praat/external/gsl/gsl_specfunc__bessel_J0.c

/* 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 "gsl__config.h"
#include "gsl_math.h"
#include "gsl_errno.h"
#include "gsl_mode.h"
#include "gsl_specfunc__bessel.h"
#include "gsl_specfunc__bessel_amp_phase.h"
#include "gsl_sf_trig.h"
#include "gsl_sf_bessel.h"

#include "gsl_specfunc__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 "gsl_specfunc__eval.h"

double gsl_sf_bessel_J0(const double x)
{
  EVAL_RESULT(gsl_sf_bessel_J0_e(x, &result));
}