11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/*- 2a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * All rights reserved. 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Redistribution and use in source and binary forms, with or without 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * modification, are permitted provided that the following conditions 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * are met: 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. Redistributions of source code must retain the above copyright 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * notice, this list of conditions and the following disclaimer. 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. Redistributions in binary form must reproduce the above copyright 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * notice, this list of conditions and the following disclaimer in the 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * documentation and/or other materials provided with the distribution. 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * SUCH DAMAGE. 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include <sys/cdefs.h> 28a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 29a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 30a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <fenv.h> 31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 32a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math.h" 33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math_private.h" 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Fused multiply-add: Compute x * y + z with a single rounding error. 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * A double has more than twice as much precision than a float, so 39a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * direct double-precision arithmetic suffices, except where double 40a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * rounding occurs. 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectfloat 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectfmaf(float x, float y, float z) 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 45a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double xy, result; 46a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes uint32_t hr, lr; 47a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes xy = (double)x * y; 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes result = xy + z; 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes EXTRACT_WORDS(hr, lr, result); 51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* Common case: The double precision result is fine. */ 52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */ 53a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */ 54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes result - xy == z || /* exact */ 55a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes fegetround() != FE_TONEAREST) /* not round-to-nearest */ 56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (result); 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 58a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* 59a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * If result is inexact, and exactly halfway between two float values, 60a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * we need to adjust the low-order bit in the direction of the error. 61a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes fesetround(FE_TOWARDZERO); 63a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes volatile double vxy = xy; /* XXX work around gcc CSE bug */ 64a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double adjusted_result = vxy + z; 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes fesetround(FE_TONEAREST); 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (result == adjusted_result) 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes SET_LOW_WORD(adjusted_result, lr + 1); 68a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (adjusted_result); 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 70