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- /* 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 3 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_expint.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__chebyshev.h"
- #include "gsl_specfunc__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 "gsl_specfunc__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));
- }
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