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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 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 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 "eval.h"
double gsl_sf_bessel_Y1(const double x)
{
EVAL_RESULT(gsl_sf_bessel_Y1_e(x, &result));
}
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