123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165 |
- /* Implementation of the ERFC_SCALED intrinsic.
- Copyright (C) 2008-2022 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
- #define ERFC_SCALED(k) \
- GFC_REAL_ ## k \
- erfc_scaled_r ## k (GFC_REAL_ ## k 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_ ## k sum = 0, oldsum; \
- GFC_REAL_ ## k inv2x2 = 1 / (2 * x * x); \
- GFC_REAL_ ## k 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); \
- } \
- }
- #if defined(_ERFC) && defined(_EXP)
- extern GFC_REAL_16 erfc_scaled_r16 (GFC_REAL_16);
- export_proto(erfc_scaled_r16);
- ERFC_SCALED(16)
- #endif
- #undef _THRESH
- #undef _M_2_SQRTPI
- #undef _INF
- #undef _ERFC
- #undef _EXP
- #endif
- #ifdef HAVE_GFC_REAL_17
- /* For quadruple-precision, netlib's implementation is
- not accurate enough. We provide another one. */
- # define _THRESH -106.566990228185312813205074546585730Q
- # define _M_2_SQRTPI M_2_SQRTPIq
- # define _INF __builtin_inff128()
- # ifdef POWER_IEEE128
- # define _ERFC(x) __erfcieee128(x)
- # define _EXP(x) __expieee128(x)
- # else
- # define _ERFC(x) erfcq(x)
- # define _EXP(x) expq(x)
- # endif
- extern GFC_REAL_17 erfc_scaled_r17 (GFC_REAL_17);
- export_proto(erfc_scaled_r17);
- ERFC_SCALED(17)
- #undef _THRESH
- #undef _M_2_SQRTPI
- #undef _INF
- #undef _ERFC
- #undef _EXP
- #undef ERFC_SCALED
- #endif
|