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1 files changed, 241 insertions, 0 deletions

diff --git a/libquadmath/math/fmaq.c b/libquadmath/math/fmaq.c
new file mode 100644
index 000000000..126b0a2d2
--- /dev/null
+++ b/libquadmath/math/fmaq.c
@@ -0,0 +1,241 @@
+/* Compute x * y + z as ternary operation.
+   Copyright (C) 2010 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#include "quadmath-imp.h"
+#include <math.h>
+#include <float.h>
+#ifdef HAVE_FENV_H
+# include <fenv.h>
+# if defined HAVE_FEHOLDEXCEPT && defined HAVE_FESETROUND \
+     && defined HAVE_FEUPDATEENV && defined HAVE_FETESTEXCEPT \
+     && defined FE_TOWARDZERO && defined FE_INEXACT
+#  define USE_FENV_H
+# endif
+#endif
+
+/* This implementation uses rounding to odd to avoid problems with
+   double rounding.  See a paper by Boldo and Melquiond:
+   http://www.lri.fr/~melquion/doc/08-tc.pdf  */
+
+__float128
+fmaq (__float128 x, __float128 y, __float128 z)
+{
+  ieee854_float128 u, v, w;
+  int adjust = 0;
+  u.value = x;
+  v.value = y;
+  w.value = z;
+  if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
+			>= 0x7fff + IEEE854_FLOAT128_BIAS
+			   - FLT128_MANT_DIG, 0)
+      || __builtin_expect (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
+      || __builtin_expect (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
+      || __builtin_expect (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
+      || __builtin_expect (u.ieee.exponent + v.ieee.exponent
+			   <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG, 0))
+    {
+      /* If z is Inf, but x and y are finite, the result should be
+	 z rather than NaN.  */
+      if (w.ieee.exponent == 0x7fff
+	  && u.ieee.exponent != 0x7fff
+          && v.ieee.exponent != 0x7fff)
+	return (z + x) + y;
+      /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
+	 or if x * y is less than half of FLT128_DENORM_MIN,
+	 compute as x * y + z.  */
+      if (u.ieee.exponent == 0x7fff
+	  || v.ieee.exponent == 0x7fff
+	  || w.ieee.exponent == 0x7fff
+	  || u.ieee.exponent + v.ieee.exponent
+	     > 0x7fff + IEEE854_FLOAT128_BIAS
+	  || u.ieee.exponent + v.ieee.exponent
+	     < IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG - 2)
+	return x * y + z;
+      if (u.ieee.exponent + v.ieee.exponent
+	  >= 0x7fff + IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG)
+	{
+	  /* Compute 1p-113 times smaller result and multiply
+	     at the end.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    u.ieee.exponent -= FLT128_MANT_DIG;
+	  else
+	    v.ieee.exponent -= FLT128_MANT_DIG;
+	  /* If x + y exponent is very large and z exponent is very small,
+	     it doesn't matter if we don't adjust it.  */
+	  if (w.ieee.exponent > FLT128_MANT_DIG)
+	    w.ieee.exponent -= FLT128_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
+	{
+	  /* Similarly.
