source: vendor/FreeBSD-msun/current/src/s_fmal.c

Last change on this file was 2006, checked in by bird, 20 years ago

Initial revision
  • Property cvs2svn:cvs-rev set to 1.1
  • Property svn:eol-style set to native
  • Property svn:executable set to *
File size: 4.8 KB
Line 
1/*-
2 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
28__FBSDID("$FreeBSD: src/lib/msun/src/s_fmal.c,v 1.2 2005/03/18 02:27:59 das Exp $");
29
30#include <fenv.h>
31#include <float.h>
32#include <math.h>
33
34/*
35 * Fused multiply-add: Compute x * y + z with a single rounding error.
36 *
37 * We use scaling to avoid overflow/underflow, along with the
38 * canonical precision-doubling technique adapted from:
39 *
40 * Dekker, T. A Floating-Point Technique for Extending the
41 * Available Precision. Numer. Math. 18, 224-242 (1971).
42 */
43long double
44fmal(long double x, long double y, long double z)
45{
46#if LDBL_MANT_DIG == 64
47 static const long double split = 0x1p32L + 1.0;
48#elif LDBL_MANT_DIG == 113
49 static const long double split = 0x1p57L + 1.0;
50#endif
51 long double xs, ys, zs;
52 long double c, cc, hx, hy, p, q, tx, ty;
53 long double r, rr, s;
54 int oround;
55 int ex, ey, ez;
56 int spread;
57
58 if (z == 0.0)
59 return (x * y);
60 if (x == 0.0 || y == 0.0)
61 return (x * y + z);
62
63 /* Results of frexp() are undefined for these cases. */
64 if (!isfinite(x) || !isfinite(y) || !isfinite(z))
65 return (x * y + z);
66
67 xs = frexpl(x, &ex);
68 ys = frexpl(y, &ey);
69 zs = frexpl(z, &ez);
70 oround = fegetround();
71 spread = ex + ey - ez;
72
73 /*
74 * If x * y and z are many orders of magnitude apart, the scaling
75 * will overflow, so we handle these cases specially. Rounding
76 * modes other than FE_TONEAREST are painful.
77 */
78 if (spread > LDBL_MANT_DIG * 2) {
79 fenv_t env;
80 feraiseexcept(FE_INEXACT);
81 switch(oround) {
82 case FE_TONEAREST:
83 return (x * y);
84 case FE_TOWARDZERO:
85 if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
86 return (x * y);
87 feholdexcept(&env);
88 r = x * y;
89 if (!fetestexcept(FE_INEXACT))
90 r = nextafterl(r, 0);
91 feupdateenv(&env);
92 return (r);
93 case FE_DOWNWARD:
94 if (z > 0.0)
95 return (x * y);
96 feholdexcept(&env);
97 r = x * y;
98 if (!fetestexcept(FE_INEXACT))
99 r = nextafterl(r, -INFINITY);
100 feupdateenv(&env);
101 return (r);
102 default: /* FE_UPWARD */
103 if (z < 0.0)
104 return (x * y);
105 feholdexcept(&env);
106 r = x * y;
107 if (!fetestexcept(FE_INEXACT))
108 r = nextafterl(r, INFINITY);
109 feupdateenv(&env);
110 return (r);
111 }
112 }
113 if (spread < -LDBL_MANT_DIG) {
114 feraiseexcept(FE_INEXACT);
115 if (!isnormal(z))
116 feraiseexcept(FE_UNDERFLOW);
117 switch (oround) {
118 case FE_TONEAREST:
119 return (z);
120 case FE_TOWARDZERO:
121 if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
122 return (z);
123 else
124 return (nextafterl(z, 0));
125 case FE_DOWNWARD:
126 if (x > 0.0 ^ y < 0.0)
127 return (z);
128 else
129 return (nextafterl(z, -INFINITY));
130 default: /* FE_UPWARD */
131 if (x > 0.0 ^ y < 0.0)
132 return (nextafterl(z, INFINITY));
133 else
134 return (z);
135 }
136 }
137
138 /*
139 * Use Dekker's algorithm to perform the multiplication and
140 * subsequent addition in twice the machine precision.
141 * Arrange so that x * y = c + cc, and x * y + z = r + rr.
142 */
143 fesetround(FE_TONEAREST);
144
145 p = xs * split;
146 hx = xs - p;
147 hx += p;
148 tx = xs - hx;
149
150 p = ys * split;
151 hy = ys - p;
152 hy += p;
153 ty = ys - hy;
154
155 p = hx * hy;
156 q = hx * ty + tx * hy;
157 c = p + q;
158 cc = p - c + q + tx * ty;
159
160 zs = ldexpl(zs, -spread);
161 r = c + zs;
162 s = r - c;
163 rr = (c - (r - s)) + (zs - s) + cc;
164
165 spread = ex + ey;
166 if (spread + ilogbl(r) > -16383) {
167 fesetround(oround);
168 r = r + rr;
169 } else {
170 /*
171 * The result is subnormal, so we round before scaling to
172 * avoid double rounding.
173 */
174 p = ldexpl(copysignl(0x1p-16382L, r), -spread);
175 c = r + p;
176 s = c - r;
177 cc = (r - (c - s)) + (p - s) + rr;
178 fesetround(oround);
179 r = (c + cc) - p;
180 }
181 return (ldexpl(r, spread));
182}
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