| 1 | /* @(#)e_fmod.c 1.3 95/01/18 */
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| 2 | /*-
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| 3 | * ====================================================
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 5 | *
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| 6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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| 7 | * Permission to use, copy, modify, and distribute this
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| 8 | * software is freely granted, provided that this notice
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| 9 | * is preserved.
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| 10 | * ====================================================
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| 11 | */
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| 12 |
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| 13 | #include <sys/cdefs.h>
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| 14 | __FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.1 2005/03/25 04:40:44 das Exp $");
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| 15 |
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| 16 | #include "math.h"
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| 17 | #include "math_private.h"
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| 18 |
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| 19 | static const double Zero[] = {0.0, -0.0,};
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| 20 |
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| 21 | /*
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| 22 | * Return the IEEE remainder and set *quo to the last n bits of the
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| 23 | * quotient, rounded to the nearest integer. We choose n=31 because
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| 24 | * we wind up computing all the integer bits of the quotient anyway as
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| 25 | * a side-effect of computing the remainder by the shift and subtract
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| 26 | * method. In practice, this is far more bits than are needed to use
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| 27 | * remquo in reduction algorithms.
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| 28 | */
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| 29 | double
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| 30 | remquo(double x, double y, int *quo)
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| 31 | {
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| 32 | int32_t n,hx,hy,hz,ix,iy,sx,i;
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| 33 | u_int32_t lx,ly,lz,q,sxy;
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| 34 |
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| 35 | EXTRACT_WORDS(hx,lx,x);
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| 36 | EXTRACT_WORDS(hy,ly,y);
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| 37 | sxy = (hx ^ hy) & 0x80000000;
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| 38 | sx = hx&0x80000000; /* sign of x */
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| 39 | hx ^=sx; /* |x| */
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| 40 | hy &= 0x7fffffff; /* |y| */
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| 41 |
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| 42 | /* purge off exception values */
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| 43 | if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
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| 44 | ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
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| 45 | return (x*y)/(x*y);
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| 46 | if(hx<=hy) {
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| 47 | if((hx<hy)||(lx<ly)) {
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| 48 | q = 0;
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| 49 | goto fixup; /* |x|<|y| return x or x-y */
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| 50 | }
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| 51 | if(lx==ly) {
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| 52 | *quo = 1;
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| 53 | return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
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| 54 | }
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| 55 | }
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| 56 |
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| 57 | /* determine ix = ilogb(x) */
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| 58 | if(hx<0x00100000) { /* subnormal x */
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| 59 | if(hx==0) {
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| 60 | for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
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| 61 | } else {
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| 62 | for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
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| 63 | }
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| 64 | } else ix = (hx>>20)-1023;
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| 65 |
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| 66 | /* determine iy = ilogb(y) */
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| 67 | if(hy<0x00100000) { /* subnormal y */
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| 68 | if(hy==0) {
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| 69 | for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
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| 70 | } else {
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| 71 | for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
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| 72 | }
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| 73 | } else iy = (hy>>20)-1023;
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| 74 |
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| 75 | /* set up {hx,lx}, {hy,ly} and align y to x */
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| 76 | if(ix >= -1022)
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| 77 | hx = 0x00100000|(0x000fffff&hx);
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| 78 | else { /* subnormal x, shift x to normal */
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| 79 | n = -1022-ix;
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| 80 | if(n<=31) {
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| 81 | hx = (hx<<n)|(lx>>(32-n));
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| 82 | lx <<= n;
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| 83 | } else {
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| 84 | hx = lx<<(n-32);
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| 85 | lx = 0;
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| 86 | }
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| 87 | }
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| 88 | if(iy >= -1022)
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| 89 | hy = 0x00100000|(0x000fffff&hy);
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| 90 | else { /* subnormal y, shift y to normal */
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| 91 | n = -1022-iy;
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| 92 | if(n<=31) {
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| 93 | hy = (hy<<n)|(ly>>(32-n));
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| 94 | ly <<= n;
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| 95 | } else {
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| 96 | hy = ly<<(n-32);
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| 97 | ly = 0;
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| 98 | }
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| 99 | }
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| 100 |
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| 101 | /* fix point fmod */
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| 102 | n = ix - iy;
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| 103 | q = 0;
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| 104 | while(n--) {
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| 105 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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| 106 | if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
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| 107 | else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
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| 108 | q <<= 1;
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| 109 | }
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| 110 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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| 111 | if(hz>=0) {hx=hz;lx=lz;q++;}
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| 112 |
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| 113 | /* convert back to floating value and restore the sign */
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| 114 | if((hx|lx)==0) { /* return sign(x)*0 */
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| 115 | *quo = (sxy ? -q : q);
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| 116 | return Zero[(u_int32_t)sx>>31];
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| 117 | }
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| 118 | while(hx<0x00100000) { /* normalize x */
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| 119 | hx = hx+hx+(lx>>31); lx = lx+lx;
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| 120 | iy -= 1;
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| 121 | }
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| 122 | if(iy>= -1022) { /* normalize output */
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| 123 | hx = ((hx-0x00100000)|((iy+1023)<<20));
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| 124 | } else { /* subnormal output */
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| 125 | n = -1022 - iy;
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| 126 | if(n<=20) {
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| 127 | lx = (lx>>n)|((u_int32_t)hx<<(32-n));
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| 128 | hx >>= n;
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| 129 | } else if (n<=31) {
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| 130 | lx = (hx<<(32-n))|(lx>>n); hx = sx;
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| 131 | } else {
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| 132 | lx = hx>>(n-32); hx = sx;
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| 133 | }
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| 134 | }
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| 135 | fixup:
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| 136 | INSERT_WORDS(x,hx,lx);
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| 137 | y = fabs(y);
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| 138 | if (y < 0x1p-1021) {
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| 139 | if (x+x>y || (x+x==y && (q & 1))) {
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| 140 | q++;
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| 141 | x-=y;
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| 142 | }
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| 143 | } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
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| 144 | q++;
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| 145 | x-=y;
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| 146 | }
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| 147 | GET_HIGH_WORD(hx,x);
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| 148 | SET_HIGH_WORD(x,hx^sx);
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| 149 | q &= 0x7fffffff;
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| 150 | *quo = (sxy ? -q : q);
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| 151 | return x;
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| 152 | }
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