/* 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 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 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));

}