1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 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 __FBSDID("$FreeBSD$"); 31 32 #include <fenv.h> 33 34 #include "math.h" 35 #include "math_private.h" 36 37 #ifdef USE_BUILTIN_FMAF 38 float 39 fmaf(float x, float y, float z) 40 { 41 return (__builtin_fmaf(x, y, z)); 42 } 43 #else 44 /* 45 * Fused multiply-add: Compute x * y + z with a single rounding error. 46 * 47 * A double has more than twice as much precision than a float, so 48 * direct double-precision arithmetic suffices, except where double 49 * rounding occurs. 50 */ 51 float 52 fmaf(float x, float y, float z) 53 { 54 double xy, result; 55 uint32_t hr, lr; 56 57 xy = (double)x * y; 58 result = xy + z; 59 EXTRACT_WORDS(hr, lr, result); 60 /* Common case: The double precision result is fine. */ 61 if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */ 62 (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */ 63 result - xy == z || /* exact */ 64 fegetround() != FE_TONEAREST) /* not round-to-nearest */ 65 return (result); 66 67 /* 68 * If result is inexact, and exactly halfway between two float values, 69 * we need to adjust the low-order bit in the direction of the error. 70 */ 71 fesetround(FE_TOWARDZERO); 72 volatile double vxy = xy; /* XXX work around gcc CSE bug */ 73 double adjusted_result = vxy + z; 74 fesetround(FE_TONEAREST); 75 if (result == adjusted_result) 76 SET_LOW_WORD(adjusted_result, lr + 1); 77 return (adjusted_result); 78 } 79 #endif /* !USE_BUILTIN_FMAF */ 80