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 #ifndef lint 14 static char rcsid[] = "$Id: e_fmod.c,v 1.4 1994/03/03 17:04:11 jtc Exp $"; 15 #endif 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 <machine/endian.h> 25 26 #if BYTE_ORDER == LITTLE_ENDIAN 27 #define n0 1 28 #define n1 0 29 #else 30 #define n0 0 31 #define n1 1 32 #endif 33 34 #ifdef __STDC__ 35 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 36 #else 37 static double one = 1.0, Zero[] = {0.0, -0.0,}; 38 #endif 39 40 #ifdef __STDC__ 41 double __ieee754_fmod(double x, double y) 42 #else 43 double __ieee754_fmod(x,y) 44 double x,y ; 45 #endif 46 { 47 int n,hx,hy,hz,ix,iy,sx,i; 48 int *px = (int*)&x, *py = (int*)&y; 49 unsigned lx,ly,lz; 50 51 hx = *( n0 + px); /* high word of x */ 52 lx = *( n1 + px); /* low word of x */ 53 hy = *( n0 + py); /* high word of y */ 54 ly = *( n1 + py); /* low word of y */ 55 sx = hx&0x80000000; /* sign of x */ 56 hx ^=sx; /* |x| */ 57 hy &= 0x7fffffff; /* |y| */ 58 59 /* purge off exception values */ 60 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 61 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 62 return (x*y)/(x*y); 63 if(hx<=hy) { 64 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ 65 if(lx==ly) 66 return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/ 67 } 68 69 /* determine ix = ilogb(x) */ 70 if(hx<0x00100000) { /* subnormal x */ 71 if(hx==0) { 72 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 73 } else { 74 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 75 } 76 } else ix = (hx>>20)-1023; 77 78 /* determine iy = ilogb(y) */ 79 if(hy<0x00100000) { /* subnormal y */ 80 if(hy==0) { 81 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 82 } else { 83 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 84 } 85 } else iy = (hy>>20)-1023; 86 87 /* set up {hx,lx}, {hy,ly} and align y to x */ 88 if(ix >= -1022) 89 hx = 0x00100000|(0x000fffff&hx); 90 else { /* subnormal x, shift x to normal */ 91 n = -1022-ix; 92 if(n<=31) { 93 hx = (hx<<n)|(lx>>(32-n)); 94 lx <<= n; 95 } else { 96 hx = lx<<(n-32); 97 lx = 0; 98 } 99 } 100 if(iy >= -1022) 101 hy = 0x00100000|(0x000fffff&hy); 102 else { /* subnormal y, shift y to normal */ 103 n = -1022-iy; 104 if(n<=31) { 105 hy = (hy<<n)|(ly>>(32-n)); 106 ly <<= n; 107 } else { 108 hy = ly<<(n-32); 109 ly = 0; 110 } 111 } 112 113 /* fix point fmod */ 114 n = ix - iy; 115 while(n--) { 116 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 117 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 118 else { 119 if((hz|lz)==0) /* return sign(x)*0 */ 120 return Zero[(unsigned)sx>>31]; 121 hx = hz+hz+(lz>>31); lx = lz+lz; 122 } 123 } 124 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 125 if(hz>=0) {hx=hz;lx=lz;} 126 127 /* convert back to floating value and restore the sign */ 128 if((hx|lx)==0) /* return sign(x)*0 */ 129 return Zero[(unsigned)sx>>31]; 130 while(hx<0x00100000) { /* normalize x */ 131 hx = hx+hx+(lx>>31); lx = lx+lx; 132 iy -= 1; 133 } 134 if(iy>= -1022) { /* normalize output */ 135 hx = ((hx-0x00100000)|((iy+1023)<<20)); 136 *(n0+px) = hx|sx; 137 *(n1+px) = lx; 138 } else { /* subnormal output */ 139 n = -1022 - iy; 140 if(n<=20) { 141 lx = (lx>>n)|((unsigned)hx<<(32-n)); 142 hx >>= n; 143 } else if (n<=31) { 144 lx = (hx<<(32-n))|(lx>>n); hx = sx; 145 } else { 146 lx = hx>>(n-32); hx = sx; 147 } 148 *(n0+px) = hx|sx; 149 *(n1+px) = lx; 150 x *= one; /* create necessary signal */ 151 } 152 return x; /* exact output */ 153 } 154