720 lines
17 KiB
C
720 lines
17 KiB
C
/**
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* This file has no copyright assigned and is placed in the Public Domain.
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* This file is part of the mingw-w64 runtime package.
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* No warranty is given; refer to the file DISCLAIMER.PD within this package.
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*/
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#ifndef _CEPHES_EMATH_H
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#define _CEPHES_EMATH_H
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/**
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* This is a workaround for a gcc bug
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*/
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#define __restrict__
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/* This file is extracted from S L Moshier's ioldoubl.c,
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* modified for use in MinGW
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*
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* Extended precision arithmetic functions for long double I/O.
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* This program has been placed in the public domain.
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*/
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/*
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* Revision history:
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*
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* 5 Jan 84 PDP-11 assembly language version
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* 6 Dec 86 C language version
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* 30 Aug 88 100 digit version, improved rounding
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* 15 May 92 80-bit long double support
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*
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* Author: S. L. Moshier.
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*
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* 6 Oct 02 Modified for MinGW by inlining utility routines,
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* removing global variables, and splitting out strtold
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* from _IO_ldtoa and _IO_ldtostr.
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*
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* Danny Smith <dannysmith@users.sourceforge.net>
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*
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*/
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/* ieee.c
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*
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* Extended precision IEEE binary floating point arithmetic routines
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*
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* Numbers are stored in C language as arrays of 16-bit unsigned
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* short integers. The arguments of the routines are pointers to
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* the arrays.
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*
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*
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* External e type data structure, simulates Intel 8087 chip
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* temporary real format but possibly with a larger significand:
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*
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* NE-1 significand words (least significant word first,
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* most significant bit is normally set)
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* exponent (value = EXONE for 1.0,
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* top bit is the sign)
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*
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*
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* Internal data structure of a number (a "word" is 16 bits):
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*
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* ei[0] sign word (0 for positive, 0xffff for negative)
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* ei[1] biased __exponent (value = EXONE for the number 1.0)
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* ei[2] high guard word (always zero after normalization)
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* ei[3]
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* to ei[NI-2] significand (NI-4 significand words,
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* most significant word first,
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* most significant bit is set)
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* ei[NI-1] low guard word (0x8000 bit is rounding place)
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*
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*
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*
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* Routines for external format numbers
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*
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* __asctoe64( string, &d ) ASCII string to long double
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* __asctoeg( string, e, prec ) ASCII string to specified precision
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* __e64toe( &d, e ) IEEE long double precision to e type
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* __eadd( a, b, c ) c = b + a
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* __eclear(e) e = 0
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* __ecmp (a, b) Returns 1 if a > b, 0 if a == b,
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* -1 if a < b, -2 if either a or b is a NaN.
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* __ediv( a, b, c ) c = b / a
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* __efloor( a, b ) truncate to integer, toward -infinity
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* __efrexp( a, exp, s ) extract exponent and significand
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* __eifrac( e, &l, frac ) e to long integer and e type fraction
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* __euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
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* __einfin( e ) set e to infinity, leaving its sign alone
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* __eldexp( a, n, b ) multiply by 2**n
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* __emov( a, b ) b = a
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* __emul( a, b, c ) c = b * a
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* __eneg(e) e = -e
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* __eround( a, b ) b = nearest integer value to a
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* __esub( a, b, c ) c = b - a
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* __e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
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* __e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
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* __e64toasc( &d, str, n ) long double to ASCII string
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* __etoasc( e, str, n ) e to ASCII string, n digits after decimal
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* __etoe24( e, &f ) convert e type to IEEE single precision
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* __etoe53( e, &d ) convert e type to IEEE double precision
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* __etoe64( e, &d ) convert e type to IEEE long double precision
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* __eisneg( e ) 1 if sign bit of e != 0, else 0
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* __eisinf( e ) 1 if e has maximum exponent (non-IEEE)
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* or is infinite (IEEE)
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* __eisnan( e ) 1 if e is a NaN
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* __esqrt( a, b ) b = square root of a
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*
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*
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* Routines for internal format numbers
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*
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* __eaddm( ai, bi ) add significands, bi = bi + ai
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* __ecleaz(ei) ei = 0
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* __ecleazs(ei) set ei = 0 but leave its sign alone
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* __ecmpm( ai, bi ) compare significands, return 1, 0, or -1
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* __edivm( ai, bi ) divide significands, bi = bi / ai
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* __emdnorm(ai,l,s,exp) normalize and round off
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* __emovi( a, ai ) convert external a to internal ai
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* __emovo( ai, a ) convert internal ai to external a
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* __emovz( ai, bi ) bi = ai, low guard word of bi = 0
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* __emulm( ai, bi ) multiply significands, bi = bi * ai
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* __enormlz(ei) left-justify the significand
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* __eshdn1( ai ) shift significand and guards down 1 bit
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* __eshdn8( ai ) shift down 8 bits
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* __eshdn6( ai ) shift down 16 bits
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* __eshift( ai, n ) shift ai n bits up (or down if n < 0)
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* __eshup1( ai ) shift significand and guards up 1 bit
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* __eshup8( ai ) shift up 8 bits
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* __eshup6( ai ) shift up 16 bits
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* __esubm( ai, bi ) subtract significands, bi = bi - ai
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*
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*
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* The result is always normalized and rounded to NI-4 word precision
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* after each arithmetic operation.
