lib/libm/src/s_fmaf.c

   1 /*      $NetBSD: s_fmaf.c,v 1.2 2013/02/11 01:29:58 christos Exp $      */
   2
   3 /*-
   4  * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
   5  * All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice, this list of conditions and the following disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  17  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  18  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  19  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  20  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  21  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  22  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  23  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  24  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  25  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  26  * SUCH DAMAGE.
  27  */
  28
  29 #include <sys/cdefs.h>
  30 #if 0
  31 __FBSDID("$FreeBSD: src/lib/msun/src/s_fmaf.c,v 1.3 2011/10/15 04:16:58 das Exp $");
  32 #else
  33 __RCSID("$NetBSD: s_fmaf.c,v 1.2 2013/02/11 01:29:58 christos Exp $");
  34 #endif
  35
  36 #include <fenv.h>
  37
  38 #include "math.h"
  39 #include "math_private.h"
  40
  41 /*
  42  * Fused multiply-add: Compute x * y + z with a single rounding error.
  43  *
  44  * A double has more than twice as much precision than a float, so
  45  * direct double-precision arithmetic suffices, except where double
  46  * rounding occurs.
  47  */
  48 float
  49 fmaf(float x, float y, float z)
  50 {
  51         double xy, result;
  52         uint32_t hr, lr;
  53
  54         xy = (double)x * y;
  55         result = xy + z;
  56         EXTRACT_WORDS(hr, lr, result);
  57         /* Common case: The double precision result is fine. */
  58         if ((lr & 0x1fffffff) != 0x10000000 ||  /* not a halfway case */
  59             (hr & 0x7ff00000) == 0x7ff00000 ||  /* NaN */
  60             result - xy == z ||                 /* exact */
  61             fegetround() != FE_TONEAREST)       /* not round-to-nearest */
  62                 return (result);
  63
  64         /*
  65          * If result is inexact, and exactly halfway between two float values,
  66          * we need to adjust the low-order bit in the direction of the error.
  67          */
  68         fesetround(FE_TOWARDZERO);
  69         volatile double vxy = xy;  /* XXX work around gcc CSE bug */
  70         double adjusted_result = vxy + z;
  71         fesetround(FE_TONEAREST);
  72         if (result == adjusted_result)
  73                 SET_LOW_WORD(adjusted_result, lr + 1);
  74         return (adjusted_result);
  75 }