127 lines
3.0 KiB
C
127 lines
3.0 KiB
C
/* Implementation of the ERFC_SCALED intrinsic.
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Copyright (C) 2008-2020 Free Software Foundation, Inc.
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This file is part of the GNU Fortran runtime library (libgfortran).
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Libgfortran is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public
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License as published by the Free Software Foundation; either
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version 3 of the License, or (at your option) any later version.
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Libgfortran is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#include "libgfortran.h"
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/* This implementation of ERFC_SCALED is based on the netlib algorithm
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available at http://www.netlib.org/specfun/erf */
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#ifdef HAVE_GFC_REAL_4
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#undef KIND
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#define KIND 4
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#include "erfc_scaled_inc.c"
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#endif
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#ifdef HAVE_GFC_REAL_8
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#undef KIND
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#define KIND 8
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#include "erfc_scaled_inc.c"
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#endif
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#ifdef HAVE_GFC_REAL_10
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#undef KIND
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#define KIND 10
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#include "erfc_scaled_inc.c"
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#endif
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#ifdef HAVE_GFC_REAL_16
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/* For quadruple-precision, netlib's implementation is
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not accurate enough. We provide another one. */
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#ifdef GFC_REAL_16_IS_FLOAT128
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# define _THRESH -106.566990228185312813205074546585730Q
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# define _M_2_SQRTPI M_2_SQRTPIq
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# define _INF __builtin_infq()
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# define _ERFC(x) erfcq(x)
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# define _EXP(x) expq(x)
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#else
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# define _THRESH -106.566990228185312813205074546585730L
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# ifndef M_2_SQRTPIl
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# define M_2_SQRTPIl 1.128379167095512573896158903121545172L
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# endif
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# define _M_2_SQRTPI M_2_SQRTPIl
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# define _INF __builtin_infl()
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# ifdef HAVE_ERFCL
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# define _ERFC(x) erfcl(x)
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# endif
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# ifdef HAVE_EXPL
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# define _EXP(x) expl(x)
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# endif
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#endif
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#if defined(_ERFC) && defined(_EXP)
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extern GFC_REAL_16 erfc_scaled_r16 (GFC_REAL_16);
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export_proto(erfc_scaled_r16);
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GFC_REAL_16
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erfc_scaled_r16 (GFC_REAL_16 x)
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{
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if (x < _THRESH)
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{
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return _INF;
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}
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if (x < 12)
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{
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/* Compute directly as ERFC_SCALED(x) = ERFC(x) * EXP(X**2).
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This is not perfect, but much better than netlib. */
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return _ERFC(x) * _EXP(x * x);
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}
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else
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{
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/* Calculate ERFC_SCALED(x) using a power series in 1/x:
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ERFC_SCALED(x) = 1 / (x * sqrt(pi))
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* (1 + Sum_n (-1)**n * (1 * 3 * 5 * ... * (2n-1))
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/ (2 * x**2)**n)
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*/
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GFC_REAL_16 sum = 0, oldsum;
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GFC_REAL_16 inv2x2 = 1 / (2 * x * x);
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GFC_REAL_16 fac = 1;
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int n = 1;
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while (n < 200)
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{
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fac *= - (2*n - 1) * inv2x2;
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oldsum = sum;
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sum += fac;
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if (sum == oldsum)
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break;
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n++;
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}
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return (1 + sum) / x * (_M_2_SQRTPI / 2);
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}
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}
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#endif
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#endif
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