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*
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* Exception flags are NOT fully supported.
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*
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* Define INFINITY in mconf.h for support of infinity; otherwise a
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* saturation arithmetic is implemented.
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*
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* Define NANS for support of Not-a-Number items; otherwise the
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* arithmetic will never produce a NaN output, and might be confused
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* by a NaN input.
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* If NaN's are supported, the output of ecmp(a,b) is -2 if
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* either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
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* may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
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* if in doubt.
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* Signaling NaN's are NOT supported; they are treated the same
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* as quiet NaN's.
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*
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* Denormals are always supported here where appropriate (e.g., not
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* for conversion to DEC numbers).
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <errno.h>
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#include <math.h>
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#include <locale.h>
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#include <ctype.h>
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#undef alloca
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#define alloca __builtin_alloca
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/* Don't build non-ANSI _IO_ldtoa. It is not thread safe. */
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#ifndef USE_LDTOA
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#define USE_LDTOA 0
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#endif
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/* Number of 16 bit words in external x type format */
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#define NE 6
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/* Number of 16 bit words in internal format */
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#define NI (NE+3)
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/* Array offset to exponent */
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#define E 1
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/* Array offset to high guard word */
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#define M 2
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/* Number of bits of precision */
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#define NBITS ((NI-4)*16)
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/* Maximum number of decimal digits in ASCII conversion
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* = NBITS*log10(2)
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*/
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#define NDEC (NBITS*8/27)
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/* The exponent of 1.0 */
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#define EXONE (0x3fff)
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#define mtherr(x,y)
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extern long double strtold (const char * __restrict__ s, char ** __restrict__ se);
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extern int __asctoe64(const char * __restrict__ ss,
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short unsigned int * __restrict__ y);
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extern void __emul(const short unsigned int * a,
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const short unsigned int * b,
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short unsigned int * c);
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extern int __ecmp(const short unsigned int * __restrict__ a,
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const short unsigned int * __restrict__ b);
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extern int __enormlz(short unsigned int *x);
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extern int __eshift(short unsigned int *x, int sc);
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extern void __eaddm(const short unsigned int * __restrict__ x,
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short unsigned int * __restrict__ y);
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extern void __esubm(const short unsigned int * __restrict__ x,
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short unsigned int * __restrict__ y);
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extern void __emdnorm(short unsigned int *s, int lost, int subflg,
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int exp, int rcntrl, const int rndprc);
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extern void __toe64(short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b);
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extern int __edivm(short unsigned int * __restrict__ den,
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short unsigned int * __restrict__ num);
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extern int __emulm(const short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b);
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extern void __emovi(const short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b);
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extern void __emovo(const short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b);
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#if USE_LDTOA
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extern char * _IO_ldtoa(long double, int, int, int *, int *, char **);
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extern void _IO_ldtostr(long double *x, char *string, int ndigs,
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int flags, char fmt);
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extern void __eiremain(short unsigned int * __restrict__ den,
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short unsigned int *__restrict__ num,
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short unsigned int *__restrict__ equot);
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extern void __efloor(short unsigned int *x, short unsigned int *y);
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extern void __eadd1(const short unsigned int * __restrict__ a,
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const short unsigned int * __restrict__ b,
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short unsigned int * __restrict__ c,
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int subflg);
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extern void __esub(const short unsigned int *a, const short unsigned int *b,
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short unsigned int *c);
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extern void __ediv(const short unsigned int *a, const short unsigned int *b,
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short unsigned int *c);
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extern void __e64toe(short unsigned int *pe, short unsigned int *y);
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#endif
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static __inline__ int __eisneg(const short unsigned int *x);
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static __inline__ int __eisinf(const short unsigned int *x);
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static __inline__ int __eisnan(const short unsigned int *x);
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static __inline__ int __eiszero(const short unsigned int *a);
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static __inline__ void __emovz(register const short unsigned int * __restrict__ a,
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register short unsigned int * __restrict__ b);
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static __inline__ void __eclear(register short unsigned int *x);
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static __inline__ void __ecleaz(register short unsigned int *xi);
