| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 1 | /*- |
| 2 | * Copyright (c) 2005-2011 David Schultz <das@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 | } |