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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
downloadglibc-zack/build-layout-experiment.tar.gz
glibc-zack/build-layout-experiment.tar.xz
glibc-zack/build-layout-experiment.zip
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage
directory, REORG.TODO, except for files that will certainly still
exist in their current form at top level when we're done (COPYING,
COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which
are moved to the new directory OldChangeLogs, instead), and the
generated file INSTALL (which is just deleted; in the new order, there
will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c')
-rw-r--r--REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c220
1 files changed, 220 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c
new file mode 100644
index 0000000000..818fa94766
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c
@@ -0,0 +1,220 @@
+/* Implementation of gamma function according to ISO C.
+   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
+
+   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>
+
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+   approximation to gamma function.  */
+
+static const double gamma_coeff[] =
+  {
+    0x1.5555555555555p-4,
+    -0xb.60b60b60b60b8p-12,
+    0x3.4034034034034p-12,
+    -0x2.7027027027028p-12,
+    0x3.72a3c5631fe46p-12,
+    -0x7.daac36664f1f4p-12,
+  };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 184, in the form R *
+   2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+   avoid overflow or underflow in intermediate calculations.  */
+
+static double
+gamma_positive (double x, int *exp2_adj)
+{
+  int local_signgam;
+  if (x < 0.5)
+    {
+      *exp2_adj = 0;
+      return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
+    }
+  else if (x <= 1.5)
+    {
+      *exp2_adj = 0;
+      return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
+    }
+  else if (x < 6.5)
+    {
+      /* Adjust into the range for using exp (lgamma).  */
+      *exp2_adj = 0;
+      double n = __ceil (x - 1.5);
+      double x_adj = x - n;
+      double eps;
+      double prod = __gamma_product (x_adj, 0, n, &eps);
+      return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
+	      * prod * (1.0 + eps));
+    }
+  else
+    {
+      double eps = 0;
+      double x_eps = 0;
+      double x_adj = x;
+      double prod = 1;
+      if (x < 12.0)
+	{
+	  /* Adjust into the range for applying Stirling's
+	     approximation.  */
+	  double n = __ceil (12.0 - x);
+	  x_adj = math_narrow_eval (x + n);
+	  x_eps = (x - (x_adj - n));
+	  prod = __gamma_product (x_adj - n, x_eps, n, &eps);
+	}
+      /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+	 Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+	 starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+	 factored out.  */
+      double exp_adj = -eps;
+      double x_adj_int = __round (x_adj);
+      double x_adj_frac = x_adj - x_adj_int;
+      int x_adj_log2;
+      double x_adj_mant = __frexp (x_adj, &x_adj_log2);
+      if (x_adj_mant < M_SQRT1_2)
+	{
+	  x_adj_log2--;
+	  x_adj_mant *= 2.0;
+	}
+      *exp2_adj = x_adj_log2 * (int) x_adj_int;
+      double ret = (__ieee754_pow (x_adj_mant, x_adj)
+		    * __ieee754_exp2 (x_adj_log2 * x_adj_frac)
+		    * __ieee754_exp (-x_adj)
+		    * __ieee754_sqrt (2 * M_PI / x_adj)
+		    / prod);
+      exp_adj += x_eps * __ieee754_log (x_adj);
+      double bsum = gamma_coeff[NCOEFF - 1];
+      double x_adj2 = x_adj * x_adj;
+      for (size_t i = 1; i <= NCOEFF - 1; i++)
+	bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+      exp_adj += bsum / x_adj;
+      return ret + ret * __expm1 (exp_adj);
+    }
+}
+
+double
+__ieee754_gamma_r (double x, int *signgamp)
+{
+  int32_t hx;
+  u_int32_t lx;
+  double ret;
+
+  EXTRACT_WORDS (hx, lx, x);
+
+  if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
+    {
+      /* Return value for x == 0 is Inf with divide by zero exception.  */
+      *signgamp = 0;
+      return 1.0 / x;
+    }
+  if (__builtin_expect (hx < 0, 0)
+      && (u_int32_t) hx < 0xfff00000 && __rint (x) == x)
+    {
+      /* Return value for integer x < 0 is NaN with invalid exception.  */
+      *signgamp = 0;
+      return (x - x) / (x - x);
+    }
+  if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0))
+    {
+      /* x == -Inf.  According to ISO this is NaN.  */
+      *signgamp = 0;
+      return x - x;
+    }
+  if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000))
+    {
+      /* Positive infinity (return positive infinity) or NaN (return
+	 NaN).  */
+      *signgamp = 0;
+      return x + x;
+    }
+
+  if (x >= 172.0)
+    {
+      /* Overflow.  */
+      *signgamp = 0;
+      ret = math_narrow_eval (DBL_MAX * DBL_MAX);
+      return ret;
+    }
+  else
+    {
+      SET_RESTORE_ROUND (FE_TONEAREST);
+      if (x > 0.0)
+	{
+	  *signgamp = 0;
+	  int exp2_adj;
+	  double tret = gamma_positive (x, &exp2_adj);
+	  ret = __scalbn (tret, exp2_adj);
+	}
+      else if (x >= -DBL_EPSILON / 4.0)
+	{
+	  *signgamp = 0;
+	  ret = 1.0 / x;
+	}
+      else
+	{
+	  double tx = __trunc (x);
+	  *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
+	  if (x <= -184.0)
+	    /* Underflow.  */
+	    ret = DBL_MIN * DBL_MIN;
+	  else
+	    {
+	      double frac = tx - x;
+	      if (frac > 0.5)
+		frac = 1.0 - frac;
+	      double sinpix = (frac <= 0.25
+			       ? __sin (M_PI * frac)
+			       : __cos (M_PI * (0.5 - frac)));
+	      int exp2_adj;
+	      double tret = M_PI / (-x * sinpix
+				    * gamma_positive (-x, &exp2_adj));
+	      ret = __scalbn (tret, -exp2_adj);
+	      math_check_force_underflow_nonneg (ret);
+	    }
+	}
+      ret = math_narrow_eval (ret);
+    }
+  if (isinf (ret) && x != 0)
+    {
+      if (*signgamp < 0)
+	{
+	  ret = math_narrow_eval (-__copysign (DBL_MAX, ret) * DBL_MAX);
+	  ret = -ret;
+	}
+      else
+	ret = math_narrow_eval (__copysign (DBL_MAX, ret) * DBL_MAX);
+      return ret;
+    }
+  else if (ret == 0)
+    {
+      if (*signgamp < 0)
+	{
+	  ret = math_narrow_eval (-__copysign (DBL_MIN, ret) * DBL_MIN);
+	  ret = -ret;
+	}
+      else
+	ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN);
+      return ret;
+    }
+  else
+    return ret;
+}
+strong_alias (__ieee754_gamma_r, __gamma_r_finite)