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GCC Code Coverage Report

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


/*	$OpenBSD: s_fmal.c,v 1.3 2013/11/12 19:00:38 martynas 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).
 */
long double
fmal(long double x, long double y, long double z)
{
#if LDBL_MANT_DIG == 64
	static const long double split = 0x1p32L + 1.0;
#elif LDBL_MANT_DIG == 113
	static const long double split = 0x1p57L + 1.0;
#endif
	long double xs, ys, zs;
	long double c, cc, hx, hy, p, q, tx, ty;
	long 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 = frexpl(x, &ex);
	ys = frexpl(y, &ey);
	zs = frexpl(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 > LDBL_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 = nextafterl(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 = nextafterl(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 = nextafterl(r, INFINITY);
			feupdateenv(&env);
			return (r);
		}
	}
	if (spread < -LDBL_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 (nextafterl(z, 0));
		case FE_DOWNWARD:
			if ((x > 0.0) ^ (y < 0.0))
				return (z);
			else
				return (nextafterl(z, -INFINITY));
		default:	/* FE_UPWARD */
			if ((x > 0.0) ^ (y < 0.0))
				return (nextafterl(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 = ldexpl(zs, -spread);
	r = c + zs;
	s = r - c;
	rr = (c - (r - s)) + (zs - s) + cc;

	spread = ex + ey;
	if (spread + ilogbl(r) > -16383) {
		fesetround(oround);
		r = r + rr;
	} else {
		/*
		 * The result is subnormal, so we round before scaling to
		 * avoid double rounding.
		 */
		p = ldexpl(copysignl(0x1p-16382L, r), -spread);
		c = r + p;
		s = c - r;
		cc = (r - (c - s)) + (p - s) + rr;
		fesetround(oround);
		r = (c + cc) - p;
	}
	return (ldexpl(r, spread));
}


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_fmal.c,v 1.3 2013/11/12 19:00:38 martynas 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			long double
43			fmal(long double x, long double y, long double z)
44			{
45			#if LDBL_MANT_DIG == 64
46			static const long double split = 0x1p32L + 1.0;
47			#elif LDBL_MANT_DIG == 113
48			static const long double split = 0x1p57L + 1.0;
49			#endif
50			long double xs, ys, zs;
51			long double c, cc, hx, hy, p, q, tx, ty;
52			long double r, rr, s;
53			int oround;
54			int ex, ey, ez;
55			int spread;
56
57			/*
58			* Handle special cases. The order of operations and the particular
59			* return values here are crucial in handling special cases involving
60			* infinities, NaNs, overflows, and signed zeroes correctly.
61			*/
62			if (x == 0.0 \|\| y == 0.0)
63			return (x * y + z);
64			if (z == 0.0)
65			return (x * y);
66			if (!isfinite(x) \|\| !isfinite(y))
67			return (x * y + z);
68			if (!isfinite(z))
69			return (z);
70
71			xs = frexpl(x, &ex);
72			ys = frexpl(y, &ey);
73			zs = frexpl(z, &ez);
74			oround = fegetround();
75			spread = ex + ey - ez;
76
77			/*
78			* If x * y and z are many orders of magnitude apart, the scaling
79			* will overflow, so we handle these cases specially. Rounding
80			* modes other than FE_TONEAREST are painful.
81			*/
82			if (spread > LDBL_MANT_DIG * 2) {
83			fenv_t env;
84			feraiseexcept(FE_INEXACT);
85			switch(oround) {
86			case FE_TONEAREST:
87			return (x * y);
88			case FE_TOWARDZERO:
89			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
90			return (x * y);
91			feholdexcept(&env);
92			r = x * y;
93			if (!fetestexcept(FE_INEXACT))
94			r = nextafterl(r, 0);
95			feupdateenv(&env);
96			return (r);
97			case FE_DOWNWARD:
98			if (z > 0.0)
99			return (x * y);
100			feholdexcept(&env);
101			r = x * y;
102			if (!fetestexcept(FE_INEXACT))
103			r = nextafterl(r, -INFINITY);
104			feupdateenv(&env);
105			return (r);
106			default: /* FE_UPWARD */
107			if (z < 0.0)
108			return (x * y);
109			feholdexcept(&env);
110			r = x * y;
111			if (!fetestexcept(FE_INEXACT))
112			r = nextafterl(r, INFINITY);
113			feupdateenv(&env);
114			return (r);
115			}
116			}
117			if (spread < -LDBL_MANT_DIG) {
118			feraiseexcept(FE_INEXACT);
119			if (!isnormal(z))
120			feraiseexcept(FE_UNDERFLOW);
121			switch (oround) {
122			case FE_TONEAREST:
123			return (z);
124			case FE_TOWARDZERO:
125			if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
126			return (z);
127			else
128			return (nextafterl(z, 0));
129			case FE_DOWNWARD:
130			if ((x > 0.0) ^ (y < 0.0))
131			return (z);
132			else
133			return (nextafterl(z, -INFINITY));
134			default: /* FE_UPWARD */
135			if ((x > 0.0) ^ (y < 0.0))
136			return (nextafterl(z, INFINITY));
137			else
138			return (z);
139			}
140			}
141
142			/*
143			* Use Dekker's algorithm to perform the multiplication and
144			* subsequent addition in twice the machine precision.
145			* Arrange so that x * y = c + cc, and x * y + z = r + rr.
146			*/
147			fesetround(FE_TONEAREST);
148
149			p = xs * split;
150			hx = xs - p;
151			hx += p;
152			tx = xs - hx;
153
154			p = ys * split;
155			hy = ys - p;
156			hy += p;
157			ty = ys - hy;
158
159			p = hx * hy;
160			q = hx * ty + tx * hy;
161			c = p + q;
162			cc = p - c + q + tx * ty;
163
164			zs = ldexpl(zs, -spread);
165			r = c + zs;
166			s = r - c;
167			rr = (c - (r - s)) + (zs - s) + cc;
168
169			spread = ex + ey;
170			if (spread + ilogbl(r) > -16383) {
171			fesetround(oround);
172			r = r + rr;
173			} else {
174			/*
175			* The result is subnormal, so we round before scaling to
176			* avoid double rounding.
177			*/
178			p = ldexpl(copysignl(0x1p-16382L, r), -spread);
179			c = r + p;
180			s = c - r;
181			cc = (r - (c - s)) + (p - s) + rr;
182			fesetround(oround);
183			r = (c + cc) - p;
184			}
185			return (ldexpl(r, spread));
186			}