|
| 5712 |
|
|
/* When rhs is at or near Nmax the estimate will be low, so we */
|
| 5713 |
|
|
/* will approach it from below, avoiding overflow when calling exp. */
|
| 5714 |
|
|
|
| 5715 |
|
|
decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */
|
| 5716 |
|
|
|
| 5717 |
|
|
/* accumulator bounds are as requested (could underflow, but */
|
| 5718 |
|
|
/* cannot overflow) */
|
| 5719 |
|
|
aset.emax=set->emax;
|
| 5720 |
|
|
aset.emin=set->emin;
|
| 5721 |
|
|
aset.clamp=0; /* no concrete format */
|
| 5722 |
|
|
/* set up a context to be used for the multiply and subtract */
|
| 5723 |
|
|
bset=aset;
|
| 5724 |
|
|
bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */
|
| 5725 |
|
|
bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */
|
| 5726 |
|
|
/* [see decExpOp call below] */
|
| 5727 |
|
|
/* for each iteration double the number of digits to calculate, */
|
| 5728 |
|
|
/* up to a maximum of p */
|
| 5729 |
|
|
pp=9; /* initial precision */
|
| 5730 |
|
|
/* [initially 9 as then the sequence starts 7+2, 16+2, and */
|
| 5731 |
|
|
/* 34+2, which is ideal for standard-sized numbers] */
|
| 5732 |
|
|
aset.digits=pp; /* working context */
|
| 5733 |
|
|
bset.digits=pp+rhs->digits; /* wider context */
|
| 5734 |
|
|
for (;;) { /* iterate */
|
| 5735 |
|
|
#if DECCHECK
|
| 5736 |
|
|
iterations++;
|
| 5737 |
|
|
if (iterations>24) break; /* consider 9 * 2**24 */
|
| 5738 |
|
|
#endif
|
| 5739 |
|
|
/* calculate the adjustment (exp(-a)*x-1) into b. This is a */
|
| 5740 |
|
|
/* catastrophic subtraction but it really is the difference */
|
| 5741 |
|
|
/* from 1 that is of interest. */
|
| 5742 |
|
|
/* Use the internal entry point to Exp as it allows the double */
|
| 5743 |
|
|
/* range for calculating exp(-a) when a is the tiniest subnormal. */
|
| 5744 |
|
|
a->bits^=DECNEG; /* make -a */
|
| 5745 |
|
|
decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */
|
| 5746 |
|
|
a->bits^=DECNEG; /* restore sign of a */
|
| 5747 |
|
|
/* now multiply by rhs and subtract 1, at the wider precision */
|
| 5748 |
|
|
decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */
|
| 5749 |
|
|
decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */
|
| 5750 |
|
|
|
| 5751 |
|
|
/* the iteration ends when the adjustment cannot affect the */
|
| 5752 |
|
|
/* result by >=0.5 ulp (at the requested digits), which */
|
| 5753 |
|
|
/* is when its value is smaller than the accumulator by */
|
| 5754 |
|
|
/* set->digits+1 digits (or it is zero) -- this is a looser */
|
| 5755 |
|
|
/* requirement than for Exp because all that happens to the */
|
| 5756 |
|
|
/* accumulator after this is the final rounding (but note that */
|
| 5757 |
|
|
/* there must also be full precision in a, or a=0). */
|
| 5758 |
|
|
|
| 5759 |
|
|
if (decNumberIsZero(b) ||
|
| 5760 |
|
|
(a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
|
| 5761 |
|
|
if (a->digits==p) break;
|
| 5762 |
|
|
if (decNumberIsZero(a)) {
|
| 5763 |
|
|
decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
|
| 5764 |
|
|
if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */
|
| 5765 |
|
|
else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */
|
| 5766 |
|
|
break;
|
| 5767 |
|
|
}
|
| 5768 |
|
|
/* force padding if adjustment has gone to 0 before full length */
|
| 5769 |
|
|
if (decNumberIsZero(b)) b->exponent=a->exponent-p;
|
| 5770 |
|
|
}
|
| 5771 |
|
|
|
| 5772 |
|
|
/* not done yet ... */
|
| 5773 |
|
|
decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */
|
| 5774 |
|
|
if (pp==p) continue; /* precision is at maximum */
|
| 5775 |
|
|
/* lengthen the next calculation */
|
| 5776 |
|
|
pp=pp*2; /* double precision */
|
| 5777 |
|
|
if (pp>p) pp=p; /* clamp to maximum */
|
| 5778 |
|
|
aset.digits=pp; /* working context */
|
| 5779 |
|
|
bset.digits=pp+rhs->digits; /* wider context */
|
| 5780 |
|
|
} /* Newton's iteration */
|
| 5781 |
|
|
|
| 5782 |
|
|
#if DECCHECK
|
| 5783 |
|
|
/* just a sanity check; remove the test to show always */
|
| 5784 |
|
|
if (iterations>24)
|
| 5785 |
|
|
printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
|
| 5786 |
|
|
(LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
|
| 5787 |
|
|
#endif
|
| 5788 |
|
|
|
| 5789 |
|
|
/* Copy and round the result to res */
|
| 5790 |
|
|
residue=1; /* indicate dirt to right */
|
| 5791 |
|
|
if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
|
| 5792 |
|
|
aset.digits=set->digits; /* [use default rounding] */
|
| 5793 |
|
|
decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
|
| 5794 |
|
|
decFinish(res, set, &residue, status); /* cleanup/set flags */
|
| 5795 |
|
|
} while(0); /* end protected */
|
| 5796 |
|
|
|
| 5797 |
|
|
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| 5798 |
|
|
if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| 5799 |
|
|
/* [status is handled by caller] */
|
| 5800 |
|
|
return res;
|
| 5801 |
|
|
} /* decLnOp */
|
| 5802 |
|
|
|
| 5803 |
|
|
/* ------------------------------------------------------------------ */
|
| 5804 |
|
|
/* decQuantizeOp -- force exponent to requested value */
|
| 5805 |
|
|
/* */
|
| 5806 |
|
|
/* This computes C = op(A, B), where op adjusts the coefficient */
|
| 5807 |
|
|
/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| 5808 |
|
|
/* of C has the value B or matches the exponent of B. */
|
| 5809 |
|
|
/* The numerical value of C will equal A, except for the effects of */
|
| 5810 |
|
|
/* any rounding that occurred. */
|
| 5811 |
|
|
/* */
|
| 5812 |
|
|
/* res is C, the result. C may be A or B */
|
| 5813 |
|
|
/* lhs is A, the number to adjust */
|
| 5814 |
|
|
/* rhs is B, the requested exponent */
|
| 5815 |
|
|
/* set is the context */
|
| 5816 |
|
|
/* quant is 1 for quantize or 0 for rescale */
|
| 5817 |
|
|
/* status is the status accumulator (this can be called without */
|
| 5818 |
|
|
/* risk of control loss) */
|
| 5819 |
|
|
/* */
|
| 5820 |
|
|
/* C must have space for set->digits digits. */
|
| 5821 |
|
|
/* */
|
| 5822 |
|
|
/* Unless there is an error or the result is infinite, the exponent */
|
| 5823 |
|
|
/* after the operation is guaranteed to be that requested. */
|
| 5824 |
|
|
/* ------------------------------------------------------------------ */
|
| 5825 |
|
|
static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
|
| 5826 |
|
|
const decNumber *rhs, decContext *set,
|
| 5827 |
|
|
Flag quant, uInt *status) {
|
| 5828 |
|
|
#if DECSUBSET
|
| 5829 |
|
|
decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| 5830 |
|
|
decNumber *allocrhs=NULL; /* .., rhs */
|
| 5831 |
|
|
#endif
|
| 5832 |
|
|
const decNumber *inrhs=rhs; /* save original rhs */
|
| 5833 |
|
|
Int reqdigits=set->digits; /* requested DIGITS */
|
| 5834 |
|
|
Int reqexp; /* requested exponent [-scale] */
|
| 5835 |
|
|
Int residue=0; /* rounding residue */
|
| 5836 |
|
|
Int etiny=set->emin-(reqdigits-1);
|
| 5837 |
|
|
|
| 5838 |
|
|
#if DECCHECK
|
| 5839 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 5840 |
|
|
#endif
|
| 5841 |
|
|
|
| 5842 |
|
|
do { /* protect allocated storage */
|
| 5843 |
|
|
#if DECSUBSET
|
| 5844 |
|
|
if (!set->extended) {
|
| 5845 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 5846 |
|
|
if (lhs->digits>reqdigits) {
|
| 5847 |
|
|
alloclhs=decRoundOperand(lhs, set, status);
|
| 5848 |
|
|
if (alloclhs==NULL) break;
|
| 5849 |
|
|
lhs=alloclhs;
|
| 5850 |
|
|
}
|
| 5851 |
|
|
if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
|
| 5852 |
|
|
allocrhs=decRoundOperand(rhs, set, status);
|
| 5853 |
|
|
if (allocrhs==NULL) break;
|
| 5854 |
|
|
rhs=allocrhs;
|
| 5855 |
|
|
}
|
| 5856 |
|
|
}
|
| 5857 |
|
|
#endif
|
| 5858 |
|
|
/* [following code does not require input rounding] */
|
| 5859 |
|
|
|
| 5860 |
|
|
/* Handle special values */
|
| 5861 |
|
|
if (SPECIALARGS) {
|
| 5862 |
|
|
/* NaNs get usual processing */
|
| 5863 |
|
|
if (SPECIALARGS & (DECSNAN | DECNAN))
|
| 5864 |
|
|
decNaNs(res, lhs, rhs, set, status);
|
| 5865 |
|
|
/* one infinity but not both is bad */
|
| 5866 |
|
|
else if ((lhs->bits ^ rhs->bits) & DECINF)
|
| 5867 |
|
|
*status|=DEC_Invalid_operation;
|
| 5868 |
|
|
/* both infinity: return lhs */
|
| 5869 |
|
|
else decNumberCopy(res, lhs); /* [nop if in place] */
|
| 5870 |
|
|
break;
|
| 5871 |
|
|
}
|
| 5872 |
|
|
|
| 5873 |
|
|
/* set requested exponent */
|
| 5874 |
|
|
if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */
|
| 5875 |
|
|
else { /* rescale -- use value of rhs */
|
| 5876 |
|
|
/* Original rhs must be an integer that fits and is in range, */
|
| 5877 |
|
|
/* which could be from -1999999997 to +999999999, thanks to */
|
| 5878 |
|
|
/* subnormals */
|
| 5879 |
|
|
reqexp=decGetInt(inrhs); /* [cannot fail] */
|
| 5880 |
|
|
}
|
| 5881 |
|
|
|
| 5882 |
|
|
#if DECSUBSET
|
| 5883 |
|
|
if (!set->extended) etiny=set->emin; /* no subnormals */
|
| 5884 |
|
|
#endif
|
| 5885 |
|
|
|
| 5886 |
|
|
if (reqexp==BADINT /* bad (rescale only) or .. */
|
| 5887 |
|
|
|| reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */
|
| 5888 |
|
|
|| (reqexp<etiny) /* < lowest */
|
| 5889 |
|
|
|| (reqexp>set->emax)) { /* > emax */
|
| 5890 |
|
|
*status|=DEC_Invalid_operation;
|
| 5891 |
|
|
break;}
|
| 5892 |
|
|
|
| 5893 |
|
|
/* the RHS has been processed, so it can be overwritten now if necessary */
|
| 5894 |
|
|
if (ISZERO(lhs)) { /* zero coefficient unchanged */
|
| 5895 |
|
|
decNumberCopy(res, lhs); /* [nop if in place] */
|
| 5896 |
|
|
res->exponent=reqexp; /* .. just set exponent */
|
| 5897 |
|
|
#if DECSUBSET
|
| 5898 |
|
|
if (!set->extended) res->bits=0; /* subset specification; no -0 */
|
| 5899 |
|
|
#endif
|
| 5900 |
|
|
}
|
| 5901 |
|
|
else { /* non-zero lhs */
|
| 5902 |
|
|
Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */
|
| 5903 |
|
|
/* if adjusted coefficient will definitely not fit, give up now */
|
| 5904 |
|
|
if ((lhs->digits-adjust)>reqdigits) {
|
| 5905 |
|
|
*status|=DEC_Invalid_operation;
|
| 5906 |
|
|
break;
|
| 5907 |
|
|
}
|
| 5908 |
|
|
|
| 5909 |
|
|
if (adjust>0) { /* increasing exponent */
|
| 5910 |
|
|
/* this will decrease the length of the coefficient by adjust */
|
| 5911 |
|
|
/* digits, and must round as it does so */
|
| 5912 |
|
|
decContext workset; /* work */
|
| 5913 |
|
|
workset=*set; /* clone rounding, etc. */
|
| 5914 |
|
|
workset.digits=lhs->digits-adjust; /* set requested length */
|
| 5915 |
|
|
/* [note that the latter can be <1, here] */
|
| 5916 |
|
|
decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
|
| 5917 |
|
|
decApplyRound(res, &workset, residue, status); /* .. and round */
|
| 5918 |
|
|
residue=0; /* [used] */
|
| 5919 |
|
|
/* If just rounded a 999s case, exponent will be off by one; */
|
| 5920 |
|
|
/* adjust back (after checking space), if so. */
|
| 5921 |
|
|
if (res->exponent>reqexp) {
|
| 5922 |
|
|
/* re-check needed, e.g., for quantize(0.9999, 0.001) under */
|
| 5923 |
|
|
/* set->digits==3 */
|
| 5924 |
|
|
if (res->digits==reqdigits) { /* cannot shift by 1 */
|
| 5925 |
|
|
*status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
|
| 5926 |
|
|
*status|=DEC_Invalid_operation;
|
| 5927 |
|
|
break;
|
| 5928 |
|
|
}
|
| 5929 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
|
| 5930 |
|
|
res->exponent--; /* (re)adjust the exponent. */
|
| 5931 |
|
|
}
|
| 5932 |
|
|
#if DECSUBSET
|
| 5933 |
|
|
if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
|
| 5934 |
|
|
#endif
|
| 5935 |
|
|
} /* increase */
|
| 5936 |
|
|
else /* adjust<=0 */ { /* decreasing or = exponent */
|
| 5937 |
|
|
/* this will increase the length of the coefficient by -adjust */
|
| 5938 |
|
|
/* digits, by adding zero or more trailing zeros; this is */
|
| 5939 |
|
|
/* already checked for fit, above */
|
| 5940 |
|
|
decNumberCopy(res, lhs); /* [it will fit] */
|
| 5941 |
|
|
/* if padding needed (adjust<0), add it now... */
|
| 5942 |
|
|
if (adjust<0) {
|
| 5943 |
|
|
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| 5944 |
|
|
res->exponent+=adjust; /* adjust the exponent */
|
| 5945 |
|
|
}
|
| 5946 |
|
|
} /* decrease */
|
| 5947 |
|
|
} /* non-zero */
|
| 5948 |
|
|
|
| 5949 |
|
|
/* Check for overflow [do not use Finalize in this case, as an */
|
| 5950 |
|
|
/* overflow here is a "don't fit" situation] */
|
| 5951 |
|
|
if (res->exponent>set->emax-res->digits+1) { /* too big */
|
| 5952 |
|
|
*status|=DEC_Invalid_operation;
|
| 5953 |
|
|
break;
|
| 5954 |
|
|
}
|
| 5955 |
|
|
else {
|
| 5956 |
|
|
decFinalize(res, set, &residue, status); /* set subnormal flags */
|
| 5957 |
|
|
*status&=~DEC_Underflow; /* suppress Underflow [as per 754] */
|
| 5958 |
|
|
}
|
| 5959 |
|
|
} while(0); /* end protected */
|
| 5960 |
|
|
|
| 5961 |
|
|
#if DECSUBSET
|
| 5962 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */
|
| 5963 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 5964 |
|
|
#endif
|
| 5965 |
|
|
return res;
|
| 5966 |
|
|
} /* decQuantizeOp */
|
| 5967 |
|
|
|
| 5968 |
|
|
/* ------------------------------------------------------------------ */
|
| 5969 |
|
|
/* decCompareOp -- compare, min, or max two Numbers */
|
| 5970 |
|
|
/* */
|
| 5971 |
|
|
/* This computes C = A ? B and carries out one of four operations: */
|
| 5972 |
|
|
/* COMPARE -- returns the signum (as a number) giving the */
|
| 5973 |
|
|
/* result of a comparison unless one or both */
|
| 5974 |
|
|
/* operands is a NaN (in which case a NaN results) */
|
| 5975 |
|
|
/* COMPSIG -- as COMPARE except that a quiet NaN raises */
|
| 5976 |
|
|
/* Invalid operation. */
|
| 5977 |
|
|
/* COMPMAX -- returns the larger of the operands, using the */
|
| 5978 |
|
|
/* 754 maxnum operation */
|
| 5979 |
|
|
/* COMPMAXMAG -- ditto, comparing absolute values */
|
| 5980 |
|
|
/* COMPMIN -- the 754 minnum operation */
|
| 5981 |
|
|
/* COMPMINMAG -- ditto, comparing absolute values */
|
| 5982 |
|
|
/* COMTOTAL -- returns the signum (as a number) giving the */
|
| 5983 |
|
|
/* result of a comparison using 754 total ordering */
|
| 5984 |
|
|
/* */
|
| 5985 |
|
|
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| 5986 |
|
|
/* lhs is A */
|
| 5987 |
|
|
/* rhs is B */
|
| 5988 |
|
|
/* set is the context */
|
| 5989 |
|
|
/* op is the operation flag */
|
| 5990 |
|
|
/* status is the usual accumulator */
|
| 5991 |
|
|
/* */
|
| 5992 |
|
|
/* C must have space for one digit for COMPARE or set->digits for */
|
| 5993 |
|
|
/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
|
| 5994 |
|
|
/* ------------------------------------------------------------------ */
|
| 5995 |
|
|
/* The emphasis here is on speed for common cases, and avoiding */
|
| 5996 |
|
