1/*-
2 * Copyright (c) 2005-2011 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("$FreeBSD$");
29
30#include <fenv.h>
31
32#include "math.h"
33#include "math_private.h"
34
35/*
36 * Fused multiply-add: Compute x * y + z with a single rounding error.
37 *
38 * A double has more than twice as much precision than a float, so
39 * direct double-precision arithmetic suffices, except where double
40 * rounding occurs.
41 */
42float
43fmaf(float x, float y, float z)
44{
45	double xy, result;
46	uint32_t hr, lr;
47
48	xy = (double)x * y;
49	result = xy + z;
50	EXTRACT_WORDS(hr, lr, result);
51	/* Common case: The double precision result is fine. */
52	if ((lr & 0x1fffffff) != 0x10000000 ||	/* not a halfway case */
53	    (hr & 0x7ff00000) == 0x7ff00000 ||	/* NaN */
54	    result - xy == z ||			/* exact */
55	    fegetround() != FE_TONEAREST)	/* not round-to-nearest */
56		return (result);
57
58	/*
59	 * If result is inexact, and exactly halfway between two float values,
60	 * we need to adjust the low-order bit in the direction of the error.
61	 */
62	fesetround(FE_TOWARDZERO);
63	volatile double vxy = xy;  /* XXX work around gcc CSE bug */
64	double adjusted_result = vxy + z;
65	fesetround(FE_TONEAREST);
66	if (result == adjusted_result)
67		SET_LOW_WORD(adjusted_result, lr + 1);
68	return (adjusted_result);
69}
70