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| 2 | /* @(#)e_fmod.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* |
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| 15 | * __ieee754_fmod(x,y) |
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| 16 | * Return x mod y in exact arithmetic |
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| 17 | * Method: shift and subtract |
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| 18 | */ |
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| 19 | |
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| 20 | #include <libm/fdlibm.h> |
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| 21 | |
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| 22 | #ifdef __STDC__ |
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| 23 | static const double one = 1.0, Zero[] = {0.0, -0.0,}; |
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| 24 | #else |
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| 25 | static double one = 1.0, Zero[] = {0.0, -0.0,}; |
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| 26 | #endif |
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| 27 | |
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| 28 | #ifdef __STDC__ |
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| 29 | double __ieee754_fmod(double x, double y) |
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| 30 | #else |
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| 31 | double __ieee754_fmod(x,y) |
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| 32 | double x,y ; |
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| 33 | #endif |
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| 34 | { |
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| 35 | int n,n0,n1,hx,hy,hz,ix,iy,sx,i; |
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| 36 | int *px = (int*)&x, *py = (int*)&y; |
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| 37 | unsigned lx,ly,lz; |
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| 38 | |
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| 39 | |
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| 40 | n0 = ((*(int*)&one)>>29)^1; /* index of high word */ |
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| 41 | n1 = 1-n0; /* index of low word */ |
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| 42 | |
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| 43 | hx = *( n0 + px); /* high word of x */ |
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| 44 | lx = *( n1 + px); /* low word of x */ |
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| 45 | hy = *( n0 + py); /* high word of y */ |
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| 46 | ly = *( n1 + py); /* low word of y */ |
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| 47 | sx = hx&0x80000000; /* sign of x */ |
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| 48 | hx ^=sx; /* |x| */ |
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| 49 | hy &= 0x7fffffff; /* |y| */ |
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| 50 | |
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| 51 | /* purge off exception values */ |
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| 52 | if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ |
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| 53 | ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ |
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| 54 | return (x*y)/(x*y); |
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| 55 | if(hx<=hy) { |
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| 56 | if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ |
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| 57 | if(lx==ly) |
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| 58 | return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/ |
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| 59 | } |
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| 60 | |
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| 61 | /* determine ix = ilogb(x) */ |
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| 62 | if(hx<0x00100000) { /* subnormal x */ |
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| 63 | if(hx==0) { |
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| 64 | for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
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| 65 | } else { |
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| 66 | for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; |
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| 67 | } |
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| 68 | } else ix = (hx>>20)-1023; |
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| 69 | |
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| 70 | /* determine iy = ilogb(y) */ |
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| 71 | if(hy<0x00100000) { /* subnormal y */ |
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| 72 | if(hy==0) { |
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| 73 | for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
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| 74 | } else { |
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| 75 | for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; |
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| 76 | } |
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| 77 | } else iy = (hy>>20)-1023; |
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| 78 | |
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| 79 | /* set up {hx,lx}, {hy,ly} and align y to x */ |
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| 80 | if(ix >= -1022) |
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| 81 | hx = 0x00100000|(0x000fffff&hx); |
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| 82 | else { /* subnormal x, shift x to normal */ |
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| 83 | n = -1022-ix; |
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| 84 | if(n<=31) { |
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| 85 | hx = (hx<<n)|(lx>>(32-n)); |
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| 86 | lx <<= n; |
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| 87 | } else { |
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| 88 | hx = lx<<(n-32); |
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| 89 | lx = 0; |
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| 90 | } |
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| 91 | } |
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| 92 | if(iy >= -1022) |
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| 93 | hy = 0x00100000|(0x000fffff&hy); |
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| 94 | else { /* subnormal y, shift y to normal */ |
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| 95 | n = -1022-iy; |
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| 96 | if(n<=31) { |
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| 97 | hy = (hy<<n)|(ly>>(32-n)); |
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| 98 | ly <<= n; |
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| 99 | } else { |
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| 100 | hy = ly<<(n-32); |
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| 101 | ly = 0; |
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| 102 | } |
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| 103 | } |
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| 104 | |
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| 105 | /* fix point fmod */ |
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| 106 | n = ix - iy; |
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| 107 | while(n--) { |
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| 108 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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| 109 | if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} |
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| 110 | else { |
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| 111 | if((hz|lz)==0) /* return sign(x)*0 */ |
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| 112 | return Zero[(unsigned)sx>>31]; |
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| 113 | hx = hz+hz+(lz>>31); lx = lz+lz; |
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| 114 | } |
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| 115 | } |
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| 116 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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| 117 | if(hz>=0) {hx=hz;lx=lz;} |
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| 118 | |
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| 119 | /* convert back to floating value and restore the sign */ |
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| 120 | if((hx|lx)==0) /* return sign(x)*0 */ |
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| 121 | return Zero[(unsigned)sx>>31]; |
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| 122 | while(hx<0x00100000) { /* normalize x */ |
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| 123 | hx = hx+hx+(lx>>31); lx = lx+lx; |
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| 124 | iy -= 1; |
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| 125 | } |
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| 126 | if(iy>= -1022) { /* normalize output */ |
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| 127 | hx = ((hx-0x00100000)|((iy+1023)<<20)); |
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| 128 | *(n0+px) = hx|sx; |
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| 129 | *(n1+px) = lx; |
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| 130 | } else { /* subnormal output */ |
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| 131 | n = -1022 - iy; |
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| 132 | if(n<=20) { |
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| 133 | lx = (lx>>n)|((unsigned)hx<<(32-n)); |
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| 134 | hx >>= n; |
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| 135 | } else if (n<=31) { |
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| 136 | lx = (hx<<(32-n))|(lx>>n); hx = sx; |
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| 137 | } else { |
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| 138 | lx = hx>>(n-32); hx = sx; |
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| 139 | } |
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| 140 | *(n0+px) = hx|sx; |
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| 141 | *(n1+px) = lx; |
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| 142 | x *= one; /* create necessary signal */ |
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| 143 | } |
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| 144 | return x; /* exact output */ |
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| 145 | } |
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