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 <float.h> 14 #include <math.h> 15 16 #include "math_private.h" 17 18 static const double Zero[] = {0.0, -0.0,}; 19 20 /* 21 * Return the IEEE remainder and set *quo to the last n bits of the 22 * quotient, rounded to the nearest integer. We choose n=31 because 23 * we wind up computing all the integer bits of the quotient anyway as 24 * a side-effect of computing the remainder by the shift and subtract 25 * method. In practice, this is far more bits than are needed to use 26 * remquo in reduction algorithms. 27 */ 28 double 29 remquo(double x, double y, int *quo) 30 { 31 int32_t n,hx,hy,hz,ix,iy,sx,i; 32 u_int32_t lx,ly,lz,q,sxy; 33 34 EXTRACT_WORDS(hx,lx,x); 35 EXTRACT_WORDS(hy,ly,y); 36 sxy = (hx ^ hy) & 0x80000000; 37 sx = hx&0x80000000; /* sign of x */ 38 hx ^=sx; /* |x| */ 39 hy &= 0x7fffffff; /* |y| */ 40 41 /* purge off exception values */ 42 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 43 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 44 return (x*y)/(x*y); 45 if(hx<=hy) { 46 if((hx<hy)||(lx<ly)) { 47 q = 0; 48 goto fixup; /* |x|<|y| return x or x-y */ 49 } 50 if(lx==ly) { 51 *quo = 1; 52 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 53 } 54 } 55 56 /* determine ix = ilogb(x) */ 57 if(hx<0x00100000) { /* subnormal x */ 58 if(hx==0) { 59 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 60 } else { 61 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 62 } 63 } else ix = (hx>>20)-1023; 64 65 /* determine iy = ilogb(y) */ 66 if(hy<0x00100000) { /* subnormal y */ 67 if(hy==0) { 68 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 69 } else { 70 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 71 } 72 } else iy = (hy>>20)-1023; 73 74 /* set up {hx,lx}, {hy,ly} and align y to x */ 75 if(ix >= -1022) 76 hx = 0x00100000|(0x000fffff&hx); 77 else { /* subnormal x, shift x to normal */ 78 n = -1022-ix; 79 if(n<=31) { 80 hx = (hx<<n)|(lx>>(32-n)); 81 lx <<= n; 82 } else { 83 hx = lx<<(n-32); 84 lx = 0; 85 } 86 } 87 if(iy >= -1022) 88 hy = 0x00100000|(0x000fffff&hy); 89 else { /* subnormal y, shift y to normal */ 90 n = -1022-iy; 91 if(n<=31) { 92 hy = (hy<<n)|(ly>>(32-n)); 93 ly <<= n; 94 } else { 95 hy = ly<<(n-32); 96 ly = 0; 97 } 98 } 99 100 /* fix point fmod */ 101 n = ix - iy; 102 q = 0; 103 while(n--) { 104 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 105 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 106 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} 107 q <<= 1; 108 } 109 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 110 if(hz>=0) {hx=hz;lx=lz;q++;} 111 112 /* convert back to floating value and restore the sign */ 113 if((hx|lx)==0) { /* return sign(x)*0 */ 114 *quo = (sxy ? -q : q); 115 return Zero[(u_int32_t)sx>>31]; 116 } 117 while(hx<0x00100000) { /* normalize x */ 118 hx = hx+hx+(lx>>31); lx = lx+lx; 119 iy -= 1; 120 } 121 if(iy>= -1022) { /* normalize output */ 122 hx = ((hx-0x00100000)|((iy+1023)<<20)); 123 } else { /* subnormal output */ 124 n = -1022 - iy; 125 if(n<=20) { 126 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 127 hx >>= n; 128 } else if (n<=31) { 129 lx = (hx<<(32-n))|(lx>>n); hx = sx; 130 } else { 131 lx = hx>>(n-32); hx = sx; 132 } 133 } 134 fixup: 135 INSERT_WORDS(x,hx,lx); 136 y = fabs(y); 137 if (y < 0x1p-1021) { 138 if (x+x>y || (x+x==y && (q & 1))) { 139 q++; 140 x-=y; 141 } 142 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 143 q++; 144 x-=y; 145 } 146 GET_HIGH_WORD(hx,x); 147 SET_HIGH_WORD(x,hx^sx); 148 q &= 0x7fffffff; 149 *quo = (sxy ? -q : q); 150 return x; 151 } 152 153 #if LDBL_MANT_DIG == DBL_MANT_DIG 154 __strong_alias(remquol, remquo); 155 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 156