/* specfunc/bessel_y.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_pow_int.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_sf_trig.h>

#include <gsl/gsl_sf_bessel.h>

#include "error.h"

#include "bessel.h"

#include "bessel_olver.h"

/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/

/* [Abramowitz+Stegun, 10.1.3]

 * with lmax=15, precision ~ 15D for x < 3

 *

 * checked OK [GJ] Wed May 13 15:41:25 MDT 1998 

 */

static int bessel_yl_small_x(int l, const double x, gsl_sf_result * result)

{

  gsl_sf_result num_fact;

  double den = gsl_sf_pow_int(x, l+1);

  int stat_df = gsl_sf_doublefact_e(2*l-1, &num_fact);

  if(stat_df != GSL_SUCCESS || den == 0.0) {

    OVERFLOW_ERROR(result);

  }

  else {

    const int lmax = 200;

    double t = -0.5*x*x;

    double sum = 1.0;

    double t_coeff = 1.0;

    double t_power = 1.0;

    double delta;

    int i;

    for(i=1; i<=lmax; i++) {

      t_coeff /= i*(2*(i-l) - 1);

      t_power *= t;

      delta = t_power*t_coeff;

      sum += delta;

      if(fabs(delta/sum) < 0.5*GSL_DBL_EPSILON) break;

    }

    result->val = -num_fact.val/den * sum;

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

    return GSL_SUCCESS;

  }

}

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

int gsl_sf_bessel_y0_e(const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x <= 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(1.0/GSL_DBL_MAX > 0.0 && x < 1.0/GSL_DBL_MAX) {

    OVERFLOW_ERROR(result);

  }

  else {

    gsl_sf_result cos_result;

    const int stat = gsl_sf_cos_e(x, &cos_result);

    result->val  = -cos_result.val/x;

    result->err  = fabs(cos_result.err/x);

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

    return stat;

  }

}

int gsl_sf_bessel_y1_e(const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x <= 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 1.0/GSL_SQRT_DBL_MAX) {

    OVERFLOW_ERROR(result);

  }

  else if(x < 0.25) {

    const double y = x*x;

    const double c1 =  1.0/2.0;

    const double c2 = -1.0/8.0;

    const double c3 =  1.0/144.0;

    const double c4 = -1.0/5760.0;

    const double c5 =  1.0/403200.0;

    const double c6 = -1.0/43545600.0;

    const double sum = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*(c5 + y*c6)))));

    result->val = -sum/y;

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

    return GSL_SUCCESS;

  }

  else {

    gsl_sf_result cos_result;

    gsl_sf_result sin_result;

    const int stat_cos = gsl_sf_cos_e(x, &cos_result);

    const int stat_sin = gsl_sf_sin_e(x, &sin_result);

    const double cx = cos_result.val;

    const double sx = sin_result.val;

    result->val  = -(cx/x + sx)/x;

    result->err  = (fabs(cos_result.err/x) + sin_result.err)/fabs(x);

    result->err += GSL_DBL_EPSILON * (fabs(sx/x) + fabs(cx/(x*x)));

    return GSL_ERROR_SELECT_2(stat_cos, stat_sin);

  }

}

int gsl_sf_bessel_y2_e(const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x <= 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 1.0/GSL_ROOT3_DBL_MAX) {

    OVERFLOW_ERROR(result);

  }

  else if(x < 0.5) {

    const double y = x*x;

    const double c1 =  1.0/6.0;

    const double c2 =  1.0/24.0;

    const double c3 = -1.0/144.0;

    const double c4 =  1.0/3456.0;

    const double c5 = -1.0/172800.0;

    const double c6 =  1.0/14515200.0;

    const double c7 = -1.0/1828915200.0;

    const double sum = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*(c5 + y*(c6 + y*c7))))));

    result->val = -3.0/(x*x*x) * sum;

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

    return GSL_SUCCESS;

