/* 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 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 <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));
}