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+/* Implementation of the ERFC_SCALED intrinsic.
+ Copyright (C) 2008-2017 Free Software Foundation, Inc.
+
+This file is part of the GNU Fortran runtime library (libgfortran).
+
+Libgfortran is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public
+License as published by the Free Software Foundation; either
+version 3 of the License, or (at your option) any later version.
+
+Libgfortran 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 General Public License for more details.
+
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
+<http://www.gnu.org/licenses/>. */
+
+#include "libgfortran.h"
+
+/* This implementation of ERFC_SCALED is based on the netlib algorithm
+ available at http://www.netlib.org/specfun/erf */
+
+#ifdef HAVE_GFC_REAL_4
+#undef KIND
+#define KIND 4
+#include "erfc_scaled_inc.c"
+#endif
+
+#ifdef HAVE_GFC_REAL_8
+#undef KIND
+#define KIND 8
+#include "erfc_scaled_inc.c"
+#endif
+
+#ifdef HAVE_GFC_REAL_10
+#undef KIND
+#define KIND 10
+#include "erfc_scaled_inc.c"
+#endif
+
+#ifdef HAVE_GFC_REAL_16
+
+/* For quadruple-precision, netlib's implementation is
+ not accurate enough. We provide another one. */
+
+#ifdef GFC_REAL_16_IS_FLOAT128
+
+# define _THRESH -106.566990228185312813205074546585730Q
+# define _M_2_SQRTPI M_2_SQRTPIq
+# define _INF __builtin_infq()
+# define _ERFC(x) erfcq(x)
+# define _EXP(x) expq(x)
+
+#else
+
+# define _THRESH -106.566990228185312813205074546585730L
+# ifndef M_2_SQRTPIl
+# define M_2_SQRTPIl 1.128379167095512573896158903121545172L
+# endif
+# define _M_2_SQRTPI M_2_SQRTPIl
+# define _INF __builtin_infl()
+# ifdef HAVE_ERFCL
+# define _ERFC(x) erfcl(x)
+# endif
+# ifdef HAVE_EXPL
+# define _EXP(x) expl(x)
+# endif
+
+#endif
+
+#if defined(_ERFC) && defined(_EXP)
+
+extern GFC_REAL_16 erfc_scaled_r16 (GFC_REAL_16);
+export_proto(erfc_scaled_r16);
+
+GFC_REAL_16
+erfc_scaled_r16 (GFC_REAL_16 x)
+{
+ if (x < _THRESH)
+ {
+ return _INF;
+ }
+ if (x < 12)
+ {
+ /* Compute directly as ERFC_SCALED(x) = ERFC(x) * EXP(X**2).
+ This is not perfect, but much better than netlib. */
+ return _ERFC(x) * _EXP(x * x);
+ }
+ else
+ {
+ /* Calculate ERFC_SCALED(x) using a power series in 1/x:
+ ERFC_SCALED(x) = 1 / (x * sqrt(pi))
+ * (1 + Sum_n (-1)**n * (1 * 3 * 5 * ... * (2n-1))
+ / (2 * x**2)**n)
+ */
+ GFC_REAL_16 sum = 0, oldsum;
+ GFC_REAL_16 inv2x2 = 1 / (2 * x * x);
+ GFC_REAL_16 fac = 1;
+ int n = 1;
+
+ while (n < 200)
+ {
+ fac *= - (2*n - 1) * inv2x2;
+ oldsum = sum;
+ sum += fac;
+
+ if (sum == oldsum)
+ break;
+
+ n++;
+ }
+
+ return (1 + sum) / x * (_M_2_SQRTPI / 2);
+ }
+}
+
+#endif
+
+#endif