/* specfunc/bessel_J0.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_mode.h>
#include "bessel.h"
#include "bessel_amp_phase.h"
#include <gsl/gsl_sf_trig.h>
#include <gsl/gsl_sf_bessel.h>
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC besj0, 1977 version, w. fullerton */
/* chebyshev expansions for Bessel functions
series for bj0 on the interval 0. to 1.60000d+01
with weighted error 7.47e-18
log weighted error 17.13
significant figures required 16.98
decimal places required 17.68
*/
static double bj0_data[13] = {
0.100254161968939137,
-0.665223007764405132,
0.248983703498281314,
-0.0332527231700357697,
0.0023114179304694015,
-0.0000991127741995080,
0.0000028916708643998,
-0.0000000612108586630,
0.0000000009838650793,
-0.0000000000124235515,
0.0000000000001265433,
-0.0000000000000010619,
0.0000000000000000074,
};
static cheb_series bj0_cs = {
bj0_data,
12,
-1, 1,
9
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_J0_e(const double x, gsl_sf_result * result)
{
double y = fabs(x);
/* CHECK_POINTER(result) */
if(y < 2.0*GSL_SQRT_DBL_EPSILON) {
result->val = 1.0;
result->err = y*y;
return GSL_SUCCESS;
}
else if(y <= 4.0) {
return cheb_eval_e(&bj0_cs, 0.125*y*y - 1.0, result);
}
else {
const double z = 32.0/(y*y) - 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_bm0_cs, z, &ca);
const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth0_cs, z, &ct);
const int stat_cp = gsl_sf_bessel_cos_pi4_e(y, ct.val/y, &cp);
const double sqrty = sqrt(y);
const double ampl = (0.75 + ca.val) / sqrty;
result->val = ampl * cp.val;
result->err = fabs(cp.val) * ca.err/sqrty + fabs(ampl) * cp.err;
result->err += GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp);
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_J0(const double x)
{
EVAL_RESULT(gsl_sf_bessel_J0_e(x, &result));
}