/* 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));

}