1 /* $NetBSD: s_fmaf.c,v 1.3 2017/05/06 18:02:52 christos Exp $ */
2
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 #if 0
31 __FBSDID("$FreeBSD: src/lib/msun/src/s_fmaf.c,v 1.3 2011/10/15 04:16:58 das Exp $");
32 #else
33 __RCSID("$NetBSD: s_fmaf.c,v 1.3 2017/05/06 18:02:52 christos Exp $");
34 #endif
35
36 #include "namespace.h"
37
38 #include <fenv.h>
39
40 #include "math.h"
41 #include "math_private.h"
42
43 /*
44 * Fused multiply-add: Compute x * y + z with a single rounding error.
45 *
46 * A double has more than twice as much precision than a float, so
47 * direct double-precision arithmetic suffices, except where double
48 * rounding occurs.
49 */
50 float
fmaf(float x,float y,float z)51 fmaf(float x, float y, float z)
52 {
53 double xy, result;
54 uint32_t hr, lr;
55
56 xy = (double)x * y;
57 result = xy + z;
58 EXTRACT_WORDS(hr, lr, result);
59 /* Common case: The double precision result is fine. */
60 if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */
61 (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */
62 result - xy == z || /* exact */
63 fegetround() != FE_TONEAREST) /* not round-to-nearest */
64 return (result);
65
66 /*
67 * If result is inexact, and exactly halfway between two float values,
68 * we need to adjust the low-order bit in the direction of the error.
69 */
70 fesetround(FE_TOWARDZERO);
71 volatile double vxy = xy; /* XXX work around gcc CSE bug */
72 double adjusted_result = vxy + z;
73 fesetround(FE_TONEAREST);
74 if (result == adjusted_result)
75 SET_LOW_WORD(adjusted_result, lr + 1);
76 return (adjusted_result);
77 }
78