| /* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */ |
| /*- |
| * 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 <fenv.h> |
| #include <math.h> |
| #include <stdint.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) |
| { |
| #pragma STDC FENV_ACCESS ON |
| double xy, result; |
| union {double f; uint64_t i;} u; |
| int e; |
| |
| xy = (double)x * y; |
| result = xy + z; |
| u.f = result; |
| e = u.i>>52 & 0x7ff; |
| /* Common case: The double precision result is fine. */ |
| if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */ |
| e == 0x7ff || /* NaN */ |
| result - xy == z || /* exact */ |
| fegetround() != FE_TONEAREST) /* not round-to-nearest */ |
| { |
| /* |
| underflow may not be raised correctly, example: |
| fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f) |
| */ |
| #if defined(FE_INEXACT) && defined(FE_UNDERFLOW) |
| if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) { |
| feclearexcept(FE_INEXACT); |
| /* TODO: gcc and clang bug workaround */ |
| volatile float vz = z; |
| result = xy + vz; |
| if (fetestexcept(FE_INEXACT)) |
| feraiseexcept(FE_UNDERFLOW); |
| else |
| feraiseexcept(FE_INEXACT); |
| } |
| #endif |
| z = result; |
| return z; |
| } |
| |
| /* |
| * 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. |
| */ |
| #ifdef FE_TOWARDZERO |
| fesetround(FE_TOWARDZERO); |
| #endif |
| volatile double vxy = xy; /* XXX work around gcc CSE bug */ |
| double adjusted_result = vxy + z; |
| fesetround(FE_TONEAREST); |
| if (result == adjusted_result) { |
| u.f = adjusted_result; |
| u.i++; |
| adjusted_result = u.f; |
| } |
| z = adjusted_result; |
| return z; |
| } |