1 /* @(#)e_fmod.c 1.3 95/01/18 */ 2 /*- 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 /* __FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.1 2005/03/25 04:40:44 das Exp $"); */ 15 16 #include "math.h" 17 #include "math_private.h" 18 19 static const double Zero[] = {0.0, -0.0,}; 20 21 /* 22 * Return the IEEE remainder and set *quo to the last n bits of the 23 * quotient, rounded to the nearest integer. We choose n=31 because 24 * we wind up computing all the integer bits of the quotient anyway as 25 * a side-effect of computing the remainder by the shift and subtract 26 * method. In practice, this is far more bits than are needed to use 27 * remquo in reduction algorithms. 28 */ 29 double 30 remquo(double x, double y, int *quo) 31 { 32 int32_t n,hx,hy,hz,ix,iy,sx,i; 33 u_int32_t lx,ly,lz,q,sxy; 34 35 EXTRACT_WORDS(hx,lx,x); 36 EXTRACT_WORDS(hy,ly,y); 37 sxy = (hx ^ hy) & 0x80000000; 38 sx = hx&0x80000000; /* sign of x */ 39 hx ^=sx; /* |x| */ 40 hy &= 0x7fffffff; /* |y| */ 41 42 /* purge off exception values */ 43 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 44 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 45 return (x*y)/(x*y); 46 if(hx<=hy) { 47 if((hx<hy)||(lx<ly)) { 48 q = 0; 49 goto fixup; /* |x|<|y| return x or x-y */ 50 } 51 if(lx==ly) { 52 *quo = (sxy ? -1 : 1); 53 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 54 } 55 } 56 57 /* determine ix = ilogb(x) */ 58 if(hx<0x00100000) { /* subnormal x */ 59 if(hx==0) { 60 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 61 } else { 62 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 63 } 64 } else ix = (hx>>20)-1023; 65 66 /* determine iy = ilogb(y) */ 67 if(hy<0x00100000) { /* subnormal y */ 68 if(hy==0) { 69 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 70 } else { 71 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 72 } 73 } else iy = (hy>>20)-1023; 74 75 /* set up {hx,lx}, {hy,ly} and align y to x */ 76 if(ix >= -1022) 77 hx = 0x00100000|(0x000fffff&hx); 78 else { /* subnormal x, shift x to normal */ 79 n = -1022-ix; 80 if(n<=31) { 81 hx = (hx<<n)|(lx>>(32-n)); 82 lx <<= n; 83 } else { 84 hx = lx<<(n-32); 85 lx = 0; 86 } 87 } 88 if(iy >= -1022) 89 hy = 0x00100000|(0x000fffff&hy); 90 else { /* subnormal y, shift y to normal */ 91 n = -1022-iy; 92 if(n<=31) { 93 hy = (hy<<n)|(ly>>(32-n)); 94 ly <<= n; 95 } else { 96 hy = ly<<(n-32); 97 ly = 0; 98 } 99 } 100 101 /* fix point fmod */ 102 n = ix - iy; 103 q = 0; 104 while(n--) { 105 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 106 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 107 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} 108 q <<= 1; 109 } 110 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 111 if(hz>=0) {hx=hz;lx=lz;q++;} 112 113 /* convert back to floating value and restore the sign */ 114 if((hx|lx)==0) { /* return sign(x)*0 */ 115 q &= 0x7fffffff; 116 *quo = (sxy ? -q : q); 117 return Zero[(u_int32_t)sx>>31]; 118 } 119 while(hx<0x00100000) { /* normalize x */ 120 hx = hx+hx+(lx>>31); lx = lx+lx; 121 iy -= 1; 122 } 123 if(iy>= -1022) { /* normalize output */ 124 hx = ((hx-0x00100000)|((iy+1023)<<20)); 125 } else { /* subnormal output */ 126 n = -1022 - iy; 127 if(n<=20) { 128 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 129 hx >>= n; 130 } else if (n<=31) { 131 lx = (hx<<(32-n))|(lx>>n); hx = 0; 132 } else { 133 lx = hx>>(n-32); hx = 0; 134 } 135 } 136 fixup: 137 INSERT_WORDS(x,hx,lx); 138 y = fabs(y); 139 if (y < 0x1p-1021) { 140 if (x+x>y || (x+x==y && (q & 1))) { 141 q++; 142 x-=y; 143 } 144 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 145 q++; 146 x-=y; 147 } 148 GET_HIGH_WORD(hx,x); 149 SET_HIGH_WORD(x,hx^sx); 150 q &= 0x7fffffff; 151 *quo = (sxy ? -q : q); 152 return x; 153 } 154
