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 #ifndef lint 15 static char rcsid[] = "$FreeBSD$"; 16 #endif 17 18 /* 19 * __ieee754_fmod(x,y) 20 * Return x mod y in exact arithmetic 21 * Method: shift and subtract 22 */ 23 24 #include "math.h" 25 #include "math_private.h" 26 27 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 28 29 double 30 __ieee754_fmod(double x, double y) 31 { 32 int32_t n,hx,hy,hz,ix,iy,sx,i; 33 u_int32_t lx,ly,lz; 34 35 EXTRACT_WORDS(hx,lx,x); 36 EXTRACT_WORDS(hy,ly,y); 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)) return x; /* |x|<|y| return x */ 47 if(lx==ly) 48 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 49 } 50 51 /* determine ix = ilogb(x) */ 52 if(hx<0x00100000) { /* subnormal x */ 53 if(hx==0) { 54 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 55 } else { 56 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 57 } 58 } else ix = (hx>>20)-1023; 59 60 /* determine iy = ilogb(y) */ 61 if(hy<0x00100000) { /* subnormal y */ 62 if(hy==0) { 63 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 64 } else { 65 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 66 } 67 } else iy = (hy>>20)-1023; 68 69 /* set up {hx,lx}, {hy,ly} and align y to x */ 70 if(ix >= -1022) 71 hx = 0x00100000|(0x000fffff&hx); 72 else { /* subnormal x, shift x to normal */ 73 n = -1022-ix; 74 if(n<=31) { 75 hx = (hx<<n)|(lx>>(32-n)); 76 lx <<= n; 77 } else { 78 hx = lx<<(n-32); 79 lx = 0; 80 } 81 } 82 if(iy >= -1022) 83 hy = 0x00100000|(0x000fffff&hy); 84 else { /* subnormal y, shift y to normal */ 85 n = -1022-iy; 86 if(n<=31) { 87 hy = (hy<<n)|(ly>>(32-n)); 88 ly <<= n; 89 } else { 90 hy = ly<<(n-32); 91 ly = 0; 92 } 93 } 94 95 /* fix point fmod */ 96 n = ix - iy; 97 while(n--) { 98 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 99 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 100 else { 101 if((hz|lz)==0) /* return sign(x)*0 */ 102 return Zero[(u_int32_t)sx>>31]; 103 hx = hz+hz+(lz>>31); lx = lz+lz; 104 } 105 } 106 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 107 if(hz>=0) {hx=hz;lx=lz;} 108 109 /* convert back to floating value and restore the sign */ 110 if((hx|lx)==0) /* return sign(x)*0 */ 111 return Zero[(u_int32_t)sx>>31]; 112 while(hx<0x00100000) { /* normalize x */ 113 hx = hx+hx+(lx>>31); lx = lx+lx; 114 iy -= 1; 115 } 116 if(iy>= -1022) { /* normalize output */ 117 hx = ((hx-0x00100000)|((iy+1023)<<20)); 118 INSERT_WORDS(x,hx|sx,lx); 119 } else { /* subnormal output */ 120 n = -1022 - iy; 121 if(n<=20) { 122 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 123 hx >>= n; 124 } else if (n<=31) { 125 lx = (hx<<(32-n))|(lx>>n); hx = sx; 126 } else { 127 lx = hx>>(n-32); hx = sx; 128 } 129 INSERT_WORDS(x,hx|sx,lx); 130 x *= one; /* create necessary signal */ 131 } 132 return x; /* exact output */ 133 } 134