github.com/afumu/libc@v0.0.6/musl/src/math/fmaf.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
     2  /*-
     3   * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
     4   * All rights reserved.
     5   *
     6   * Redistribution and use in source and binary forms, with or without
     7   * modification, are permitted provided that the following conditions
     8   * are met:
     9   * 1. Redistributions of source code must retain the above copyright
    10   *    notice, this list of conditions and the following disclaimer.
    11   * 2. Redistributions in binary form must reproduce the above copyright
    12   *    notice, this list of conditions and the following disclaimer in the
    13   *    documentation and/or other materials provided with the distribution.
    14   *
    15   * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
    16   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
    17   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
    18   * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
    19   * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
    20   * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
    21   * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
    22   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
    23   * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
    24   * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
    25   * SUCH DAMAGE.
    26   */
    27  
    28  #include <fenv.h>
    29  #include <math.h>
    30  #include <stdint.h>
    31  
    32  /*
    33   * Fused multiply-add: Compute x * y + z with a single rounding error.
    34   *
    35   * A double has more than twice as much precision than a float, so
    36   * direct double-precision arithmetic suffices, except where double
    37   * rounding occurs.
    38   */
    39  float fmaf(float x, float y, float z)
    40  {
    41  	#pragma STDC FENV_ACCESS ON
    42  	double xy, result;
    43  	union {double f; uint64_t i;} u;
    44  	int e;
    45  
    46  	xy = (double)x * y;
    47  	result = xy + z;
    48  	u.f = result;
    49  	e = u.i>>52 & 0x7ff;
    50  	/* Common case: The double precision result is fine. */
    51  	if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */
    52  		e == 0x7ff ||                   /* NaN */
    53  		(result - xy == z && result - z == xy) || /* exact */
    54  		fegetround() != FE_TONEAREST)       /* not round-to-nearest */
    55  	{
    56  		/*
    57  		underflow may not be raised correctly, example:
    58  		fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
    59  		*/
    60  #if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
    61  		if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) {
    62  			feclearexcept(FE_INEXACT);
    63  			/* TODO: gcc and clang bug workaround */
    64  			volatile float vz = z;
    65  			result = xy + vz;
    66  			if (fetestexcept(FE_INEXACT))
    67  				feraiseexcept(FE_UNDERFLOW);
    68  			else
    69  				feraiseexcept(FE_INEXACT);
    70  		}
    71  #endif
    72  		z = result;
    73  		return z;
    74  	}
    75  
    76  	/*
    77  	 * If result is inexact, and exactly halfway between two float values,
    78  	 * we need to adjust the low-order bit in the direction of the error.
    79  	 */
    80  #ifdef FE_TOWARDZERO
    81  	fesetround(FE_TOWARDZERO);
    82  #endif
    83  	volatile double vxy = xy;  /* XXX work around gcc CSE bug */
    84  	double adjusted_result = vxy + z;
    85  	fesetround(FE_TONEAREST);
    86  	if (result == adjusted_result) {
    87  		u.f = adjusted_result;
    88  		u.i++;
    89  		adjusted_result = u.f;
    90  	}
    91  	z = adjusted_result;
    92  	return z;
    93  }