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- /* specfunc/bessel_Y1.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"
- /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
- /* based on SLATEC besy1, 1977 version, w. fullerton */
- /* chebyshev expansions
- series for by1 on the interval 0. to 1.60000d+01
- with weighted error 1.87e-18
- log weighted error 17.73
- significant figures required 17.83
- decimal places required 18.30
- */
- static double by1_data[14] = {
- 0.03208047100611908629,
- 1.262707897433500450,
- 0.00649996189992317500,
- -0.08936164528860504117,
- 0.01325088122175709545,
- -0.00089790591196483523,
- 0.00003647361487958306,
- -0.00000100137438166600,
- 0.00000001994539657390,
- -0.00000000030230656018,
- 0.00000000000360987815,
- -0.00000000000003487488,
- 0.00000000000000027838,
- -0.00000000000000000186
- };
- static cheb_series by1_cs = {
- by1_data,
- 13,
- -1, 1,
- 10
- };
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result)
- {
- const double two_over_pi = 2.0/M_PI;
- const double xmin = 1.571*GSL_DBL_MIN; /*exp ( amax1(alog(r1mach(1)), -alog(r1mach(2)))+.01) */
- const double x_small = 2.0 * GSL_SQRT_DBL_EPSILON;
- const double xmax = 1.0/GSL_DBL_EPSILON;
- /* CHECK_POINTER(result) */
- if(x <= 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x < xmin) {
- OVERFLOW_ERROR(result);
- }
- else if(x < x_small) {
- const double lnterm = log(0.5*x);
- gsl_sf_result J1;
- gsl_sf_result c;
- int status = gsl_sf_bessel_J1_e(x, &J1);
- cheb_eval_e(&by1_cs, -1.0, &c);
- result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
- result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
- return status;
- }
- else if(x < 4.0) {
- const double lnterm = log(0.5*x);
- int status;
- gsl_sf_result J1;
- gsl_sf_result c;
- cheb_eval_e(&by1_cs, 0.125*x*x-1.0, &c);
- status = gsl_sf_bessel_J1_e(x, &J1);
- result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
- result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
- return status;
- }
- else if(x < xmax) {
- const double z = 32.0/(x*x) - 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_bm1_cs, z, &ca);
- const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth1_cs, z, &ct);
- const int stat_cp = gsl_sf_bessel_cos_pi4_e(x, ct.val/x, &cp);
- const double sqrtx = sqrt(x);
- const double ampl = (0.75 + ca.val) / sqrtx;
- result->val = -ampl * cp.val;
- result->err = fabs(cp.val) * ca.err/sqrtx + fabs(ampl) * cp.err;
- result->err += GSL_DBL_EPSILON * fabs(result->val);
- return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp);
- }
- else {
- UNDERFLOW_ERROR(result);
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_bessel_Y1(const double x)
- {
- EVAL_RESULT(gsl_sf_bessel_Y1_e(x, &result));
- }
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