  }

  else {

    gsl_sf_result cos_result;

    gsl_sf_result sin_result;

    const int stat_cos = gsl_sf_cos_e(x, &cos_result);

    const int stat_sin = gsl_sf_sin_e(x, &sin_result);

    const double sx = sin_result.val;

    const double cx = cos_result.val;

    const double a  = 3.0/(x*x);

    result->val  = (1.0 - a)/x * cx - a * sx;

    result->err  = cos_result.err * fabs((1.0 - a)/x) + sin_result.err * fabs(a);

    result->err += GSL_DBL_EPSILON * (fabs(cx/x) + fabs(sx/(x*x)));

    return GSL_ERROR_SELECT_2(stat_cos, stat_sin);

  }

}

int gsl_sf_bessel_yl_e(int l, const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(l < 0 || x <= 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(l == 0) {

    return gsl_sf_bessel_y0_e(x, result);

  }

  else if(l == 1) {

    return gsl_sf_bessel_y1_e(x, result);

  }

  else if(l == 2) {

    return gsl_sf_bessel_y2_e(x, result);

  }

  else if(x < 3.0) {

    return bessel_yl_small_x(l, x, result);

  }

  else if(GSL_ROOT3_DBL_EPSILON * x > (l*l + l + 1.0)) {

    int status = gsl_sf_bessel_Ynu_asympx_e(l + 0.5, x, result);

    double pre = sqrt((0.5*M_PI)/x);

    result->val *= pre;

    result->err *= pre;

    return status;

  }

  else if(l > 40) {

    int status = gsl_sf_bessel_Ynu_asymp_Olver_e(l + 0.5, x, result);

    double pre = sqrt((0.5*M_PI)/x);

    result->val *= pre;

    result->err *= pre;

    return status;

  }

  else {

    /* recurse upward */

    gsl_sf_result r_by;

    gsl_sf_result r_bym;

    int stat_1 = gsl_sf_bessel_y1_e(x, &r_by);

    int stat_0 = gsl_sf_bessel_y0_e(x, &r_bym);

    double bym = r_bym.val;

    double by  = r_by.val;

    double byp;

    int j;

    for(j=1; j

      byp = (2*j+1)/x*by - bym;

      bym = by;

      by  = byp;

    }

    result->val = by;

    result->err = fabs(result->val) * (GSL_DBL_EPSILON + fabs(r_by.err/r_by.val) + fabs(r_bym.err/r_bym.val));

    return GSL_ERROR_SELECT_2(stat_1, stat_0);

  }

}

int gsl_sf_bessel_yl_array(const int lmax, const double x, double * result_array)

{

  /* CHECK_POINTER(result_array) */

  if(lmax < 0 || x <= 0.0) {

    GSL_ERROR ("error", GSL_EDOM);

  } else if (lmax == 0) {

    gsl_sf_result result;

    int stat = gsl_sf_bessel_y0_e(x, &result);

    result_array[0] = result.val;

    return stat;

  } else {

    gsl_sf_result r_yell;

    gsl_sf_result r_yellm1;

    int stat_1 = gsl_sf_bessel_y1_e(x, &r_yell);

    int stat_0 = gsl_sf_bessel_y0_e(x, &r_yellm1);

    double yellp1;

    double yell   = r_yell.val;

    double yellm1 = r_yellm1.val;

    int ell;

    result_array[0] = yellm1;

    result_array[1] = yell;

    for(ell = 1; ell < lmax; ell++) {

      yellp1 = (2*ell+1)/x * yell - yellm1;

      result_array[ell+1] = yellp1;

      yellm1 = yell;

      yell   = yellp1;

    }

    return GSL_ERROR_SELECT_2(stat_0, stat_1);

  }

}

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

#include "eval.h"

double gsl_sf_bessel_y0(const double x)

{

  EVAL_RESULT(gsl_sf_bessel_y0_e(x, &result));

}

double gsl_sf_bessel_y1(const double x)

{

  EVAL_RESULT(gsl_sf_bessel_y1_e(x, &result));

}

double gsl_sf_bessel_y2(const double x)

{

  EVAL_RESULT(gsl_sf_bessel_y2_e(x, &result));

}

double gsl_sf_bessel_yl(const int l, const double x)

{

  EVAL_RESULT(gsl_sf_bessel_yl_e(l, x, &result));

}