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("$FreeBSD$"); 15 16 #include <float.h> 17 18 #include "math.h" 19 #include "math_private.h" 20 21 static const double Zero[] = {0.0, -0.0,}; 22 23 /* 24 * Return the IEEE remainder and set *quo to the last n bits of the 25 * quotient, rounded to the nearest integer. We choose n=31 because 26 * we wind up computing all the integer bits of the quotient anyway as 27 * a side-effect of computing the remainder by the shift and subtract 28 * method. In practice, this is far more bits than are needed to use 29 * remquo in reduction algorithms. 30 */ 31 double 32 remquo(double x, double y, int *quo) 33 { 34 int32_t n,hx,hy,hz,ix,iy,sx,i; 35 u_int32_t lx,ly,lz,q,sxy; 36 37 EXTRACT_WORDS(hx,lx,x); 38 EXTRACT_WORDS(hy,ly,y); 39 sxy = (hx ^ hy) & 0x80000000; 40 sx = hx&0x80000000; /* sign of x */ 41 hx ^=sx; /* |x| */ 42 hy &= 0x7fffffff; /* |y| */ 43 44 /* purge off exception values */ 45 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 46 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 47 return (x*y)/(x*y); 48 if(hx<=hy) { 49 if((hx<hy)||(lx<ly)) { 50 q = 0; 51 goto fixup; /* |x|<|y| return x or x-y */ 52 } 53 if(lx==ly) { 54 *quo = (sxy ? -1 : 1); 55 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 56 } 57 } 58 59 /* determine ix = ilogb(x) */ 60 if(hx<0x00100000) { /* subnormal x */ 61 if(hx==0) { 62 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 63 } else { 64 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 65 } 66 } else ix = (hx>>20)-1023; 67 68 /* determine iy = ilogb(y) */ 69 if(hy<0x00100000) { /* subnormal y */ 70 if(hy==0) { 71 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 72 } else { 73 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 74 } 75 } else iy = (hy>>20)-1023; 76 77 /* set up {hx,lx}, {hy,ly} and align y to x */ 78 if(ix >= -1022) 79 hx = 0x00100000|(0x000fffff&hx); 80 else { /* subnormal x, shift x to normal */ 81 n = -1022-ix; 82 if(n<=31) { 83 hx = (hx<<n)|(lx>>(32-n)); 84 lx <<= n; 85 } else { 86 hx = lx<<(n-32); 87 lx = 0; 88 } 89 } 90 if(iy >= -1022) 91 hy = 0x00100000|(0x000fffff&hy); 92 else { /* subnormal y, shift y to normal */ 93 n = -1022-iy; 94 if(n<=31) { 95 hy = (hy<<n)|(ly>>(32-n)); 96 ly <<= n; 97 } else { 98 hy = ly<<(n-32); 99 ly = 0; 100 } 101 } 102 103 /* fix point fmod */ 104 n = ix - iy; 105 q = 0; 106 while(n--) { 107 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 108 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 109 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} 110 q <<= 1; 111 } 112 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 113 if(hz>=0) {hx=hz;lx=lz;q++;} 114 115 /* convert back to floating value and restore the sign */ 116 if((hx|lx)==0) { /* return sign(x)*0 */ 117 q &= 0x7fffffff; 118 *quo = (sxy ? -q : q); 119 return Zero[(u_int32_t)sx>>31]; 120 } 121 while(hx<0x00100000) { /* normalize x */ 122 hx = hx+hx+(lx>>31); lx = lx+lx; 123 iy -= 1; 124 } 125 if(iy>= -1022) { /* normalize output */ 126 hx = ((hx-0x00100000)|((iy+1023)<<20)); 127 } else { /* subnormal output */ 128 n = -1022 - iy; 129 if(n<=20) { 130 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 131 hx >>= n; 132 } else if (n<=31) { 133 lx = (hx<<(32-n))|(lx>>n); hx = 0; 134 } else { 135 lx = hx>>(n-32); hx = 0; 136 } 137 } 138 fixup: 139 INSERT_WORDS(x,hx,lx); 140 y = fabs(y); 141 if (y < 0x1p-1021) { 142 if (x+x>y || (x+x==y && (q & 1))) { 143 q++; 144 x-=y; 145 } 146 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 147 q++; 148 x-=y; 149 } 150 GET_HIGH_WORD(hx,x); 151 SET_HIGH_WORD(x,hx^sx); 152 q &= 0x7fffffff; 153 *quo = (sxy ? -q : q); 154 return x; 155 } 156 157 #if LDBL_MANT_DIG == 53 158 __weak_reference(remquo, remquol); 159 #endif 160