/* 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 <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"
#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 "eval.h"
double gsl_sf_bessel_J1(const double x)
{
EVAL_RESULT(gsl_sf_bessel_J1_e(x, &result));
}