|
/* coefficient comparison if possible. */
|
| 5997 |
|
|
/* ------------------------------------------------------------------ */
|
| 5998 |
|
|
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
|
| 5999 |
|
|
const decNumber *rhs, decContext *set,
|
| 6000 |
|
|
Flag op, uInt *status) {
|
| 6001 |
|
|
#if DECSUBSET
|
| 6002 |
|
|
decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| 6003 |
|
|
decNumber *allocrhs=NULL; /* .., rhs */
|
| 6004 |
|
|
#endif
|
| 6005 |
|
|
Int result=0; /* default result value */
|
| 6006 |
|
|
uByte merged; /* work */
|
| 6007 |
|
|
|
| 6008 |
|
|
#if DECCHECK
|
| 6009 |
|
|
if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| 6010 |
|
|
#endif
|
| 6011 |
|
|
|
| 6012 |
|
|
do { /* protect allocated storage */
|
| 6013 |
|
|
#if DECSUBSET
|
| 6014 |
|
|
if (!set->extended) {
|
| 6015 |
|
|
/* reduce operands and set lostDigits status, as needed */
|
| 6016 |
|
|
if (lhs->digits>set->digits) {
|
| 6017 |
|
|
alloclhs=decRoundOperand(lhs, set, status);
|
| 6018 |
|
|
if (alloclhs==NULL) {result=BADINT; break;}
|
| 6019 |
|
|
lhs=alloclhs;
|
| 6020 |
|
|
}
|
| 6021 |
|
|
if (rhs->digits>set->digits) {
|
| 6022 |
|
|
allocrhs=decRoundOperand(rhs, set, status);
|
| 6023 |
|
|
if (allocrhs==NULL) {result=BADINT; break;}
|
| 6024 |
|
|
rhs=allocrhs;
|
| 6025 |
|
|
}
|
| 6026 |
|
|
}
|
| 6027 |
|
|
#endif
|
| 6028 |
|
|
/* [following code does not require input rounding] */
|
| 6029 |
|
|
|
| 6030 |
|
|
/* If total ordering then handle differing signs 'up front' */
|
| 6031 |
|
|
if (op==COMPTOTAL) { /* total ordering */
|
| 6032 |
|
|
if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
|
| 6033 |
|
|
result=-1;
|
| 6034 |
|
|
break;
|
| 6035 |
|
|
}
|
| 6036 |
|
|
if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
|
| 6037 |
|
|
result=+1;
|
| 6038 |
|
|
break;
|
| 6039 |
|
|
}
|
| 6040 |
|
|
}
|
| 6041 |
|
|
|
| 6042 |
|
|
/* handle NaNs specially; let infinities drop through */
|
| 6043 |
|
|
/* This assumes sNaN (even just one) leads to NaN. */
|
| 6044 |
|
|
merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
|
| 6045 |
|
|
if (merged) { /* a NaN bit set */
|
| 6046 |
|
|
if (op==COMPARE); /* result will be NaN */
|
| 6047 |
|
|
else if (op==COMPSIG) /* treat qNaN as sNaN */
|
| 6048 |
|
|
*status|=DEC_Invalid_operation | DEC_sNaN;
|
| 6049 |
|
|
else if (op==COMPTOTAL) { /* total ordering, always finite */
|
| 6050 |
|
|
/* signs are known to be the same; compute the ordering here */
|
| 6051 |
|
|
/* as if the signs are both positive, then invert for negatives */
|
| 6052 |
|
|
if (!decNumberIsNaN(lhs)) result=-1;
|
| 6053 |
|
|
else if (!decNumberIsNaN(rhs)) result=+1;
|
| 6054 |
|
|
/* here if both NaNs */
|
| 6055 |
|
|
else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
|
| 6056 |
|
|
else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
|
| 6057 |
|
|
else { /* both NaN or both sNaN */
|
| 6058 |
|
|
/* now it just depends on the payload */
|
| 6059 |
|
|
result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
|
| 6060 |
|
|
rhs->lsu, D2U(rhs->digits), 0);
|
| 6061 |
|
|
/* [Error not possible, as these are 'aligned'] */
|
| 6062 |
|
|
} /* both same NaNs */
|
| 6063 |
|
|
if (decNumberIsNegative(lhs)) result=-result;
|
| 6064 |
|
|
break;
|
| 6065 |
|
|
} /* total order */
|
| 6066 |
|
|
|
| 6067 |
|
|
else if (merged & DECSNAN); /* sNaN -> qNaN */
|
| 6068 |
|
|
else { /* here if MIN or MAX and one or two quiet NaNs */
|
| 6069 |
|
|
/* min or max -- 754 rules ignore single NaN */
|
| 6070 |
|
|
if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
|
| 6071 |
|
|
/* just one NaN; force choice to be the non-NaN operand */
|
| 6072 |
|
|
op=COMPMAX;
|
| 6073 |
|
|
if (lhs->bits & DECNAN) result=-1; /* pick rhs */
|
| 6074 |
|
|
else result=+1; /* pick lhs */
|
| 6075 |
|
|
break;
|
| 6076 |
|
|
}
|
| 6077 |
|
|
} /* max or min */
|
| 6078 |
|
|
op=COMPNAN; /* use special path */
|
| 6079 |
|
|
decNaNs(res, lhs, rhs, set, status); /* propagate NaN */
|
| 6080 |
|
|
break;
|
| 6081 |
|
|
}
|
| 6082 |
|
|
/* have numbers */
|
| 6083 |
|
|
if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
|
| 6084 |
|
|
else result=decCompare(lhs, rhs, 0); /* sign matters */
|
| 6085 |
|
|
} while(0); /* end protected */
|
| 6086 |
|
|
|
| 6087 |
|
|
if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
|
| 6088 |
|
|
else {
|
| 6089 |
|
|
if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
|
| 6090 |
|
|
if (op==COMPTOTAL && result==0) {
|
| 6091 |
|
|
/* operands are numerically equal or same NaN (and same sign, */
|
| 6092 |
|
|
/* tested first); if identical, leave result 0 */
|
| 6093 |
|
|
if (lhs->exponent!=rhs->exponent) {
|
| 6094 |
|
|
if (lhs->exponent<rhs->exponent) result=-1;
|
| 6095 |
|
|
else result=+1;
|
| 6096 |
|
|
if (decNumberIsNegative(lhs)) result=-result;
|
| 6097 |
|
|
} /* lexp!=rexp */
|
| 6098 |
|
|
} /* total-order by exponent */
|
| 6099 |
|
|
decNumberZero(res); /* [always a valid result] */
|
| 6100 |
|
|
if (result!=0) { /* must be -1 or +1 */
|
| 6101 |
|
|
*res->lsu=1;
|
| 6102 |
|
|
if (result<0) res->bits=DECNEG;
|
| 6103 |
|
|
}
|
| 6104 |
|
|
}
|
| 6105 |
|
|
else if (op==COMPNAN); /* special, drop through */
|
| 6106 |
|
|
else { /* MAX or MIN, non-NaN result */
|
| 6107 |
|
|
Int residue=0; /* rounding accumulator */
|
| 6108 |
|
|
/* choose the operand for the result */
|
| 6109 |
|
|
const decNumber *choice;
|
| 6110 |
|
|
if (result==0) { /* operands are numerically equal */
|
| 6111 |
|
|
/* choose according to sign then exponent (see 754) */
|
| 6112 |
|
|
uByte slhs=(lhs->bits & DECNEG);
|
| 6113 |
|
|
uByte srhs=(rhs->bits & DECNEG);
|
| 6114 |
|
|
#if DECSUBSET
|
| 6115 |
|
|
if (!set->extended) { /* subset: force left-hand */
|
| 6116 |
|
|
op=COMPMAX;
|
| 6117 |
|
|
result=+1;
|
| 6118 |
|
|
}
|
| 6119 |
|
|
else
|
| 6120 |
|
|
#endif
|
| 6121 |
|
|
if (slhs!=srhs) { /* signs differ */
|
| 6122 |
|
|
if (slhs) result=-1; /* rhs is max */
|
| 6123 |
|
|
else result=+1; /* lhs is max */
|
| 6124 |
|
|
}
|
| 6125 |
|
|
else if (slhs && srhs) { /* both negative */
|
| 6126 |
|
|
if (lhs->exponent<rhs->exponent) result=+1;
|
| 6127 |
|
|
else result=-1;
|
| 6128 |
|
|
/* [if equal, use lhs, technically identical] */
|
| 6129 |
|
|
}
|
| 6130 |
|
|
else { /* both positive */
|
| 6131 |
|
|
if (lhs->exponent>rhs->exponent) result=+1;
|
| 6132 |
|
|
else result=-1;
|
| 6133 |
|
|
/* [ditto] */
|
| 6134 |
|
|
}
|
| 6135 |
|
|
} /* numerically equal */
|
| 6136 |
|
|
/* here result will be non-0; reverse if looking for MIN */
|
| 6137 |
|
|
if (op==COMPMIN || op==COMPMINMAG) result=-result;
|
| 6138 |
|
|
choice=(result>0 ? lhs : rhs); /* choose */
|
| 6139 |
|
|
/* copy chosen to result, rounding if need be */
|
| 6140 |
|
|
decCopyFit(res, choice, set, &residue, status);
|
| 6141 |
|
|
decFinish(res, set, &residue, status);
|
| 6142 |
|
|
}
|
| 6143 |
|
|
}
|
| 6144 |
|
|
#if DECSUBSET
|
| 6145 |
|
|
if (allocrhs!=NULL) free(allocrhs); /* free any storage used */
|
| 6146 |
|
|
if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| 6147 |
|
|
#endif
|
| 6148 |
|
|
return res;
|
| 6149 |
|
|
} /* decCompareOp */
|
| 6150 |
|
|
|
| 6151 |
|
|
/* ------------------------------------------------------------------ */
|
| 6152 |
|
|
/* decCompare -- compare two decNumbers by numerical value */
|
| 6153 |
|
|
/* */
|
| 6154 |
|
|
/* This routine compares A ? B without altering them. */
|
| 6155 |
|
|
/* */
|
| 6156 |
|
|
/* Arg1 is A, a decNumber which is not a NaN */
|
| 6157 |
|
|
/* Arg2 is B, a decNumber which is not a NaN */
|
| 6158 |
|
|
/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
|
| 6159 |
|
|
/* */
|
| 6160 |
|
|
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| 6161 |
|
|
/* (the only possible failure is an allocation error) */
|
| 6162 |
|
|
/* ------------------------------------------------------------------ */
|
| 6163 |
|
|
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
|
| 6164 |
|
|
Flag abs) {
|
| 6165 |
|
|
Int result; /* result value */
|
| 6166 |
|
|
Int sigr; /* rhs signum */
|
| 6167 |
|
|
Int compare; /* work */
|
| 6168 |
|
|
|
| 6169 |
|
|
result=1; /* assume signum(lhs) */
|
| 6170 |
|
|
if (ISZERO(lhs)) result=0;
|
| 6171 |
|
|
if (abs) {
|
| 6172 |
|
|
if (ISZERO(rhs)) return result; /* LHS wins or both 0 */
|
| 6173 |
|
|
/* RHS is non-zero */
|
| 6174 |
|
|
if (result==0) return -1; /* LHS is 0; RHS wins */
|
| 6175 |
|
|
/* [here, both non-zero, result=1] */
|
| 6176 |
|
|
}
|
| 6177 |
|
|
else { /* signs matter */
|
| 6178 |
|
|
if (result && decNumberIsNegative(lhs)) result=-1;
|
| 6179 |
|
|
sigr=1; /* compute signum(rhs) */
|
| 6180 |
|
|
if (ISZERO(rhs)) sigr=0;
|
| 6181 |
|
|
else if (decNumberIsNegative(rhs)) sigr=-1;
|
| 6182 |
|
|
if (result > sigr) return +1; /* L > R, return 1 */
|
| 6183 |
|
|
if (result < sigr) return -1; /* L < R, return -1 */
|
| 6184 |
|
|
if (result==0) return 0; /* both 0 */
|
| 6185 |
|
|
}
|
| 6186 |
|
|
|
| 6187 |
|
|
/* signums are the same; both are non-zero */
|
| 6188 |
|
|
if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */
|
| 6189 |
|
|
if (decNumberIsInfinite(rhs)) {
|
| 6190 |
|
|
if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
|
| 6191 |
|
|
else result=-result; /* only rhs infinite */
|
| 6192 |
|
|
}
|
| 6193 |
|
|
return result;
|
| 6194 |
|
|
}
|
| 6195 |
|
|
/* must compare the coefficients, allowing for exponents */
|
| 6196 |
|
|
if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */
|
| 6197 |
|
|
/* swap sides, and sign */
|
| 6198 |
|
|
const decNumber *temp=lhs;
|
| 6199 |
|
|
lhs=rhs;
|
| 6200 |
|
|
rhs=temp;
|
| 6201 |
|
|
result=-result;
|
| 6202 |
|
|
}
|
| 6203 |
|
|
compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
|
| 6204 |
|
|
rhs->lsu, D2U(rhs->digits),
|
| 6205 |
|
|
rhs->exponent-lhs->exponent);
|
| 6206 |
|
|
if (compare!=BADINT) compare*=result; /* comparison succeeded */
|
| 6207 |
|
|
return compare;
|
| 6208 |
|
|
} /* decCompare */
|
| 6209 |
|
|
|
| 6210 |
|
|
/* ------------------------------------------------------------------ */
|
| 6211 |
|
|
/* decUnitCompare -- compare two >=0 integers in Unit arrays */
|
| 6212 |
|
|
/* */
|
| 6213 |
|
|
/* This routine compares A ? B*10**E where A and B are unit arrays */
|
| 6214 |
|
|
/* A is a plain integer */
|
| 6215 |
|
|
/* B has an exponent of E (which must be non-negative) */
|
| 6216 |
|
|
/* */
|
| 6217 |
|
|
/* Arg1 is A first Unit (lsu) */
|
| 6218 |
|
|
/* Arg2 is A length in Units */
|
| 6219 |
|
|
/* Arg3 is B first Unit (lsu) */
|
| 6220 |
|
|
/* Arg4 is B length in Units */
|
| 6221 |
|
|
/* Arg5 is E (0 if the units are aligned) */
|
| 6222 |
|
|
/* */
|
| 6223 |
|
|
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| 6224 |
|
|
/* (the only possible failure is an allocation error, which can */
|
| 6225 |
|
|
/* only occur if E!=0) */
|
| 6226 |
|
|
/* ------------------------------------------------------------------ */
|
| 6227 |
|
|
static Int decUnitCompare(const Unit *a, Int alength,
|
| 6228 |
|
|
const Unit *b, Int blength, Int exp) {
|
| 6229 |
|
|
Unit *acc; /* accumulator for result */
|
| 6230 |
|
|
Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
|
| 6231 |
|
|
Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
|
| 6232 |
|
|
Int accunits, need; /* units in use or needed for acc */
|
| 6233 |
|
|
const Unit *l, *r, *u; /* work */
|
| 6234 |
|
|
Int expunits, exprem, result; /* .. */
|
| 6235 |
|
|
|
| 6236 |
|
|
if (exp==0) { /* aligned; fastpath */
|
| 6237 |
|
|
if (alength>blength) return 1;
|
| 6238 |
|
|
if (alength<blength) return -1;
|
| 6239 |
|
|
/* same number of units in both -- need unit-by-unit compare */
|
| 6240 |
|
|
l=a+alength-1;
|
| 6241 |
|
|
r=b+alength-1;
|
| 6242 |
|
|
for (;l>=a; l--, r--) {
|
| 6243 |
|
|
if (*l>*r) return 1;
|
| 6244 |
|
|
if (*l<*r) return -1;
|
| 6245 |
|
|
}
|
| 6246 |
|
|
return 0; /* all units match */
|
| 6247 |
|
|
} /* aligned */
|
| 6248 |
|
|
|
| 6249 |
|
|
/* Unaligned. If one is >1 unit longer than the other, padded */
|
| 6250 |
|
|
/* approximately, then can return easily */
|
| 6251 |
|
|
if (alength>blength+(Int)D2U(exp)) return 1;
|
| 6252 |
|
|
if (alength+1<blength+(Int)D2U(exp)) return -1;
|
| 6253 |
|
|
|
| 6254 |
|
|
/* Need to do a real subtract. For this, a result buffer is needed */
|
| 6255 |
|
|
/* even though only the sign is of interest. Its length needs */
|
| 6256 |
|
|
/* to be the larger of alength and padded blength, +2 */
|
| 6257 |
|
|
need=blength+D2U(exp); /* maximum real length of B */
|
| 6258 |
|
|
if (need<alength) need=alength;
|
| 6259 |
|
|
need+=2;
|
| 6260 |
|
|
acc=accbuff; /* assume use local buffer */
|
| 6261 |
|
|
if (need*sizeof(Unit)>sizeof(accbuff)) {
|
| 6262 |
|
|
allocacc=(Unit *)malloc(need*sizeof(Unit));
|
| 6263 |
|
|
if (allocacc==NULL) return BADINT; /* hopeless -- abandon */
|
| 6264 |
|
|
acc=allocacc;
|
| 6265 |
|
|
}
|
| 6266 |
|
|
/* Calculate units and remainder from exponent. */
|
| 6267 |
|
|
expunits=exp/DECDPUN;
|
| 6268 |
|
|
exprem=exp%DECDPUN;
|
| 6269 |
|
|
/* subtract [A+B*(-m)] */
|
| 6270 |
|
|
accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
|
| 6271 |
|
|
-(Int)powers[exprem]);
|
| 6272 |
|
|
/* [UnitAddSub result may have leading zeros, even on zero] */
|
| 6273 |
|
|
if (accunits<0) result=-1; /* negative result */
|
| 6274 |
|
|
else { /* non-negative result */
|
| 6275 |
|
|
/* check units of the result before freeing any storage */
|
| 6276 |
|
|
for (u=acc; u<acc+accunits-1 && *u==0;) u++;
|
| 6277 |
|
|
result=(*u==0 ? 0 : +1);
|
| 6278 |
|
|
}
|
| 6279 |
|
|
/* clean up and return the result */
|
| 6280 |
|
|
if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| 6281 |
|
|
return result;
|
| 6282 |
|
|
} /* decUnitCompare */
|
| 6283 |
|
|
|
| 6284 |
|
|
/* ------------------------------------------------------------------ */
|
| 6285 |
|
|
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
|
| 6286 |
|
|
/* */
|
| 6287 |
|
|
/* This routine performs the calculation: */
|
| 6288 |
|
|
/* */
|
| 6289 |
|
|
/* C=A+(B*M) */
|
| 6290 |
|
|
/* */
|
| 6291 |
|
|
/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
|
| 6292 |
|
|
/* */
|
| 6293 |
|
|
/* A may be shorter or longer than B. */
|
| 6294 |
|
|
/* */
|
| 6295 |
|
|
/* Leading zeros are not removed after a calculation. The result is */
|
| 6296 |
|
|
/* either the same length as the longer of A and B (adding any */
|
| 6297 |
|
|
/* shift), or one Unit longer than that (if a Unit carry occurred). */
|
| 6298 |
|
|
/* */
|
| 6299 |
|
|
/* A and B content are not altered unless C is also A or B. */