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static __inline__ void __ecleazs(register short unsigned int *xi);
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static __inline__ int __eiisinf(const short unsigned int *x);
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static __inline__ int __eiisnan(const short unsigned int *x);
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static __inline__ int __eiiszero(const short unsigned int *x);
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static __inline__ void __enan_64(short unsigned int *nanptr);
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static __inline__ void __enan_NBITS (short unsigned int *nanptr);
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static __inline__ void __enan_NI16 (short unsigned int *nanptr);
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static __inline__ void __einfin(register short unsigned int *x);
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static __inline__ void __eneg(short unsigned int *x);
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static __inline__ void __eshup1(register short unsigned int *x);
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static __inline__ void __eshup8(register short unsigned int *x);
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static __inline__ void __eshup6(register short unsigned int *x);
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static __inline__ void __eshdn1(register short unsigned int *x);
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static __inline__ void __eshdn8(register short unsigned int *x);
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static __inline__ void __eshdn6(register short unsigned int *x);
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/* Intel IEEE, low order words come first:
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*/
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#define IBMPC 1
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/* Define 1 for ANSI C atan2() function
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* See atan.c and clog.c.
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*/
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#define ANSIC 1
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/*define VOLATILE volatile*/
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#define VOLATILE
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/* For 12-byte long doubles on an i386, pad a 16-bit short 0
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* to the end of real constants initialized by integer arrays.
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*
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* #define XPD 0,
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*
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* Otherwise, the type is 10 bytes long and XPD should be
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* defined blank.
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*
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* #define XPD
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*/
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#define XPD 0,
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/* #define XPD */
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#define NANS
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/* NaN's require infinity support. */
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#ifdef NANS
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#ifndef INFINITY
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#define INFINITY
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#endif
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#endif
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/* This handles 64-bit long ints. */
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#define LONGBITS (8 * sizeof(long))
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#define NTEN 12
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#define MAXP 4096
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/*
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; Clear out entire external format number.
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;
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; unsigned short x[];
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; eclear( x );
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*/
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static __inline__ void __eclear(register short unsigned int *x)
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{
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memset(x, 0, NE * sizeof(unsigned short));
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}
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/* Move external format number from a to b.
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*
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* emov( a, b );
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*/
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static __inline__ void __emov(register const short unsigned int * __restrict__ a,
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register short unsigned int * __restrict__ b)
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{
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memcpy(b, a, NE * sizeof(unsigned short));
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}
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/*
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; Negate external format number
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;
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; unsigned short x[NE];
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; eneg( x );
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*/
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static __inline__ void __eneg(short unsigned int *x)
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{
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#ifdef NANS
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if (__eisnan(x))
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return;
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#endif
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x[NE-1] ^= 0x8000; /* Toggle the sign bit */
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}
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/* Return 1 if external format number is negative,
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* else return zero.
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*/
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static __inline__ int __eisneg(const short unsigned int *x)
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{
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#ifdef NANS
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if (__eisnan(x))
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return (0);
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#endif
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if (x[NE-1] & 0x8000)
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return (1);
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else
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return (0);
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}
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/* Return 1 if external format number has maximum possible exponent,
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* else return zero.
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*/
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static __inline__ int __eisinf(const short unsigned int *x)
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{
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if ((x[NE - 1] & 0x7fff) == 0x7fff)
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{
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#ifdef NANS
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if (__eisnan(x))
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return (0);
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#endif
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return (1);
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}
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else
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return (0);
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}
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/* Check if e-type number is not a number.
