Merge changes between r20863 and r21108 from /fsf/trunk.

git-svn-id: svn://svn.eglibc.org/trunk@21109 7b3dc134-2b1b-0410-93df-9e9f96275f8d

15 files changed, 590 insertions, 173 deletions

diff --git a/libc/sysdeps/ieee754/dbl-64/s_fma.c b/libc/sysdeps/ieee754/dbl-64/s_fma.c
index ce3bd36fa..5e21461a4 100644
--- a/libc/sysdeps/ieee754/dbl-64/s_fma.c
+++ b/libc/sysdeps/ieee754/dbl-64/s_fma.c
@@ -49,6 +49,11 @@ __fma (double x, double y, double z)
 	  && u.ieee.exponent != 0x7ff
 	  && v.ieee.exponent != 0x7ff)
 	return (z + x) + y;
+      /* If z is zero and x are y are nonzero, compute the result
+	 as x * y to avoid the wrong sign of a zero result if x * y
+	 underflows to 0.  */
+      if (z == 0 && x != 0 && y != 0)
+	return 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 DBL_DENORM_MIN,
 	 compute as x * y + z.  */
@@ -128,6 +133,11 @@ __fma (double x, double y, double z)
       y = v.d;
       z = w.d;
     }
+
+  /* Ensure correct sign of exact 0 + 0.  */
+  if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
+    return x * y + z;
+
   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
 #define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
   double x1 = x * C;
diff --git a/libc/sysdeps/ieee754/dbl-64/s_fmaf.c b/libc/sysdeps/ieee754/dbl-64/s_fmaf.c
index e7a0650f0..a4f12d9f7 100644
--- a/libc/sysdeps/ieee754/dbl-64/s_fmaf.c
+++ b/libc/sysdeps/ieee754/dbl-64/s_fmaf.c
@@ -32,8 +32,15 @@ float
 __fmaf (float x, float y, float z)
 {
   fenv_t env;
+
   /* Multiplication is always exact.  */
   double temp = (double) x * (double) y;
+
+  /* Ensure correct sign of an exact zero result by performing the
+     addition in the original rounding mode in that case.  */
+  if (temp == -z)
+    return (float) temp + z;
+
   union ieee754_double u;
 
   libc_feholdexcept_setround (&env, FE_TOWARDZERO);
diff --git a/libc/sysdeps/ieee754/dbl-64/x2y2m1.c b/libc/sysdeps/ieee754/dbl-64/x2y2m1.c
new file mode 100644
index 000000000..4badde3be
--- /dev/null
+++ b/libc/sysdeps/ieee754/dbl-64/x2y2m1.c
@@ -0,0 +1,111 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+#include <stdlib.h>
+
+/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
+   given that |X| >= |Y| and the values are small enough that no
+   overflow occurs.  */
+
+static inline void
+add_split (double *hi, double *lo, double x, double y)
+{
+  /* Apply Dekker's algorithm.  */
+  *hi = x + y;
+  *lo = (x - *hi) + y;
+}
+
+/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
+   given that the values are small enough that no overflow occurs and
+   large enough (or zero) that no underflow occurs.  */
+
+static inline void
+mul_split (double *hi, double *lo, double x, double y)
+{
+#ifdef __FP_FAST_FMA
+  /* Fast built-in fused multiply-add.  */
+  *hi = x * y;
+  *lo = __builtin_fma (x, y, -*hi);
+#elif defined FP_FAST_FMA
+  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
+  *hi = x * y;
+  *lo = __fma (x, y, -*hi);
+#else
+  /* Apply Dekker's algorithm.  */
+  *hi = x * y;
+# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+  double x1 = x * C;