|
| 6300 |
|
|
/* C may be the same array as A or B, but only if no zero padding is */
|
| 6301 |
|
|
/* requested (that is, C may be B only if bshift==0). */
|
| 6302 |
|
|
/* C is filled from the lsu; only those units necessary to complete */
|
| 6303 |
|
|
/* the calculation are referenced. */
|
| 6304 |
|
|
/* */
|
| 6305 |
|
|
/* Arg1 is A first Unit (lsu) */
|
| 6306 |
|
|
/* Arg2 is A length in Units */
|
| 6307 |
|
|
/* Arg3 is B first Unit (lsu) */
|
| 6308 |
|
|
/* Arg4 is B length in Units */
|
| 6309 |
|
|
/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
|
| 6310 |
|
|
/* Arg6 is C first Unit (lsu) */
|
| 6311 |
|
|
/* Arg7 is M, the multiplier */
|
| 6312 |
|
|
/* */
|
| 6313 |
|
|
/* returns the count of Units written to C, which will be non-zero */
|
| 6314 |
|
|
/* and negated if the result is negative. That is, the sign of the */
|
| 6315 |
|
|
/* returned Int is the sign of the result (positive for zero) and */
|
| 6316 |
|
|
/* the absolute value of the Int is the count of Units. */
|
| 6317 |
|
|
/* */
|
| 6318 |
|
|
/* It is the caller's responsibility to make sure that C size is */
|
| 6319 |
|
|
/* safe, allowing space if necessary for a one-Unit carry. */
|
| 6320 |
|
|
/* */
|
| 6321 |
|
|
/* This routine is severely performance-critical; *any* change here */
|
| 6322 |
|
|
/* must be measured (timed) to assure no performance degradation. */
|
| 6323 |
|
|
/* In particular, trickery here tends to be counter-productive, as */
|
| 6324 |
|
|
/* increased complexity of code hurts register optimizations on */
|
| 6325 |
|
|
/* register-poor architectures. Avoiding divisions is nearly */
|
| 6326 |
|
|
/* always a Good Idea, however. */
|
| 6327 |
|
|
/* */
|
| 6328 |
|
|
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
|
| 6329 |
|
|
/* (IBM Warwick, UK) for some of the ideas used in this routine. */
|
| 6330 |
|
|
/* ------------------------------------------------------------------ */
|
| 6331 |
|
|
static Int decUnitAddSub(const Unit *a, Int alength,
|
| 6332 |
|
|
const Unit *b, Int blength, Int bshift,
|
| 6333 |
|
|
Unit *c, Int m) {
|
| 6334 |
|
|
const Unit *alsu=a; /* A lsu [need to remember it] */
|
| 6335 |
|
|
Unit *clsu=c; /* C ditto */
|
| 6336 |
|
|
Unit *minC; /* low water mark for C */
|
| 6337 |
|
|
Unit *maxC; /* high water mark for C */
|
| 6338 |
|
|
eInt carry=0; /* carry integer (could be Long) */
|
| 6339 |
|
|
Int add; /* work */
|
| 6340 |
|
|
#if DECDPUN<=4 /* myriadal, millenary, etc. */
|
| 6341 |
|
|
Int est; /* estimated quotient */
|
| 6342 |
|
|
#endif
|
| 6343 |
|
|
|
| 6344 |
|
|
#if DECTRACE
|
| 6345 |
|
|
if (alength<1 || blength<1)
|
| 6346 |
|
|
printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
|
| 6347 |
|
|
#endif
|
| 6348 |
|
|
|
| 6349 |
|
|
maxC=c+alength; /* A is usually the longer */
|
| 6350 |
|
|
minC=c+blength; /* .. and B the shorter */
|
| 6351 |
|
|
if (bshift!=0) { /* B is shifted; low As copy across */
|
| 6352 |
|
|
minC+=bshift;
|
| 6353 |
|
|
/* if in place [common], skip copy unless there's a gap [rare] */
|
| 6354 |
|
|
if (a==c && bshift<=alength) {
|
| 6355 |
|
|
c+=bshift;
|
| 6356 |
|
|
a+=bshift;
|
| 6357 |
|
|
}
|
| 6358 |
|
|
else for (; c<clsu+bshift; a++, c++) { /* copy needed */
|
| 6359 |
|
|
if (a<alsu+alength) *c=*a;
|
| 6360 |
|
|
else *c=0;
|
| 6361 |
|
|
}
|
| 6362 |
|
|
}
|
| 6363 |
|
|
if (minC>maxC) { /* swap */
|
| 6364 |
|
|
Unit *hold=minC;
|
| 6365 |
|
|
minC=maxC;
|
| 6366 |
|
|
maxC=hold;
|
| 6367 |
|
|
}
|
| 6368 |
|
|
|
| 6369 |
|
|
/* For speed, do the addition as two loops; the first where both A */
|
| 6370 |
|
|
/* and B contribute, and the second (if necessary) where only one or */
|
| 6371 |
|
|
/* other of the numbers contribute. */
|
| 6372 |
|
|
/* Carry handling is the same (i.e., duplicated) in each case. */
|
| 6373 |
|
|
for (; c<minC; c++) {
|
| 6374 |
|
|
carry+=*a;
|
| 6375 |
|
|
a++;
|
| 6376 |
|
|
carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */
|
| 6377 |
|
|
b++; /* here is not a win] */
|
| 6378 |
|
|
/* here carry is new Unit of digits; it could be +ve or -ve */
|
| 6379 |
|
|
if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
|
| 6380 |
|
|
*c=(Unit)carry;
|
| 6381 |
|
|
carry=0;
|
| 6382 |
|
|
continue;
|
| 6383 |
|
|
}
|
| 6384 |
|
|
#if DECDPUN==4 /* use divide-by-multiply */
|
| 6385 |
|
|
if (carry>=0) {
|
| 6386 |
|
|
est=(((ueInt)carry>>11)*53687)>>18;
|
| 6387 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6388 |
|
|
carry=est; /* likely quotient [89%] */
|
| 6389 |
|
|
if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| 6390 |
|
|
carry++;
|
| 6391 |
|
|
*c-=DECDPUNMAX+1;
|
| 6392 |
|
|
continue;
|
| 6393 |
|
|
}
|
| 6394 |
|
|
/* negative case */
|
| 6395 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6396 |
|
|
est=(((ueInt)carry>>11)*53687)>>18;
|
| 6397 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6398 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6399 |
|
|
if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| 6400 |
|
|
carry++;
|
| 6401 |
|
|
*c-=DECDPUNMAX+1;
|
| 6402 |
|
|
#elif DECDPUN==3
|
| 6403 |
|
|
if (carry>=0) {
|
| 6404 |
|
|
est=(((ueInt)carry>>3)*16777)>>21;
|
| 6405 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6406 |
|
|
carry=est; /* likely quotient [99%] */
|
| 6407 |
|
|
if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| 6408 |
|
|
carry++;
|
| 6409 |
|
|
*c-=DECDPUNMAX+1;
|
| 6410 |
|
|
continue;
|
| 6411 |
|
|
}
|
| 6412 |
|
|
/* negative case */
|
| 6413 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6414 |
|
|
est=(((ueInt)carry>>3)*16777)>>21;
|
| 6415 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6416 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6417 |
|
|
if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| 6418 |
|
|
carry++;
|
| 6419 |
|
|
*c-=DECDPUNMAX+1;
|
| 6420 |
|
|
#elif DECDPUN<=2
|
| 6421 |
|
|
/* Can use QUOT10 as carry <= 4 digits */
|
| 6422 |
|
|
if (carry>=0) {
|
| 6423 |
|
|
est=QUOT10(carry, DECDPUN);
|
| 6424 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6425 |
|
|
carry=est; /* quotient */
|
| 6426 |
|
|
continue;
|
| 6427 |
|
|
}
|
| 6428 |
|
|
/* negative case */
|
| 6429 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6430 |
|
|
est=QUOT10(carry, DECDPUN);
|
| 6431 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6432 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6433 |
|
|
#else
|
| 6434 |
|
|
/* remainder operator is undefined if negative, so must test */
|
| 6435 |
|
|
if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */
|
| 6436 |
|
|
*c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */
|
| 6437 |
|
|
carry=1;
|
| 6438 |
|
|
continue;
|
| 6439 |
|
|
}
|
| 6440 |
|
|
if (carry>=0) {
|
| 6441 |
|
|
*c=(Unit)(carry%(DECDPUNMAX+1));
|
| 6442 |
|
|
carry=carry/(DECDPUNMAX+1);
|
| 6443 |
|
|
continue;
|
| 6444 |
|
|
}
|
| 6445 |
|
|
/* negative case */
|
| 6446 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6447 |
|
|
*c=(Unit)(carry%(DECDPUNMAX+1));
|
| 6448 |
|
|
carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
|
| 6449 |
|
|
#endif
|
| 6450 |
|
|
} /* c */
|
| 6451 |
|
|
|
| 6452 |
|
|
/* now may have one or other to complete */
|
| 6453 |
|
|
/* [pretest to avoid loop setup/shutdown] */
|
| 6454 |
|
|
if (c<maxC) for (; c<maxC; c++) {
|
| 6455 |
|
|
if (a<alsu+alength) { /* still in A */
|
| 6456 |
|
|
carry+=*a;
|
| 6457 |
|
|
a++;
|
| 6458 |
|
|
}
|
| 6459 |
|
|
else { /* inside B */
|
| 6460 |
|
|
carry+=((eInt)*b)*m;
|
| 6461 |
|
|
b++;
|
| 6462 |
|
|
}
|
| 6463 |
|
|
/* here carry is new Unit of digits; it could be +ve or -ve and */
|
| 6464 |
|
|
/* magnitude up to DECDPUNMAX squared */
|
| 6465 |
|
|
if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
|
| 6466 |
|
|
*c=(Unit)carry;
|
| 6467 |
|
|
carry=0;
|
| 6468 |
|
|
continue;
|
| 6469 |
|
|
}
|
| 6470 |
|
|
/* result for this unit is negative or >DECDPUNMAX */
|
| 6471 |
|
|
#if DECDPUN==4 /* use divide-by-multiply */
|
| 6472 |
|
|
if (carry>=0) {
|
| 6473 |
|
|
est=(((ueInt)carry>>11)*53687)>>18;
|
| 6474 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6475 |
|
|
carry=est; /* likely quotient [79.7%] */
|
| 6476 |
|
|
if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| 6477 |
|
|
carry++;
|
| 6478 |
|
|
*c-=DECDPUNMAX+1;
|
| 6479 |
|
|
continue;
|
| 6480 |
|
|
}
|
| 6481 |
|
|
/* negative case */
|
| 6482 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6483 |
|
|
est=(((ueInt)carry>>11)*53687)>>18;
|
| 6484 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6485 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6486 |
|
|
if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| 6487 |
|
|
carry++;
|
| 6488 |
|
|
*c-=DECDPUNMAX+1;
|
| 6489 |
|
|
#elif DECDPUN==3
|
| 6490 |
|
|
if (carry>=0) {
|
| 6491 |
|
|
est=(((ueInt)carry>>3)*16777)>>21;
|
| 6492 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6493 |
|
|
carry=est; /* likely quotient [99%] */
|
| 6494 |
|
|
if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| 6495 |
|
|
carry++;
|
| 6496 |
|
|
*c-=DECDPUNMAX+1;
|
| 6497 |
|
|
continue;
|
| 6498 |
|
|
}
|
| 6499 |
|
|
/* negative case */
|
| 6500 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6501 |
|
|
est=(((ueInt)carry>>3)*16777)>>21;
|
| 6502 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6503 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6504 |
|
|
if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| 6505 |
|
|
carry++;
|
| 6506 |
|
|
*c-=DECDPUNMAX+1;
|
| 6507 |
|
|
#elif DECDPUN<=2
|
| 6508 |
|
|
if (carry>=0) {
|
| 6509 |
|
|
est=QUOT10(carry, DECDPUN);
|
| 6510 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| 6511 |
|
|
carry=est; /* quotient */
|
| 6512 |
|
|
continue;
|
| 6513 |
|
|
}
|
| 6514 |
|
|
/* negative case */
|
| 6515 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6516 |
|
|
est=QUOT10(carry, DECDPUN);
|
| 6517 |
|
|
*c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| 6518 |
|
|
carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| 6519 |
|
|
#else
|
| 6520 |
|
|
if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */
|
| 6521 |
|
|
*c=(Unit)(carry-(DECDPUNMAX+1));
|
| 6522 |
|
|
carry=1;
|
| 6523 |
|
|
continue;
|
| 6524 |
|
|
}
|
| 6525 |
|
|
/* remainder operator is undefined if negative, so must test */
|
| 6526 |
|
|
if (carry>=0) {
|
| 6527 |
|
|
*c=(Unit)(carry%(DECDPUNMAX+1));
|
| 6528 |
|
|
carry=carry/(DECDPUNMAX+1);
|
| 6529 |
|
|
continue;
|
| 6530 |
|
|
}
|
| 6531 |
|
|
/* negative case */
|
| 6532 |
|
|
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| 6533 |
|
|
*c=(Unit)(carry%(DECDPUNMAX+1));
|
| 6534 |
|
|
carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
|
| 6535 |
|
|
#endif
|
| 6536 |
|
|
} /* c */
|
| 6537 |
|
|
|
| 6538 |
|
|
/* OK, all A and B processed; might still have carry or borrow */
|
| 6539 |
|
|
/* return number of Units in the result, negated if a borrow */
|
| 6540 |
|
|
if (carry==0) return c-clsu; /* no carry, so no more to do */
|
| 6541 |
|
|
if (carry>0) { /* positive carry */
|
| 6542 |
|
|
*c=(Unit)carry; /* place as new unit */
|
| 6543 |
|
|
c++; /* .. */
|
| 6544 |
|
|
return c-clsu;
|
| 6545 |
|
|
}
|
| 6546 |
|
|
/* -ve carry: it's a borrow; complement needed */
|
| 6547 |
|
|
add=1; /* temporary carry... */
|
| 6548 |
|
|
for (c=clsu; c<maxC; c++) {
|
| 6549 |
|
|
add=DECDPUNMAX+add-*c;
|
| 6550 |
|
|
if (add<=DECDPUNMAX) {
|
| 6551 |
|
|
*c=(Unit)add;
|
| 6552 |
|
|
add=0;
|
| 6553 |
|
|
}
|
| 6554 |
|
|
else {
|
| 6555 |
|
|
*c=0;
|
| 6556 |
|
|
add=1;
|
| 6557 |
|
|
}
|
| 6558 |
|
|
}
|
| 6559 |
|
|
/* add an extra unit iff it would be non-zero */
|
| 6560 |
|
|
#if DECTRACE
|
| 6561 |
|
|
printf("UAS borrow: add %ld, carry %ld\n", add, carry);
|
| 6562 |
|
|
#endif
|
| 6563 |
|
|
if ((add-carry-1)!=0) {
|
| 6564 |
|
|
*c=(Unit)(add-carry-1);
|
| 6565 |
|
|
c++; /* interesting, include it */
|
| 6566 |
|
|
}
|
| 6567 |
|
|
return clsu-c; /* -ve result indicates borrowed */
|
| 6568 |
|
|
} /* decUnitAddSub */
|
| 6569 |
|
|
|
| 6570 |
|
|
/* ------------------------------------------------------------------ */
|
| 6571 |
|
|
/* decTrim -- trim trailing zeros or normalize */
|
| 6572 |
|
|
/* */
|
| 6573 |
|
|
/* dn is the number to trim or normalize */
|
| 6574 |
|
|
/* set is the context to use to check for clamp */
|
| 6575 |
|
|
/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
|
| 6576 |
|
|
/* noclamp is 1 to unconditional (unclamped) trim */
|
| 6577 |
|
|
/* dropped returns the number of discarded trailing zeros */
|
| 6578 |
|
|
/* returns dn */
|
| 6579 |
|
|
/* */
|
| 6580 |
|
|
/* If clamp is set in the context then the number of zeros trimmed */
|
| 6581 |
|
|
/* may be limited if the exponent is high. */
|
| 6582 |
|
|
/* All fields are updated as required. This is a utility operation, */
|
| 6583 |
|
|
/* so special values are unchanged and no error is possible. */
|
| 6584 |
|
|
/* ------------------------------------------------------------------ */
|
| 6585 |
|
|
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
|
| 6586 |
|
|
Flag noclamp, Int *dropped) {
|
| 6587 |
|
|
Int d, exp; /* work */
|
| 6588 |
|
|
uInt cut; /* .. */
|
| 6589 |
|
|
Unit *up; /* -> current Unit */
|
| 6590 |
|
|
|
| 6591 |
|
|
#if DECCHECK
|
| 6592 |
|
|
if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
|
| 6593 |
|
|
#endif
|
| 6594 |
|
|
|
| 6595 |
|
|
*dropped=0; /* assume no zeros dropped */
|
| 6596 |
|
|
if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
|
| 6597 |
|
|
|| (*dn->lsu & 0x01)) return dn; /* .. or odd */
|
| 6598 |
|
|
if (ISZERO(dn)) { /* .. or 0 */
|
| 6599 |
|
|
dn->exponent=0; /* (sign is preserved) */
|
| 6600 |
|
|
return dn;
|
| 6601 |
|
|
}
|
| 6602 |
|
|
|
| 6603 |
|
|
/* have a finite number which is even */
|
| 6604 |
|
|
exp=dn->exponent;
|
| 6605 |
|
|
cut=1; /* digit (1-DECDPUN) in Unit */
|
| 6606 |
|
|
up=dn->lsu; /* -> current Unit */
|
| 6607 |
|
|
for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
|
| 6608 |
|
|
/* slice by powers */
|
| 6609 |
|
|
#if DECDPUN<=4
|
| 6610 |
|
|
uInt quot=QUOT10(*up, cut);
|
| 6611 |
|
|
if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */
|
| 6612 |
|
|
#else
|
| 6613 |
|
|
if (*up%powers[cut]!=0) break; /* found non-0 digit */
|
| 6614 |
|
|
#endif
|
| 6615 |
|
|
/* have a trailing 0 */
|
| 6616 |
|
|
if (!all) { /* trimming */
|
| 6617 |
|
|
/* [if exp>0 then all trailing 0s are significant for trim] */
|
| 6618 |
|
|
if (exp<=0) { /* if digit might be significant */
|
| 6619 |
|
|
if (exp==0) break; /* then quit */
|
| 6620 |
|
|
exp++; /* next digit might be significant */
