xref: /freebsd/lib/msun/src/s_fmaf.c (revision 5e3190f700637fcfc1a52daeaa4a031fdd2557c7)
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 #include <fenv.h>
31 
32 #include "math.h"
33 #include "math_private.h"
34 
35 #ifdef USE_BUILTIN_FMAF
36 float
37 fmaf(float x, float y, float z)
38 {
39 	return (__builtin_fmaf(x, y, z));
40 }
41 #else
42 /*
43  * Fused multiply-add: Compute x * y + z with a single rounding error.
44  *
45  * A double has more than twice as much precision than a float, so
46  * direct double-precision arithmetic suffices, except where double
47  * rounding occurs.
48  */
49 float
50 fmaf(float x, float y, float z)
51 {
52 	double xy, result;
53 	uint32_t hr, lr;
54 
55 	xy = (double)x * y;
56 	result = xy + z;
57 	EXTRACT_WORDS(hr, lr, result);
58 	/* Common case: The double precision result is fine. */
59 	if ((lr & 0x1fffffff) != 0x10000000 ||	/* not a halfway case */
60 	    (hr & 0x7ff00000) == 0x7ff00000 ||	/* NaN */
61 	    result - xy == z ||			/* exact */
62 	    fegetround() != FE_TONEAREST)	/* not round-to-nearest */
63 		return (result);
64 
65 	/*
66 	 * If result is inexact, and exactly halfway between two float values,
67 	 * we need to adjust the low-order bit in the direction of the error.
68 	 */
69 	fesetround(FE_TOWARDZERO);
70 	volatile double vxy = xy;  /* XXX work around gcc CSE bug */
71 	double adjusted_result = vxy + z;
72 	fesetround(FE_TONEAREST);
73 	if (result == adjusted_result)
74 		SET_LOW_WORD(adjusted_result, lr + 1);
75 	return (adjusted_result);
76 }
77 #endif /* !USE_BUILTIN_FMAF */
78