+  double y1 = y * C;
+# undef C
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  double x2 = x - x1;
+  double y2 = y - y1;
+  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compare absolute values of floating-point values pointed to by P
+   and Q for qsort.  */
+
+static int
+compare (const void *p, const void *q)
+{
+  double pd = fabs (*(const double *) p);
+  double qd = fabs (*(const double *) q);
+  if (pd < qd)
+    return -1;
+  else if (pd == qd)
+    return 0;
+  else
+    return 1;
+}
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+double
+__x2y2m1 (double x, double y)
+{
+  double vals[4];
+  SET_RESTORE_ROUND (FE_TONEAREST);
+  mul_split (&vals[1], &vals[0], x, x);
+  mul_split (&vals[3], &vals[2], y, y);
+  if (x >= 0.75)
+    vals[1] -= 1.0;
+  else
+    {
+      vals[1] -= 0.5;
+      vals[3] -= 0.5;
+    }
+  qsort (vals, 4, sizeof (double), compare);
+  /* Add up the values so that each element of VALS has absolute value
+     at most equal to the last set bit of the next nonzero
+     element.  */
+  for (size_t i = 0; i <= 2; i++)
+    {
+      add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
+      qsort (vals + i + 1, 3 - i, sizeof (double), compare);
+    }
+  /* Now any error from this addition will be small.  */
+  return vals[3] + vals[2] + vals[1] + vals[0];
+}
diff --git a/libc/sysdeps/ieee754/dbl-64/x2y2m1f.c b/libc/sysdeps/ieee754/dbl-64/x2y2m1f.c
new file mode 100644
index 000000000..fcaa70851
--- /dev/null
+++ b/libc/sysdeps/ieee754/dbl-64/x2y2m1f.c
@@ -0,0 +1,32 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+float
+__x2y2m1f (float x, float y)
+{
+  double dx = x, dy = y;
+  return (float) ((dx - 1) * (dx + 1) + dy * dy);
+}
diff --git a/libc/sysdeps/ieee754/flt-32/s_sincosf.c b/libc/sysdeps/ieee754/flt-32/s_sincosf.c
index 1b4d000e1..c3bd998ab 100644
--- a/libc/sysdeps/ieee754/flt-32/s_sincosf.c
+++ b/libc/sysdeps/ieee754/flt-32/s_sincosf.c
@@ -21,9 +21,14 @@
 
 #include <math_private.h>
 
+#ifndef SINCOSF
+# define SINCOSF_FUNC __sincosf
+#else
+# define SINCOSF_FUNC SINCOSF
+#endif
 
 void
-__sincosf (float x, float *sinx, float *cosx)
+SINCOSF_FUNC (float x, float *sinx, float *cosx)
 {
   int32_t ix;
 
@@ -70,4 +75,7 @@ __sincosf (float x, float *sinx, float *cosx)
 	}
     }
 }
+
+#ifndef SINCOSF
 weak_alias (__sincosf, sincosf)
+#endif
diff --git a/libc/sysdeps/ieee754/ldbl-128/bits/huge_vall.h b/libc/sysdeps/ieee754/ldbl-128/bits/huge_vall.h
deleted file mode 100644
index 89b207331..000000000
--- a/libc/sysdeps/ieee754/ldbl-128/bits/huge_vall.h
+++ /dev/null
@@ -1,50 +0,0 @@
-/* `HUGE_VALL' constant for IEEE 754 machines (where it is infinity).
-   Used by <stdlib.h> and <math.h> functions for overflow.
-   Copyright (C) 1992, 1995, 1996, 1997, 1999, 2000, 2004
-   Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-
-   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, see
-   <http://www.gnu.org/licenses/>.  */
-
-#ifndef _MATH_H
-# error "Never use <bits/huge_vall.h> directly; include <math.h> instead."
