GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_fma.c Lines: 0 87 0.0 %
Date: 2017-11-13 Branches: 0 44 0.0 %

Line Branch Exec Source
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/*	$OpenBSD: s_fma.c,v 1.7 2016/09/12 19:47:02 guenther Exp $	*/
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/*-
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 * Copyright (c) 2005 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 <float.h>
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#include <math.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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 * We use scaling to avoid overflow/underflow, along with the
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 * canonical precision-doubling technique adapted from:
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 *
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 *	Dekker, T.  A Floating-Point Technique for Extending the
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 *	Available Precision.  Numer. Math. 18, 224-242 (1971).
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 *
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 * This algorithm is sensitive to the rounding precision.  FPUs such
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 * as the i387 must be set in double-precision mode if variables are
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 * to be stored in FP registers in order to avoid incorrect results.
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 * This is the default on FreeBSD, but not on many other systems.
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 *
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 * Hardware instructions should be used on architectures that support it,
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 * since this implementation will likely be several times slower.
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 */
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#if LDBL_MANT_DIG != 113
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double
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fma(double x, double y, double z)
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{
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	static const double split = 0x1p27 + 1.0;
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	double xs, ys, zs;
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	double c, cc, hx, hy, p, q, tx, ty;
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	double r, rr, s;
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	int oround;
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	int ex, ey, ez;
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	int spread;
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	/*
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	 * Handle special cases. The order of operations and the particular
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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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	xs = frexp(x, &ex);
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	ys = frexp(y, &ey);
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	zs = frexp(z, &ez);
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	oround = fegetround();
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	spread = ex + ey - ez;
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	/*
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	 * If x * y and z are many orders of magnitude apart, the scaling
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	 * will overflow, so we handle these cases specially.  Rounding
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	 * modes other than FE_TONEAREST are painful.
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	 */
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	if (spread > DBL_MANT_DIG * 2) {
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		fenv_t env;
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		feraiseexcept(FE_INEXACT);
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		switch(oround) {
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		case FE_TONEAREST:
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			return (x * y);
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		case FE_TOWARDZERO:
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			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
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				return (x * y);
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			feholdexcept(&env);
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			r = x * y;
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			if (!fetestexcept(FE_INEXACT))
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				r = nextafter(r, 0);
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			feupdateenv(&env);
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			return (r);
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		case FE_DOWNWARD:
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			if (z > 0.0)
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				return (x * y);
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			feholdexcept(&env);
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			r = x * y;
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			if (!fetestexcept(FE_INEXACT))
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				r = nextafter(r, -INFINITY);
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			feupdateenv(&env);
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			return (r);
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		default:	/* FE_UPWARD */
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			if (z < 0.0)
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				return (x * y);
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			feholdexcept(&env);
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			r = x * y;
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			if (!fetestexcept(FE_INEXACT))
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				r = nextafter(r, INFINITY);
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			feupdateenv(&env);
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			return (r);
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		}
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	}
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	if (spread < -DBL_MANT_DIG) {
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		feraiseexcept(FE_INEXACT);
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		if (!isnormal(z))
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			feraiseexcept(FE_UNDERFLOW);
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		switch (oround) {
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		case FE_TONEAREST:
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			return (z);
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		case FE_TOWARDZERO:
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			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
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				return (z);
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			else
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				return (nextafter(z, 0));
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		case FE_DOWNWARD:
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			if ((x > 0.0) ^ (y < 0.0))
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				return (z);
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			else
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				return (nextafter(z, -INFINITY));
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		default:	/* FE_UPWARD */
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			if ((x > 0.0) ^ (y < 0.0))
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				return (nextafter(z, INFINITY));
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			else
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				return (z);
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		}
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	}
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	/*
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	 * Use Dekker's algorithm to perform the multiplication and
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	 * subsequent addition in twice the machine precision.
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	 * Arrange so that x * y = c + cc, and x * y + z = r + rr.
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	 */
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	fesetround(FE_TONEAREST);
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	p = xs * split;
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	hx = xs - p;
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	hx += p;
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	tx = xs - hx;
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	p = ys * split;
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	hy = ys - p;
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	hy += p;
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	ty = ys - hy;
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	p = hx * hy;
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	q = hx * ty + tx * hy;
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	c = p + q;
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	cc = p - c + q + tx * ty;
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	zs = ldexp(zs, -spread);
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	r = c + zs;
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	s = r - c;
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	rr = (c - (r - s)) + (zs - s) + cc;
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	spread = ex + ey;
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	if (spread + ilogb(r) > -1023) {
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		fesetround(oround);
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		r = r + rr;
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	} else {
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		/*
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		 * The result is subnormal, so we round before scaling to
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		 * avoid double rounding.
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		 */
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		p = ldexp(copysign(0x1p-1022, r), -spread);
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		c = r + p;
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		s = c - r;
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		cc = (r - (c - s)) + (p - s) + rr;
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		fesetround(oround);
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		r = (c + cc) - p;
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	}
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	return (ldexp(r, spread));
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}
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#else	/* LDBL_MANT_DIG == 113 */
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/*
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 * 113 bits of precision is more than twice the precision of a double,
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 * so it is enough to represent the intermediate product exactly.
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 */
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double
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fma(double x, double y, double z)
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{
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	return ((long double)x * y + z);
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}
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#endif	/* LDBL_MANT_DIG != 113 */
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DEF_STD(fma);
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LDBL_MAYBE_UNUSED_CLONE(fma);