| /* specfunc/bessel_Y0.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_trig.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "error.h" |
| |
| #include "bessel.h" |
| #include "bessel_amp_phase.h" |
| #include "cheb_eval.c" |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| /* based on SLATEC besy0, 1980 version, w. fullerton */ |
| |
| /* chebyshev expansions |
| |
| series for by0 on the interval 0. to 1.60000d+01 |
| with weighted error 1.20e-17 |
| log weighted error 16.92 |
| significant figures required 16.15 |
| decimal places required 17.48 |
| */ |
| |
| static double by0_data[13] = { |
| -0.011277839392865573, |
| -0.128345237560420350, |
| -0.104378847997942490, |
| 0.023662749183969695, |
| -0.002090391647700486, |
| 0.000103975453939057, |
| -0.000003369747162423, |
| 0.000000077293842676, |
| -0.000000001324976772, |
| 0.000000000017648232, |
| -0.000000000000188105, |
| 0.000000000000001641, |
| -0.000000000000000011 |
| }; |
| static cheb_series by0_cs = { |
| by0_data, |
| 12, |
| -1, 1, |
| 8 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int gsl_sf_bessel_Y0_e(const double x, gsl_sf_result * result) |
| { |
| const double two_over_pi = 2.0/M_PI; |
| const double xmax = 1.0/GSL_DBL_EPSILON; |
| |
| /* CHECK_POINTER(result) */ |
| |
| if (x <= 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| else if(x < 4.0) { |
| gsl_sf_result J0; |
| gsl_sf_result c; |
| int stat_J0 = gsl_sf_bessel_J0_e(x, &J0); |
| cheb_eval_e(&by0_cs, 0.125*x*x-1.0, &c); |
| result->val = two_over_pi*(-M_LN2 + log(x))*J0.val + 0.375 + c.val; |
| result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) + c.err; |
| return stat_J0; |
| } |
| else if(x < xmax) { |
| /* Leading behaviour of phase is x, which is exact, |
| * so the error is bounded. |
| */ |
| const double z = 32.0/(x*x) - 1.0; |
| gsl_sf_result c1; |
| gsl_sf_result c2; |
| gsl_sf_result sp; |
| const int stat_c1 = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm0_cs, z, &c1); |
| const int stat_c2 = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth0_cs, z, &c2); |
| const int stat_sp = gsl_sf_bessel_sin_pi4_e(x, c2.val/x, &sp); |
| const double sqrtx = sqrt(x); |
| const double ampl = (0.75 + c1.val) / sqrtx; |
| result->val = ampl * sp.val; |
| result->err = fabs(sp.val) * c1.err/sqrtx + fabs(ampl) * sp.err; |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_ERROR_SELECT_3(stat_sp, stat_c1, stat_c2); |
| } |
| else { |
| UNDERFLOW_ERROR(result); |
| } |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_Y0(const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Y0_e(x, &result)); |
| } |