-#endif
-
-/* IEEE positive infinity (-HUGE_VAL is negative infinity).  */
-
-#if __GNUC_PREREQ(3,3)
-# define HUGE_VALL	(__builtin_huge_vall())
-#elif __GNUC_PREREQ(2,96)
-# define HUGE_VALL	(__extension__ 0x1.0p32767L)
-#else
-# include <endian.h>
-
-typedef union { unsigned char __c[16]; long double __ld; } __huge_vall_t;
-
-# if __BYTE_ORDER == __BIG_ENDIAN
-#  define __HUGE_VALL_bytes	{ 0x7f, 0xff, 0,0,0,0,0,0,0,0,0,0,0,0,0,0 }
-# endif
-# if __BYTE_ORDER == __LITTLE_ENDIAN
-#  define __HUGE_VALL_bytes	{ 0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0xff, 0x7f }
-# endif
-
-# ifdef __GNUC__
-#  define HUGE_VALL	(__extension__ \
-			 ((__huge_vall_t) { __c : __HUGE_VALL_bytes }).__ld)
-# else
-static __huge_vall_t __huge_vall = { __HUGE_VALL_bytes };
-#  define HUGE_VALL	(__huge_vall.__ld)
-# endif
-#endif 
diff --git a/libc/sysdeps/ieee754/ldbl-128/s_fma.c b/libc/sysdeps/ieee754/ldbl-128/s_fma.c
index 355b60ebb..b08ff29c0 100644
--- a/libc/sysdeps/ieee754/ldbl-128/s_fma.c
+++ b/libc/sysdeps/ieee754/ldbl-128/s_fma.c
@@ -1,5 +1,5 @@
 /* Compute x * y + z as ternary operation.
-   Copyright (C) 2010 Free Software Foundation, Inc.
+   Copyright (C) 2010-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
 
@@ -33,6 +33,12 @@ __fma (double x, double y, double z)
   fenv_t env;
   /* Multiplication is always exact.  */
   long double temp = (long double) x * (long double) y;
+
+  /* Ensure correct sign of an exact zero result by performing the
+     addition in the original rounding mode in that case.  */
+  if (temp == -z)
+    return (double) temp + z;
+
   union ieee854_long_double u;
   feholdexcept (&env);
   fesetround (FE_TOWARDZERO);
diff --git a/libc/sysdeps/ieee754/ldbl-128/s_fmal.c b/libc/sysdeps/ieee754/ldbl-128/s_fmal.c
index 963bbd734..46b3d81ce 100644
--- a/libc/sysdeps/ieee754/ldbl-128/s_fmal.c
+++ b/libc/sysdeps/ieee754/ldbl-128/s_fmal.c
@@ -50,6 +50,11 @@ __fmal (long double x, long double y, long double z)
 	  && u.ieee.exponent != 0x7fff
           && v.ieee.exponent != 0x7fff)
 	return (z + x) + y;
+      /* If z is zero and x are y are nonzero, compute the result
+	 as x * y to avoid the wrong sign of a zero result if x * y
+	 underflows to 0.  */
+      if (z == 0 && x != 0 && y != 0)
+	return 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 LDBL_DENORM_MIN,
 	 compute as x * y + z.  */
@@ -129,6 +134,11 @@ __fmal (long double x, long double y, long double z)
       y = v.d;
       z = w.d;
     }
+
+  /* Ensure correct sign of exact 0 + 0.  */
+  if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
+    return x * y + z;
+
   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
 #define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
   long double x1 = x * C;
diff --git a/libc/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/libc/sysdeps/ieee754/ldbl-128/x2y2m1l.c
new file mode 100644
index 000000000..a249cd347
--- /dev/null
+++ b/libc/sysdeps/ieee754/ldbl-128/x2y2m1l.c
@@ -0,0 +1,111 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+#include <stdlib.h>
+
+/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
+   given that |X| >= |Y| and the values are small enough that no
+   overflow occurs.  */
+
+static inline void
+add_split (long double *hi, long double *lo, long double x, long double y)
+{
+  /* Apply Dekker's algorithm.  */
+  *hi = x + y;
+  *lo = (x - *hi) + y;
+}
+
+/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
+   given that the values are small enough that no overflow occurs and
+   large enough (or zero) that no underflow occurs.  */
