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[/] [openrisc/] [trunk/] [gnu-dev/] [or1k-gcc/] [libquadmath/] [math/] [fmaq.c] - Blame information for rev 847

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1 740 jeremybenn
/* Compute x * y + z as ternary operation.
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   Copyright (C) 2010 Free Software Foundation, Inc.
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   This file is part of the GNU C Library.
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   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
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   The GNU C Library is free software; you can redistribute it and/or
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   modify it under the terms of the GNU Lesser General Public
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   License as published by the Free Software Foundation; either
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   version 2.1 of the License, or (at your option) any later version.
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   The GNU C Library is distributed in the hope that it will be useful,
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   but WITHOUT ANY WARRANTY; without even the implied warranty of
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   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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   Lesser General Public License for more details.
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   You should have received a copy of the GNU Lesser General Public
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   License along with the GNU C Library; if not, write to the Free
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   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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   02111-1307 USA.  */
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#include "quadmath-imp.h"
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#include <math.h>
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#include <float.h>
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#ifdef HAVE_FENV_H
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# include <fenv.h>
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# if defined HAVE_FEHOLDEXCEPT && defined HAVE_FESETROUND \
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     && defined HAVE_FEUPDATEENV && defined HAVE_FETESTEXCEPT \
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     && defined FE_TOWARDZERO && defined FE_INEXACT
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#  define USE_FENV_H
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# endif
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#endif
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/* This implementation uses rounding to odd to avoid problems with
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   double rounding.  See a paper by Boldo and Melquiond:
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   http://www.lri.fr/~melquion/doc/08-tc.pdf  */
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__float128
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fmaq (__float128 x, __float128 y, __float128 z)
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{
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  ieee854_float128 u, v, w;
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  int adjust = 0;
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  u.value = x;
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  v.value = y;
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  w.value = z;
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  if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
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                        >= 0x7fff + IEEE854_FLOAT128_BIAS
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                           - FLT128_MANT_DIG, 0)
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      || __builtin_expect (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
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      || __builtin_expect (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
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      || __builtin_expect (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
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      || __builtin_expect (u.ieee.exponent + v.ieee.exponent
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                           <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG, 0))
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    {
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      /* If z is Inf, but x and y are finite, the result should be
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         z rather than NaN.  */
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      if (w.ieee.exponent == 0x7fff
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          && u.ieee.exponent != 0x7fff
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          && v.ieee.exponent != 0x7fff)
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        return (z + x) + y;
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      /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
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         or if x * y is less than half of FLT128_DENORM_MIN,
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         compute as x * y + z.  */
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      if (u.ieee.exponent == 0x7fff
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          || v.ieee.exponent == 0x7fff
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          || w.ieee.exponent == 0x7fff
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          || u.ieee.exponent + v.ieee.exponent
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             > 0x7fff + IEEE854_FLOAT128_BIAS
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          || u.ieee.exponent + v.ieee.exponent
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             < IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG - 2)
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        return x * y + z;
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      if (u.ieee.exponent + v.ieee.exponent
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          >= 0x7fff + IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG)
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        {
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          /* Compute 1p-113 times smaller result and multiply
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             at the end.  */
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          if (u.ieee.exponent > v.ieee.exponent)
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            u.ieee.exponent -= FLT128_MANT_DIG;
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          else
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            v.ieee.exponent -= FLT128_MANT_DIG;
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          /* If x + y exponent is very large and z exponent is very small,
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             it doesn't matter if we don't adjust it.  */
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          if (w.ieee.exponent > FLT128_MANT_DIG)
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            w.ieee.exponent -= FLT128_MANT_DIG;
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          adjust = 1;
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        }
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      else if (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
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        {
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          /* Similarly.
