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path: root/src/math/remquo.c
blob: 085466e6a2f84ba16bdabfe8eb6d94bfa7e8a7b1 (plain) (blame)
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 ``` ``````/* origin: FreeBSD /usr/src/lib/msun/src/s_remquo.c */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* * Return the IEEE remainder and set *quo to the last n bits of the * quotient, rounded to the nearest integer. We choose n=31 because * we wind up computing all the integer bits of the quotient anyway as * a side-effect of computing the remainder by the shift and subtract * method. In practice, this is far more bits than are needed to use * remquo in reduction algorithms. */ #include "libm.h" static const double Zero[] = {0.0, -0.0,}; double remquo(double x, double y, int *quo) { int32_t n,hx,hy,hz,ix,iy,sx,i; uint32_t lx,ly,lz,q,sxy; EXTRACT_WORDS(hx, lx, x); EXTRACT_WORDS(hy, ly, y); sxy = (hx ^ hy) & 0x80000000; sx = hx & 0x80000000; /* sign of x */ hx ^= sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if ((hy|ly) == 0 || hx >= 0x7ff00000 || /* y = 0, or x not finite */ (hy|((ly|-ly)>>31)) > 0x7ff00000) /* or y is NaN */ return (x*y)/(x*y); if (hx <= hy) { if (hx < hy || lx < ly) { /* |x| < |y| return x or x-y */ q = 0; goto fixup; } if (lx == ly) { /* |x| = |y| return x*0 */ *quo = sxy ? -1 : 1; return Zero[(uint32_t)sx>>31]; } } // FIXME: use ilogb? /* determine ix = ilogb(x) */ if (hx < 0x00100000) { /* subnormal x */ if (hx == 0) { for (ix = -1043, i=lx; i>0; i<<=1) ix--; } else { for (ix = -1022, i=hx<<11; i>0; i<<=1) ix--; } } else ix = (hx>>20) - 1023; /* determine iy = ilogb(y) */ if (hy < 0x00100000) { /* subnormal y */ if (hy == 0) { for (iy = -1043, i=ly; i>0; i<<=1) iy--; } else { for (iy = -1022, i=hy<<11; i>0; i<<=1) iy--; } } else iy = (hy>>20) - 1023; /* set up {hx,lx}, {hy,ly} and align y to x */ if (ix >= -1022) hx = 0x00100000|(0x000fffff&hx); else { /* subnormal x, shift x to normal */ n = -1022 - ix; if (n <= 31) { hx = (hx<>(32-n)); lx <<= n; } else { hx = lx<<(n-32); lx = 0; } } if (iy >= -1022) hy = 0x00100000|(0x000fffff&hy); else { /* subnormal y, shift y to normal */ n = -1022 - iy; if (n <= 31) { hy = (hy<>(32-n)); ly <<= n; } else { hy = ly<<(n-32); ly = 0; } } /* fix point fmod */ n = ix - iy; q = 0; while (n--) { hz = hx - hy; lz = lx - ly; if (lx < ly) hz--; if (hz < 0) { hx = hx + hx + (lx>>31); lx = lx + lx; } else { hx = hz + hz + (lz>>31); lx = lz + lz; q++; } q <<= 1; } hz = hx - hy; lz = lx - ly; if (lx < ly) hz--; if (hz >= 0) { hx = hz; lx = lz; q++; } /* convert back to floating value and restore the sign */ if ((hx|lx) == 0) { /* return sign(x)*0 */ q &= 0x7fffffff; *quo = sxy ? -q : q; return Zero[(uint32_t)sx>>31]; } while (hx < 0x00100000) { /* normalize x */ hx = hx + hx + (lx>>31); lx = lx + lx; iy--; } if (iy >= -1022) { /* normalize output */ hx = (hx-0x00100000)|((iy+1023)<<20); } else { /* subnormal output */ n = -1022 - iy; if (n <= 20) { lx = (lx>>n)|((uint32_t)hx<<(32-n)); hx >>= n; } else if (n <= 31) { lx = (hx<<(32-n))|(lx>>n); hx = 0; } else { lx = hx>>(n-32); hx = 0; } } fixup: INSERT_WORDS(x, hx, lx); y = fabs(y); if (y < 0x1p-1021) { if (x + x > y || (x + x == y && (q & 1))) { q++; x -= y; } } else if (x > 0.5*y || (x == 0.5*y && (q & 1))) { q++; x -= y; } GET_HIGH_WORD(hx, x); SET_HIGH_WORD(x, hx ^ sx); q &= 0x7fffffff; *quo = sxy ? -q : q; return x; } ``````