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Diffstat (limited to 'src/math/remquo.c')
| -rw-r--r-- | src/math/remquo.c | 171 |
1 files changed, 171 insertions, 0 deletions
diff --git a/src/math/remquo.c b/src/math/remquo.c new file mode 100644 index 00000000..79c9a55e --- /dev/null +++ b/src/math/remquo.c @@ -0,0 +1,171 @@ +/* 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 */ + // FIXME: signed shift + 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 = 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<<n)|(lx>>(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<<n)|(ly>>(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 */ + *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 = sx; + } else { + lx = hx>>(n-32); + hx = sx; + } + } +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; +} |