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       1                 :             : /*-
       2                 :             :  * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
       3                 :             :  * All rights reserved.
       4                 :             :  *
       5                 :             :  * Redistribution and use in source and binary forms, with or without
       6                 :             :  * modification, are permitted provided that the following conditions
       7                 :             :  * are met:
       8                 :             :  * 1. Redistributions of source code must retain the above copyright
       9                 :             :  *    notice, this list of conditions and the following disclaimer.
      10                 :             :  * 2. Redistributions in binary form must reproduce the above copyright
      11                 :             :  *    notice, this list of conditions and the following disclaimer in the
      12                 :             :  *    documentation and/or other materials provided with the distribution.
      13                 :             :  *
      14                 :             :  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
      15                 :             :  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
      16                 :             :  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
      17                 :             :  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
      18                 :             :  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
      19                 :             :  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
      20                 :             :  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
      21                 :             :  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
      22                 :             :  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
      23                 :             :  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
      24                 :             :  * SUCH DAMAGE.
      25                 :             :  */
      26                 :             : 
      27                 :             : #include "cdefs-compat.h"
      28                 :             : //__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaf.c,v 1.3 2011/10/15 04:16:58 das Exp $");
      29                 :             : 
      30                 :             : #include <openlibm_fenv.h>
      31                 :             : #include <openlibm_math.h>
      32                 :             : 
      33                 :             : #include "math_private.h"
      34                 :             : 
      35                 :             : /*
      36                 :             :  * Fused multiply-add: Compute x * y + z with a single rounding error.
      37                 :             :  *
      38                 :             :  * A double has more than twice as much precision than a float, so
      39                 :             :  * direct double-precision arithmetic suffices, except where double
      40                 :             :  * rounding occurs.
      41                 :             :  */
      42                 :             : OLM_DLLEXPORT float
      43                 :          16 : fmaf(float x, float y, float z)
      44                 :             : {
      45                 :             :         double xy, result;
      46                 :             :         u_int32_t hr, lr;
      47                 :             : 
      48                 :          16 :         xy = (double)x * y;
      49                 :          16 :         result = xy + z;
      50                 :          16 :         EXTRACT_WORDS(hr, lr, result);
      51                 :             :         /* Common case: The double precision result is fine. */
      52         [ -  + ]:          16 :         if ((lr & 0x1fffffff) != 0x10000000 ||      /* not a halfway case */
      53         [ #  # ]:           0 :             (hr & 0x7ff00000) == 0x7ff00000 ||      /* NaN */
      54   [ #  #  #  # ]:           0 :             result - xy == z ||                 /* exact */
      55                 :           0 :             fegetround() != FE_TONEAREST)       /* not round-to-nearest */
      56                 :          16 :                 return (result);
      57                 :             : 
      58                 :             :         /*
      59                 :             :          * If result is inexact, and exactly halfway between two float values,
      60                 :             :          * we need to adjust the low-order bit in the direction of the error.
      61                 :             :          */
      62                 :           0 :         fesetround(FE_TOWARDZERO);
      63                 :           0 :         volatile double vxy = xy;  /* XXX work around gcc CSE bug */
      64                 :           0 :         double adjusted_result = vxy + z;
      65                 :           0 :         fesetround(FE_TONEAREST);
      66         [ #  # ]:           0 :         if (result == adjusted_result)
      67                 :           0 :                 SET_LOW_WORD(adjusted_result, lr + 1);
      68                 :           0 :         return (adjusted_result);
      69                 :             : }