|
| 6621 |
|
|
}
|
| 6622 |
|
|
}
|
| 6623 |
|
|
cut++; /* next power */
|
| 6624 |
|
|
if (cut>DECDPUN) { /* need new Unit */
|
| 6625 |
|
|
up++;
|
| 6626 |
|
|
cut=1;
|
| 6627 |
|
|
}
|
| 6628 |
|
|
} /* d */
|
| 6629 |
|
|
if (d==0) return dn; /* none to drop */
|
| 6630 |
|
|
|
| 6631 |
|
|
/* may need to limit drop if clamping */
|
| 6632 |
|
|
if (set->clamp && !noclamp) {
|
| 6633 |
|
|
Int maxd=set->emax-set->digits+1-dn->exponent;
|
| 6634 |
|
|
if (maxd<=0) return dn; /* nothing possible */
|
| 6635 |
|
|
if (d>maxd) d=maxd;
|
| 6636 |
|
|
}
|
| 6637 |
|
|
|
| 6638 |
|
|
/* effect the drop */
|
| 6639 |
|
|
decShiftToLeast(dn->lsu, D2U(dn->digits), d);
|
| 6640 |
|
|
dn->exponent+=d; /* maintain numerical value */
|
| 6641 |
|
|
dn->digits-=d; /* new length */
|
| 6642 |
|
|
*dropped=d; /* report the count */
|
| 6643 |
|
|
return dn;
|
| 6644 |
|
|
} /* decTrim */
|
| 6645 |
|
|
|
| 6646 |
|
|
/* ------------------------------------------------------------------ */
|
| 6647 |
|
|
/* decReverse -- reverse a Unit array in place */
|
| 6648 |
|
|
/* */
|
| 6649 |
|
|
/* ulo is the start of the array */
|
| 6650 |
|
|
/* uhi is the end of the array (highest Unit to include) */
|
| 6651 |
|
|
/* */
|
| 6652 |
|
|
/* The units ulo through uhi are reversed in place (if the number */
|
| 6653 |
|
|
/* of units is odd, the middle one is untouched). Note that the */
|
| 6654 |
|
|
/* digit(s) in each unit are unaffected. */
|
| 6655 |
|
|
/* ------------------------------------------------------------------ */
|
| 6656 |
|
|
static void decReverse(Unit *ulo, Unit *uhi) {
|
| 6657 |
|
|
Unit temp;
|
| 6658 |
|
|
for (; ulo<uhi; ulo++, uhi--) {
|
| 6659 |
|
|
temp=*ulo;
|
| 6660 |
|
|
*ulo=*uhi;
|
| 6661 |
|
|
*uhi=temp;
|
| 6662 |
|
|
}
|
| 6663 |
|
|
return;
|
| 6664 |
|
|
} /* decReverse */
|
| 6665 |
|
|
|
| 6666 |
|
|
/* ------------------------------------------------------------------ */
|
| 6667 |
|
|
/* decShiftToMost -- shift digits in array towards most significant */
|
| 6668 |
|
|
/* */
|
| 6669 |
|
|
/* uar is the array */
|
| 6670 |
|
|
/* digits is the count of digits in use in the array */
|
| 6671 |
|
|
/* shift is the number of zeros to pad with (least significant); */
|
| 6672 |
|
|
/* it must be zero or positive */
|
| 6673 |
|
|
/* */
|
| 6674 |
|
|
/* returns the new length of the integer in the array, in digits */
|
| 6675 |
|
|
/* */
|
| 6676 |
|
|
/* No overflow is permitted (that is, the uar array must be known to */
|
| 6677 |
|
|
/* be large enough to hold the result, after shifting). */
|
| 6678 |
|
|
/* ------------------------------------------------------------------ */
|
| 6679 |
|
|
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
|
| 6680 |
|
|
Unit *target, *source, *first; /* work */
|
| 6681 |
|
|
Int cut; /* odd 0's to add */
|
| 6682 |
|
|
uInt next; /* work */
|
| 6683 |
|
|
|
| 6684 |
|
|
if (shift==0) return digits; /* [fastpath] nothing to do */
|
| 6685 |
|
|
if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */
|
| 6686 |
|
|
*uar=(Unit)(*uar*powers[shift]);
|
| 6687 |
|
|
return digits+shift;
|
| 6688 |
|
|
}
|
| 6689 |
|
|
|
| 6690 |
|
|
next=0; /* all paths */
|
| 6691 |
|
|
source=uar+D2U(digits)-1; /* where msu comes from */
|
| 6692 |
|
|
target=source+D2U(shift); /* where upper part of first cut goes */
|
| 6693 |
|
|
cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
|
| 6694 |
|
|
if (cut==0) { /* unit-boundary case */
|
| 6695 |
|
|
for (; source>=uar; source--, target--) *target=*source;
|
| 6696 |
|
|
}
|
| 6697 |
|
|
else {
|
| 6698 |
|
|
first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
|
| 6699 |
|
|
for (; source>=uar; source--, target--) {
|
| 6700 |
|
|
/* split the source Unit and accumulate remainder for next */
|
| 6701 |
|
|
#if DECDPUN<=4
|
| 6702 |
|
|
uInt quot=QUOT10(*source, cut);
|
| 6703 |
|
|
uInt rem=*source-quot*powers[cut];
|
| 6704 |
|
|
next+=quot;
|
| 6705 |
|
|
#else
|
| 6706 |
|
|
uInt rem=*source%powers[cut];
|
| 6707 |
|
|
next+=*source/powers[cut];
|
| 6708 |
|
|
#endif
|
| 6709 |
|
|
if (target<=first) *target=(Unit)next; /* write to target iff valid */
|
| 6710 |
|
|
next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */
|
| 6711 |
|
|
}
|
| 6712 |
|
|
} /* shift-move */
|
| 6713 |
|
|
|
| 6714 |
|
|
/* propagate any partial unit to one below and clear the rest */
|
| 6715 |
|
|
for (; target>=uar; target--) {
|
| 6716 |
|
|
*target=(Unit)next;
|
| 6717 |
|
|
next=0;
|
| 6718 |
|
|
}
|
| 6719 |
|
|
return digits+shift;
|
| 6720 |
|
|
} /* decShiftToMost */
|
| 6721 |
|
|
|
| 6722 |
|
|
/* ------------------------------------------------------------------ */
|
| 6723 |
|
|
/* decShiftToLeast -- shift digits in array towards least significant */
|
| 6724 |
|
|
/* */
|
| 6725 |
|
|
/* uar is the array */
|
| 6726 |
|
|
/* units is length of the array, in units */
|
| 6727 |
|
|
/* shift is the number of digits to remove from the lsu end; it */
|
| 6728 |
|
|
/* must be zero or positive and <= than units*DECDPUN. */
|
| 6729 |
|
|
/* */
|
| 6730 |
|
|
/* returns the new length of the integer in the array, in units */
|
| 6731 |
|
|
/* */
|
| 6732 |
|
|
/* Removed digits are discarded (lost). Units not required to hold */
|
| 6733 |
|
|
/* the final result are unchanged. */
|
| 6734 |
|
|
/* ------------------------------------------------------------------ */
|
| 6735 |
|
|
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
|
| 6736 |
|
|
Unit *target, *up; /* work */
|
| 6737 |
|
|
Int cut, count; /* work */
|
| 6738 |
|
|
Int quot, rem; /* for division */
|
| 6739 |
|
|
|
| 6740 |
|
|
if (shift==0) return units; /* [fastpath] nothing to do */
|
| 6741 |
|
|
if (shift==units*DECDPUN) { /* [fastpath] little to do */
|
| 6742 |
|
|
*uar=0; /* all digits cleared gives zero */
|
| 6743 |
|
|
return 1; /* leaves just the one */
|
| 6744 |
|
|
}
|
| 6745 |
|
|
|
| 6746 |
|
|
target=uar; /* both paths */
|
| 6747 |
|
|
cut=MSUDIGITS(shift);
|
| 6748 |
|
|
if (cut==DECDPUN) { /* unit-boundary case; easy */
|
| 6749 |
|
|
up=uar+D2U(shift);
|
| 6750 |
|
|
for (; up<uar+units; target++, up++) *target=*up;
|
| 6751 |
|
|
return target-uar;
|
| 6752 |
|
|
}
|
| 6753 |
|
|
|
| 6754 |
|
|
/* messier */
|
| 6755 |
|
|
up=uar+D2U(shift-cut); /* source; correct to whole Units */
|
| 6756 |
|
|
count=units*DECDPUN-shift; /* the maximum new length */
|
| 6757 |
|
|
#if DECDPUN<=4
|
| 6758 |
|
|
quot=QUOT10(*up, cut);
|
| 6759 |
|
|
#else
|
| 6760 |
|
|
quot=*up/powers[cut];
|
| 6761 |
|
|
#endif
|
| 6762 |
|
|
for (; ; target++) {
|
| 6763 |
|
|
*target=(Unit)quot;
|
| 6764 |
|
|
count-=(DECDPUN-cut);
|
| 6765 |
|
|
if (count<=0) break;
|
| 6766 |
|
|
up++;
|
| 6767 |
|
|
quot=*up;
|
| 6768 |
|
|
#if DECDPUN<=4
|
| 6769 |
|
|
quot=QUOT10(quot, cut);
|
| 6770 |
|
|
rem=*up-quot*powers[cut];
|
| 6771 |
|
|
#else
|
| 6772 |
|
|
rem=quot%powers[cut];
|
| 6773 |
|
|
quot=quot/powers[cut];
|
| 6774 |
|
|
#endif
|
| 6775 |
|
|
*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
|
| 6776 |
|
|
count-=cut;
|
| 6777 |
|
|
if (count<=0) break;
|
| 6778 |
|
|
}
|
| 6779 |
|
|
return target-uar+1;
|
| 6780 |
|
|
} /* decShiftToLeast */
|
| 6781 |
|
|
|
| 6782 |
|
|
#if DECSUBSET
|
| 6783 |
|
|
/* ------------------------------------------------------------------ */
|
| 6784 |
|
|
/* decRoundOperand -- round an operand [used for subset only] */
|
| 6785 |
|
|
/* */
|
| 6786 |
|
|
/* dn is the number to round (dn->digits is > set->digits) */
|
| 6787 |
|
|
/* set is the relevant context */
|
| 6788 |
|
|
/* status is the status accumulator */
|
| 6789 |
|
|
/* */
|
| 6790 |
|
|
/* returns an allocated decNumber with the rounded result. */
|
| 6791 |
|
|
/* */
|
| 6792 |
|
|
/* lostDigits and other status may be set by this. */
|
| 6793 |
|
|
/* */
|
| 6794 |
|
|
/* Since the input is an operand, it must not be modified. */
|
| 6795 |
|
|
/* Instead, return an allocated decNumber, rounded as required. */
|
| 6796 |
|
|
/* It is the caller's responsibility to free the allocated storage. */
|
| 6797 |
|
|
/* */
|
| 6798 |
|
|
/* If no storage is available then the result cannot be used, so NULL */
|
| 6799 |
|
|
/* is returned. */
|
| 6800 |
|
|
/* ------------------------------------------------------------------ */
|
| 6801 |
|
|
static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
|
| 6802 |
|
|
uInt *status) {
|
| 6803 |
|
|
decNumber *res; /* result structure */
|
| 6804 |
|
|
uInt newstatus=0; /* status from round */
|
| 6805 |
|
|
Int residue=0; /* rounding accumulator */
|
| 6806 |
|
|
|
| 6807 |
|
|
/* Allocate storage for the returned decNumber, big enough for the */
|
| 6808 |
|
|
/* length specified by the context */
|
| 6809 |
|
|
res=(decNumber *)malloc(sizeof(decNumber)
|
| 6810 |
|
|
+(D2U(set->digits)-1)*sizeof(Unit));
|
| 6811 |
|
|
if (res==NULL) {
|
| 6812 |
|
|
*status|=DEC_Insufficient_storage;
|
| 6813 |
|
|
return NULL;
|
| 6814 |
|
|
}
|
| 6815 |
|
|
decCopyFit(res, dn, set, &residue, &newstatus);
|
| 6816 |
|
|
decApplyRound(res, set, residue, &newstatus);
|
| 6817 |
|
|
|
| 6818 |
|
|
/* If that set Inexact then "lost digits" is raised... */
|
| 6819 |
|
|
if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
|
| 6820 |
|
|
*status|=newstatus;
|
| 6821 |
|
|
return res;
|
| 6822 |
|
|
} /* decRoundOperand */
|
| 6823 |
|
|
#endif
|
| 6824 |
|
|
|
| 6825 |
|
|
/* ------------------------------------------------------------------ */
|
| 6826 |
|
|
/* decCopyFit -- copy a number, truncating the coefficient if needed */
|
| 6827 |
|
|
/* */
|
| 6828 |
|
|
/* dest is the target decNumber */
|
| 6829 |
|
|
/* src is the source decNumber */
|
| 6830 |
|
|
/* set is the context [used for length (digits) and rounding mode] */
|
| 6831 |
|
|
/* residue is the residue accumulator */
|
| 6832 |
|
|
/* status contains the current status to be updated */
|
| 6833 |
|
|
/* */
|
| 6834 |
|
|
/* (dest==src is allowed and will be a no-op if fits) */
|
| 6835 |
|
|
/* All fields are updated as required. */
|
| 6836 |
|
|
/* ------------------------------------------------------------------ */
|
| 6837 |
|
|
static void decCopyFit(decNumber *dest, const decNumber *src,
|
| 6838 |
|
|
decContext *set, Int *residue, uInt *status) {
|
| 6839 |
|
|
dest->bits=src->bits;
|
| 6840 |
|
|
dest->exponent=src->exponent;
|
| 6841 |
|
|
decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
|
| 6842 |
|
|
} /* decCopyFit */
|
| 6843 |
|
|
|
| 6844 |
|
|
/* ------------------------------------------------------------------ */
|
| 6845 |
|
|
/* decSetCoeff -- set the coefficient of a number */
|
| 6846 |
|
|
/* */
|
| 6847 |
|
|
/* dn is the number whose coefficient array is to be set. */
|
| 6848 |
|
|
/* It must have space for set->digits digits */
|
| 6849 |
|
|
/* set is the context [for size] */
|
| 6850 |
|
|
/* lsu -> lsu of the source coefficient [may be dn->lsu] */
|
| 6851 |
|
|
/* len is digits in the source coefficient [may be dn->digits] */
|
| 6852 |
|
|
/* residue is the residue accumulator. This has values as in */
|
| 6853 |
|
|
/* decApplyRound, and will be unchanged unless the */
|
| 6854 |
|
|
/* target size is less than len. In this case, the */
|
| 6855 |
|
|
/* coefficient is truncated and the residue is updated to */
|
| 6856 |
|
|
/* reflect the previous residue and the dropped digits. */
|
| 6857 |
|
|
/* status is the status accumulator, as usual */
|
| 6858 |
|
|
/* */
|
| 6859 |
|
|
/* The coefficient may already be in the number, or it can be an */
|
| 6860 |
|
|
/* external intermediate array. If it is in the number, lsu must == */
|
| 6861 |
|
|
/* dn->lsu and len must == dn->digits. */
|
| 6862 |
|
|
/* */
|
| 6863 |
|
|
/* Note that the coefficient length (len) may be < set->digits, and */
|
| 6864 |
|
|
/* in this case this merely copies the coefficient (or is a no-op */
|
| 6865 |
|
|
/* if dn->lsu==lsu). */
|
| 6866 |
|
|
/* */
|
| 6867 |
|
|
/* Note also that (only internally, from decQuantizeOp and */
|
| 6868 |
|
|
/* decSetSubnormal) the value of set->digits may be less than one, */
|
| 6869 |
|
|
/* indicating a round to left. This routine handles that case */
|
| 6870 |
|
|
/* correctly; caller ensures space. */
|
| 6871 |
|
|
/* */
|
| 6872 |
|
|
/* dn->digits, dn->lsu (and as required), and dn->exponent are */
|
| 6873 |
|
|
/* updated as necessary. dn->bits (sign) is unchanged. */
|
| 6874 |
|
|
/* */
|
| 6875 |
|
|
/* DEC_Rounded status is set if any digits are discarded. */
|
| 6876 |
|
|
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
|
| 6877 |
|
|
/* incoming residue was non-0 (implies rounded) */
|
| 6878 |
|
|
/* ------------------------------------------------------------------ */
|
| 6879 |
|
|
/* mapping array: maps 0-9 to canonical residues, so that a residue */
|
| 6880 |
|
|
/* can be adjusted in the range [-1, +1] and achieve correct rounding */
|
| 6881 |
|
|
/* 0 1 2 3 4 5 6 7 8 9 */
|
| 6882 |
|
|
static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
|
| 6883 |
|
|
static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
|
| 6884 |
|
|
Int len, Int *residue, uInt *status) {
|
| 6885 |
|
|
Int discard; /* number of digits to discard */
|
| 6886 |
|
|
uInt cut; /* cut point in Unit */
|
| 6887 |
|
|
const Unit *up; /* work */
|
| 6888 |
|
|
Unit *target; /* .. */
|
| 6889 |
|
|
Int count; /* .. */
|
| 6890 |
|
|
#if DECDPUN<=4
|
| 6891 |
|
|
uInt temp; /* .. */
|
| 6892 |
|
|
#endif
|
| 6893 |
|
|
|
| 6894 |
|
|
discard=len-set->digits; /* digits to discard */
|
| 6895 |
|
|
if (discard<=0) { /* no digits are being discarded */
|
| 6896 |
|
|
if (dn->lsu!=lsu) { /* copy needed */
|
| 6897 |
|
|
/* copy the coefficient array to the result number; no shift needed */
|
| 6898 |
|
|
count=len; /* avoids D2U */
|
| 6899 |
|
|
up=lsu;
|
| 6900 |
|
|
for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
|
| 6901 |
|
|
*target=*up;
|
| 6902 |
|
|
dn->digits=len; /* set the new length */
|
| 6903 |
|
|
}
|
| 6904 |
|
|
/* dn->exponent and residue are unchanged, record any inexactitude */
|
| 6905 |
|
|
if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
|
| 6906 |
|
|
return;
|
| 6907 |
|
|
}
|
| 6908 |
|
|
|
| 6909 |
|
|
/* some digits must be discarded ... */
|
| 6910 |
|
|
dn->exponent+=discard; /* maintain numerical value */
|
| 6911 |
|
|
*status|=DEC_Rounded; /* accumulate Rounded status */
|
| 6912 |
|
|
if (*residue>1) *residue=1; /* previous residue now to right, so reduce */
|
| 6913 |
|
|
|
| 6914 |
|
|
if (discard>len) { /* everything, +1, is being discarded */
|
| 6915 |
|
|
/* guard digit is 0 */
|
| 6916 |
|
|
/* residue is all the number [NB could be all 0s] */