+
+static inline void
+mul_split (long double *hi, long double *lo, long double x, long double y)
+{
+#ifdef __FP_FAST_FMAL
+  /* Fast built-in fused multiply-add.  */
+  *hi = x * y;
+  *lo = __builtin_fmal (x, y, -*hi);
+#elif defined FP_FAST_FMAL
+  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
+  *hi = x * y;
+  *lo = __fmal (x, y, -*hi);
+#else
+  /* Apply Dekker's algorithm.  */
+  *hi = x * y;
+# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
+  long double x1 = x * C;
+  long double y1 = y * C;
+# undef C
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  long double x2 = x - x1;
+  long double y2 = y - y1;
+  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compare absolute values of floating-point values pointed to by P
+   and Q for qsort.  */
+
+static int
+compare (const void *p, const void *q)
+{
+  long double pld = fabsl (*(const long double *) p);
+  long double qld = fabsl (*(const long double *) q);
+  if (pld < qld)
+    return -1;
+  else if (pld == qld)
+    return 0;
+  else
+    return 1;
+}
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+long double
+__x2y2m1l (long double x, long double y)
+{
+  long double vals[4];
+  SET_RESTORE_ROUNDL (FE_TONEAREST);
+  mul_split (&vals[1], &vals[0], x, x);
+  mul_split (&vals[3], &vals[2], y, y);
+  if (x >= 0.75L)
+    vals[1] -= 1.0L;
+  else
+    {
+      vals[1] -= 0.5L;
+      vals[3] -= 0.5L;
+    }
+  qsort (vals, 4, sizeof (long double), compare);
+  /* Add up the values so that each element of VALS has absolute value
+     at most equal to the last set bit of the next nonzero
+     element.  */
+  for (size_t i = 0; i <= 2; i++)
+    {
+      add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
+      qsort (vals + i + 1, 3 - i, sizeof (long double), compare);
+    }
+  /* Now any error from this addition will be small.  */
+  return vals[3] + vals[2] + vals[1] + vals[0];
+}
diff --git a/libc/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/libc/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c
new file mode 100644
index 000000000..4379b68c3
--- /dev/null
+++ b/libc/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c
@@ -0,0 +1,128 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
+   given that |X| >= |Y| and the values are small enough that no
+   overflow occurs.  */
+
+static inline void
+add_split (double *hi, double *lo, double x, double y)
+{
+  /* Apply Dekker's algorithm.  */
+  *hi = x + y;
+  *lo = (x - *hi) + y;
+}
+
+/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
+   given that the values are small enough that no overflow occurs and
+   large enough (or zero) that no underflow occurs.  */
+
+static inline void
+mul_split (double *hi, double *lo, double x, double y)
+{
+#ifdef __FP_FAST_FMA
+  /* Fast built-in fused multiply-add.  */
+  *hi = x * y;
+  *lo = __builtin_fma (x, y, -*hi);
+#elif defined FP_FAST_FMA
+  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
+  *hi = x * y;
+  *lo = __fma (x, y, -*hi);
+#else
+  /* Apply Dekker's algorithm.  */
+  *hi = x * y;
+# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+  double x1 = x * C;
+  double y1 = y * C;
+# undef C
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  double x2 = x - x1;
+  double y2 = y - y1;
+  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compare absolute values of floating-point values pointed to by P
+   and Q for qsort.  */
+
+static int
+compare (const void *p, const void *q)
+{
+  double pd = fabs (*(const double *) p);
