/* 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));

}