|
| 6917 |
|
|
if (*residue<=0) { /* not already positive */
|
| 6918 |
|
|
count=len; /* avoids D2U */
|
| 6919 |
|
|
for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
|
| 6920 |
|
|
*residue=1;
|
| 6921 |
|
|
break; /* no need to check any others */
|
| 6922 |
|
|
}
|
| 6923 |
|
|
}
|
| 6924 |
|
|
if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
|
| 6925 |
|
|
*dn->lsu=0; /* coefficient will now be 0 */
|
| 6926 |
|
|
dn->digits=1; /* .. */
|
| 6927 |
|
|
return;
|
| 6928 |
|
|
} /* total discard */
|
| 6929 |
|
|
|
| 6930 |
|
|
/* partial discard [most common case] */
|
| 6931 |
|
|
/* here, at least the first (most significant) discarded digit exists */
|
| 6932 |
|
|
|
| 6933 |
|
|
/* spin up the number, noting residue during the spin, until get to */
|
| 6934 |
|
|
/* the Unit with the first discarded digit. When reach it, extract */
|
| 6935 |
|
|
/* it and remember its position */
|
| 6936 |
|
|
count=0;
|
| 6937 |
|
|
for (up=lsu;; up++) {
|
| 6938 |
|
|
count+=DECDPUN;
|
| 6939 |
|
|
if (count>=discard) break; /* full ones all checked */
|
| 6940 |
|
|
if (*up!=0) *residue=1;
|
| 6941 |
|
|
} /* up */
|
| 6942 |
|
|
|
| 6943 |
|
|
/* here up -> Unit with first discarded digit */
|
| 6944 |
|
|
cut=discard-(count-DECDPUN)-1;
|
| 6945 |
|
|
if (cut==DECDPUN-1) { /* unit-boundary case (fast) */
|
| 6946 |
|
|
Unit half=(Unit)powers[DECDPUN]>>1;
|
| 6947 |
|
|
/* set residue directly */
|
| 6948 |
|
|
if (*up>=half) {
|
| 6949 |
|
|
if (*up>half) *residue=7;
|
| 6950 |
|
|
else *residue+=5; /* add sticky bit */
|
| 6951 |
|
|
}
|
| 6952 |
|
|
else { /* <half */
|
| 6953 |
|
|
if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
|
| 6954 |
|
|
}
|
| 6955 |
|
|
if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
|
| 6956 |
|
|
*dn->lsu=0; /* .. result is 0 */
|
| 6957 |
|
|
dn->digits=1; /* .. */
|
| 6958 |
|
|
}
|
| 6959 |
|
|
else { /* shift to least */
|
| 6960 |
|
|
count=set->digits; /* now digits to end up with */
|
| 6961 |
|
|
dn->digits=count; /* set the new length */
|
| 6962 |
|
|
up++; /* move to next */
|
| 6963 |
|
|
/* on unit boundary, so shift-down copy loop is simple */
|
| 6964 |
|
|
for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
|
| 6965 |
|
|
*target=*up;
|
| 6966 |
|
|
}
|
| 6967 |
|
|
} /* unit-boundary case */
|
| 6968 |
|
|
|
| 6969 |
|
|
else { /* discard digit is in low digit(s), and not top digit */
|
| 6970 |
|
|
uInt discard1; /* first discarded digit */
|
| 6971 |
|
|
uInt quot, rem; /* for divisions */
|
| 6972 |
|
|
if (cut==0) quot=*up; /* is at bottom of unit */
|
| 6973 |
|
|
else /* cut>0 */ { /* it's not at bottom of unit */
|
| 6974 |
|
|
#if DECDPUN<=4
|
| 6975 |
|
|
quot=QUOT10(*up, cut);
|
| 6976 |
|
|
rem=*up-quot*powers[cut];
|
| 6977 |
|
|
#else
|
| 6978 |
|
|
rem=*up%powers[cut];
|
| 6979 |
|
|
quot=*up/powers[cut];
|
| 6980 |
|
|
#endif
|
| 6981 |
|
|
if (rem!=0) *residue=1;
|
| 6982 |
|
|
}
|
| 6983 |
|
|
/* discard digit is now at bottom of quot */
|
| 6984 |
|
|
#if DECDPUN<=4
|
| 6985 |
|
|
temp=(quot*6554)>>16; /* fast /10 */
|
| 6986 |
|
|
/* Vowels algorithm here not a win (9 instructions) */
|
| 6987 |
|
|
discard1=quot-X10(temp);
|
| 6988 |
|
|
quot=temp;
|
| 6989 |
|
|
#else
|
| 6990 |
|
|
discard1=quot%10;
|
| 6991 |
|
|
quot=quot/10;
|
| 6992 |
|
|
#endif
|
| 6993 |
|
|
/* here, discard1 is the guard digit, and residue is everything */
|
| 6994 |
|
|
/* else [use mapping array to accumulate residue safely] */
|
| 6995 |
|
|
*residue+=resmap[discard1];
|
| 6996 |
|
|
cut++; /* update cut */
|
| 6997 |
|
|
/* here: up -> Unit of the array with bottom digit */
|
| 6998 |
|
|
/* cut is the division point for each Unit */
|
| 6999 |
|
|
/* quot holds the uncut high-order digits for the current unit */
|
| 7000 |
|
|
if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
|
| 7001 |
|
|
*dn->lsu=0; /* .. result is 0 */
|
| 7002 |
|
|
dn->digits=1; /* .. */
|
| 7003 |
|
|
}
|
| 7004 |
|
|
else { /* shift to least needed */
|
| 7005 |
|
|
count=set->digits; /* now digits to end up with */
|
| 7006 |
|
|
dn->digits=count; /* set the new length */
|
| 7007 |
|
|
/* shift-copy the coefficient array to the result number */
|
| 7008 |
|
|
for (target=dn->lsu; ; target++) {
|
| 7009 |
|
|
*target=(Unit)quot;
|
| 7010 |
|
|
count-=(DECDPUN-cut);
|
| 7011 |
|
|
if (count<=0) break;
|
| 7012 |
|
|
up++;
|
| 7013 |
|
|
quot=*up;
|
| 7014 |
|
|
#if DECDPUN<=4
|
| 7015 |
|
|
quot=QUOT10(quot, cut);
|
| 7016 |
|
|
rem=*up-quot*powers[cut];
|
| 7017 |
|
|
#else
|
| 7018 |
|
|
rem=quot%powers[cut];
|
| 7019 |
|
|
quot=quot/powers[cut];
|
| 7020 |
|
|
#endif
|
| 7021 |
|
|
*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
|
| 7022 |
|
|
count-=cut;
|
| 7023 |
|
|
if (count<=0) break;
|
| 7024 |
|
|
} /* shift-copy loop */
|
| 7025 |
|
|
} /* shift to least */
|
| 7026 |
|
|
} /* not unit boundary */
|
| 7027 |
|
|
|
| 7028 |
|
|
if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
|
| 7029 |
|
|
return;
|
| 7030 |
|
|
} /* decSetCoeff */
|
| 7031 |
|
|
|
| 7032 |
|
|
/* ------------------------------------------------------------------ */
|
| 7033 |
|
|
/* decApplyRound -- apply pending rounding to a number */
|
| 7034 |
|
|
/* */
|
| 7035 |
|
|
/* dn is the number, with space for set->digits digits */
|
| 7036 |
|
|
/* set is the context [for size and rounding mode] */
|
| 7037 |
|
|
/* residue indicates pending rounding, being any accumulated */
|
| 7038 |
|
|
/* guard and sticky information. It may be: */
|
| 7039 |
|
|
/* 6-9: rounding digit is >5 */
|
| 7040 |
|
|
/* 5: rounding digit is exactly half-way */
|
| 7041 |
|
|
/* 1-4: rounding digit is <5 and >0 */
|
| 7042 |
|
|
/* 0: the coefficient is exact */
|
| 7043 |
|
|
/* -1: as 1, but the hidden digits are subtractive, that */
|
| 7044 |
|
|
/* is, of the opposite sign to dn. In this case the */
|
| 7045 |
|
|
/* coefficient must be non-0. This case occurs when */
|
| 7046 |
|
|
/* subtracting a small number (which can be reduced to */
|
| 7047 |
|
|
/* a sticky bit); see decAddOp. */
|
| 7048 |
|
|
/* status is the status accumulator, as usual */
|
| 7049 |
|
|
/* */
|
| 7050 |
|
|
/* This routine applies rounding while keeping the length of the */
|
| 7051 |
|
|
/* coefficient constant. The exponent and status are unchanged */
|
| 7052 |
|
|
/* except if: */
|
| 7053 |
|
|
/* */
|
| 7054 |
|
|
/* -- the coefficient was increased and is all nines (in which */
|
| 7055 |
|
|
/* case Overflow could occur, and is handled directly here so */
|
| 7056 |
|
|
/* the caller does not need to re-test for overflow) */
|
| 7057 |
|
|
/* */
|
| 7058 |
|
|
/* -- the coefficient was decreased and becomes all nines (in which */
|
| 7059 |
|
|
/* case Underflow could occur, and is also handled directly). */
|
| 7060 |
|
|
/* */
|
| 7061 |
|
|
/* All fields in dn are updated as required. */
|
| 7062 |
|
|
/* */
|
| 7063 |
|
|
/* ------------------------------------------------------------------ */
|
| 7064 |
|
|
static void decApplyRound(decNumber *dn, decContext *set, Int residue,
|
| 7065 |
|
|
uInt *status) {
|
| 7066 |
|
|
Int bump; /* 1 if coefficient needs to be incremented */
|
| 7067 |
|
|
/* -1 if coefficient needs to be decremented */
|
| 7068 |
|
|
|
| 7069 |
|
|
if (residue==0) return; /* nothing to apply */
|
| 7070 |
|
|
|
| 7071 |
|
|
bump=0; /* assume a smooth ride */
|
| 7072 |
|
|
|
| 7073 |
|
|
/* now decide whether, and how, to round, depending on mode */
|
| 7074 |
|
|
switch (set->round) {
|
| 7075 |
|
|
case DEC_ROUND_05UP: { /* round zero or five up (for reround) */
|
| 7076 |
|
|
/* This is the same as DEC_ROUND_DOWN unless there is a */
|
| 7077 |
|
|
/* positive residue and the lsd of dn is 0 or 5, in which case */
|
| 7078 |
|
|
/* it is bumped; when residue is <0, the number is therefore */
|
| 7079 |
|
|
/* bumped down unless the final digit was 1 or 6 (in which */
|
| 7080 |
|
|
/* case it is bumped down and then up -- a no-op) */
|
| 7081 |
|
|
Int lsd5=*dn->lsu%5; /* get lsd and quintate */
|
| 7082 |
|
|
if (residue<0 && lsd5!=1) bump=-1;
|
| 7083 |
|
|
else if (residue>0 && lsd5==0) bump=1;
|
| 7084 |
|
|
/* [bump==1 could be applied directly; use common path for clarity] */
|
| 7085 |
|
|
break;} /* r-05 */
|
| 7086 |
|
|
|
| 7087 |
|
|
case DEC_ROUND_DOWN: {
|
| 7088 |
|
|
/* no change, except if negative residue */
|
| 7089 |
|
|
if (residue<0) bump=-1;
|
| 7090 |
|
|
break;} /* r-d */
|
| 7091 |
|
|
|
| 7092 |
|
|
case DEC_ROUND_HALF_DOWN: {
|
| 7093 |
|
|
if (residue>5) bump=1;
|
| 7094 |
|
|
break;} /* r-h-d */
|
| 7095 |
|
|
|
| 7096 |
|
|
case DEC_ROUND_HALF_EVEN: {
|
| 7097 |
|
|
if (residue>5) bump=1; /* >0.5 goes up */
|
| 7098 |
|
|
else if (residue==5) { /* exactly 0.5000... */
|
| 7099 |
|
|
/* 0.5 goes up iff [new] lsd is odd */
|
| 7100 |
|
|
if (*dn->lsu & 0x01) bump=1;
|
| 7101 |
|
|
}
|
| 7102 |
|
|
break;} /* r-h-e */
|
| 7103 |
|
|
|
| 7104 |
|
|
case DEC_ROUND_HALF_UP: {
|
| 7105 |
|
|
if (residue>=5) bump=1;
|
| 7106 |
|
|
break;} /* r-h-u */
|
| 7107 |
|
|
|
| 7108 |
|
|
case DEC_ROUND_UP: {
|
| 7109 |
|
|
if (residue>0) bump=1;
|
| 7110 |
|
|
break;} /* r-u */
|
| 7111 |
|
|
|
| 7112 |
|
|
case DEC_ROUND_CEILING: {
|
| 7113 |
|
|
/* same as _UP for positive numbers, and as _DOWN for negatives */
|
| 7114 |
|
|
/* [negative residue cannot occur on 0] */
|
| 7115 |
|
|
if (decNumberIsNegative(dn)) {
|
| 7116 |
|
|
if (residue<0) bump=-1;
|
| 7117 |
|
|
}
|
| 7118 |
|
|
else {
|
| 7119 |
|
|
if (residue>0) bump=1;
|
| 7120 |
|
|
}
|
| 7121 |
|
|
break;} /* r-c */
|
| 7122 |
|
|
|
| 7123 |
|
|
case DEC_ROUND_FLOOR: {
|
| 7124 |
|
|
/* same as _UP for negative numbers, and as _DOWN for positive */
|
| 7125 |
|
|
/* [negative residue cannot occur on 0] */
|
| 7126 |
|
|
if (!decNumberIsNegative(dn)) {
|
| 7127 |
|
|
if (residue<0) bump=-1;
|
| 7128 |
|
|
}
|
| 7129 |
|
|
else {
|
| 7130 |
|
|
if (residue>0) bump=1;
|
| 7131 |
|
|
}
|
| 7132 |
|
|
break;} /* r-f */
|
| 7133 |
|
|
|
| 7134 |
|
|
default: { /* e.g., DEC_ROUND_MAX */
|
| 7135 |
|
|
*status|=DEC_Invalid_context;
|
| 7136 |
|
|
#if DECTRACE || (DECCHECK && DECVERB)
|
| 7137 |
|
|
printf("Unknown rounding mode: %d\n", set->round);
|
| 7138 |
|
|
#endif
|
| 7139 |
|
|
break;}
|
| 7140 |
|
|
} /* switch */
|
| 7141 |
|
|
|
| 7142 |
|
|
/* now bump the number, up or down, if need be */
|
| 7143 |
|
|
if (bump==0) return; /* no action required */
|
| 7144 |
|
|
|
| 7145 |
|
|
/* Simply use decUnitAddSub unless bumping up and the number is */
|
| 7146 |
|
|
/* all nines. In this special case set to 100... explicitly */
|
| 7147 |
|
|
/* and adjust the exponent by one (as otherwise could overflow */
|
| 7148 |
|
|
/* the array) */
|
| 7149 |
|
|
/* Similarly handle all-nines result if bumping down. */
|
| 7150 |
|
|
if (bump>0) {
|
| 7151 |
|
|
Unit *up; /* work */
|
| 7152 |
|
|
uInt count=dn->digits; /* digits to be checked */
|
| 7153 |
|
|
for (up=dn->lsu; ; up++) {
|
| 7154 |
|
|
if (count<=DECDPUN) {
|
| 7155 |
|
|
/* this is the last Unit (the msu) */
|
| 7156 |
|
|
if (*up!=powers[count]-1) break; /* not still 9s */
|
| 7157 |
|
|
/* here if it, too, is all nines */
|
| 7158 |
|
|
*up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */
|
| 7159 |
|
|
for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
|
| 7160 |
|
|
dn->exponent++; /* and bump exponent */
|
| 7161 |
|
|
/* [which, very rarely, could cause Overflow...] */
|
| 7162 |
|
|
if ((dn->exponent+dn->digits)>set->emax+1) {
|
| 7163 |
|
|
decSetOverflow(dn, set, status);
|
| 7164 |
|
|
}
|
| 7165 |
|
|
return; /* done */
|
| 7166 |
|
|
}
|
| 7167 |
|
|
/* a full unit to check, with more to come */
|
| 7168 |
|
|
if (*up!=DECDPUNMAX) break; /* not still 9s */
|
| 7169 |
|
|
count-=DECDPUN;
|
| 7170 |
|
|
} /* up */
|
| 7171 |
|
|
} /* bump>0 */
|
| 7172 |
|
|
else { /* -1 */
|
| 7173 |
|
|
/* here checking for a pre-bump of 1000... (leading 1, all */
|
| 7174 |
|
|
/* other digits zero) */
|
| 7175 |
|
|
Unit *up, *sup; /* work */
|
| 7176 |
|
|
uInt count=dn->digits; /* digits to be checked */
|
| 7177 |
|
|
for (up=dn->lsu; ; up++) {
|
| 7178 |
|
|
if (count<=DECDPUN) {
|
| 7179 |
|
|
/* this is the last Unit (the msu) */
|
| 7180 |
|
|
if (*up!=powers[count-1]) break; /* not 100.. */
|
| 7181 |
|
|
/* here if have the 1000... case */
|
| 7182 |
|
|
sup=up; /* save msu pointer */
|
| 7183 |
|
|
*up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */
|
| 7184 |
|
|
/* others all to all-nines, too */
|
| 7185 |
|
|
for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
|
| 7186 |
|
|
dn->exponent--; /* and bump exponent */
|
| 7187 |
|
|
|
| 7188 |
|
|
/* iff the number was at the subnormal boundary (exponent=etiny) */
|
| 7189 |
|
|
/* then the exponent is now out of range, so it will in fact get */
|
| 7190 |
|
|
/* clamped to etiny and the final 9 dropped. */
|
| 7191 |
|
|
/* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
|
| 7192 |
|
|
/* dn->exponent, set->digits); */
|
| 7193 |
|
|
if (dn->exponent+1==set->emin-set->digits+1) {
|
| 7194 |
|
|
if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */
|
| 7195 |
|
|
else {
|
| 7196 |
|
|
*sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */
|
| 7197 |
|
|
dn->digits--;
|
| 7198 |
|
|
}
|
| 7199 |
|
|
dn->exponent++;
|
| 7200 |
|
|
*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| 7201 |
|
|
}
|
| 7202 |
|
|
return; /* done */
|
| 7203 |
|
|
}
|
| 7204 |
|
|
|
| 7205 |
|
|
/* a full unit to check, with more to come */
|
| 7206 |
|
|
if (*up!=0) break; /* not still 0s */
|
| 7207 |
|
|
count-=DECDPUN;
|
| 7208 |
|
|
} /* up */
|
| 7209 |
|
|
|
| 7210 |
|
|
} /* bump<0 */
|
| 7211 |
|
|
|
| 7212 |
|
|
/* Actual bump needed. Do it. */
|
| 7213 |
|
|
decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
|
| 7214 |
|
|
} /* decApplyRound */
|
| 7215 |
|
|
|
| 7216 |
|
|
#if DECSUBSET
|
| 7217 |
|
|
/* ------------------------------------------------------------------ */
|
| 7218 |
|
|
/* decFinish -- finish processing a number */
|
| 7219 |
|
|
/* */
|
| 7220 |
|
|
/* dn is the number */
|
| 7221 |
|
|
/* set is the context */
|
| 7222 |
|
|
/* residue is the rounding accumulator (as in decApplyRound) */
|
| 7223 |
|
|
/* status is the accumulator */
|
| 7224 |
|
|
/* */
|
| 7225 |
|
|
/* This finishes off the current number by: */
|
| 7226 |
|
|
/* 1. If not extended: */
|
| 7227 |
|
|
/* a. Converting a zero result to clean '0' */
|
| 7228 |
|
|
/* b. Reducing positive exponents to 0, if would fit in digits */
|
| 7229 |
|
|
/* 2. Checking for overflow and subnormals (always) */
|
| 7230 |
|
|
/* Note this is just Finalize when no subset arithmetic. */
|
