1 /* @(#)e_fmod.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, 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 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_fmod.c,v 1.9 1997/10/09 11:29:00 lukem Exp $"); 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 #ifdef __STDC__ 28 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 29 #else 30 static double one = 1.0, Zero[] = {0.0, -0.0,}; 31 #endif 32 33 #ifdef __STDC__ 34 double __ieee754_fmod(double x, double y) 35 #else 36 double __ieee754_fmod(x,y) 37 double x,y ; 38 #endif 39 { 40 int32_t n,hx,hy,hz,ix,iy,sx,i; 41 u_int32_t lx,ly,lz; 42 43 EXTRACT_WORDS(hx,lx,x); 44 EXTRACT_WORDS(hy,ly,y); 45 sx = hx&0x80000000; /* sign of x */ 46 hx ^=sx; /* |x| */ 47 hy &= 0x7fffffff; /* |y| */ 48 49 /* purge off exception values */ 50 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 51 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 52 return (x*y)/(x*y); 53 if(hx<=hy) { 54 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ 55 if(lx==ly) 56 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 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 while(n--) { 106 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 107 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 108 else { 109 if((hz|lz)==0) /* return sign(x)*0 */ 110 return Zero[(u_int32_t)sx>>31]; 111 hx = hz+hz+(lz>>31); lx = lz+lz; 112 } 113 } 114 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 115 if(hz>=0) {hx=hz;lx=lz;} 116 117 /* convert back to floating value and restore the sign */ 118 if((hx|lx)==0) /* return sign(x)*0 */ 119 return Zero[(u_int32_t)sx>>31]; 120 while(hx<0x00100000) { /* normalize x */ 121 hx = hx+hx+(lx>>31); lx = lx+lx; 122 iy -= 1; 123 } 124 if(iy>= -1022) { /* normalize output */ 125 hx = ((hx-0x00100000)|((iy+1023)<<20)); 126 INSERT_WORDS(x,hx|sx,lx); 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 = sx; 134 } else { 135 lx = hx>>(n-32); hx = sx; 136 } 137 INSERT_WORDS(x,hx|sx,lx); 138 x *= one; /* create necessary signal */ 139 } 140 return x; /* exact output */ 141 } 142