1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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/*
38 * Fused multiply-add: Compute x * y + z with a single rounding error.
39 *
40 * A double has more than twice as much precision than a float, so
41 * direct double-precision arithmetic suffices, except where double
42 * rounding occurs.
43 */
44float
45fmaf(float x, float y, float z)
46{
47	double xy, result;
48	uint32_t hr, lr;
49
50	xy = (double)x * y;
51	result = xy + z;
52	EXTRACT_WORDS(hr, lr, result);
53	/* Common case: The double precision result is fine. */
54	if ((lr & 0x1fffffff) != 0x10000000 ||	/* not a halfway case */
55	    (hr & 0x7ff00000) == 0x7ff00000 ||	/* NaN */
56	    result - xy == z ||			/* exact */
57	    fegetround() != FE_TONEAREST)	/* not round-to-nearest */
58		return (result);
59
60	/*
61	 * If result is inexact, and exactly halfway between two float values,
62	 * we need to adjust the low-order bit in the direction of the error.
63	 */
64	fesetround(FE_TOWARDZERO);
65	volatile double vxy = xy;  /* XXX work around gcc CSE bug */
66	double adjusted_result = vxy + z;
67	fesetround(FE_TONEAREST);
68	if (result == adjusted_result)
69		SET_LOW_WORD(adjusted_result, lr + 1);
70	return (adjusted_result);
71}
72