1 /*- 2 * Copyright (c) 2005-2011 David Schultz <das (at) 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 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