| 7231 |
|
|
/* All fields are updated as required. */
|
| 7232 |
|
|
/* ------------------------------------------------------------------ */
|
| 7233 |
|
|
static void decFinish(decNumber *dn, decContext *set, Int *residue,
|
| 7234 |
|
|
uInt *status) {
|
| 7235 |
|
|
if (!set->extended) {
|
| 7236 |
|
|
if ISZERO(dn) { /* value is zero */
|
| 7237 |
|
|
dn->exponent=0; /* clean exponent .. */
|
| 7238 |
|
|
dn->bits=0; /* .. and sign */
|
| 7239 |
|
|
return; /* no error possible */
|
| 7240 |
|
|
}
|
| 7241 |
|
|
if (dn->exponent>=0) { /* non-negative exponent */
|
| 7242 |
|
|
/* >0; reduce to integer if possible */
|
| 7243 |
|
|
if (set->digits >= (dn->exponent+dn->digits)) {
|
| 7244 |
|
|
dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
|
| 7245 |
|
|
dn->exponent=0;
|
| 7246 |
|
|
}
|
| 7247 |
|
|
}
|
| 7248 |
|
|
} /* !extended */
|
| 7249 |
|
|
|
| 7250 |
|
|
decFinalize(dn, set, residue, status);
|
| 7251 |
|
|
} /* decFinish */
|
| 7252 |
|
|
#endif
|
| 7253 |
|
|
|
| 7254 |
|
|
/* ------------------------------------------------------------------ */
|
| 7255 |
|
|
/* decFinalize -- final check, clamp, and round of a number */
|
| 7256 |
|
|
/* */
|
| 7257 |
|
|
/* dn is the number */
|
| 7258 |
|
|
/* set is the context */
|
| 7259 |
|
|
/* residue is the rounding accumulator (as in decApplyRound) */
|
| 7260 |
|
|
/* status is the status accumulator */
|
| 7261 |
|
|
/* */
|
| 7262 |
|
|
/* This finishes off the current number by checking for subnormal */
|
| 7263 |
|
|
/* results, applying any pending rounding, checking for overflow, */
|
| 7264 |
|
|
/* and applying any clamping. */
|
| 7265 |
|
|
/* Underflow and overflow conditions are raised as appropriate. */
|
| 7266 |
|
|
/* All fields are updated as required. */
|
| 7267 |
|
|
/* ------------------------------------------------------------------ */
|
| 7268 |
|
|
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
|
| 7269 |
|
|
uInt *status) {
|
| 7270 |
|
|
Int shift; /* shift needed if clamping */
|
| 7271 |
|
|
Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */
|
| 7272 |
|
|
|
| 7273 |
|
|
/* Must be careful, here, when checking the exponent as the */
|
| 7274 |
|
|
/* adjusted exponent could overflow 31 bits [because it may already */
|
| 7275 |
|
|
/* be up to twice the expected]. */
|
| 7276 |
|
|
|
| 7277 |
|
|
/* First test for subnormal. This must be done before any final */
|
| 7278 |
|
|
/* round as the result could be rounded to Nmin or 0. */
|
| 7279 |
|
|
if (dn->exponent<=tinyexp) { /* prefilter */
|
| 7280 |
|
|
Int comp;
|
| 7281 |
|
|
decNumber nmin;
|
| 7282 |
|
|
/* A very nasty case here is dn == Nmin and residue<0 */
|
| 7283 |
|
|
if (dn->exponent<tinyexp) {
|
| 7284 |
|
|
/* Go handle subnormals; this will apply round if needed. */
|
| 7285 |
|
|
decSetSubnormal(dn, set, residue, status);
|
| 7286 |
|
|
return;
|
| 7287 |
|
|
}
|
| 7288 |
|
|
/* Equals case: only subnormal if dn=Nmin and negative residue */
|
| 7289 |
|
|
decNumberZero(&nmin);
|
| 7290 |
|
|
nmin.lsu[0]=1;
|
| 7291 |
|
|
nmin.exponent=set->emin;
|
| 7292 |
|
|
comp=decCompare(dn, &nmin, 1); /* (signless compare) */
|
| 7293 |
|
|
if (comp==BADINT) { /* oops */
|
| 7294 |
|
|
*status|=DEC_Insufficient_storage; /* abandon... */
|
| 7295 |
|
|
return;
|
| 7296 |
|
|
}
|
| 7297 |
|
|
if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */
|
| 7298 |
|
|
decApplyRound(dn, set, *residue, status); /* might force down */
|
| 7299 |
|
|
decSetSubnormal(dn, set, residue, status);
|
| 7300 |
|
|
return;
|
| 7301 |
|
|
}
|
| 7302 |
|
|
}
|
| 7303 |
|
|
|
| 7304 |
|
|
/* now apply any pending round (this could raise overflow). */
|
| 7305 |
|
|
if (*residue!=0) decApplyRound(dn, set, *residue, status);
|
| 7306 |
|
|
|
| 7307 |
|
|
/* Check for overflow [redundant in the 'rare' case] or clamp */
|
| 7308 |
|
|
if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */
|
| 7309 |
|
|
|
| 7310 |
|
|
|
| 7311 |
|
|
/* here when might have an overflow or clamp to do */
|
| 7312 |
|
|
if (dn->exponent>set->emax-dn->digits+1) { /* too big */
|
| 7313 |
|
|
decSetOverflow(dn, set, status);
|
| 7314 |
|
|
return;
|
| 7315 |
|
|
}
|
| 7316 |
|
|
/* here when the result is normal but in clamp range */
|
| 7317 |
|
|
if (!set->clamp) return;
|
| 7318 |
|
|
|
| 7319 |
|
|
/* here when need to apply the IEEE exponent clamp (fold-down) */
|
| 7320 |
|
|
shift=dn->exponent-(set->emax-set->digits+1);
|
| 7321 |
|
|
|
| 7322 |
|
|
/* shift coefficient (if non-zero) */
|
| 7323 |
|
|
if (!ISZERO(dn)) {
|
| 7324 |
|
|
dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
|
| 7325 |
|
|
}
|
| 7326 |
|
|
dn->exponent-=shift; /* adjust the exponent to match */
|
| 7327 |
|
|
*status|=DEC_Clamped; /* and record the dirty deed */
|
| 7328 |
|
|
return;
|
| 7329 |
|
|
} /* decFinalize */
|
| 7330 |
|
|
|
| 7331 |
|
|
/* ------------------------------------------------------------------ */
|
| 7332 |
|
|
/* decSetOverflow -- set number to proper overflow value */
|
| 7333 |
|
|
/* */
|
| 7334 |
|
|
/* dn is the number (used for sign [only] and result) */
|
| 7335 |
|
|
/* set is the context [used for the rounding mode, etc.] */
|
| 7336 |
|
|
/* status contains the current status to be updated */
|
| 7337 |
|
|
/* */
|
| 7338 |
|
|
/* This sets the sign of a number and sets its value to either */
|
| 7339 |
|
|
/* Infinity or the maximum finite value, depending on the sign of */
|
| 7340 |
|
|
/* dn and the rounding mode, following IEEE 754 rules. */
|
| 7341 |
|
|
/* ------------------------------------------------------------------ */
|
| 7342 |
|
|
static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
|
| 7343 |
|
|
Flag needmax=0; /* result is maximum finite value */
|
| 7344 |
|
|
uByte sign=dn->bits&DECNEG; /* clean and save sign bit */
|
| 7345 |
|
|
|
| 7346 |
|
|
if (ISZERO(dn)) { /* zero does not overflow magnitude */
|
| 7347 |
|
|
Int emax=set->emax; /* limit value */
|
| 7348 |
|
|
if (set->clamp) emax-=set->digits-1; /* lower if clamping */
|
| 7349 |
|
|
if (dn->exponent>emax) { /* clamp required */
|
| 7350 |
|
|
dn->exponent=emax;
|
| 7351 |
|
|
*status|=DEC_Clamped;
|
| 7352 |
|
|
}
|
| 7353 |
|
|
return;
|
| 7354 |
|
|
}
|
| 7355 |
|
|
|
| 7356 |
|
|
decNumberZero(dn);
|
| 7357 |
|
|
switch (set->round) {
|
| 7358 |
|
|
case DEC_ROUND_DOWN: {
|
| 7359 |
|
|
needmax=1; /* never Infinity */
|
| 7360 |
|
|
break;} /* r-d */
|
| 7361 |
|
|
case DEC_ROUND_05UP: {
|
| 7362 |
|
|
needmax=1; /* never Infinity */
|
| 7363 |
|
|
break;} /* r-05 */
|
| 7364 |
|
|
case DEC_ROUND_CEILING: {
|
| 7365 |
|
|
if (sign) needmax=1; /* Infinity if non-negative */
|
| 7366 |
|
|
break;} /* r-c */
|
| 7367 |
|
|
case DEC_ROUND_FLOOR: {
|
| 7368 |
|
|
if (!sign) needmax=1; /* Infinity if negative */
|
| 7369 |
|
|
break;} /* r-f */
|
| 7370 |
|
|
default: break; /* Infinity in all other cases */
|
| 7371 |
|
|
}
|
| 7372 |
|
|
if (needmax) {
|
| 7373 |
|
|
decSetMaxValue(dn, set);
|
| 7374 |
|
|
dn->bits=sign; /* set sign */
|
| 7375 |
|
|
}
|
| 7376 |
|
|
else dn->bits=sign|DECINF; /* Value is +/-Infinity */
|
| 7377 |
|
|
*status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
|
| 7378 |
|
|
} /* decSetOverflow */
|
| 7379 |
|
|
|
| 7380 |
|
|
/* ------------------------------------------------------------------ */
|
| 7381 |
|
|
/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
|
| 7382 |
|
|
/* */
|
| 7383 |
|
|
/* dn is the number to set */
|
| 7384 |
|
|
/* set is the context [used for digits and emax] */
|
| 7385 |
|
|
/* */
|
| 7386 |
|
|
/* This sets the number to the maximum positive value. */
|
| 7387 |
|
|
/* ------------------------------------------------------------------ */
|
| 7388 |
|
|
static void decSetMaxValue(decNumber *dn, decContext *set) {
|
| 7389 |
|
|
Unit *up; /* work */
|
| 7390 |
|
|
Int count=set->digits; /* nines to add */
|
| 7391 |
|
|
dn->digits=count;
|
| 7392 |
|
|
/* fill in all nines to set maximum value */
|
| 7393 |
|
|
for (up=dn->lsu; ; up++) {
|
| 7394 |
|
|
if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */
|
| 7395 |
|
|
else { /* this is the msu */
|
| 7396 |
|
|
*up=(Unit)(powers[count]-1);
|
| 7397 |
|
|
break;
|
| 7398 |
|
|
}
|
| 7399 |
|
|
count-=DECDPUN; /* filled those digits */
|
| 7400 |
|
|
} /* up */
|
| 7401 |
|
|
dn->bits=0; /* + sign */
|
| 7402 |
|
|
dn->exponent=set->emax-set->digits+1;
|
| 7403 |
|
|
} /* decSetMaxValue */
|
| 7404 |
|
|
|
| 7405 |
|
|
/* ------------------------------------------------------------------ */
|
| 7406 |
|
|
/* decSetSubnormal -- process value whose exponent is <Emin */
|
| 7407 |
|
|
/* */
|
| 7408 |
|
|
/* dn is the number (used as input as well as output; it may have */
|
| 7409 |
|
|
/* an allowed subnormal value, which may need to be rounded) */
|
| 7410 |
|
|
/* set is the context [used for the rounding mode] */
|
| 7411 |
|
|
/* residue is any pending residue */
|
| 7412 |
|
|
/* status contains the current status to be updated */
|
| 7413 |
|
|
/* */
|
| 7414 |
|
|
/* If subset mode, set result to zero and set Underflow flags. */
|
| 7415 |
|
|
/* */
|
| 7416 |
|
|
/* Value may be zero with a low exponent; this does not set Subnormal */
|
| 7417 |
|
|
/* but the exponent will be clamped to Etiny. */
|
| 7418 |
|
|
/* */
|
| 7419 |
|
|
/* Otherwise ensure exponent is not out of range, and round as */
|
| 7420 |
|
|
/* necessary. Underflow is set if the result is Inexact. */
|
| 7421 |
|
|
/* ------------------------------------------------------------------ */
|
| 7422 |
|
|
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
|
| 7423 |
|
|
uInt *status) {
|
| 7424 |
|
|
decContext workset; /* work */
|
| 7425 |
|
|
Int etiny, adjust; /* .. */
|
| 7426 |
|
|
|
| 7427 |
|
|
#if DECSUBSET
|
| 7428 |
|
|
/* simple set to zero and 'hard underflow' for subset */
|
| 7429 |
|
|
if (!set->extended) {
|
| 7430 |
|
|
decNumberZero(dn);
|
| 7431 |
|
|
/* always full overflow */
|
| 7432 |
|
|
*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| 7433 |
|
|
return;
|
| 7434 |
|
|
}
|
| 7435 |
|
|
#endif
|
| 7436 |
|
|
|
| 7437 |
|
|
/* Full arithmetic -- allow subnormals, rounded to minimum exponent */
|
| 7438 |
|
|
/* (Etiny) if needed */
|
| 7439 |
|
|
etiny=set->emin-(set->digits-1); /* smallest allowed exponent */
|
| 7440 |
|
|
|
| 7441 |
|
|
if ISZERO(dn) { /* value is zero */
|
| 7442 |
|
|
/* residue can never be non-zero here */
|
| 7443 |
|
|
#if DECCHECK
|
| 7444 |
|
|
if (*residue!=0) {
|
| 7445 |
|
|
printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
|
| 7446 |
|
|
*status|=DEC_Invalid_operation;
|
| 7447 |
|
|
}
|
| 7448 |
|
|
#endif
|
| 7449 |
|
|
if (dn->exponent<etiny) { /* clamp required */
|
| 7450 |
|
|
dn->exponent=etiny;
|
| 7451 |
|
|
*status|=DEC_Clamped;
|
| 7452 |
|
|
}
|
| 7453 |
|
|
return;
|
| 7454 |
|
|
}
|
| 7455 |
|
|
|
| 7456 |
|
|
*status|=DEC_Subnormal; /* have a non-zero subnormal */
|
| 7457 |
|
|
adjust=etiny-dn->exponent; /* calculate digits to remove */
|
| 7458 |
|
|
if (adjust<=0) { /* not out of range; unrounded */
|
| 7459 |
|
|
/* residue can never be non-zero here, except in the Nmin-residue */
|
| 7460 |
|
|
/* case (which is a subnormal result), so can take fast-path here */
|
| 7461 |
|
|
/* it may already be inexact (from setting the coefficient) */
|
| 7462 |
|
|
if (*status&DEC_Inexact) *status|=DEC_Underflow;
|
| 7463 |
|
|
return;
|
| 7464 |
|
|
}
|
| 7465 |
|
|
|
| 7466 |
|
|
/* adjust>0, so need to rescale the result so exponent becomes Etiny */
|
| 7467 |
|
|
/* [this code is similar to that in rescale] */
|
| 7468 |
|
|
workset=*set; /* clone rounding, etc. */
|
| 7469 |
|
|
workset.digits=dn->digits-adjust; /* set requested length */
|
| 7470 |
|
|
workset.emin-=adjust; /* and adjust emin to match */
|
| 7471 |
|
|
/* [note that the latter can be <1, here, similar to Rescale case] */
|
| 7472 |
|
|
decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
|
| 7473 |
|
|
decApplyRound(dn, &workset, *residue, status);
|
| 7474 |
|
|
|
| 7475 |
|
|
/* Use 754 default rule: Underflow is set iff Inexact */
|
| 7476 |
|
|
/* [independent of whether trapped] */
|
| 7477 |
|
|
if (*status&DEC_Inexact) *status|=DEC_Underflow;
|
| 7478 |
|
|
|
| 7479 |
|
|
/* if rounded up a 999s case, exponent will be off by one; adjust */
|
| 7480 |
|
|
/* back if so [it will fit, because it was shortened earlier] */
|
| 7481 |
|
|
if (dn->exponent>etiny) {
|
| 7482 |
|
|
dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
|
| 7483 |
|
|
dn->exponent--; /* (re)adjust the exponent. */
|
| 7484 |
|
|
}
|
| 7485 |
|
|
|
| 7486 |
|
|
/* if rounded to zero, it is by definition clamped... */
|
| 7487 |
|
|
if (ISZERO(dn)) *status|=DEC_Clamped;
|
| 7488 |
|
|
} /* decSetSubnormal */
|
| 7489 |
|
|
|
| 7490 |
|
|
/* ------------------------------------------------------------------ */
|
| 7491 |
|
|
/* decCheckMath - check entry conditions for a math function */
|
| 7492 |
|
|
/* */
|
| 7493 |
|
|
/* This checks the context and the operand */
|
| 7494 |
|
|
/* */
|
| 7495 |
|
|
/* rhs is the operand to check */
|
| 7496 |
|
|
/* set is the context to check */
|
| 7497 |
|
|
/* status is unchanged if both are good */
|
| 7498 |
|
|
/* */
|
| 7499 |
|
|
/* returns non-zero if status is changed, 0 otherwise */
|
| 7500 |
|
|
/* */
|
| 7501 |
|
|
/* Restrictions enforced: */
|
| 7502 |
|
|
/* */
|
| 7503 |
|
|
/* digits, emax, and -emin in the context must be less than */
|
| 7504 |
|
|
/* DEC_MAX_MATH (999999), and A must be within these bounds if */
|
| 7505 |
|
|
/* non-zero. Invalid_operation is set in the status if a */
|
| 7506 |
|
|
/* restriction is violated. */
|
| 7507 |
|
|
/* ------------------------------------------------------------------ */
|
| 7508 |
|
|
static uInt decCheckMath(const decNumber *rhs, decContext *set,
|
| 7509 |
|
|
uInt *status) {
|
| 7510 |
|
|
uInt save=*status; /* record */
|
| 7511 |
|
|
if (set->digits>DEC_MAX_MATH
|
| 7512 |
|
|
|| set->emax>DEC_MAX_MATH
|
| 7513 |
|
|
|| -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
|
| 7514 |
|
|
else if ((rhs->digits>DEC_MAX_MATH
|
| 7515 |
|
|
|| rhs->exponent+rhs->digits>DEC_MAX_MATH+1
|
| 7516 |
|
|
|| rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
|
| 7517 |
|
|
&& !ISZERO(rhs)) *status|=DEC_Invalid_operation;
|
| 7518 |
|
|
return (*status!=save);
|
| 7519 |
|
|
} /* decCheckMath */
|
| 7520 |
|
|
|
| 7521 |
|
|
/* ------------------------------------------------------------------ */
|
| 7522 |
|
|
/* decGetInt -- get integer from a number */
|
| 7523 |
|
|
/* */
|
| 7524 |
|
|
/* dn is the number [which will not be altered] */
|
| 7525 |
|
|
/* */
|