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*/
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static __inline__ int __eisnan(const short unsigned int *x)
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{
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#ifdef NANS
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int i;
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/* NaN has maximum __exponent */
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if ((x[NE - 1] & 0x7fff) == 0x7fff)
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/* ... and non-zero significand field. */
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for (i = 0; i < NE - 1; i++)
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{
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if (*x++ != 0)
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return (1);
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}
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#endif
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return (0);
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}
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/*
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; Fill __entire number, including __exponent and significand, with
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; largest possible number. These programs implement a saturation
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; value that is an ordinary, legal number. A special value
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; "infinity" may also be implemented; this would require tests
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; for that value and implementation of special rules for arithmetic
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; operations involving inifinity.
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*/
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static __inline__ void __einfin(register short unsigned int *x)
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{
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register int i;
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#ifdef INFINITY
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for (i = 0; i < NE - 1; i++)
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*x++ = 0;
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*x |= 32767;
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#else
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for (i = 0; i < NE - 1; i++)
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*x++ = 0xffff;
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*x |= 32766;
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*(x - 5) = 0;
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#endif
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}
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/* Clear out internal format number.
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*/
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static __inline__ void __ecleaz(register short unsigned int *xi)
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{
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memset(xi, 0, NI * sizeof(unsigned short));
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}
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/* same, but don't touch the sign. */
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static __inline__ void __ecleazs(register short unsigned int *xi)
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{
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++xi;
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memset(xi, 0, (NI-1) * sizeof(unsigned short));
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}
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/* Move internal format number from a to b.
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*/
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static __inline__ void __emovz(register const short unsigned int * __restrict__ a,
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register short unsigned int * __restrict__ b)
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{
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memcpy(b, a, (NI-1) * sizeof(unsigned short));
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b[NI - 1] = 0;
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}
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/* Return nonzero if internal format number is a NaN.
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*/
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static __inline__ int __eiisnan (const short unsigned int *x)
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{
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int i;
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if ((x[E] & 0x7fff) == 0x7fff)
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{
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for (i = M + 1; i < NI; i++ )
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{
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if (x[i] != 0)
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return (1);
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}
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}
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return (0);
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}
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/* Return nonzero if external format number is zero. */
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static __inline__ int
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__eiszero(const short unsigned int * a)
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{
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union {
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long double ld;
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unsigned short sh[8];
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} av;
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av.ld = 0.0;
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memcpy (av.sh, a, 12);
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if (av.ld == 0.0)
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return (1);
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return (0);
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}
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/* Return nonzero if internal format number is zero. */
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static __inline__ int
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__eiiszero(const short unsigned int * ai)
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{
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int i;
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/* skip the sign word */
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for (i = 1; i < NI - 1; i++ )
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{
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if (ai[i] != 0)
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return (0);
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}
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return (1);
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}
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/* Return nonzero if internal format number is infinite. */
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static __inline__ int
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__eiisinf (const unsigned short *x)
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{
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#ifdef NANS
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if (__eiisnan (x))
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return (0);
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#endif
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if ((x[E] & 0x7fff) == 0x7fff)
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return (1);
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return (0);
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}
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/*
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; Compare significands of numbers in internal format.
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; Guard words are included in the comparison.
