src/math/fmaf.c

   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         double err;
  81         int neg = u.i >> 63;
  82         if (neg == (z > xy))
  83                 err = xy - result + z;
  84         else
  85                 err = z - result + xy;
  86         if (neg == (err < 0))
  87                 u.i++;
  88         else
  89                 u.i--;
  90         z = u.f;
  91         return z;
  92 }