Improve tgamma accuracy (bugs 2546, 2560, 5159, 15426).

1 files changed, 75 insertions, 0 deletions

diff --git a/sysdeps/ieee754/dbl-64/gamma_product.c b/sysdeps/ieee754/dbl-64/gamma_product.c
new file mode 100644
index 0000000000..2a3fc1aff8
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/gamma_product.c
@@ -0,0 +1,75 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+   Copyright (C) 2013 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 the values are small enough that no overflow occurs and
+   large enough (or zero) that no underflow occurs.  */
+
+static 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
+}
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+   - 1, in the form R * (1 + *EPS) where the return value R is an
+   approximation to the product and *EPS is set to indicate the
+   approximate error in the return value.  X is such that all the
+   values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+   X is small enough that factors quadratic in it can be
+   neglected.  */
+
+double
+__gamma_product (double x, double x_eps, int n, double *eps)
+{
+  SET_RESTORE_ROUND (FE_TONEAREST);
+  double ret = x;
+  *eps = x_eps / x;
+  for (int i = 1; i < n; i++)
+    {
+      *eps += x_eps / (x + i);
+      double lo;
+      mul_split (&ret, &lo, ret, x + i);
+      *eps += lo / ret;
+    }
+  return ret;
+}