| /* specfunc/atanint.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_mode.h> |
| #include <gsl/gsl_sf_expint.h> |
| |
| #include "chebyshev.h" |
| #include "cheb_eval.c" |
| |
| |
| static double atanint_data[21] = { |
| 1.91040361296235937512, |
| -0.4176351437656746940e-01, |
| 0.275392550786367434e-02, |
| -0.25051809526248881e-03, |
| 0.2666981285121171e-04, |
| -0.311890514107001e-05, |
| 0.38833853132249e-06, |
| -0.5057274584964e-07, |
| 0.681225282949e-08, |
| -0.94212561654e-09, |
| 0.13307878816e-09, |
| -0.1912678075e-10, |
| 0.278912620e-11, |
| -0.41174820e-12, |
| 0.6142987e-13, |
| -0.924929e-14, |
| 0.140387e-14, |
| -0.21460e-15, |
| 0.3301e-16, |
| -0.511e-17, |
| 0.79e-18, |
| }; |
| static cheb_series atanint_cs = { |
| atanint_data, |
| 20, |
| -1, 1, |
| 10 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| int |
| gsl_sf_atanint_e(const double x, gsl_sf_result * result) |
| { |
| const double ax = fabs(x); |
| const double sgn = GSL_SIGN(x); |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(ax == 0.0) { |
| result->val = 0.0; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| else if(ax < 0.5*GSL_SQRT_DBL_EPSILON) { |
| result->val = x; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| else if(ax <= 1.0) { |
| const double t = 2.0 * (x*x - 0.5); |
| gsl_sf_result result_c; |
| cheb_eval_e(&atanint_cs, t, &result_c); |
| result->val = x * result_c.val; |
| result->err = x * result_c.err; |
| result->err += GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_SUCCESS; |
| } |
| else if(ax < 1.0/GSL_SQRT_DBL_EPSILON) { |
| const double t = 2.0 * (1.0/(x*x) - 0.5); |
| gsl_sf_result result_c; |
| cheb_eval_e(&atanint_cs, t, &result_c); |
| result->val = sgn * (0.5*M_PI*log(ax) + result_c.val/ax); |
| result->err = result_c.err/ax + fabs(result->val*GSL_DBL_EPSILON); |
| result->err += GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_SUCCESS; |
| } |
| else { |
| result->val = sgn * 0.5*M_PI*log(ax); |
| result->err = 2.0 * fabs(result->val * GSL_DBL_EPSILON); |
| return GSL_SUCCESS; |
| } |
| } |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_atanint(const double x) |
| { |
| EVAL_RESULT(gsl_sf_atanint_e(x, &result)); |
| } |