diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_Y0.c')
| -rw-r--r-- | gsl-1.9/specfunc/bessel_Y0.c | 122 |
1 files changed, 122 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_Y0.c b/gsl-1.9/specfunc/bessel_Y0.c new file mode 100644 index 0000000..0ed50ef --- /dev/null +++ b/gsl-1.9/specfunc/bessel_Y0.c @@ -0,0 +1,122 @@ +/* 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)); +} |