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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/s_fma.c	Lines:	0	87	0.0 %
Date:	2017-11-07	Branches:	0	44	0.0 %


/*	$OpenBSD: s_fma.c,v 1.7 2016/09/12 19:47:02 guenther Exp $	*/

/*-
 * 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.
 */

#include <fenv.h>
#include <float.h>
#include <math.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.
 */
#if LDBL_MANT_DIG != 113
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;

	/*
	 * Handle special cases. The order of operations and the particular
	 * return values here are crucial in handling special cases involving
	 * infinities, NaNs, overflows, and signed zeroes correctly.
	 */
	if (x == 0.0 || y == 0.0)
		return (x * y + z);
	if (z == 0.0)
		return (x * y);
	if (!isfinite(x) || !isfinite(y))
		return (x * y + z);
	if (!isfinite(z))
		return (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));
}
#else	/* LDBL_MANT_DIG == 113 */
/*
 * 113 bits of precision is more than twice the precision of a double,
 * so it is enough to represent the intermediate product exactly.
 */
double
fma(double x, double y, double z)
{
	return ((long double)x * y + z);
}
#endif	/* LDBL_MANT_DIG != 113 */
DEF_STD(fma);
LDBL_MAYBE_UNUSED_CLONE(fma);


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_fma.c,v 1.7 2016/09/12 19:47:02 guenther Exp $ */
2
3			/*-
4			* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
5			* All rights reserved.
6			*
7			* Redistribution and use in source and binary forms, with or without
8			* modification, are permitted provided that the following conditions
9			* are met:
10			* 1. Redistributions of source code must retain the above copyright
11			* notice, this list of conditions and the following disclaimer.
12			* 2. Redistributions in binary form must reproduce the above copyright
13			* notice, this list of conditions and the following disclaimer in the
14			* documentation and/or other materials provided with the distribution.
15			*
16			* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17			* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18			* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19			* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20			* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21			* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22			* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23			* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24			* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25			* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26			* SUCH DAMAGE.
27			*/
28
29			#include <fenv.h>
30			#include <float.h>
31			#include <math.h>
32
33			/*
34			* Fused multiply-add: Compute x * y + z with a single rounding error.
35			*
36			* We use scaling to avoid overflow/underflow, along with the
37			* canonical precision-doubling technique adapted from:
38			*
39			* Dekker, T. A Floating-Point Technique for Extending the
40			* Available Precision. Numer. Math. 18, 224-242 (1971).
41			*
42			* This algorithm is sensitive to the rounding precision. FPUs such
43			* as the i387 must be set in double-precision mode if variables are
44			* to be stored in FP registers in order to avoid incorrect results.
45			* This is the default on FreeBSD, but not on many other systems.
46			*
47			* Hardware instructions should be used on architectures that support it,
48			* since this implementation will likely be several times slower.
49			*/
50			#if LDBL_MANT_DIG != 113
51			double
52			fma(double x, double y, double z)
53			{
54			static const double split = 0x1p27 + 1.0;
55			double xs, ys, zs;
56			double c, cc, hx, hy, p, q, tx, ty;
57			double r, rr, s;
58			int oround;
59			int ex, ey, ez;
