1 2 /* @(#)e_fmod.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 16 17 /* 18 * __ieee754_fmod(x,y) 19 * Return x mod y in exact arithmetic 20 * Method: shift and subtract 21 */ 22 23 #include "math.h" 24 #include "math_private.h" 25 26 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 27 28 double 29 __ieee754_fmod(double x, double y) 30 { 31 int32_t n,hx,hy,hz,ix,iy,sx,i; 32 u_int32_t lx,ly,lz; 33 34 EXTRACT_WORDS(hx,lx,x); 35 EXTRACT_WORDS(hy,ly,y); 36 sx = hx&0x80000000; /* sign of x */ 37 hx ^=sx; /* |x| */ 38 hy &= 0x7fffffff; /* |y| */ 39 40 /* purge off exception values */ 41 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 42 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 43 return (x*y)/(x*y); 44 if(hx<=hy) { 45 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ 46 if(lx==ly) 47 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 48 } 49 50 /* determine ix = ilogb(x) */ 51 if(hx<0x00100000) { /* subnormal x */ 52 if(hx==0) { 53 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 54 } else { 55 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 56 } 57 } else ix = (hx>>20)-1023; 58 59 /* determine iy = ilogb(y) */ 60 if(hy<0x00100000) { /* subnormal y */ 61 if(hy==0) { 62 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 63 } else { 64 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 65 } 66 } else iy = (hy>>20)-1023; 67 68 /* set up {hx,lx}, {hy,ly} and align y to x */ 69 if(ix >= -1022) 70 hx = 0x00100000|(0x000fffff&hx); 71 else { /* subnormal x, shift x to normal */ 72 n = -1022-ix; 73 if(n<=31) { 74 hx = (hx<<n)|(lx>>(32-n)); 75 lx <<= n; 76 } else { 77 hx = lx<<(n-32); 78 lx = 0; 79 } 80 } 81 if(iy >= -1022) 82 hy = 0x00100000|(0x000fffff&hy); 83 else { /* subnormal y, shift y to normal */ 84 n = -1022-iy; 85 if(n<=31) { 86 hy = (hy<<n)|(ly>>(32-n)); 87 ly <<= n; 88 } else { 89 hy = ly<<(n-32); 90 ly = 0; 91 } 92 } 93 94 /* fix point fmod */ 95 n = ix - iy; 96 while(n--) { 97 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 98 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 99 else { 100 if((hz|lz)==0) /* return sign(x)*0 */ 101 return Zero[(u_int32_t)sx>>31]; 102 hx = hz+hz+(lz>>31); lx = lz+lz; 103 } 104 } 105 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 106 if(hz>=0) {hx=hz;lx=lz;} 107 108 /* convert back to floating value and restore the sign */ 109 if((hx|lx)==0) /* return sign(x)*0 */ 110 return Zero[(u_int32_t)sx>>31]; 111 while(hx<0x00100000) { /* normalize x */ 112 hx = hx+hx+(lx>>31); lx = lx+lx; 113 iy -= 1; 114 } 115 if(iy>= -1022) { /* normalize output */ 116 hx = ((hx-0x00100000)|((iy+1023)<<20)); 117 INSERT_WORDS(x,hx|sx,lx); 118 } else { /* subnormal output */ 119 n = -1022 - iy; 120 if(n<=20) { 121 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 122 hx >>= n; 123 } else if (n<=31) { 124 lx = (hx<<(32-n))|(lx>>n); hx = sx; 125 } else { 126 lx = hx>>(n-32); hx = sx; 127 } 128 INSERT_WORDS(x,hx|sx,lx); 129 x *= one; /* create necessary signal */ 130 } 131 return x; /* exact output */ 132 } 133