/*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * 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" #ifdef USE_BUILTIN_FMAF float fmaf(float x, float y, float z) { return (__builtin_fmaf(x, y, z)); } #else /* * 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); } #endif /* !USE_BUILTIN_FMAF */