| /* specfunc/bessel_J0.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 "bessel.h" |
| #include "bessel_amp_phase.h" |
| #include <gsl/gsl_sf_trig.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "cheb_eval.c" |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| |
| /* based on SLATEC besj0, 1977 version, w. fullerton */ |
| |
| /* chebyshev expansions for Bessel functions |
| |
| series for bj0 on the interval 0. to 1.60000d+01 |
| with weighted error 7.47e-18 |
| log weighted error 17.13 |
| significant figures required 16.98 |
| decimal places required 17.68 |
| |
| */ |
| |
| static double bj0_data[13] = { |
| 0.100254161968939137, |
| -0.665223007764405132, |
| 0.248983703498281314, |
| -0.0332527231700357697, |
| 0.0023114179304694015, |
| -0.0000991127741995080, |
| 0.0000028916708643998, |
| -0.0000000612108586630, |
| 0.0000000009838650793, |
| -0.0000000000124235515, |
| 0.0000000000001265433, |
| -0.0000000000000010619, |
| 0.0000000000000000074, |
| }; |
| static cheb_series bj0_cs = { |
| bj0_data, |
| 12, |
| -1, 1, |
| 9 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int gsl_sf_bessel_J0_e(const double x, gsl_sf_result * result) |
| { |
| double y = fabs(x); |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(y < 2.0*GSL_SQRT_DBL_EPSILON) { |
| result->val = 1.0; |
| result->err = y*y; |
| return GSL_SUCCESS; |
| } |
| else if(y <= 4.0) { |
| return cheb_eval_e(&bj0_cs, 0.125*y*y - 1.0, result); |
| } |
| else { |
| const double z = 32.0/(y*y) - 1.0; |
| gsl_sf_result ca; |
| gsl_sf_result ct; |
| gsl_sf_result cp; |
| const int stat_ca = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm0_cs, z, &ca); |
| const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth0_cs, z, &ct); |
| const int stat_cp = gsl_sf_bessel_cos_pi4_e(y, ct.val/y, &cp); |
| const double sqrty = sqrt(y); |
| const double ampl = (0.75 + ca.val) / sqrty; |
| result->val = ampl * cp.val; |
| result->err = fabs(cp.val) * ca.err/sqrty + fabs(ampl) * cp.err; |
| result->err += GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp); |
| } |
| } |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_J0(const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_J0_e(x, &result)); |
| } |