+	     If z exponent is very large and x and y exponents are
+	     very small, it doesn't matter if we don't adjust it.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    {
+	      if (u.ieee.exponent > FLT128_MANT_DIG)
+		u.ieee.exponent -= FLT128_MANT_DIG;
+	    }
+	  else if (v.ieee.exponent > FLT128_MANT_DIG)
+	    v.ieee.exponent -= FLT128_MANT_DIG;
+	  w.ieee.exponent -= FLT128_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
+	{
+	  u.ieee.exponent -= FLT128_MANT_DIG;
+	  if (v.ieee.exponent)
+	    v.ieee.exponent += FLT128_MANT_DIG;
+	  else
+	    v.value *= 0x1p113Q;
+	}
+      else if (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
+	{
+	  v.ieee.exponent -= FLT128_MANT_DIG;
+	  if (u.ieee.exponent)
+	    u.ieee.exponent += FLT128_MANT_DIG;
+	  else
+	    u.value *= 0x1p113Q;
+	}
+      else /* if (u.ieee.exponent + v.ieee.exponent
+		  <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG) */
+	{
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    u.ieee.exponent += 2 * FLT128_MANT_DIG;
+	  else
+	    v.ieee.exponent += 2 * FLT128_MANT_DIG;
+	  if (w.ieee.exponent <= 4 * FLT128_MANT_DIG + 4)
+	    {
+	      if (w.ieee.exponent)
+		w.ieee.exponent += 2 * FLT128_MANT_DIG;
+	      else
+		w.value *= 0x1p226Q;
+	      adjust = -1;
+	    }
+	  /* Otherwise x * y should just affect inexact
+	     and nothing else.  */
+	}
+      x = u.value;
+      y = v.value;
+      z = w.value;
+    }
+  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
+#define C ((1LL << (FLT128_MANT_DIG + 1) / 2) + 1)
+  __float128 x1 = x * C;
+  __float128 y1 = y * C;
+  __float128 m1 = x * y;
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  __float128 x2 = x - x1;
+  __float128 y2 = y - y1;
+  __float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
+
+  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
+  __float128 a1 = z + m1;
+  __float128 t1 = a1 - z;
+  __float128 t2 = a1 - t1;
+  t1 = m1 - t1;
+  t2 = z - t2;
+  __float128 a2 = t1 + t2;
+
+#ifdef USE_FENV_H
+  fenv_t env;
+  feholdexcept (&env);
+  fesetround (FE_TOWARDZERO);
+#endif
+  /* Perform m2 + a2 addition with round to odd.  */
+  u.value = a2 + m2;
+
+  if (__builtin_expect (adjust == 0, 1))
+    {
+#ifdef USE_FENV_H
+      if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
+	u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
+      feupdateenv (&env);
+#endif
+      /* Result is a1 + u.value.  */
+      return a1 + u.value;
+    }
+  else if (__builtin_expect (adjust > 0, 1))
+    {
+#ifdef USE_FENV_H
+      if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
+	u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
+      feupdateenv (&env);
+#endif
+      /* Result is a1 + u.value, scaled up.  */
+      return (a1 + u.value) * 0x1p113Q;
+    }
+  else
+    {
+#ifdef USE_FENV_H
+      if ((u.ieee.mant_low & 1) == 0)
+	u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
+#endif
+      v.value = a1 + u.value;
+      /* Ensure the addition is not scheduled after fetestexcept call.  */
+      asm volatile ("" : : "m" (v));
+#ifdef USE_FENV_H
+      int j = fetestexcept (FE_INEXACT) != 0;
+      feupdateenv (&env);
+#else
+      int j = 0;
+#endif
+      /* Ensure the following computations are performed in default rounding
+	 mode instead of just reusing the round to zero computation.  */
+      asm volatile ("" : "=m" (u) : "m" (u));
+      /* If a1 + u.value is exact, the only rounding happens during
+	 scaling down.  */
+      if (j == 0)
+	return v.value * 0x1p-226Q;
+      /* If result rounded to zero is not subnormal, no double
+	 rounding will occur.  */
+      if (v.ieee.exponent > 226)
+	return (a1 + u.value) * 0x1p-226Q;
+      /* If v.value * 0x1p-226Q with round to zero is a subnormal above
+	 or equal to FLT128_MIN / 2, then v.value * 0x1p-226Q shifts mantissa
+	 down just by 1 bit, which means v.ieee.mant_low |= j would
+	 change the round bit, not sticky or guard bit.
+	 v.value * 0x1p-226Q never normalizes by shifting up,
+	 so round bit plus sticky bit should be already enough
+	 for proper rounding.  */
+      if (v.ieee.exponent == 226)
+	{
+	  /* v.ieee.mant_low & 2 is LSB bit of the result before rounding,
+	     v.ieee.mant_low & 1 is the round bit and j is our sticky
+	     bit.  In round-to-nearest 001 rounds down like 00,
+	     011 rounds up, even though 01 rounds down (thus we need
+	     to adjust), 101 rounds down like 10 and 111 rounds up
+	     like 11.  */
+	  if ((v.ieee.mant_low & 3) == 1)
+	    {
+	      v.value *= 0x1p-226Q;
+	      if (v.ieee.negative)
+		return v.value - 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
+	      else
+		return v.value + 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
+	    }
+	  else
+	    return v.value * 0x1p-226Q;
+	}
+      v.ieee.mant_low |= j;
+      return v.value * 0x1p-226Q;
+    }
+}