209 lines
5.7 KiB
C
209 lines
5.7 KiB
C
/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
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* errors to make test scripts easier.) */
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/* @(#)e_fmod.c 1.3 95/01/18 */
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/*-
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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FUNCTION
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<<remquo>>, <<remquof>>--remainder and part of quotient
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INDEX
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remquo
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INDEX
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remquof
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ANSI_SYNOPSIS
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#include <math.h>
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double remquo(double <[x]>, double <[y]>, int *<[quo]>);
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float remquof(float <[x]>, float <[y]>, int *<[quo]>);
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DESCRIPTION
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The <<remquo>> functions compute the same remainder as the <<remainder>>
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functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object
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pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>>
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and whose magnitude is congruent modulo 2**n to the magnitude of the integral
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quotient of <<x>>/<<y>>. (That is, <<quo>> is given the n lsbs of the
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quotient, not counting the sign.) This implementation uses n=31 if int is 32
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bits or more, otherwise, n is 1 less than the width of int.
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For example:
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. remquo(-29.0, 3.0, &<[quo]>)
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returns -1.0 and sets <[quo]>=10, and
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. remquo(-98307.0, 3.0, &<[quo]>)
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returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In
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the latter case, the actual quotient of -(32769=0x8001) is reduced to -1
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because of the 15-bit limitation for the quotient.
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RETURNS
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When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is
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infinite (and neither is NaN), a domain error occurs (i.e. the "invalid"
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floating point exception is raised or errno is set to EDOM), and NaN is
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returned.
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Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.
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BUGS
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IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"
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floating-point exception. This implementation does not.
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PORTABILITY
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C99, POSIX.
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*/
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#include <limits.h>
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#include <math.h>
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#include "fdlibm.h"
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/* For quotient, return either all 31 bits that can from calculation (using
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* int32_t), or as many as can fit into an int that is smaller than 32 bits. */
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#if INT_MAX > 0x7FFFFFFFL
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#define QUO_MASK 0x7FFFFFFF
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# else
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#define QUO_MASK INT_MAX
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#endif
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static const double Zero[] = {0.0, -0.0,};
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/*
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* Return the IEEE remainder and set *quo to the last n bits of the
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* quotient, rounded to the nearest integer. We choose n=31--if that many fit--
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* because we wind up computing all the integer bits of the quotient anyway as
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* a side-effect of computing the remainder by the shift and subtract
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* method. In practice, this is far more bits than are needed to use
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* remquo in reduction algorithms.
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*/
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double
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remquo(double x, double y, int *quo)
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{
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__int32_t n,hx,hy,hz,ix,iy,sx,i;
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__uint32_t lx,ly,lz,q,sxy;
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EXTRACT_WORDS(hx,lx,x);
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EXTRACT_WORDS(hy,ly,y);
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sxy = (hx ^ hy) & 0x80000000;
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sx = hx&0x80000000; /* sign of x */
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hx ^=sx; /* |x| */
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hy &= 0x7fffffff; /* |y| */
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/* purge off exception values */
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if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
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((hy|((ly|-ly)>>31))>0x7ff00000)) { /* or y is NaN */
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*quo = 0; /* Not necessary, but return consistent value */
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return (x*y)/(x*y);
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}
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if(hx<=hy) {
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if((hx<hy)||(lx<ly)) {
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q = 0;
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goto fixup; /* |x|<|y| return x or x-y */
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}
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if(lx==ly) {
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*quo = (sxy ? -1 : 1);
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return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0 */
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}
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}
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/* determine ix = ilogb(x) */
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if(hx<0x00100000) { /* subnormal x */
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if(hx==0) {
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for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
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} else {
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for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
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}
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} else ix = (hx>>20)-1023;
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/* determine iy = ilogb(y) */
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if(hy<0x00100000) { /* subnormal y */
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if(hy==0) {
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for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
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} else {
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for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
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}
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} else iy = (hy>>20)-1023;
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/* set up {hx,lx}, {hy,ly} and align y to x */
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if(ix >= -1022)
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hx = 0x00100000|(0x000fffff&hx);
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else { /* subnormal x, shift x to normal */
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n = -1022-ix;
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if(n<=31) {
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hx = (hx<<n)|(lx>>(32-n));
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lx <<= n;
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} else {
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hx = lx<<(n-32);
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lx = 0;
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}
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}
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if(iy >= -1022)
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hy = 0x00100000|(0x000fffff&hy);
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else { /* subnormal y, shift y to normal */
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n = -1022-iy;
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if(n<=31) {
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hy = (hy<<n)|(ly>>(32-n));
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ly <<= n;
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} else {
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hy = ly<<(n-32);
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ly = 0;
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}
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}
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/* fix point fmod */
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n = ix - iy;
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q = 0;
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while(n--) {
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hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
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else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
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q <<= 1;
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}
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hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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if(hz>=0) {hx=hz;lx=lz;q++;}
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/* convert back to floating value and restore the sign */
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if((hx|lx)==0) { /* return sign(x)*0 */
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q &= QUO_MASK;
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*quo = (sxy ? -q : q);
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return Zero[(__uint32_t)sx>>31];
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}
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while(hx<0x00100000) { /* normalize x */
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hx = hx+hx+(lx>>31); lx = lx+lx;
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iy -= 1;
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}
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if(iy>= -1022) { /* normalize output */
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hx = ((hx-0x00100000)|((iy+1023)<<20));
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} else { /* subnormal output */
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n = -1022 - iy;
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if(n<=20) {
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lx = (lx>>n)|((__uint32_t)hx<<(32-n));
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hx >>= n;
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} else if (n<=31) {
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lx = (hx<<(32-n))|(lx>>n); hx = sx;
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} else {
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lx = hx>>(n-32); hx = sx;
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}
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}
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fixup:
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INSERT_WORDS(x,hx,lx);
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y = fabs(y);
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if (y < 0x1p-1021) {
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if (x+x>y || (x+x==y && (q & 1))) {
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q++;
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x-=y;
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}
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} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
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q++;
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x-=y;
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}
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GET_HIGH_WORD(hx,x);
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SET_HIGH_WORD(x,hx^sx);
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q &= QUO_MASK;
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*quo = (sxy ? -q : q);
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return x;
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}
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