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