+  double qd = fabs (*(const double *) q);
+  if (pd < qd)
+    return -1;
+  else if (pd == qd)
+    return 0;
+  else
+    return 1;
+}
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+long double
+__x2y2m1l (long double x, long double y)
+{
+  double vals[12];
+  SET_RESTORE_ROUND (FE_TONEAREST);
+  union ibm_extended_long_double xu, yu;
+  xu.d = x;
+  yu.d = y;
+  if (fabs (xu.dd[1]) < 0x1p-500)
+    xu.dd[1] = 0.0;
+  if (fabs (yu.dd[1]) < 0x1p-500)
+    yu.dd[1] = 0.0;
+  mul_split (&vals[1], &vals[0], xu.dd[0], xu.dd[0]);
+  mul_split (&vals[3], &vals[2], xu.dd[0], xu.dd[1]);
+  vals[2] *= 2.0;
+  vals[3] *= 2.0;
+  mul_split (&vals[5], &vals[4], xu.dd[1], xu.dd[1]);
+  mul_split (&vals[7], &vals[6], yu.dd[0], yu.dd[0]);
+  mul_split (&vals[9], &vals[8], yu.dd[0], yu.dd[1]);
+  vals[8] *= 2.0;
+  vals[9] *= 2.0;
+  mul_split (&vals[11], &vals[10], yu.dd[1], yu.dd[1]);
+  if (xu.dd[0] >= 0.75)
+    vals[1] -= 1.0;
+  else
+    {
+      vals[1] -= 0.5;
+      vals[7] -= 0.5;
+    }
+  qsort (vals, 12, sizeof (double), compare);
+  /* Add up the values so that each element of VALS has absolute value
+     at most equal to the last set bit of the next nonzero
+     element.  */
+  for (size_t i = 0; i <= 10; i++)
+    {
+      add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
+      qsort (vals + i + 1, 11 - i, sizeof (double), compare);
+    }
+  /* Now any error from this addition will be small.  */
+  long double retval = (long double) vals[11];
+  for (size_t i = 10; i != (size_t) -1; i--)
+    retval += (long double) vals[i];
+  return retval;
+}
diff --git a/libc/sysdeps/ieee754/ldbl-96/s_fma.c b/libc/sysdeps/ieee754/ldbl-96/s_fma.c
index 78c0b0db1..001d8063d 100644
--- a/libc/sysdeps/ieee754/ldbl-96/s_fma.c
+++ b/libc/sysdeps/ieee754/ldbl-96/s_fma.c
@@ -1,5 +1,5 @@
 /* Compute x * y + z as ternary operation.
-   Copyright (C) 2010 Free Software Foundation, Inc.
+   Copyright (C) 2010-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
 
@@ -38,6 +38,10 @@ __fma (double x, double y, double z)
       return (x * y) + z;
     }
 
+  /* Ensure correct sign of exact 0 + 0.  */
+  if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
+    return x * y + z;
+
   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
   long double x1 = (long double) x * C;
diff --git a/libc/sysdeps/ieee754/ldbl-96/s_fmal.c b/libc/sysdeps/ieee754/ldbl-96/s_fmal.c
index ca1e0905a..d12512428 100644
--- a/libc/sysdeps/ieee754/ldbl-96/s_fmal.c
+++ b/libc/sysdeps/ieee754/ldbl-96/s_fmal.c
@@ -50,6 +50,11 @@ __fmal (long double x, long double y, long double z)
 	  && u.ieee.exponent != 0x7fff
           && v.ieee.exponent != 0x7fff)
 	return (z + x) + y;
+      /* If z is zero and x are y are nonzero, compute the result
+	 as x * y to avoid the wrong sign of a zero result if x * y
+	 underflows to 0.  */
+      if (z == 0 && x != 0 && y != 0)
+	return 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 LDBL_DENORM_MIN,
 	 compute as x * y + z.  */
@@ -129,6 +134,11 @@ __fmal (long double x, long double y, long double z)
       y = v.d;
       z = w.d;
     }
+
+  /* Ensure correct sign of exact 0 + 0.  */
+  if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
+    return x * y + z;
+
   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
 #define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
   long double x1 = x * C;
diff --git a/libc/sysdeps/ieee754/ldbl-96/x2y2m1.c b/libc/sysdeps/ieee754/ldbl-96/x2y2m1.c
new file mode 100644
index 000000000..3086fa2c8
--- /dev/null
+++ b/libc/sysdeps/ieee754/ldbl-96/x2y2m1.c
