Merge remote branch 'nsz/master'
This commit is contained in:
Rich Felker
commit
da7458a602
5 changed files with 208 additions and 163 deletions
146
src/math/fma.c
146
src/math/fma.c
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@ -1,3 +1,137 @@
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#include <fenv.h>
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#include "libm.h"
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#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
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union ld80 {
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long double x;
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struct {
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uint64_t m;
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uint16_t e : 15;
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uint16_t s : 1;
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uint16_t pad;
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} bits;
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};
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/* exact add, assumes exponent_x >= exponent_y */
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static void add(long double *hi, long double *lo, long double x, long double y)
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{
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long double r;
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r = x + y;
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*hi = r;
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r -= x;
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*lo = y - r;
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}
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/* exact mul, assumes no over/underflow */
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static void mul(long double *hi, long double *lo, long double x, long double y)
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{
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static const long double c = 1.0 + 0x1p32L;
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long double cx, xh, xl, cy, yh, yl;
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cx = c*x;
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xh = (x - cx) + cx;
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xl = x - xh;
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cy = c*y;
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yh = (y - cy) + cy;
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yl = y - yh;
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*hi = x*y;
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*lo = (xh*yh - *hi) + xh*yl + xl*yh + xl*yl;
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}
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/*
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assume (long double)(hi+lo) == hi
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return an adjusted hi so that rounding it to double is correct
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*/
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static long double adjust(long double hi, long double lo)
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{
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union ld80 uhi, ulo;
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if (lo == 0)
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return hi;
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uhi.x = hi;
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if (uhi.bits.m & 0x3ff)
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return hi;
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ulo.x = lo;
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if (uhi.bits.s == ulo.bits.s)
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uhi.bits.m++;
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else
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uhi.bits.m--;
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return uhi.x;
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}
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static long double dadd(long double x, long double y)
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{
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add(&x, &y, x, y);
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return adjust(x, y);
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}
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static long double dmul(long double x, long double y)
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{
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mul(&x, &y, x, y);
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return adjust(x, y);
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}
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static int getexp(long double x)
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{
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union ld80 u;
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u.x = x;
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return u.bits.e;
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}
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double fma(double x, double y, double z)
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{
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long double hi, lo1, lo2, xy;
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int round, ez, exy;
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/* handle +-inf,nan */
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if (!isfinite(x) || !isfinite(y))
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return x*y + z;
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if (!isfinite(z))
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return z;
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/* handle +-0 */
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if (x == 0.0 || y == 0.0)
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return x*y + z;
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round = fegetround();
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if (z == 0.0) {
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if (round == FE_TONEAREST)
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return dmul(x, y);
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return x*y;
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}
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/* exact mul and add require nearest rounding */
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/* spurious inexact exceptions may be raised */
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fesetround(FE_TONEAREST);
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mul(&xy, &lo1, x, y);
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exy = getexp(xy);
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ez = getexp(z);
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if (ez > exy) {
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add(&hi, &lo2, z, xy);
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} else if (ez > exy - 12) {
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add(&hi, &lo2, xy, z);
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if (hi == 0) {
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fesetround(round);
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/* make sure that the sign of 0 is correct */
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return (xy + z) + lo1;
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}
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} else {
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/*
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ez <= exy - 12
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the 12 extra bits (1guard, 11round+sticky) are needed so with
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lo = dadd(lo1, lo2)
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elo <= ehi - 11, and we use the last 10 bits in adjust so
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dadd(hi, lo)
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gives correct result when rounded to double
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*/
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hi = xy;
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lo2 = z;
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}
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fesetround(round);
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if (round == FE_TONEAREST)
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return dadd(hi, dadd(lo1, lo2));
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return hi + (lo1 + lo2);
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}
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#else
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/* origin: FreeBSD /usr/src/lib/msun/src/s_fma.c */
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/*-
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* Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
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@ -25,9 +159,6 @@
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* SUCH DAMAGE.
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*/
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#include <fenv.h>
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#include "libm.h"
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/*
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* A struct dd represents a floating-point number with twice the precision
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* of a double. We maintain the invariant that "hi" stores the 53 high-order
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@ -178,14 +309,14 @@ double fma(double x, double y, double z)
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* return values here are crucial in handling special cases involving
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* infinities, NaNs, overflows, and signed zeroes correctly.
