| /* specfunc/expint3.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" |
| |
| static double expint3_data[24] = { |
| 1.269198414221126014, |
| -0.248846446384140982, |
| 0.80526220717231041e-01, |
| -0.25772733251968330e-01, |
| 0.7599878873073774e-02, |
| -0.2030695581940405e-02, |
| 0.490834586699330e-03, |
| -0.107682239142021e-03, |
| 0.21551726264290e-04, |
| -0.3956705137384e-05, |
| 0.6699240933896e-06, |
| -0.105132180807e-06, |
| 0.15362580199e-07, |
| -0.20990960364e-08, |
| 0.2692109538e-09, |
| -0.325195242e-10, |
| 0.37114816e-11, |
| -0.4013652e-12, |
| 0.412334e-13, |
| -0.40338e-14, |
| 0.3766e-15, |
| -0.336e-16, |
| 0.29e-17, |
| -0.2e-18 |
| }; |
| static cheb_series expint3_cs = { |
| expint3_data, |
| 23, |
| -1.0, 1.0, |
| 15 |
| }; |
| |
| static double expint3a_data[23] = { |
| 1.9270464955068273729, |
| -0.349293565204813805e-01, |
| 0.14503383718983009e-02, |
| -0.8925336718327903e-04, |
| 0.70542392191184e-05, |
| -0.6671727454761e-06, |
| 0.724267589982e-07, |
| -0.87825825606e-08, |
| 0.11672234428e-08, |
| -0.1676631281e-09, |
| 0.257550158e-10, |
| -0.41957888e-11, |
| 0.7201041e-12, |
| -0.1294906e-12, |
| 0.24287e-13, |
| -0.47331e-14, |
| 0.95531e-15, |
| -0.1991e-15, |
| 0.428e-16, |
| -0.94e-17, |
| 0.21e-17, |
| -0.5e-18, |
| 0.1e-18 |
| }; |
| static cheb_series expint3a_cs = { |
| expint3a_data, |
| 22, |
| -1.0, 1.0, |
| 10 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int gsl_sf_expint_3_e(const double x, gsl_sf_result * result) |
| { |
| const double val_infinity = 0.892979511569249211; |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(x < 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| else if(x < 1.6*GSL_ROOT3_DBL_EPSILON) { |
| result->val = x; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| else if(x <= 2.0) { |
| const double t = x*x*x/4.0 - 1.0; |
| gsl_sf_result result_c; |
| cheb_eval_e(&expint3_cs, t, &result_c); |
| result->val = x * result_c.val; |
| result->err = x * result_c.err; |
| return GSL_SUCCESS; |
| } |
| else if(x < pow(-GSL_LOG_DBL_EPSILON, 1.0/3.0)) { |
| const double t = 16.0/(x*x*x) - 1.0; |
| const double s = exp(-x*x*x)/(3.0*x*x); |
| gsl_sf_result result_c; |
| cheb_eval_e(&expint3a_cs, t, &result_c); |
| result->val = val_infinity - result_c.val * s; |
| result->err = val_infinity * GSL_DBL_EPSILON + s * result_c.err; |
| return GSL_SUCCESS; |
| } |
| else { |
| result->val = val_infinity; |
| result->err = val_infinity * GSL_DBL_EPSILON; |
| return GSL_SUCCESS; |
| } |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_expint_3(double x) |
| { |
| EVAL_RESULT(gsl_sf_expint_3_e(x, &result)); |
| } |