| /*- |
| * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include <fenv.h> |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| /* |
| * Fused multiply-add: Compute x * y + z with a single rounding error. |
| * |
| * A double has more than twice as much precision than a float, so |
| * direct double-precision arithmetic suffices, except where double |
| * rounding occurs. |
| */ |
| float |
| fmaf(float x, float y, float z) |
| { |
| double xy, result; |
| uint32_t hr, lr; |
| |
| xy = (double)x * y; |
| result = xy + z; |
| EXTRACT_WORDS(hr, lr, result); |
| /* Common case: The double precision result is fine. */ |
| if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */ |
| (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */ |
| result - xy == z || /* exact */ |
| fegetround() != FE_TONEAREST) /* not round-to-nearest */ |
| return (result); |
| |
| /* |
| * If result is inexact, and exactly halfway between two float values, |
| * we need to adjust the low-order bit in the direction of the error. |
| */ |
| fesetround(FE_TOWARDZERO); |
| volatile double vxy = xy; /* XXX work around gcc CSE bug */ |
| double adjusted_result = vxy + z; |
| fesetround(FE_TONEAREST); |
| if (result == adjusted_result) |
| SET_LOW_WORD(adjusted_result, lr + 1); |
| return (adjusted_result); |
| } |