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*/
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if (x == 0.0 || y == 0.0)
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return (x * y + z);
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if (z == 0.0)
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return (x * y);
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if (!isfinite(x) || !isfinite(y))
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return (x * y + z);
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if (!isfinite(z))
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return (z);
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if (x == 0.0 || y == 0.0)
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return (x * y + z);
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if (z == 0.0)
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return (x * y);
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xs = frexp(x, &ex);
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ys = frexp(y, &ey);
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@ -278,3 +409,4 @@ double fma(double x, double y, double z)
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else
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return (add_and_denormalize(r.hi, adj, spread));
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}
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#endif
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@ -173,14 +173,14 @@ long double fmal(long double x, long double y, long double z)
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* return values here are crucial in handling special cases involving
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* infinities, NaNs, overflows, and signed zeroes correctly.
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*/
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if (x == 0.0 || y == 0.0)
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return (x * y + z);
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if (z == 0.0)
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return (x * y);
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if (!isfinite(x) || !isfinite(y))
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return (x * y + z);
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if (!isfinite(z))
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return (z);
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if (x == 0.0 || y == 0.0)
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return (x * y + z);
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if (z == 0.0)
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return (x * y);
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xs = frexpl(x, &ex);
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ys = frexpl(y, &ey);
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@ -1,62 +1,28 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbn.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* scalbn (double x, int n)
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* scalbn(x,n) returns x* 2**n computed by exponent
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* manipulation rather than by actually performing an
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* exponentiation or a multiplication.
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*/
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#include "libm.h"
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
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huge = 1.0e+300,
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tiny = 1.0e-300;
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double scalbn(double x, int n)
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{
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// FIXME: k+n check depends on signed int overflow.. use unsigned hx
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// TODO: when long != int:
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// scalbln(x,long n) { if(n>9999)n=9999; else if(n<-9999)n=-9999; return scalbn(x,n); }
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// TODO: n < -50000 ...
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int32_t k,hx,lx;
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double scale;
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EXTRACT_WORDS(hx, lx, x);
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k = (hx&0x7ff00000)>>20; /* extract exponent */
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if (k == 0) { /* 0 or subnormal x */
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if ((lx|(hx&0x7fffffff)) == 0) /* +-0 */
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return x;
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x *= two54;
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GET_HIGH_WORD(hx, x);
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k = ((hx&0x7ff00000)>>20) - 54;
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if (n < -50000)
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return tiny*x; /*underflow*/
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if (n > 1023) {
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x *= 0x1p1023;
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n -= 1023;
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if (n > 1023) {
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x *= 0x1p1023;
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n -= 1023;
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if (n > 1023)
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return x * 0x1p1023;
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}
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} else if (n < -1022) {
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x *= 0x1p-1022;
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n += 1022;
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if (n < -1022) {
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x *= 0x1p-1022;
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n += 1022;
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if (n < -1022)
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return x * 0x1p-1022;
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}
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}
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if (k == 0x7ff) /* NaN or Inf */
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return x + x;
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k = k + n;
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if (k > 0x7fe)
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return huge*copysign(huge, x); /* overflow */
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if (k > 0) { /* normal result */
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SET_HIGH_WORD(x, (hx&0x800fffff)|(k<<20));
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return x;
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}
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if (k <= -54)
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if (n > 50000) /* in case integer overflow in n+k */
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return huge*copysign(huge, x); /*overflow*/
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return tiny*copysign(tiny, x); /*underflow*/
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k += 54; /* subnormal result */
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SET_HIGH_WORD(x, (hx&0x800fffff)|(k<<20));
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return x*twom54;
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INSERT_WORDS(scale, (uint32_t)(0x3ff+n)<<20, 0);
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return x * scale;
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}
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@ -1,54 +1,28 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbnf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "libm.h"
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static const float
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two25 = 3.355443200e+07, /* 0x4c000000 */
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twom25 = 2.9802322388e-08, /* 0x33000000 */
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huge = 1.0e+30,
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tiny = 1.0e-30;
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float scalbnf(float x, int n)
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{
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int32_t k, ix;
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GET_FLOAT_WORD(ix, x);
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k = (ix&0x7f800000)>>23; /* extract exponent */
