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Diffstat (limited to 'gsl-1.9/specfunc/shint.c')
| -rw-r--r-- | gsl-1.9/specfunc/shint.c | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/shint.c b/gsl-1.9/specfunc/shint.c new file mode 100644 index 0000000..24deffc --- /dev/null +++ b/gsl-1.9/specfunc/shint.c @@ -0,0 +1,135 @@ +/* specfunc/shint.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman + * + * This program 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 2 of the License, or (at + * your option) any later version. + * + * This program 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. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +/* Author: G. Jungman */ + +#include <config.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_sf_expint.h> + +#include "error.h" + +#include "chebyshev.h" +#include "cheb_eval.c" + +/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ + +/* based on SLATEC shi.f, W. Fullerton + + series for shi on the interval 0.00000e+00 to 1.40625e-01 + with weighted error 4.67e-20 + log weighted error 19.33 + significant figures required 17.07 + decimal places required 19.75 +*/ +static double shi_data[7] = { + 0.0078372685688900950695, + 0.0039227664934234563973, + 0.0000041346787887617267, + 0.0000000024707480372883, + 0.0000000000009379295591, + 0.0000000000000002451817, + 0.0000000000000000000467 +}; +static cheb_series shi_cs = { + shi_data, + 6, + -1, 1, + 6 +}; + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + +int gsl_sf_Shi_e(const double x, gsl_sf_result * result) +{ + const double xsml = GSL_SQRT_DBL_EPSILON; /* sqrt (r1mach(3)) */ + const double ax = fabs(x); + + if(ax < xsml) { + result->val = x; + result->err = 0.0; + return GSL_SUCCESS; + } + else if(ax <= 0.375) { + gsl_sf_result result_c; + cheb_eval_e(&shi_cs, 128.0*x*x/9.0-1.0, &result_c); + result->val = x * (1.0 + result_c.val); + result->err = x * result_c.err; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else { + gsl_sf_result result_Ei; + gsl_sf_result result_E1; + int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei); + int status_E1 = gsl_sf_expint_E1_e(x, &result_E1); + result->val = 0.5*(result_Ei.val + result_E1.val); + result->err = 0.5*(result_Ei.err + result_E1.err); + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) { + GSL_ERROR ("underflow", GSL_EUNDRFLW); + } + else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) { + GSL_ERROR ("overflow", GSL_EOVRFLW); + } + else { + return GSL_SUCCESS; + } + } +} + + +int gsl_sf_Chi_e(const double x, gsl_sf_result * result) +{ + gsl_sf_result result_Ei; + gsl_sf_result result_E1; + int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei); + int status_E1 = gsl_sf_expint_E1_e(x, &result_E1); + if(status_Ei == GSL_EDOM || status_E1 == GSL_EDOM) { + DOMAIN_ERROR(result); + } + else if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) { + UNDERFLOW_ERROR(result); + } + else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) { + OVERFLOW_ERROR(result); + } + else { + result->val = 0.5 * (result_Ei.val - result_E1.val); + result->err = 0.5 * (result_Ei.err + result_E1.err); + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } +} + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_Shi(const double x) +{ + EVAL_RESULT(gsl_sf_Shi_e(x, &result)); +} + +double gsl_sf_Chi(const double x) +{ + EVAL_RESULT(gsl_sf_Chi_e(x, &result)); +} |