/* 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));

}