@@ -0,0 +1,39 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+#if FLT_EVAL_METHOD == 0
+
+# include <sysdeps/ieee754/dbl-64/x2y2m1.c>
+
+#else
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+double
+__x2y2m1 (double x, double y)
+{
+  return (double) __x2y2m1l (x, y);
+}
+
+#endif
diff --git a/libc/sysdeps/ieee754/ldbl-96/x2y2m1l.c b/libc/sysdeps/ieee754/ldbl-96/x2y2m1l.c
new file mode 100644
index 000000000..a249cd347
--- /dev/null
+++ b/libc/sysdeps/ieee754/ldbl-96/x2y2m1l.c
@@ -0,0 +1,111 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+#include <stdlib.h>
+
+/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
+   given that |X| >= |Y| and the values are small enough that no
+   overflow occurs.  */
+
+static inline void
+add_split (long double *hi, long double *lo, long double x, long double y)
+{
+  /* Apply Dekker's algorithm.  */
+  *hi = x + y;
+  *lo = (x - *hi) + y;
+}
+
+/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
+   given that the values are small enough that no overflow occurs and
+   large enough (or zero) that no underflow occurs.  */
+
+static inline void
+mul_split (long double *hi, long double *lo, long double x, long double y)
+{
+#ifdef __FP_FAST_FMAL
+  /* Fast built-in fused multiply-add.  */
+  *hi = x * y;
+  *lo = __builtin_fmal (x, y, -*hi);
+#elif defined FP_FAST_FMAL
+  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
+  *hi = x * y;
+  *lo = __fmal (x, y, -*hi);
+#else
+  /* Apply Dekker's algorithm.  */
+  *hi = x * y;
+# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
+  long double x1 = x * C;
+  long double y1 = y * C;
+# undef C
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  long double x2 = x - x1;
+  long double y2 = y - y1;
+  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compare absolute values of floating-point values pointed to by P
+   and Q for qsort.  */
+
+static int
+compare (const void *p, const void *q)
+{
+  long double pld = fabsl (*(const long double *) p);
+  long double qld = fabsl (*(const long double *) q);
+  if (pld < qld)
+    return -1;
+  else if (pld == qld)
+    return 0;
+  else
+    return 1;
+}
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
+   0.75 or Y >= 0.5.  */
+
+long double
+__x2y2m1l (long double x, long double y)
+{
+  long double vals[4];
+  SET_RESTORE_ROUNDL (FE_TONEAREST);
+  mul_split (&vals[1], &vals[0], x, x);
+  mul_split (&vals[3], &vals[2], y, y);
+  if (x >= 0.75L)
+    vals[1] -= 1.0L;
+  else
+    {
+      vals[1] -= 0.5L;
+      vals[3] -= 0.5L;
+    }
+  qsort (vals, 4, sizeof (long double), compare);
+  /* Add up the values so that each element of VALS has absolute value
+     at most equal to the last set bit of the next nonzero
+     element.  */
+  for (size_t i = 0; i <= 2; i++)
+    {
+      add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
+      qsort (vals + i + 1, 3 - i, sizeof (long double), compare);
+    }
+  /* Now any error from this addition will be small.  */
+  return vals[3] + vals[2] + vals[1] + vals[0];
+}
diff --git a/libc/sysdeps/ieee754/ldbl-opt/configure b/libc/sysdeps/ieee754/ldbl-opt/configure
index d1f3177cf..6e69038b9 100755
--- a/libc/sysdeps/ieee754/ldbl-opt/configure
+++ b/libc/sysdeps/ieee754/ldbl-opt/configure
@@ -1,123 +1,3 @@
-
-# as_fn_set_status STATUS
-# -----------------------
-# Set $? to STATUS, without forking.
-as_fn_set_status ()
-{
-  return $1
-} # as_fn_set_status
-
-# as_fn_exit STATUS
-# -----------------
-# Exit the shell with STATUS, even in a "trap 0" or "set -e" context.
