blob: 1f8c778eb651b638f7b1a3b5614966537baca19c (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
|
/* Implementation of the ERFC_SCALED intrinsic.
Copyright (C) 2008-2013 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
#if defined(HAVE_GFC_REAL_16) && defined(GFC_REAL_16_IS_LONG_DOUBLE)
#undef KIND
#define KIND 16
#include "erfc_scaled_inc.c"
#endif
/* For quadruple-precision (__float128), netlib's implementation is
not accurate enough. We provide another one. */
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 < -106.566990228185312813205074546585730Q)
{
return __builtin_infq();
}
if (x < 12)
{
/* Compute directly as ERFC_SCALED(x) = ERFC(x) * EXP(X**2).
This is not perfect, but much better than netlib. */
return erfcq(x) * expq(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_SQRTPIq / 2);
}
}
|
