1/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
2/*-
3 * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28#include <fenv.h>
29#include <math.h>
30#include <stdint.h>
31
32/*
33 * Fused multiply-add: Compute x * y + z with a single rounding error.
34 *
35 * A double has more than twice as much precision than a float, so
36 * direct double-precision arithmetic suffices, except where double
37 * rounding occurs.
38 */
39float fmaf(float x, float y, float z)
40{
41	#pragma STDC FENV_ACCESS ON
42	double xy, result;
43	union {double f; uint64_t i;} u;
44	int e;
45
46	xy = (double)x * y;
47	result = xy + z;
48	u.f = result;
49	e = u.i>>52 & 0x7ff;
50	/* Common case: The double precision result is fine. */
51	if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */
52		e == 0x7ff ||                   /* NaN */
53		(result - xy == z && result - z == xy) || /* exact */
54		fegetround() != FE_TONEAREST)       /* not round-to-nearest */
55	{
56		/*
57		underflow may not be raised correctly, example:
58		fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
59		*/
60#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
61		if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) {
62			feclearexcept(FE_INEXACT);
63			/* TODO: gcc and clang bug workaround */
64			volatile float vz = z;
65			result = xy + vz;
66			if (fetestexcept(FE_INEXACT))
67				feraiseexcept(FE_UNDERFLOW);
68			else
69				feraiseexcept(FE_INEXACT);
70		}
71#endif
72		z = result;
73		return z;
74	}
75
76	/*
77	 * If result is inexact, and exactly halfway between two float values,
78	 * we need to adjust the low-order bit in the direction of the error.
79	 */
80#ifdef FE_TOWARDZERO
81	fesetround(FE_TOWARDZERO);
82#endif
83	volatile double vxy = xy;  /* XXX work around gcc CSE bug */
84	double adjusted_result = vxy + z;
85	fesetround(FE_TONEAREST);
86	if (result == adjusted_result) {
87		u.f = adjusted_result;
88		u.i++;
89		adjusted_result = u.f;
90	}
91	z = adjusted_result;
92	return z;
93}
94