2 * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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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
26 * FreeBSD SVN: 226371 (2011-10-15)
31 #include "math_private.h"
34 * Fused multiply-add: Compute x * y + z with a single rounding error.
36 * A double has more than twice as much precision than a float, so
37 * direct double-precision arithmetic suffices, except where double
41 fmaf(float x, float y, float z)
48 EXTRACT_WORDS(hr, lr, result);
49 /* Common case: The double precision result is fine. */
50 if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */
51 (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */
52 result - xy == z || /* exact */
53 fegetround() != FE_TONEAREST) /* not round-to-nearest */
57 * If result is inexact, and exactly halfway between two float values,
58 * we need to adjust the low-order bit in the direction of the error.
60 fesetround(FE_TOWARDZERO);
61 volatile double vxy = xy; /* XXX work around gcc CSE bug */
62 double adjusted_result = vxy + z;
63 fesetround(FE_TONEAREST);
64 if (result == adjusted_result)
65 SET_LOW_WORD(adjusted_result, lr + 1);
66 return (adjusted_result);