/* specfunc/bessel_Y0.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 besy0, 1980 version, w. fullerton */

/* chebyshev expansions

 series for by0        on the interval  0.          to  1.60000d+01

                                        with weighted error   1.20e-17

                                         log weighted error  16.92

                               significant figures required  16.15

                                    decimal places required  17.48

*/

static double by0_data[13] = {

  -0.011277839392865573,

  -0.128345237560420350,

  -0.104378847997942490,

   0.023662749183969695,

  -0.002090391647700486,

   0.000103975453939057,

  -0.000003369747162423,

   0.000000077293842676,

  -0.000000001324976772,

   0.000000000017648232,

  -0.000000000000188105,

   0.000000000000001641,

  -0.000000000000000011

};

static cheb_series by0_cs = {

  by0_data,

  12,

  -1, 1,

  8

};

/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/

int gsl_sf_bessel_Y0_e(const double x, gsl_sf_result * result)

{

  const double two_over_pi = 2.0/M_PI;

  const double xmax        = 1.0/GSL_DBL_EPSILON;

  /* CHECK_POINTER(result) */

  if (x <= 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 4.0) {

    gsl_sf_result J0;

    gsl_sf_result c;

    int stat_J0 = gsl_sf_bessel_J0_e(x, &J0;;

    cheb_eval_e(&by0_cs, 0.125*x*x-1.0, &c);

    result->val = two_over_pi*(-M_LN2 + log(x))*J0.val + 0.375 + c.val;

    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) + c.err;

    return stat_J0;

  }

  else if(x < xmax) {

    /* Leading behaviour of phase is x, which is exact,

     * so the error is bounded.

     */

    const double z  = 32.0/(x*x) - 1.0;

    gsl_sf_result c1;

    gsl_sf_result c2;

    gsl_sf_result sp;

    const int stat_c1 = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm0_cs,  z, &c1;;

    const int stat_c2 = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth0_cs, z, &c2;;

    const int stat_sp = gsl_sf_bessel_sin_pi4_e(x, c2.val/x, &sp);

    const double sqrtx = sqrt(x);

    const double ampl  = (0.75 + c1.val) / sqrtx;

    result->val  = ampl * sp.val;

    result->err  = fabs(sp.val) * c1.err/sqrtx + fabs(ampl) * sp.err;

    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

    return GSL_ERROR_SELECT_3(stat_sp, stat_c1, stat_c2);

  }

  else {

    UNDERFLOW_ERROR(result);

  }

}

/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_bessel_Y0(const double x)

{

  EVAL_RESULT(gsl_sf_bessel_Y0_e(x, &result));

}