-as_fn_exit ()
-{
-  set +e
-  as_fn_set_status $1
-  exit $1
-} # as_fn_exit
-if expr a : '\(a\)' >/dev/null 2>&1 &&
-   test "X`expr 00001 : '.*\(...\)'`" = X001; then
-  as_expr=expr
-else
-  as_expr=false
-fi
-
-if (basename -- /) >/dev/null 2>&1 && test "X`basename -- / 2>&1`" = "X/"; then
-  as_basename=basename
-else
-  as_basename=false
-fi
-
-as_me=`$as_basename -- "$0" ||
-$as_expr X/"$0" : '.*/\([^/][^/]*\)/*$' \| \
-	 X"$0" : 'X\(//\)$' \| \
-	 X"$0" : 'X\(/\)' \| . 2>/dev/null ||
-$as_echo X/"$0" |
-    sed '/^.*\/\([^/][^/]*\)\/*$/{
-	    s//\1/
-	    q
-	  }
-	  /^X\/\(\/\/\)$/{
-	    s//\1/
-	    q
-	  }
-	  /^X\/\(\/\).*/{
-	    s//\1/
-	    q
-	  }
-	  s/.*/./; q'`
-
-
-  as_lineno_1=$LINENO as_lineno_1a=$LINENO
-  as_lineno_2=$LINENO as_lineno_2a=$LINENO
-  eval 'test "x$as_lineno_1'$as_run'" != "x$as_lineno_2'$as_run'" &&
-  test "x`expr $as_lineno_1'$as_run' + 1`" = "x$as_lineno_2'$as_run'"' || {
-  # Blame Lee E. McMahon (1931-1989) for sed's syntax.  :-)
-  sed -n '
-    p
-    /[$]LINENO/=
-  ' <$as_myself |
-    sed '
-      s/[$]LINENO.*/&-/
-      t lineno
-      b
-      :lineno
-      N
-      :loop
-      s/[$]LINENO\([^'$as_cr_alnum'_].*\n\)\(.*\)/\2\1\2/
-      t loop
-      s/-\n.*//
-    ' >$as_me.lineno &&
-  chmod +x "$as_me.lineno" ||
-    { $as_echo "$as_me: error: cannot create $as_me.lineno; rerun with a POSIX shell" >&2; as_fn_exit 1; }
-
-  # Don't try to exec as it changes $[0], causing all sort of problems
-  # (the dirname of $[0] is not the place where we might find the
-  # original and so on.  Autoconf is especially sensitive to this).
-  . "./$as_me.lineno"
-  # Exit status is that of the last command.
-  exit
-}
-
-
-# ac_fn_c_try_compile LINENO
-# --------------------------
-# Try to compile conftest.$ac_ext, and return whether this succeeded.
-ac_fn_c_try_compile ()
-{
-  as_lineno=${as_lineno-"$1"} as_lineno_stack=as_lineno_stack=$as_lineno_stack
-  rm -f conftest.$ac_objext
-  if { { ac_try="$ac_compile"
-case "(($ac_try" in
-  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
-  *) ac_try_echo=$ac_try;;
-esac
-eval ac_try_echo="\"\$as_me:${as_lineno-$LINENO}: $ac_try_echo\""
-$as_echo "$ac_try_echo"; } >&5
-  (eval "$ac_compile") 2>conftest.err
-  ac_status=$?
-  if test -s conftest.err; then
-    grep -v '^ *+' conftest.err >conftest.er1
-    cat conftest.er1 >&5
-    mv -f conftest.er1 conftest.err
-  fi
-  $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5
-  test $ac_status = 0; } && {
-	 test -z "$ac_c_werror_flag" ||
-	 test ! -s conftest.err
-       } && test -s conftest.$ac_objext; then :
-  ac_retval=0
-else
-  $as_echo "$as_me: failed program was:" >&5
-sed 's/^/| /' conftest.$ac_ext >&5
-
-	ac_retval=1
-fi
-  eval $as_lineno_stack; ${as_lineno_stack:+:} unset as_lineno
-  as_fn_set_status $ac_retval
-
-} # ac_fn_c_try_compile
 # This file is generated from configure.in by Autoconf.  DO NOT EDIT!
  # Local configure fragment for sysdeps/ieee754/ldbl-opt/.