60			int spread;
61
62			/*
63			* Handle special cases. The order of operations and the particular
64			* return values here are crucial in handling special cases involving
65			* infinities, NaNs, overflows, and signed zeroes correctly.
66			*/
67			if (x == 0.0 \|\| y == 0.0)
68			return (x * y + z);
69			if (z == 0.0)
70			return (x * y);
71			if (!isfinite(x) \|\| !isfinite(y))
72			return (x * y + z);
73			if (!isfinite(z))
74			return (z);
75
76			xs = frexp(x, &ex);
77			ys = frexp(y, &ey);
78			zs = frexp(z, &ez);
79			oround = fegetround();
80			spread = ex + ey - ez;
81
82			/*
83			* If x * y and z are many orders of magnitude apart, the scaling
84			* will overflow, so we handle these cases specially. Rounding
85			* modes other than FE_TONEAREST are painful.
86			*/
87			if (spread > DBL_MANT_DIG * 2) {
88			fenv_t env;
89			feraiseexcept(FE_INEXACT);
90			switch(oround) {
91			case FE_TONEAREST:
92			return (x * y);
93			case FE_TOWARDZERO:
94			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
95			return (x * y);
96			feholdexcept(&env);
97			r = x * y;
98			if (!fetestexcept(FE_INEXACT))
99			r = nextafter(r, 0);
100			feupdateenv(&env);
101			return (r);
102			case FE_DOWNWARD:
103			if (z > 0.0)
104			return (x * y);
105			feholdexcept(&env);
106			r = x * y;
107			if (!fetestexcept(FE_INEXACT))
108			r = nextafter(r, -INFINITY);
109			feupdateenv(&env);
110			return (r);
111			default: /* FE_UPWARD */
112			if (z < 0.0)
113			return (x * y);
114			feholdexcept(&env);
115			r = x * y;
116			if (!fetestexcept(FE_INEXACT))
117			r = nextafter(r, INFINITY);
118			feupdateenv(&env);
119			return (r);
120			}
121			}
122			if (spread < -DBL_MANT_DIG) {
123			feraiseexcept(FE_INEXACT);
124			if (!isnormal(z))
125			feraiseexcept(FE_UNDERFLOW);
126			switch (oround) {
127			case FE_TONEAREST:
128			return (z);
129			case FE_TOWARDZERO:
130			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
131			return (z);
132			else
133			return (nextafter(z, 0));
134			case FE_DOWNWARD:
135			if ((x > 0.0) ^ (y < 0.0))
136			return (z);
137			else
138			return (nextafter(z, -INFINITY));
139			default: /* FE_UPWARD */
140			if ((x > 0.0) ^ (y < 0.0))
141			return (nextafter(z, INFINITY));
142			else
143			return (z);
144			}
145			}
146
147			/*
148			* Use Dekker's algorithm to perform the multiplication and
149			* subsequent addition in twice the machine precision.
150			* Arrange so that x * y = c + cc, and x * y + z = r + rr.
151			*/
152			fesetround(FE_TONEAREST);
153
154			p = xs * split;
155			hx = xs - p;
156			hx += p;
157			tx = xs - hx;
158
159			p = ys * split;
160			hy = ys - p;
161			hy += p;
162			ty = ys - hy;
163
164			p = hx * hy;
165			q = hx * ty + tx * hy;
166			c = p + q;
167			cc = p - c + q + tx * ty;
168
169			zs = ldexp(zs, -spread);
170			r = c + zs;
171			s = r - c;
172			rr = (c - (r - s)) + (zs - s) + cc;
173
174			spread = ex + ey;
175			if (spread + ilogb(r) > -1023) {
176			fesetround(oround);
177			r = r + rr;
178			} else {
179			/*
180			* The result is subnormal, so we round before scaling to
181			* avoid double rounding.
182			*/
183			p = ldexp(copysign(0x1p-1022, r), -spread);
184			c = r + p;
185			s = c - r;
186			cc = (r - (c - s)) + (p - s) + rr;
187			fesetround(oround);
188			r = (c + cc) - p;
189			}
190			return (ldexp(r, spread));
191			}
192			#else /* LDBL_MANT_DIG == 113 */
193			/*
194			* 113 bits of precision is more than twice the precision of a double,
195			* so it is enough to represent the intermediate product exactly.
196			*/
197			double
198			fma(double x, double y, double z)
199			{
200			return ((long double)x * y + z);
201			}
202			#endif /* LDBL_MANT_DIG != 113 */
203			DEF_STD(fma);
204			LDBL_MAYBE_UNUSED_CLONE(fma);