/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ Musl Libc │
│ Copyright © 2005-2014 Rich Felker, et al. │
│ │
│ Permission is hereby granted, free of charge, to any person obtaining │
│ a copy of this software and associated documentation files (the │
│ "Software"), to deal in the Software without restriction, including │
│ without limitation the rights to use, copy, modify, merge, publish, │
│ distribute, sublicense, and/or sell copies of the Software, and to │
│ permit persons to whom the Software is furnished to do so, subject to │
│ the following conditions: │
│ │
│ The above copyright notice and this permission notice shall be │
│ included in all copies or substantial portions of the Software. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
asm(".ident\t\"\\n\\n\
Fused Multiply Add (MIT License)\\n\
Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* 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.
*/
/**
* Performs fused multiply add.
*
* @return `𝑥 * 𝑦 + 𝑧` with a single rounding error
*/
float fmaf(float x, float y, float z)
{
#if defined(__x86_64__) && defined(__FMA__)
// Intel Haswell+ (c. 2013)
// AMD Piledriver+ (c. 2011)
asm("vfmadd132ss\t%1,%2,%0" : "+x"(x) : "x"(y), "x"(z));
return x;
#elif defined(__x86_64__) && defined(__FMA4__)
// AMD Bulldozer+ (c. 2011)
asm("vfmaddss\t%3,%2,%1,%0" : "=x"(x) : "x"(x), "x"(y), "x"(z));
return x;
#elif defined(__aarch64__)
asm("fmadd\t%s0,%s1,%s2,%s3" : "=w"(x) : "w"(x), "w"(y), "w"(z));
return x;
#elif defined(__powerpc64__)
asm("fmadds\t%0,%1,%2,%3" : "=f"(x) : "f"(x), "f"(y), "f"(z));
return x;
#elif defined(__riscv) && __riscv_flen >= 32
asm("fmadd.s\t%0,%1,%2,%3" : "=f"(x) : "f"(x), "f"(y), "f"(z));
return x;
#elif defined(__s390x__)
asm("maebr\t%0,%1,%2" : "+f"(z) : "f"(x), "f"(y));
return z;
#else
/* A double has more than twice as much precision than a float,
so direct double-precision arithmetic suffices, except where
double rounding occurs. */
/* #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 && result - z == xy) || /* 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.
*/
double err;
int neg = u.i >> 63;
if (neg == (z > xy))
err = xy - result + z;
else
err = z - result + xy;
if (neg == (err < 0))
u.i++;
else
u.i--;
z = u.f;
return z;
#endif /* __x86_64__ */
}