fma_freeBSD.c   [plain text]

#include "math.h"

#if !defined(__VFP_FP__) || defined(__SOFTFP__)

#warning VERY SKETCHY FMA
double fma(double x, double y, double z) {
	return x*y + z;
}

#else

/*-
 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#define __ISO_C_VISIBLE 1999
#include <sys/cdefs.h>

#include <fenv.h>
#include <float.h>

/*
 * Fused multiply-add: Compute x * y + z with a single rounding error.
 *
 * We use scaling to avoid overflow/underflow, along with the
 * canonical precision-doubling technique adapted from:
 *
 *	Dekker, T.  A Floating-Point Technique for Extending the
 *	Available Precision.  Numer. Math. 18, 224-242 (1971).
 *
 * This algorithm is sensitive to the rounding precision.  FPUs such
 * as the i387 must be set in double-precision mode if variables are
 * to be stored in FP registers in order to avoid incorrect results.
 * This is the default on FreeBSD, but not on many other systems.
 *
 * Hardware instructions should be used on architectures that support it,
 * since this implementation will likely be several times slower.
 */

double
fma(double x, double y, double z)
{
	static const double split = 0x1p27 + 1.0;
	double xs, ys, zs;
	double c, cc, hx, hy, p, q, tx, ty;
	double r, rr, s;
	int oround;
	int ex, ey, ez;
	int spread;
	
	if (z == 0.0)
		return (x * y);
	if (x == 0.0 || y == 0.0)
		return (x * y + z);
	
	/* Results of frexp() are undefined for these cases. */
	if (!isfinite(x) || !isfinite(y) || !isfinite(z))
		return (x * y + z);
	
	xs = frexp(x, &ex);
	ys = frexp(y, &ey);
	zs = frexp(z, &ez);
	oround = fegetround();
	spread = ex + ey - ez;
	
	/*
	 * If x * y and z are many orders of magnitude apart, the scaling
	 * will overflow, so we handle these cases specially.  Rounding
	 * modes other than FE_TONEAREST are painful.
	 */
	if (spread > DBL_MANT_DIG * 2) {
		fenv_t env;
		feraiseexcept(FE_INEXACT);
		switch(oround) {
			case FE_TONEAREST:
				return (x * y);
			case FE_TOWARDZERO:
				if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
					return (x * y);
				feholdexcept(&env);
				r = x * y;
				if (!fetestexcept(FE_INEXACT))
					r = nextafter(r, 0);
				feupdateenv(&env);
				return (r);
			case FE_DOWNWARD:
				if (z > 0.0)
					return (x * y);
				feholdexcept(&env);
				r = x * y;
				if (!fetestexcept(FE_INEXACT))
					r = nextafter(r, -INFINITY);
				feupdateenv(&env);
				return (r);
			default:	/* FE_UPWARD */
				if (z < 0.0)
					return (x * y);
				feholdexcept(&env);
				r = x * y;
				if (!fetestexcept(FE_INEXACT))
					r = nextafter(r, INFINITY);
				feupdateenv(&env);
				return (r);
		}
	}
	if (spread < -DBL_MANT_DIG) {
		feraiseexcept(FE_INEXACT);
		if (!isnormal(z))
			feraiseexcept(FE_UNDERFLOW);
		switch (oround) {
			case FE_TONEAREST:
				return (z);
			case FE_TOWARDZERO:
				if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
					return (z);
				else
					return (nextafter(z, 0));
			case FE_DOWNWARD:
				if (x > 0.0 ^ y < 0.0)
					return (z);
				else
					return (nextafter(z, -INFINITY));
			default:	/* FE_UPWARD */
				if (x > 0.0 ^ y < 0.0)
					return (nextafter(z, INFINITY));
				else
					return (z);
		}
	}
	
	/*
	 * Use Dekker's algorithm to perform the multiplication and
	 * subsequent addition in twice the machine precision.
	 * Arrange so that x * y = c + cc, and x * y + z = r + rr.
	 */
	fesetround(FE_TONEAREST);
	
	p = xs * split;
	hx = xs - p;
	hx += p;
	tx = xs - hx;
	
	p = ys * split;
	hy = ys - p;
	hy += p;
	ty = ys - hy;
	
	p = hx * hy;
	q = hx * ty + tx * hy;
	c = p + q;
	cc = p - c + q + tx * ty;
	
	zs = ldexp(zs, -spread);
	r = c + zs;
	s = r - c;
	rr = (c - (r - s)) + (zs - s) + cc;
	
	spread = ex + ey;
	if (spread + ilogb(r) > -1023) {
		fesetround(oround);
		r = r + rr;
	} else {
		/*
		 * The result is subnormal, so we round before scaling to
		 * avoid double rounding.
		 */
		p = ldexp(copysign(0x1p-1022, r), -spread);
		c = r + p;
		s = c - r;
		cc = (r - (c - s)) + (p - s) + rr;
		fesetround(oround);
		r = (c + cc) - p;
	}
	return (ldexp(r, spread));
}

#endif