1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2005-2011 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 <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 #include <fenv.h>
33
34 #include "math.h"
35 #include "math_private.h"
36
37 #ifdef USE_BUILTIN_FMAF
38 float
fmaf(float x,float y,float z)39 fmaf(float x, float y, float z)
40 {
41 return (__builtin_fmaf(x, y, z));
42 }
43 #else
44 /*
45 * Fused multiply-add: Compute x * y + z with a single rounding error.
46 *
47 * A double has more than twice as much precision than a float, so
48 * direct double-precision arithmetic suffices, except where double
49 * rounding occurs.
50 */
51 float
fmaf(float x,float y,float z)52 fmaf(float x, float y, float z)
53 {
54 double xy, result;
55 uint32_t hr, lr;
56
57 xy = (double)x * y;
58 result = xy + z;
59 EXTRACT_WORDS(hr, lr, result);
60 /* Common case: The double precision result is fine. */
61 if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */
62 (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */
63 result - xy == z || /* exact */
64 fegetround() != FE_TONEAREST) /* not round-to-nearest */
65 return (result);
66
67 /*
68 * If result is inexact, and exactly halfway between two float values,
69 * we need to adjust the low-order bit in the direction of the error.
70 */
71 fesetround(FE_TOWARDZERO);
72 volatile double vxy = xy; /* XXX work around gcc CSE bug */
73 double adjusted_result = vxy + z;
74 fesetround(FE_TONEAREST);
75 if (result == adjusted_result)
76 SET_LOW_WORD(adjusted_result, lr + 1);
77 return (adjusted_result);
78 }
79 #endif /* !USE_BUILTIN_FMAF */
80