| 7526 |
|
|
/* returns one of: */
|
| 7527 |
|
|
/* BADINT if there is a non-zero fraction */
|
| 7528 |
|
|
/* the converted integer */
|
| 7529 |
|
|
/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
|
| 7530 |
|
|
/* BIGODD if the integer is odd and magnitude > 2*10**9 */
|
| 7531 |
|
|
/* */
|
| 7532 |
|
|
/* This checks and gets a whole number from the input decNumber. */
|
| 7533 |
|
|
/* The sign can be determined from dn by the caller when BIGEVEN or */
|
| 7534 |
|
|
/* BIGODD is returned. */
|
| 7535 |
|
|
/* ------------------------------------------------------------------ */
|
| 7536 |
|
|
static Int decGetInt(const decNumber *dn) {
|
| 7537 |
|
|
Int theInt; /* result accumulator */
|
| 7538 |
|
|
const Unit *up; /* work */
|
| 7539 |
|
|
Int got; /* digits (real or not) processed */
|
| 7540 |
|
|
Int ilength=dn->digits+dn->exponent; /* integral length */
|
| 7541 |
|
|
Flag neg=decNumberIsNegative(dn); /* 1 if -ve */
|
| 7542 |
|
|
|
| 7543 |
|
|
/* The number must be an integer that fits in 10 digits */
|
| 7544 |
|
|
/* Assert, here, that 10 is enough for any rescale Etiny */
|
| 7545 |
|
|
#if DEC_MAX_EMAX > 999999999
|
| 7546 |
|
|
#error GetInt may need updating [for Emax]
|
| 7547 |
|
|
#endif
|
| 7548 |
|
|
#if DEC_MIN_EMIN < -999999999
|
| 7549 |
|
|
#error GetInt may need updating [for Emin]
|
| 7550 |
|
|
#endif
|
| 7551 |
|
|
if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */
|
| 7552 |
|
|
|
| 7553 |
|
|
up=dn->lsu; /* ready for lsu */
|
| 7554 |
|
|
theInt=0; /* ready to accumulate */
|
| 7555 |
|
|
if (dn->exponent>=0) { /* relatively easy */
|
| 7556 |
|
|
/* no fractional part [usual]; allow for positive exponent */
|
| 7557 |
|
|
got=dn->exponent;
|
| 7558 |
|
|
}
|
| 7559 |
|
|
else { /* -ve exponent; some fractional part to check and discard */
|
| 7560 |
|
|
Int count=-dn->exponent; /* digits to discard */
|
| 7561 |
|
|
/* spin up whole units until reach the Unit with the unit digit */
|
| 7562 |
|
|
for (; count>=DECDPUN; up++) {
|
| 7563 |
|
|
if (*up!=0) return BADINT; /* non-zero Unit to discard */
|
| 7564 |
|
|
count-=DECDPUN;
|
| 7565 |
|
|
}
|
| 7566 |
|
|
if (count==0) got=0; /* [a multiple of DECDPUN] */
|
| 7567 |
|
|
else { /* [not multiple of DECDPUN] */
|
| 7568 |
|
|
Int rem; /* work */
|
| 7569 |
|
|
/* slice off fraction digits and check for non-zero */
|
| 7570 |
|
|
#if DECDPUN<=4
|
| 7571 |
|
|
theInt=QUOT10(*up, count);
|
| 7572 |
|
|
rem=*up-theInt*powers[count];
|
| 7573 |
|
|
#else
|
| 7574 |
|
|
rem=*up%powers[count]; /* slice off discards */
|
| 7575 |
|
|
theInt=*up/powers[count];
|
| 7576 |
|
|
#endif
|
| 7577 |
|
|
if (rem!=0) return BADINT; /* non-zero fraction */
|
| 7578 |
|
|
/* it looks good */
|
| 7579 |
|
|
got=DECDPUN-count; /* number of digits so far */
|
| 7580 |
|
|
up++; /* ready for next */
|
| 7581 |
|
|
}
|
| 7582 |
|
|
}
|
| 7583 |
|
|
/* now it's known there's no fractional part */
|
| 7584 |
|
|
|
| 7585 |
|
|
/* tricky code now, to accumulate up to 9.3 digits */
|
| 7586 |
|
|
if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */
|
| 7587 |
|
|
|
| 7588 |
|
|
if (ilength<11) {
|
| 7589 |
|
|
Int save=theInt;
|
| 7590 |
|
|
/* collect any remaining unit(s) */
|
| 7591 |
|
|
for (; got<ilength; up++) {
|
| 7592 |
|
|
theInt+=*up*powers[got];
|
| 7593 |
|
|
got+=DECDPUN;
|
| 7594 |
|
|
}
|
| 7595 |
|
|
if (ilength==10) { /* need to check for wrap */
|
| 7596 |
|
|
if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
|
| 7597 |
|
|
/* [that test also disallows the BADINT result case] */
|
| 7598 |
|
|
else if (neg && theInt>1999999997) ilength=11;
|
| 7599 |
|
|
else if (!neg && theInt>999999999) ilength=11;
|
| 7600 |
|
|
if (ilength==11) theInt=save; /* restore correct low bit */
|
| 7601 |
|
|
}
|
| 7602 |
|
|
}
|
| 7603 |
|
|
|
| 7604 |
|
|
if (ilength>10) { /* too big */
|
| 7605 |
|
|
if (theInt&1) return BIGODD; /* bottom bit 1 */
|
| 7606 |
|
|
return BIGEVEN; /* bottom bit 0 */
|
| 7607 |
|
|
}
|
| 7608 |
|
|
|
| 7609 |
|
|
if (neg) theInt=-theInt; /* apply sign */
|
| 7610 |
|
|
return theInt;
|
| 7611 |
|
|
} /* decGetInt */
|
| 7612 |
|
|
|
| 7613 |
|
|
/* ------------------------------------------------------------------ */
|
| 7614 |
|
|
/* decDecap -- decapitate the coefficient of a number */
|
| 7615 |
|
|
/* */
|
| 7616 |
|
|
/* dn is the number to be decapitated */
|
| 7617 |
|
|
/* drop is the number of digits to be removed from the left of dn; */
|
| 7618 |
|
|
/* this must be <= dn->digits (if equal, the coefficient is */
|
| 7619 |
|
|
/* set to 0) */
|
| 7620 |
|
|
/* */
|
| 7621 |
|
|
/* Returns dn; dn->digits will be <= the initial digits less drop */
|
| 7622 |
|
|
/* (after removing drop digits there may be leading zero digits */
|
| 7623 |
|
|
/* which will also be removed). Only dn->lsu and dn->digits change. */
|
| 7624 |
|
|
/* ------------------------------------------------------------------ */
|
| 7625 |
|
|
static decNumber *decDecap(decNumber *dn, Int drop) {
|
| 7626 |
|
|
Unit *msu; /* -> target cut point */
|
| 7627 |
|
|
Int cut; /* work */
|
| 7628 |
|
|
if (drop>=dn->digits) { /* losing the whole thing */
|
| 7629 |
|
|
#if DECCHECK
|
| 7630 |
|
|
if (drop>dn->digits)
|
| 7631 |
|
|
printf("decDecap called with drop>digits [%ld>%ld]\n",
|
| 7632 |
|
|
(LI)drop, (LI)dn->digits);
|
| 7633 |
|
|
#endif
|
| 7634 |
|
|
dn->lsu[0]=0;
|
| 7635 |
|
|
dn->digits=1;
|
| 7636 |
|
|
return dn;
|
| 7637 |
|
|
}
|
| 7638 |
|
|
msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */
|
| 7639 |
|
|
cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */
|
| 7640 |
|
|
if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */
|
| 7641 |
|
|
/* that may have left leading zero digits, so do a proper count... */
|
| 7642 |
|
|
dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
|
| 7643 |
|
|
return dn;
|
| 7644 |
|
|
} /* decDecap */
|
| 7645 |
|
|
|
| 7646 |
|
|
/* ------------------------------------------------------------------ */
|
| 7647 |
|
|
/* decBiStr -- compare string with pairwise options */
|
| 7648 |
|
|
/* */
|
| 7649 |
|
|
/* targ is the string to compare */
|
| 7650 |
|
|
/* str1 is one of the strings to compare against (length may be 0) */
|
| 7651 |
|
|
/* str2 is the other; it must be the same length as str1 */
|
| 7652 |
|
|
/* */
|
| 7653 |
|
|
/* returns 1 if strings compare equal, (that is, it is the same */
|
| 7654 |
|
|
/* length as str1 and str2, and each character of targ is in either */
|
| 7655 |
|
|
/* str1 or str2 in the corresponding position), or 0 otherwise */
|
| 7656 |
|
|
/* */
|
| 7657 |
|
|
/* This is used for generic caseless compare, including the awkward */
|
| 7658 |
|
|
/* case of the Turkish dotted and dotless Is. Use as (for example): */
|
| 7659 |
|
|
/* if (decBiStr(test, "mike", "MIKE")) ... */
|
| 7660 |
|
|
/* ------------------------------------------------------------------ */
|
| 7661 |
|
|
static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
|
| 7662 |
|
|
for (;;targ++, str1++, str2++) {
|
| 7663 |
|
|
if (*targ!=*str1 && *targ!=*str2) return 0;
|
| 7664 |
|
|
/* *targ has a match in one (or both, if terminator) */
|
| 7665 |
|
|
if (*targ=='\0') break;
|
| 7666 |
|
|
} /* forever */
|
| 7667 |
|
|
return 1;
|
| 7668 |
|
|
} /* decBiStr */
|
| 7669 |
|
|
|
| 7670 |
|
|
/* ------------------------------------------------------------------ */
|
| 7671 |
|
|
/* decNaNs -- handle NaN operand or operands */
|
| 7672 |
|
|
/* */
|
| 7673 |
|
|
/* res is the result number */
|
| 7674 |
|
|
/* lhs is the first operand */
|
| 7675 |
|
|
/* rhs is the second operand, or NULL if none */
|
| 7676 |
|
|
/* context is used to limit payload length */
|
| 7677 |
|
|
/* status contains the current status */
|
| 7678 |
|
|
/* returns res in case convenient */
|
| 7679 |
|
|
/* */
|
| 7680 |
|
|
/* Called when one or both operands is a NaN, and propagates the */
|
| 7681 |
|
|
/* appropriate result to res. When an sNaN is found, it is changed */
|
| 7682 |
|
|
/* to a qNaN and Invalid operation is set. */
|
| 7683 |
|
|
/* ------------------------------------------------------------------ */
|
| 7684 |
|
|
static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
|
| 7685 |
|
|
const decNumber *rhs, decContext *set,
|
| 7686 |
|
|
uInt *status) {
|
| 7687 |
|
|
/* This decision tree ends up with LHS being the source pointer, */
|
| 7688 |
|
|
/* and status updated if need be */
|
| 7689 |
|
|
if (lhs->bits & DECSNAN)
|
| 7690 |
|
|
*status|=DEC_Invalid_operation | DEC_sNaN;
|
| 7691 |
|
|
else if (rhs==NULL);
|
| 7692 |
|
|
else if (rhs->bits & DECSNAN) {
|
| 7693 |
|
|
lhs=rhs;
|
| 7694 |
|
|
*status|=DEC_Invalid_operation | DEC_sNaN;
|
| 7695 |
|
|
}
|
| 7696 |
|
|
else if (lhs->bits & DECNAN);
|
| 7697 |
|
|
else lhs=rhs;
|
| 7698 |
|
|
|
| 7699 |
|
|
/* propagate the payload */
|
| 7700 |
|
|
if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */
|
| 7701 |
|
|
else { /* too long */
|
| 7702 |
|
|
const Unit *ul;
|
| 7703 |
|
|
Unit *ur, *uresp1;
|
| 7704 |
|
|
/* copy safe number of units, then decapitate */
|
| 7705 |
|
|
res->bits=lhs->bits; /* need sign etc. */
|
| 7706 |
|
|
uresp1=res->lsu+D2U(set->digits);
|
| 7707 |
|
|
for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
|
| 7708 |
|
|
res->digits=D2U(set->digits)*DECDPUN;
|
| 7709 |
|
|
/* maybe still too long */
|
| 7710 |
|
|
if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
|
| 7711 |
|
|
}
|
| 7712 |
|
|
|
| 7713 |
|
|
res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */
|
| 7714 |
|
|
res->bits|=DECNAN; /* .. preserving sign */
|
| 7715 |
|
|
res->exponent=0; /* clean exponent */
|
| 7716 |
|
|
/* [coefficient was copied/decapitated] */
|
| 7717 |
|
|
return res;
|
| 7718 |
|
|
} /* decNaNs */
|
| 7719 |
|
|
|
| 7720 |
|
|
/* ------------------------------------------------------------------ */
|
| 7721 |
|
|
/* decStatus -- apply non-zero status */
|
| 7722 |
|
|
/* */
|
| 7723 |
|
|
/* dn is the number to set if error */
|
| 7724 |
|
|
/* status contains the current status (not yet in context) */
|
| 7725 |
|
|
/* set is the context */
|
| 7726 |
|
|
/* */
|
| 7727 |
|
|
/* If the status is an error status, the number is set to a NaN, */
|
| 7728 |
|
|
/* unless the error was an overflow, divide-by-zero, or underflow, */
|
| 7729 |
|
|
/* in which case the number will have already been set. */
|
| 7730 |
|
|
/* */
|
| 7731 |
|
|
/* The context status is then updated with the new status. Note that */
|
| 7732 |
|
|
/* this may raise a signal, so control may never return from this */
|
| 7733 |
|
|
/* routine (hence resources must be recovered before it is called). */
|
| 7734 |
|
|
/* ------------------------------------------------------------------ */
|
| 7735 |
|
|
static void decStatus(decNumber *dn, uInt status, decContext *set) {
|
| 7736 |
|
|
if (status & DEC_NaNs) { /* error status -> NaN */
|
| 7737 |
|
|
/* if cause was an sNaN, clear and propagate [NaN is already set up] */
|
| 7738 |
|
|
if (status & DEC_sNaN) status&=~DEC_sNaN;
|
| 7739 |
|
|
else {
|
| 7740 |
|
|
decNumberZero(dn); /* other error: clean throughout */
|
| 7741 |
|
|
dn->bits=DECNAN; /* and make a quiet NaN */
|
| 7742 |
|
|
}
|
| 7743 |
|
|
}
|
| 7744 |
|
|
decContextSetStatus(set, status); /* [may not return] */
|
| 7745 |
|
|
return;
|
| 7746 |
|
|
} /* decStatus */
|
| 7747 |
|
|
|
| 7748 |
|
|
/* ------------------------------------------------------------------ */
|
| 7749 |
|
|
/* decGetDigits -- count digits in a Units array */
|
| 7750 |
|
|
/* */
|
| 7751 |
|
|
/* uar is the Unit array holding the number (this is often an */
|
| 7752 |
|
|
/* accumulator of some sort) */
|
| 7753 |
|
|
/* len is the length of the array in units [>=1] */
|
| 7754 |
|
|
/* */
|
| 7755 |
|
|
/* returns the number of (significant) digits in the array */
|
| 7756 |
|
|
/* */
|
| 7757 |
|
|
/* All leading zeros are excluded, except the last if the array has */
|
| 7758 |
|
|
/* only zero Units. */
|
| 7759 |
|
|
/* ------------------------------------------------------------------ */
|
| 7760 |
|
|
/* This may be called twice during some operations. */
|
| 7761 |
|
|
static Int decGetDigits(Unit *uar, Int len) {
|
| 7762 |
|
|
Unit *up=uar+(len-1); /* -> msu */
|
| 7763 |
|
|
Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */
|
| 7764 |
|
|
#if DECDPUN>4
|
| 7765 |
|
|
uInt const *pow; /* work */
|
| 7766 |
|
|
#endif
|
| 7767 |
|
|
/* (at least 1 in final msu) */
|
| 7768 |
|
|
#if DECCHECK
|
| 7769 |
|
|
if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
|
| 7770 |
|
|
#endif
|
| 7771 |
|
|
|
| 7772 |
|
|
for (; up>=uar; up--) {
|
| 7773 |
|
|
if (*up==0) { /* unit is all 0s */
|
| 7774 |
|
|
if (digits==1) break; /* a zero has one digit */
|
| 7775 |
|
|
digits-=DECDPUN; /* adjust for 0 unit */
|
| 7776 |
|
|
continue;}
|
| 7777 |
|
|
/* found the first (most significant) non-zero Unit */
|
| 7778 |
|
|
#if DECDPUN>1 /* not done yet */
|
| 7779 |
|
|
if (*up<10) break; /* is 1-9 */
|
| 7780 |
|
|
digits++;
|
| 7781 |
|
|
#if DECDPUN>2 /* not done yet */
|
| 7782 |
|
|
if (*up<100) break; /* is 10-99 */
|
| 7783 |
|
|
digits++;
|
| 7784 |
|
|
#if DECDPUN>3 /* not done yet */
|
| 7785 |
|
|
if (*up<1000) break; /* is 100-999 */
|
| 7786 |
|
|
digits++;
|
| 7787 |
|
|
#if DECDPUN>4 /* count the rest ... */
|
| 7788 |
|
|
for (pow=&powers[4]; *up>=*pow; pow++) digits++;
|
| 7789 |
|
|
#endif
|
| 7790 |
|
|
#endif
|
| 7791 |
|
|
#endif
|
| 7792 |
|
|
#endif
|
| 7793 |
|
|
break;
|
| 7794 |
|
|
} /* up */
|
| 7795 |
|
|
return digits;
|
| 7796 |
|
|
} /* decGetDigits */
|
| 7797 |
|
|
|
| 7798 |
|
|
#if DECTRACE | DECCHECK
|
| 7799 |
|
|
/* ------------------------------------------------------------------ */
|
| 7800 |
|
|
/* decNumberShow -- display a number [debug aid] */
|
| 7801 |
|
|
/* dn is the number to show */
|
| 7802 |
|
|
/* */
|
| 7803 |
|
|
/* Shows: sign, exponent, coefficient (msu first), digits */
|
| 7804 |
|
|
/* or: sign, special-value */
|
| 7805 |
|
|
/* ------------------------------------------------------------------ */
|
| 7806 |
|
|
/* this is public so other modules can use it */
|
| 7807 |
|
|
void decNumberShow(const decNumber *dn) {
|
| 7808 |
|
|
const Unit *up; /* work */
|
| 7809 |
|
|
uInt u, d; /* .. */
|
| 7810 |
|
|
Int cut; /* .. */
|
| 7811 |
|
|
char isign='+'; /* main sign */
|
| 7812 |
|
|
if (dn==NULL) {
|
| 7813 |
|
|
printf("NULL\n");
|
| 7814 |
|
|
return;}
|
| 7815 |
|
|
if (decNumberIsNegative(dn)) isign='-';
|
| 7816 |
|
|
printf(" >> %c ", isign);
|
| 7817 |
|
|
if (dn->bits&DECSPECIAL) { /* Is a special value */
|
| 7818 |
|
|
