127 lines
3.0 KiB
C
127 lines
3.0 KiB
C
/* Implementation of the ERFC_SCALED intrinsic.
|
|
Copyright (C) 2008-2018 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
|