/* specfunc/bessel_Inu.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_exp.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_sf_bessel.h>

#include "error.h"

#include "bessel.h"

#include "bessel_temme.h"

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

int

gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x < 0.0 || nu < 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x*x < 10.0*(nu+1.0)) {

    gsl_sf_result b;

    double ex = exp(-x);

    int stat = gsl_sf_bessel_IJ_taylor_e(nu, x, 1, 100, GSL_DBL_EPSILON, &b);

    result->val  = b.val * ex;

    result->err  = b.err * ex;

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

    return stat;

  }

  else if(0.5/(nu*nu + x*x) < GSL_ROOT3_DBL_EPSILON) {

    return gsl_sf_bessel_Inu_scaled_asymp_unif_e(nu, x, result);

  }

  else {

    int N = (int)(nu + 0.5);

    double mu = nu - N;      /* -1/2 <= mu <= 1/2 */ 

    double K_mu, K_mup1, Kp_mu;

    double K_nu, K_nup1, K_num1;

    double I_nu_ratio;

    int stat_Irat;

    int stat_Kmu;

    int n;

    /* obtain K_mu, K_mup1 */

    if(x < 2.0) {

      stat_Kmu = gsl_sf_bessel_K_scaled_temme(mu, x, &K_mu, &K_mup1, &Kp_mu);

    }

    else {

      stat_Kmu = gsl_sf_bessel_K_scaled_steed_temme_CF2(mu, x, &K_mu, &K_mup1, &Kp_mu);

    }

    /* recurse forward to obtain K_num1, K_nu */

    K_nu   = K_mu;

    K_nup1 = K_mup1;

    for(n=0; n

      K_num1 = K_nu;

      K_nu   = K_nup1;

      K_nup1 = 2.0*(mu+n+1)/x * K_nu + K_num1;

    }

    /* calculate I_{nu+1}/I_nu */

    stat_Irat = gsl_sf_bessel_I_CF1_ser(nu, x, &I_nu_ratio);

    /* solve for I_nu */

    result->val = 1.0/(x * (K_nup1 + I_nu_ratio * K_nu));

    result->err = GSL_DBL_EPSILON * (0.5*N + 2.0) * fabs(result->val);

    return GSL_ERROR_SELECT_2(stat_Kmu, stat_Irat);

  }

}

int

gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result)

{

  gsl_sf_result b;

  int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &b);

  int stat_e = gsl_sf_exp_mult_err_e(x, fabs(x*GSL_DBL_EPSILON),

                                        b.val, b.err,

                                        result);

  return GSL_ERROR_SELECT_2(stat_e, stat_I);

}

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

#include "eval.h"

double gsl_sf_bessel_Inu_scaled(double nu, double x)

{

  EVAL_RESULT(gsl_sf_bessel_Inu_scaled_e(nu, x, &result));

}

double gsl_sf_bessel_Inu(double nu, double x)

{

  EVAL_RESULT(gsl_sf_bessel_Inu_e(nu, x, &result));

}