if (decNumberIsInfinite(dn)) printf("Infinity");
|
| 7819 |
|
|
else { /* a NaN */
|
| 7820 |
|
|
if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */
|
| 7821 |
|
|
else printf("NaN");
|
| 7822 |
|
|
}
|
| 7823 |
|
|
/* if coefficient and exponent are 0, no more to do */
|
| 7824 |
|
|
if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
|
| 7825 |
|
|
printf("\n");
|
| 7826 |
|
|
return;}
|
| 7827 |
|
|
/* drop through to report other information */
|
| 7828 |
|
|
printf(" ");
|
| 7829 |
|
|
}
|
| 7830 |
|
|
|
| 7831 |
|
|
/* now carefully display the coefficient */
|
| 7832 |
|
|
up=dn->lsu+D2U(dn->digits)-1; /* msu */
|
| 7833 |
|
|
printf("%ld", (LI)*up);
|
| 7834 |
|
|
for (up=up-1; up>=dn->lsu; up--) {
|
| 7835 |
|
|
u=*up;
|
| 7836 |
|
|
printf(":");
|
| 7837 |
|
|
for (cut=DECDPUN-1; cut>=0; cut--) {
|
| 7838 |
|
|
d=u/powers[cut];
|
| 7839 |
|
|
u-=d*powers[cut];
|
| 7840 |
|
|
printf("%ld", (LI)d);
|
| 7841 |
|
|
} /* cut */
|
| 7842 |
|
|
} /* up */
|
| 7843 |
|
|
if (dn->exponent!=0) {
|
| 7844 |
|
|
char esign='+';
|
| 7845 |
|
|
if (dn->exponent<0) esign='-';
|
| 7846 |
|
|
printf(" E%c%ld", esign, (LI)abs(dn->exponent));
|
| 7847 |
|
|
}
|
| 7848 |
|
|
printf(" [%ld]\n", (LI)dn->digits);
|
| 7849 |
|
|
} /* decNumberShow */
|
| 7850 |
|
|
#endif
|
| 7851 |
|
|
|
| 7852 |
|
|
#if DECTRACE || DECCHECK
|
| 7853 |
|
|
/* ------------------------------------------------------------------ */
|
| 7854 |
|
|
/* decDumpAr -- display a unit array [debug/check aid] */
|
| 7855 |
|
|
/* name is a single-character tag name */
|
| 7856 |
|
|
/* ar is the array to display */
|
| 7857 |
|
|
/* len is the length of the array in Units */
|
| 7858 |
|
|
/* ------------------------------------------------------------------ */
|
| 7859 |
|
|
static void decDumpAr(char name, const Unit *ar, Int len) {
|
| 7860 |
|
|
Int i;
|
| 7861 |
|
|
const char *spec;
|
| 7862 |
|
|
#if DECDPUN==9
|
| 7863 |
|
|
spec="%09d ";
|
| 7864 |
|
|
#elif DECDPUN==8
|
| 7865 |
|
|
spec="%08d ";
|
| 7866 |
|
|
#elif DECDPUN==7
|
| 7867 |
|
|
spec="%07d ";
|
| 7868 |
|
|
#elif DECDPUN==6
|
| 7869 |
|
|
spec="%06d ";
|
| 7870 |
|
|
#elif DECDPUN==5
|
| 7871 |
|
|
spec="%05d ";
|
| 7872 |
|
|
#elif DECDPUN==4
|
| 7873 |
|
|
spec="%04d ";
|
| 7874 |
|
|
#elif DECDPUN==3
|
| 7875 |
|
|
spec="%03d ";
|
| 7876 |
|
|
#elif DECDPUN==2
|
| 7877 |
|
|
spec="%02d ";
|
| 7878 |
|
|
#else
|
| 7879 |
|
|
spec="%d ";
|
| 7880 |
|
|
#endif
|
| 7881 |
|
|
printf(" :%c: ", name);
|
| 7882 |
|
|
for (i=len-1; i>=0; i--) {
|
| 7883 |
|
|
if (i==len-1) printf("%ld ", (LI)ar[i]);
|
| 7884 |
|
|
else printf(spec, ar[i]);
|
| 7885 |
|
|
}
|
| 7886 |
|
|
printf("\n");
|
| 7887 |
|
|
return;}
|
| 7888 |
|
|
#endif
|
| 7889 |
|
|
|
| 7890 |
|
|
#if DECCHECK
|
| 7891 |
|
|
/* ------------------------------------------------------------------ */
|
| 7892 |
|
|
/* decCheckOperands -- check operand(s) to a routine */
|
| 7893 |
|
|
/* res is the result structure (not checked; it will be set to */
|
| 7894 |
|
|
/* quiet NaN if error found (and it is not NULL)) */
|
| 7895 |
|
|
/* lhs is the first operand (may be DECUNRESU) */
|
| 7896 |
|
|
/* rhs is the second (may be DECUNUSED) */
|
| 7897 |
|
|
/* set is the context (may be DECUNCONT) */
|
| 7898 |
|
|
/* returns 0 if both operands, and the context are clean, or 1 */
|
| 7899 |
|
|
/* otherwise (in which case the context will show an error, */
|
| 7900 |
|
|
/* unless NULL). Note that res is not cleaned; caller should */
|
| 7901 |
|
|
/* handle this so res=NULL case is safe. */
|
| 7902 |
|
|
/* The caller is expected to abandon immediately if 1 is returned. */
|
| 7903 |
|
|
/* ------------------------------------------------------------------ */
|
| 7904 |
|
|
static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
|
| 7905 |
|
|
const decNumber *rhs, decContext *set) {
|
| 7906 |
|
|
Flag bad=0;
|
| 7907 |
|
|
if (set==NULL) { /* oops; hopeless */
|
| 7908 |
|
|
#if DECTRACE || DECVERB
|
| 7909 |
|
|
printf("Reference to context is NULL.\n");
|
| 7910 |
|
|
#endif
|
| 7911 |
|
|
bad=1;
|
| 7912 |
|
|
return 1;}
|
| 7913 |
|
|
else if (set!=DECUNCONT
|
| 7914 |
|
|
&& (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
|
| 7915 |
|
|
bad=1;
|
| 7916 |
|
|
#if DECTRACE || DECVERB
|
| 7917 |
|
|
printf("Bad context [digits=%ld round=%ld].\n",
|
| 7918 |
|
|
(LI)set->digits, (LI)set->round);
|
| 7919 |
|
|
#endif
|
| 7920 |
|
|
}
|
| 7921 |
|
|
else {
|
| 7922 |
|
|
if (res==NULL) {
|
| 7923 |
|
|
bad=1;
|
| 7924 |
|
|
#if DECTRACE
|
| 7925 |
|
|
/* this one not DECVERB as standard tests include NULL */
|
| 7926 |
|
|
printf("Reference to result is NULL.\n");
|
| 7927 |
|
|
#endif
|
| 7928 |
|
|
}
|
| 7929 |
|
|
if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
|
| 7930 |
|
|
if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
|
| 7931 |
|
|
}
|
| 7932 |
|
|
if (bad) {
|
| 7933 |
|
|
if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
|
| 7934 |
|
|
if (res!=DECUNRESU && res!=NULL) {
|
| 7935 |
|
|
decNumberZero(res);
|
| 7936 |
|
|
res->bits=DECNAN; /* qNaN */
|
| 7937 |
|
|
}
|
| 7938 |
|
|
}
|
| 7939 |
|
|
return bad;
|
| 7940 |
|
|
} /* decCheckOperands */
|
| 7941 |
|
|
|
| 7942 |
|
|
/* ------------------------------------------------------------------ */
|
| 7943 |
|
|
/* decCheckNumber -- check a number */
|
| 7944 |
|
|
/* dn is the number to check */
|
| 7945 |
|
|
/* returns 0 if the number is clean, or 1 otherwise */
|
| 7946 |
|
|
/* */
|
| 7947 |
|
|
/* The number is considered valid if it could be a result from some */
|
| 7948 |
|
|
/* operation in some valid context. */
|
| 7949 |
|
|
/* ------------------------------------------------------------------ */
|
| 7950 |
|
|
static Flag decCheckNumber(const decNumber *dn) {
|
| 7951 |
|
|
const Unit *up; /* work */
|
| 7952 |
|
|
uInt maxuint; /* .. */
|
| 7953 |
|
|
Int ae, d, digits; /* .. */
|
| 7954 |
|
|
Int emin, emax; /* .. */
|
| 7955 |
|
|
|
| 7956 |
|
|
if (dn==NULL) { /* hopeless */
|
| 7957 |
|
|
#if DECTRACE
|
| 7958 |
|
|
/* this one not DECVERB as standard tests include NULL */
|
| 7959 |
|
|
printf("Reference to decNumber is NULL.\n");
|
| 7960 |
|
|
#endif
|
| 7961 |
|
|
return 1;}
|
| 7962 |
|
|
|
| 7963 |
|
|
/* check special values */
|
| 7964 |
|
|
if (dn->bits & DECSPECIAL) {
|
| 7965 |
|
|
if (dn->exponent!=0) {
|
| 7966 |
|
|
#if DECTRACE || DECVERB
|
| 7967 |
|
|
printf("Exponent %ld (not 0) for a special value [%02x].\n",
|
| 7968 |
|
|
(LI)dn->exponent, dn->bits);
|
| 7969 |
|
|
#endif
|
| 7970 |
|
|
return 1;}
|
| 7971 |
|
|
|
| 7972 |
|
|
/* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
|
| 7973 |
|
|
if (decNumberIsInfinite(dn)) {
|
| 7974 |
|
|
if (dn->digits!=1) {
|
| 7975 |
|
|
#if DECTRACE || DECVERB
|
| 7976 |
|
|
printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
|
| 7977 |
|
|
#endif
|
| 7978 |
|
|
return 1;}
|
| 7979 |
|
|
if (*dn->lsu!=0) {
|
| 7980 |
|
|
#if DECTRACE || DECVERB
|
| 7981 |
|
|
printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
|
| 7982 |
|
|
#endif
|
| 7983 |
|
|
decDumpAr('I', dn->lsu, D2U(dn->digits));
|
| 7984 |
|
|
return 1;}
|
| 7985 |
|
|
} /* Inf */
|
| 7986 |
|
|
/* 2002.12.26: negative NaNs can now appear through proposed IEEE */
|
| 7987 |
|
|
/* concrete formats (decimal64, etc.). */
|
| 7988 |
|
|
return 0;
|
| 7989 |
|
|
}
|
| 7990 |
|
|
|
| 7991 |
|
|
/* check the coefficient */
|
| 7992 |
|
|
if (dn->digits<1 || dn->digits>DECNUMMAXP) {
|
| 7993 |
|
|
#if DECTRACE || DECVERB
|
| 7994 |
|
|
printf("Digits %ld in number.\n", (LI)dn->digits);
|
| 7995 |
|
|
#endif
|
| 7996 |
|
|
return 1;}
|
| 7997 |
|
|
|
| 7998 |
|
|
d=dn->digits;
|
| 7999 |
|
|
|
| 8000 |
|
|
for (up=dn->lsu; d>0; up++) {
|
| 8001 |
|
|
if (d>DECDPUN) maxuint=DECDPUNMAX;
|
| 8002 |
|
|
else { /* reached the msu */
|
| 8003 |
|
|
maxuint=powers[d]-1;
|
| 8004 |
|
|
if (dn->digits>1 && *up<powers[d-1]) {
|
| 8005 |
|
|
#if DECTRACE || DECVERB
|
| 8006 |
|
|
printf("Leading 0 in number.\n");
|
| 8007 |
|
|
decNumberShow(dn);
|
| 8008 |
|
|
#endif
|
| 8009 |
|
|
return 1;}
|
| 8010 |
|
|
}
|
| 8011 |
|
|
if (*up>maxuint) {
|
| 8012 |
|
|
#if DECTRACE || DECVERB
|
| 8013 |
|
|
printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
|
| 8014 |
|
|
(LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
|
| 8015 |
|
|
#endif
|
| 8016 |
|
|
return 1;}
|
| 8017 |
|
|
d-=DECDPUN;
|
| 8018 |
|
|
}
|
| 8019 |
|
|
|
| 8020 |
|
|
/* check the exponent. Note that input operands can have exponents */
|
| 8021 |
|
|
/* which are out of the set->emin/set->emax and set->digits range */
|
| 8022 |
|
|
/* (just as they can have more digits than set->digits). */
|
| 8023 |
|
|
ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| 8024 |
|
|
emax=DECNUMMAXE;
|
| 8025 |
|
|
emin=DECNUMMINE;
|
| 8026 |
|
|
digits=DECNUMMAXP;
|
| 8027 |
|
|
if (ae<emin-(digits-1)) {
|
| 8028 |
|
|
#if DECTRACE || DECVERB
|
| 8029 |
|
|
printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
|
| 8030 |
|
|
decNumberShow(dn);
|
| 8031 |
|
|
#endif
|
| 8032 |
|
|
return 1;}
|
| 8033 |
|
|
if (ae>+emax) {
|
| 8034 |
|
|
#if DECTRACE || DECVERB
|
| 8035 |
|
|
printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
|
| 8036 |
|
|
decNumberShow(dn);
|
| 8037 |
|
|
#endif
|
| 8038 |
|
|
return 1;}
|
| 8039 |
|
|
|
| 8040 |
|
|
return 0; /* it's OK */
|
| 8041 |
|
|
} /* decCheckNumber */
|
| 8042 |
|
|
|
| 8043 |
|
|
/* ------------------------------------------------------------------ */
|
| 8044 |
|
|
/* decCheckInexact -- check a normal finite inexact result has digits */
|
| 8045 |
|
|
/* dn is the number to check */
|
| 8046 |
|
|
/* set is the context (for status and precision) */
|
| 8047 |
|
|
/* sets Invalid operation, etc., if some digits are missing */
|
| 8048 |
|
|
/* [this check is not made for DECSUBSET compilation or when */
|
| 8049 |
|
|
/* subnormal is not set] */
|
| 8050 |
|
|
/* ------------------------------------------------------------------ */
|
| 8051 |
|
|
static void decCheckInexact(const decNumber *dn, decContext *set) {
|
| 8052 |
|
|
#if !DECSUBSET && DECEXTFLAG
|
| 8053 |
|
|
if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
|
| 8054 |
|
|
&& (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
|
| 8055 |
|
|
#if DECTRACE || DECVERB
|
| 8056 |
|
|
printf("Insufficient digits [%ld] on normal Inexact result.\n",
|
| 8057 |
|
|
(LI)dn->digits);
|
| 8058 |
|
|
decNumberShow(dn);
|
| 8059 |
|
|
#endif
|
| 8060 |
|
|
decContextSetStatus(set, DEC_Invalid_operation);
|
| 8061 |
|
|
}
|
| 8062 |
|
|
#else
|
| 8063 |
|
|
/* next is a noop for quiet compiler */
|
| 8064 |
|
|
if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
|
| 8065 |
|
|
#endif
|
| 8066 |
|
|
return;
|
| 8067 |
|
|
} /* decCheckInexact */
|
| 8068 |
|
|
#endif
|
| 8069 |
|
|
|
| 8070 |
|
|
#if DECALLOC
|
| 8071 |
|
|
#undef malloc
|
| 8072 |
|
|
#undef free
|
| 8073 |
|
|
/* ------------------------------------------------------------------ */
|
| 8074 |
|
|
/* decMalloc -- accountable allocation routine */
|
| 8075 |
|
|
/* n is the number of bytes to allocate */
|
| 8076 |
|
|
/* */
|
| 8077 |
|
|
/* Semantics is the same as the stdlib malloc routine, but bytes */
|
| 8078 |
|
|
/* allocated are accounted for globally, and corruption fences are */
|
| 8079 |
|
|
/* added before and after the 'actual' storage. */
|
| 8080 |
|
|
/* ------------------------------------------------------------------ */
|
| 8081 |
|
|
/* This routine allocates storage with an extra twelve bytes; 8 are */
|
| 8082 |
|
|
/* at the start and hold: */
|
| 8083 |
|
|
/* 0-3 the original length requested */
|
| 8084 |
|
|
/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
|
| 8085 |
|
|
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
|
| 8086 |
|
|
/* ------------------------------------------------------------------ */
|
| 8087 |
|
|
static void *decMalloc(size_t n) {
|
| 8088 |
|
|
uInt size=n+12; /* true size */
|
| 8089 |
|
|
void *alloc; /* -> allocated storage */
|
| 8090 |
|
|
uByte *b, *b0; /* work */
|
| 8091 |
|
|
uInt uiwork; /* for macros */
|
| 8092 |
|
|
|
| 8093 |
|
|
alloc=malloc(size); /* -> allocated storage */
|
| 8094 |
|
|
if (alloc==NULL) return NULL; /* out of strorage */
|
| 8095 |
|
|
b0=(uByte *)alloc; /* as bytes */
|
| 8096 |
|
|
decAllocBytes+=n; /* account for storage */
|
| 8097 |
|
|
UBFROMUI(alloc, n); /* save n */
|
| 8098 |
|
|
/* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */
|
| 8099 |
|
|
for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
|
| 8100 |
|
|
for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
|
| 8101 |
|
|
return b0+8; /* -> play area */
|
| 8102 |
|
|
} /* decMalloc */
|
| 8103 |
|
|
|
| 8104 |
|
|
/* ------------------------------------------------------------------ */
|
| 8105 |
|
|
/* decFree -- accountable free routine */
|
| 8106 |
|
|
/* alloc is the storage to free */
|
| 8107 |
|
|
/* */
|
| 8108 |
|
|
/* Semantics is the same as the stdlib malloc routine, except that */
|
| 8109 |
|
|
/* the global storage accounting is updated and the fences are */
|
| 8110 |
|
|
/* checked to ensure that no routine has written 'out of bounds'. */
|
| 8111 |
|
|
/* ------------------------------------------------------------------ */
|
| 8112 |
|
|
/* This routine first checks that the fences have not been corrupted. */
|
| 8113 |
|
|
/* It then frees the storage using the 'truw' storage address (that */
|
| 8114 |
|
|
/* is, offset by 8). */
|
| 8115 |
|
|
/* ------------------------------------------------------------------ */
|
| 8116 |
|
|
static void decFree(void *alloc) {
|
| 8117 |
|
|
uInt n; /* original length */
|
| 8118 |
|
|
uByte *b, *b0; /* work */
|
| 8119 |
|
|
uInt uiwork; /* for macros */
|
| 8120 |
|
|
|
| 8121 |
|
|
if (alloc==NULL) return; /* allowed; it's a nop */
|
| 8122 |
|
|
b0=(uByte *)alloc; /* as bytes */
|
| 8123 |
|
|
b0-=8; /* -> true start of storage */
|
| 8124 |
|
|
n=UBTOUI(b0); /* lift length */
|
| 8125 |
|
|
for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
|
| 8126 |
|
|
printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
|
| 8127 |
|
|
b-b0-8, (LI)b0);
|
| 8128 |
|
|
for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
|
| 8129 |
|
|
printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
|
| 8130 |
|
|
b-b0-8, (LI)b0, (LI)n);
|
| 8131 |
|
|
free(b0); /* drop the storage */
|
| 8132 |
|
|
decAllocBytes-=n; /* account for storage */
|
| 8133 |
|
|
/* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
|
| 8134 |
|
|
} /* decFree */
|
| 8135 |
|
|
#define malloc(a) decMalloc(a)
|
| 8136 |
|
|
#define free(a) decFree(a)
|
| 8137 |
|
|
#endif
|
