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

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
}