/* 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.
 */

#include <fenv.h>
#include <math.h>
#include <stdint.h>
#include "libm.h"

/*
 * Fused multiply-add: Compute x * y + z with a single rounding error.
 *
 * A double has more than twice as much precision than a float, so
 * direct double-precision arithmetic suffices, except where double
 * rounding occurs.
 */
float fmaf(float x, float y, float z) {
  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 ||                 /* 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.
 */
#ifdef FE_TOWARDZERO
  fesetround(FE_TOWARDZERO);
#endif
  volatile double vxy = xy; /* XXX work around gcc CSE bug */
  double adjusted_result = vxy + z;
  fesetround(FE_TONEAREST);
  if (result == adjusted_result) {
    u.f = adjusted_result;
    u.i++;
    adjusted_result = u.f;
  }
  z = adjusted_result;
  return z;
}