| /* specfunc/bessel_J1.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" |
| |
| #define ROOT_EIGHT (2.0*M_SQRT2) |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| |
| /* based on SLATEC besj1, 1983 version, w. fullerton */ |
| |
| /* chebyshev expansions |
| |
| series for bj1 on the interval 0. to 1.60000d+01 |
| with weighted error 4.48e-17 |
| log weighted error 16.35 |
| significant figures required 15.77 |
| decimal places required 16.89 |
| |
| */ |
| static double bj1_data[12] = { |
| -0.11726141513332787, |
| -0.25361521830790640, |
| 0.050127080984469569, |
| -0.004631514809625081, |
| 0.000247996229415914, |
| -0.000008678948686278, |
| 0.000000214293917143, |
| -0.000000003936093079, |
| 0.000000000055911823, |
| -0.000000000000632761, |
| 0.000000000000005840, |
| -0.000000000000000044, |
| }; |
| static cheb_series bj1_cs = { |
| bj1_data, |
| 11, |
| -1, 1, |
| 8 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int gsl_sf_bessel_J1_e(const double x, gsl_sf_result * result) |
| { |
| double y = fabs(x); |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(y == 0.0) { |
| result->val = 0.0; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| else if(y < 2.0*GSL_DBL_MIN) { |
| UNDERFLOW_ERROR(result); |
| } |
| else if(y < ROOT_EIGHT * GSL_SQRT_DBL_EPSILON) { |
| result->val = 0.5*x; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| else if(y < 4.0) { |
| gsl_sf_result c; |
| cheb_eval_e(&bj1_cs, 0.125*y*y-1.0, &c); |
| result->val = x * (0.25 + c.val); |
| result->err = fabs(x * c.err); |
| return GSL_SUCCESS; |
| } |
| else { |
| /* Because the leading term in the phase is y, |
| * which we assume is exactly known, the error |
| * in the cos() evaluation is bounded. |
| */ |
| const double z = 32.0/(y*y) - 1.0; |
| gsl_sf_result ca; |
| gsl_sf_result ct; |
| gsl_sf_result sp; |
| const int stat_ca = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm1_cs, z, &ca); |
| const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth1_cs, z, &ct); |
| const int stat_sp = gsl_sf_bessel_sin_pi4_e(y, ct.val/y, &sp); |
| const double sqrty = sqrt(y); |
| const double ampl = (0.75 + ca.val) / sqrty; |
| result->val = (x < 0.0 ? -ampl : ampl) * sp.val; |
| result->err = fabs(sp.val) * ca.err/sqrty + fabs(ampl) * sp.err; |
| result->err += GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_sp); |
| } |
| } |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_J1(const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_J1_e(x, &result)); |
| } |