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if (k == 0) { /* 0 or subnormal x */
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if ((ix&0x7fffffff) == 0) /* +-0 */
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return x;
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x *= two25;
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GET_FLOAT_WORD(ix, x);
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k = ((ix&0x7f800000)>>23) - 25;
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if (n < -50000)
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return tiny*x; /*underflow*/
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float scale;
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if (n > 127) {
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x *= 0x1p127f;
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n -= 127;
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if (n > 127) {
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x *= 0x1p127f;
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n -= 127;
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if (n > 127)
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return x * 0x1p127f;
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}
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} else if (n < -126) {
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x *= 0x1p-126f;
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n += 126;
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if (n < -126) {
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x *= 0x1p-126f;
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n += 126;
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if (n < -126)
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return x * 0x1p-126f;
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}
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}
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if (k == 0xff) /* NaN or Inf */
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return x + x;
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k = k + n;
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if (k > 0xfe)
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return huge*copysignf(huge, x); /* overflow */
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if (k > 0) { /* normal result */
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SET_FLOAT_WORD(x, (ix&0x807fffff)|(k<<23));
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return x;
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}
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if (k <= -25)
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if (n > 50000) /* in case integer overflow in n+k */
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return huge*copysignf(huge,x); /*overflow*/
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return tiny*copysignf(tiny, x); /*underflow*/
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k += 25; /* subnormal result */
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SET_FLOAT_WORD(x, (ix&0x807fffff)|(k<<23));
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return x*twom25;
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SET_FLOAT_WORD(scale, (uint32_t)(0x7f+n)<<23);
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return x * scale;
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}
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@ -1,21 +1,3 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/s_scalbnl.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
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* ====================================================
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*/
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/*
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* scalbnl (long double x, int n)
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* scalbnl(x,n) returns x* 2**n computed by exponent
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* manipulation rather than by actually performing an
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* exponentiation or a multiplication.
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*/
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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@ -24,40 +6,31 @@ long double scalbnl(long double x, int n)
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return scalbn(x, n);
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}
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#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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static const long double
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huge = 0x1p16000L,
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tiny = 0x1p-16000L;
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long double scalbnl(long double x, int n)
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{
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union IEEEl2bits u;
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int k;
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union IEEEl2bits scale;
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u.e = x;
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k = u.bits.exp; /* extract exponent */
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if (k == 0) { /* 0 or subnormal x */
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if ((u.bits.manh|u.bits.manl) == 0) /* +-0 */
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return x;
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u.e *= 0x1p128;
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k = u.bits.exp - 128;
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if (n < -50000)
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return tiny*x; /*underflow*/
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if (n > 16383) {
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x *= 0x1p16383L;
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n -= 16383;
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if (n > 16383) {
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x *= 0x1p16383L;
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n -= 16383;
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if (n > 16383)
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return x * 0x1p16383L;
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}
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} else if (n < -16382) {
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x *= 0x1p-16382L;
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n += 16382;
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if (n < -16382) {
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x *= 0x1p-16382L;
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n += 16382;
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if (n < -16382)
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return x * 0x1p-16382L;
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}
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}
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if (k == 0x7fff) /* NaN or Inf */
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return x + x;
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k = k + n;
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if (k >= 0x7fff)
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return huge*copysignl(huge, x); /* overflow */
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if (k > 0) { /* normal result */
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u.bits.exp = k;
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return u.e;
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}
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if (k <= -128)
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if (n > 50000) /* in case integer overflow in n+k */
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return huge*copysign(huge, x); /*overflow*/
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return tiny*copysign(tiny, x); /*underflow*/
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k += 128; /* subnormal result */
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u.bits.exp = k;
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return u.e*0x1p-128;
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scale.e = 1.0L;
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scale.bits.exp = 0x3fff + n;
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return x * scale.e;
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}
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#endif
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||||
|
|
|
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