| /* 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)); |
| } |