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             If z exponent is very large and x and y exponents are
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             very small, it doesn't matter if we don't adjust it.  */
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          if (u.ieee.exponent > v.ieee.exponent)
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            {
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              if (u.ieee.exponent > FLT128_MANT_DIG)
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                u.ieee.exponent -= FLT128_MANT_DIG;
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            }
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          else if (v.ieee.exponent > FLT128_MANT_DIG)
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            v.ieee.exponent -= FLT128_MANT_DIG;
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          w.ieee.exponent -= FLT128_MANT_DIG;
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          adjust = 1;
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        }
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      else if (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
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        {
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          u.ieee.exponent -= FLT128_MANT_DIG;
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          if (v.ieee.exponent)
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            v.ieee.exponent += FLT128_MANT_DIG;
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          else
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            v.value *= 0x1p113Q;
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        }
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      else if (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
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        {
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          v.ieee.exponent -= FLT128_MANT_DIG;
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          if (u.ieee.exponent)
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            u.ieee.exponent += FLT128_MANT_DIG;
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          else
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            u.value *= 0x1p113Q;
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        }
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      else /* if (u.ieee.exponent + v.ieee.exponent
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                  <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG) */
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        {
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          if (u.ieee.exponent > v.ieee.exponent)
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            u.ieee.exponent += 2 * FLT128_MANT_DIG;
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          else
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            v.ieee.exponent += 2 * FLT128_MANT_DIG;
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          if (w.ieee.exponent <= 4 * FLT128_MANT_DIG + 4)
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            {
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              if (w.ieee.exponent)
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                w.ieee.exponent += 2 * FLT128_MANT_DIG;
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              else
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                w.value *= 0x1p226Q;
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              adjust = -1;
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            }
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          /* Otherwise x * y should just affect inexact
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             and nothing else.  */
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        }
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      x = u.value;
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      y = v.value;
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      z = w.value;
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    }
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  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
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#define C ((1LL << (FLT128_MANT_DIG + 1) / 2) + 1)
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  __float128 x1 = x * C;
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  __float128 y1 = y * C;
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  __float128 m1 = x * y;
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  x1 = (x - x1) + x1;
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  y1 = (y - y1) + y1;
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  __float128 x2 = x - x1;
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  __float128 y2 = y - y1;
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  __float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
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  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
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  __float128 a1 = z + m1;
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  __float128 t1 = a1 - z;
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  __float128 t2 = a1 - t1;
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  t1 = m1 - t1;
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  t2 = z - t2;
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  __float128 a2 = t1 + t2;
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#ifdef USE_FENV_H
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  fenv_t env;
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  feholdexcept (&env);
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  fesetround (FE_TOWARDZERO);
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#endif
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  /* Perform m2 + a2 addition with round to odd.  */
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  u.value = a2 + m2;
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  if (__builtin_expect (adjust == 0, 1))
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    {
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#ifdef USE_FENV_H
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      if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
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        u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
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      feupdateenv (&env);
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#endif
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      /* Result is a1 + u.value.  */
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      return a1 + u.value;
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    }
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  else if (__builtin_expect (adjust > 0, 1))
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    {
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#ifdef USE_FENV_H
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      if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
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        u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
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      feupdateenv (&env);
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#endif
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      /* Result is a1 + u.value, scaled up.  */
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      return (a1 + u.value) * 0x1p113Q;
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    }
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  else
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    {
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#ifdef USE_FENV_H
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      if ((u.ieee.mant_low & 1) == 0)
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        u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
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#endif
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      v.value = a1 + u.value;
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      /* Ensure the addition is not scheduled after fetestexcept call.  */
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      asm volatile ("" : : "m" (v));
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#ifdef USE_FENV_H
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      int j = fetestexcept (FE_INEXACT) != 0;
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      feupdateenv (&env);
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#else
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      int j = 0;
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#endif
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      /* Ensure the following computations are performed in default rounding
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         mode instead of just reusing the round to zero computation.  */
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      asm volatile ("" : "=m" (u) : "m" (u));
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      /* If a1 + u.value is exact, the only rounding happens during
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         scaling down.  */
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      if (j == 0)
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        return v.value * 0x1p-226Q;
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      /* If result rounded to zero is not subnormal, no double
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         rounding will occur.  */
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      if (v.ieee.exponent > 226)
211
        return (a1 + u.value) * 0x1p-226Q;
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      /* If v.value * 0x1p-226Q with round to zero is a subnormal above
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         or equal to FLT128_MIN / 2, then v.value * 0x1p-226Q shifts mantissa
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         down just by 1 bit, which means v.ieee.mant_low |= j would
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         change the round bit, not sticky or guard bit.
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         v.value * 0x1p-226Q never normalizes by shifting up,
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         so round bit plus sticky bit should be already enough
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         for proper rounding.  */
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      if (v.ieee.exponent == 226)
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        {
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          /* v.ieee.mant_low & 2 is LSB bit of the result before rounding,
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             v.ieee.mant_low & 1 is the round bit and j is our sticky
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             bit.  In round-to-nearest 001 rounds down like 00,
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             011 rounds up, even though 01 rounds down (thus we need
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             to adjust), 101 rounds down like 10 and 111 rounds up
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             like 11.  */
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          if ((v.ieee.mant_low & 3) == 1)
228
            {
229
              v.value *= 0x1p-226Q;
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              if (v.ieee.negative)
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                return v.value - 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
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              else
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                return v.value + 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
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            }
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          else
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            return v.value * 0x1p-226Q;
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        }
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      v.ieee.mant_low |= j;
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      return v.value * 0x1p-226Q;
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    }
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}

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