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- /* 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 3 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_trig.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__bessel.h"
- #include "gsl_specfunc__bessel_amp_phase.h"
- #include "gsl_specfunc__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 "gsl_specfunc__eval.h"
- double gsl_sf_bessel_J1(const double x)
- {
- EVAL_RESULT(gsl_sf_bessel_J1_e(x, &result));
- }
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