1/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
2/*-
3 * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28#include <fenv.h>
29#include <math.h>
30#include <stdint.h>
31
32/*
33 * Fused multiply-add: Compute x * y + z with a single rounding error.
34 *
35 * A double has more than twice as much precision than a float, so
36 * direct double-precision arithmetic suffices, except where double
37 * rounding occurs.
38 */
39float fmaf(float x, float y, float z)
40{
41 #pragma STDC FENV_ACCESS ON
42 double xy, result;
43 union {double f; uint64_t i;} u;
44 int e;
45
46 xy = (double)x * y;
47 result = xy + z;
48 u.f = result;
49 e = u.i>>52 & 0x7ff;
50 /* Common case: The double precision result is fine. */
51 if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */
52 e == 0x7ff || /* NaN */
53 (result - xy == z && result - z == xy) || /* exact */
54 fegetround() != FE_TONEAREST) /* not round-to-nearest */
55 {
56 /*
57 underflow may not be raised correctly, example:
58 fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
59 */
60#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
61 if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) {
62 feclearexcept(FE_INEXACT);
63 /* TODO: gcc and clang bug workaround */
64 volatile float vz = z;
65 result = xy + vz;
66 if (fetestexcept(FE_INEXACT))
67 feraiseexcept(FE_UNDERFLOW);
68 else
69 feraiseexcept(FE_INEXACT);
70 }
71#endif
72 z = result;
73 return z;
74 }
75
76 /*
77 * If result is inexact, and exactly halfway between two float values,
78 * we need to adjust the low-order bit in the direction of the error.
79 */
80 double err;
81 int neg = u.i >> 63;
82 if (neg == (z > xy))
83 err = xy - result + z;
84 else
85 err = z - result + xy;
86 if (neg == (err < 0))
87 u.i++;
88 else
89 u.i--;
90 z = u.f;
91 return z;
92}