94 lines
3.1 KiB
C
94 lines
3.1 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
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/*-
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* Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <fenv.h>
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#include <math.h>
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#include <stdint.h>
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/*
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* Fused multiply-add: Compute x * y + z with a single rounding error.
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*
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* A double has more than twice as much precision than a float, so
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* direct double-precision arithmetic suffices, except where double
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* rounding occurs.
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*/
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float fmaf(float x, float y, float z)
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{
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#pragma STDC FENV_ACCESS ON
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double xy, result;
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union {double f; uint64_t i;} u;
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int e;
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xy = (double)x * y;
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result = xy + z;
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u.f = result;
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e = u.i>>52 & 0x7ff;
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/* Common case: The double precision result is fine. */
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if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */
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e == 0x7ff || /* NaN */
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(result - xy == z && result - z == xy) || /* exact */
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fegetround() != FE_TONEAREST) /* not round-to-nearest */
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{
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/*
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underflow may not be raised correctly, example:
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fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
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*/
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#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
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if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) {
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feclearexcept(FE_INEXACT);
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/* TODO: gcc and clang bug workaround */
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volatile float vz = z;
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result = xy + vz;
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if (fetestexcept(FE_INEXACT))
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feraiseexcept(FE_UNDERFLOW);
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else
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feraiseexcept(FE_INEXACT);
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}
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#endif
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z = result;
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return z;
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}
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/*
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* If result is inexact, and exactly halfway between two float values,
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* we need to adjust the low-order bit in the direction of the error.
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*/
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#ifdef FE_TOWARDZERO
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fesetround(FE_TOWARDZERO);
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#endif
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volatile double vxy = xy; /* XXX work around gcc CSE bug */
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double adjusted_result = vxy + z;
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fesetround(FE_TONEAREST);
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if (result == adjusted_result) {
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u.f = adjusted_result;
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u.i++;
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adjusted_result = u.f;
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}
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z = adjusted_result;
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return z;
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}
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