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 */
42 float
fmaf(float x,float y,float z)43 fmaf(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