|
|
;
|
|
; unsigned short a[NI], b[NI];
|
|
; cmpm( a, b );
|
|
;
|
|
; for the significands:
|
|
; returns +1 if a > b
|
|
; 0 if a == b
|
|
; -1 if a < b
|
|
*/
|
|
static __inline__ int __ecmpm(register const short unsigned int * __restrict__ a,
|
|
register const short unsigned int * __restrict__ b)
|
|
{
|
|
int i;
|
|
|
|
a += M; /* skip up to significand area */
|
|
b += M;
|
|
for (i = M; i < NI; i++)
|
|
{
|
|
if( *a++ != *b++ )
|
|
goto difrnt;
|
|
}
|
|
return(0);
|
|
|
|
difrnt:
|
|
if ( *(--a) > *(--b) )
|
|
return (1);
|
|
else
|
|
return (-1);
|
|
}
|
|
|
|
|
|
/*
|
|
; Shift significand down by 1 bit
|
|
*/
|
|
|
|
static __inline__ void __eshdn1(register short unsigned int *x)
|
|
{
|
|
register unsigned short bits;
|
|
int i;
|
|
|
|
x += M; /* point to significand area */
|
|
|
|
bits = 0;
|
|
for (i = M; i < NI; i++ )
|
|
{
|
|
if (*x & 1)
|
|
bits |= 1;
|
|
*x >>= 1;
|
|
if (bits & 2)
|
|
*x |= 0x8000;
|
|
bits <<= 1;
|
|
++x;
|
|
}
|
|
}
|
|
|
|
/*
|
|
; Shift significand up by 1 bit
|
|
*/
|
|
|
|
static __inline__ void __eshup1(register short unsigned int *x)
|
|
{
|
|
register unsigned short bits;
|
|
int i;
|
|
|
|
x += NI-1;
|
|
bits = 0;
|
|
|
|
for (i = M; i < NI; i++)
|
|
{
|
|
if (*x & 0x8000)
|
|
bits |= 1;
|
|
*x <<= 1;
|
|
if (bits & 2)
|
|
*x |= 1;
|
|
bits <<= 1;
|
|
--x;
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
; Shift significand down by 8 bits
|
|
*/
|
|
|
|
static __inline__ void __eshdn8(register short unsigned int *x)
|
|
{
|
|
register unsigned short newbyt, oldbyt;
|
|
int i;
|
|
|
|
x += M;
|
|
oldbyt = 0;
|
|
for (i = M; i < NI; i++)
|
|
{
|
|
newbyt = *x << 8;
|
|
*x >>= 8;
|
|
*x |= oldbyt;
|
|
oldbyt = newbyt;
|
|
++x;
|
|
}
|
|
}
|
|
|
|
/*
|
|
; Shift significand up by 8 bits
|
|
*/
|
|
|
|
static __inline__ void __eshup8(register short unsigned int *x)
|
|
{
|
|
int i;
|
|
register unsigned short newbyt, oldbyt;
|
|
|
|
x += NI - 1;
|
|
oldbyt = 0;
|
|
|
|
for (i = M; i < NI; i++)
|
|
{
|
|
newbyt = *x >> 8;
|
|
*x <<= 8;
|
|
*x |= oldbyt;
|
|
oldbyt = newbyt;
|
|
--x;
|
|
}
|
|
}
|
|
|
|
/*
|
|
; Shift significand up by 16 bits
|
|
*/
|
|
|
|
static __inline__ void __eshup6(register short unsigned int *x)
|
|
{
|
|
int i;
|
|
register unsigned short *p;
|
|
|
|
p = x + M;
|
|
x += M + 1;
|
|
|
|
for (i = M; i < NI - 1; i++)
|
|
*p++ = *x++;
|
|
|
|
*p = 0;
|
|
}
|
|
|
|
/*
|
|
; Shift significand down by 16 bits
|
|
*/
|
|
|
|
static __inline__ void __eshdn6(register short unsigned int *x)
|
|
{
|
|
int i;
|
|
register unsigned short *p;
|
|
|
|
x += NI - 1;
|
|
p = x + 1;
|
|
|
|
for (i = M; i < NI - 1; i++)
|
|
*(--p) = *(--x);
|
|
|
|
*(--p) = 0;
|
|
}
|
|
|
|
/*
|
|
; Add significands
|
|
; x + y replaces y
|
|
*/
|
|
|
|
static __inline__ void __enan_64(unsigned short* nanptr)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 3; i++)
|
|
*nanptr++ = 0;
|
|
*nanptr++ = 0xc000;
|
|
*nanptr++ = 0x7fff;
|
|
*nanptr = 0;
|
|
return;
|
|
}
|
|
|
|
static __inline__ void __enan_NBITS(unsigned short* nanptr)
|
|
{
|
|
int i;
|
|
for (i = 0; i < NE - 2; i++)
|
|
*nanptr++ = 0;
|
|
*nanptr++ = 0xc000;
|
|
*nanptr = 0x7fff;
|
|
return;
|
|
}
|
|
|
|
static __inline__ void __enan_NI16(unsigned short* nanptr)
|
|
{
|
|
int i;
|
|
*nanptr++ = 0;
|
|
*nanptr++ = 0x7fff;
|
|
*nanptr++ = 0;
|
|
*nanptr++ = 0xc000;
|
|
for (i = 4; i < NI; i++)
|
|
*nanptr++ = 0;
|
|
return;
|
|
}
|
|
|
|
#endif /* _CEPHES_EMATH_H */
|
|
|