/* specfunc/shint.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_expint.h>

#include "error.h"

#include "chebyshev.h"

#include "cheb_eval.c"

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

/* based on SLATEC shi.f, W. Fullerton

 series for shi  on the interval  0.00000e+00 to  1.40625e-01

                                        with weighted error   4.67e-20

                                         log weighted error  19.33

                               significant figures required  17.07

                                    decimal places required  19.75

*/

static double shi_data[7] = {

   0.0078372685688900950695,

   0.0039227664934234563973,

   0.0000041346787887617267,

   0.0000000024707480372883,

   0.0000000000009379295591,

   0.0000000000000002451817,

   0.0000000000000000000467

};

static cheb_series shi_cs = {

  shi_data,

  6,

  -1, 1,

  6

};

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

int gsl_sf_Shi_e(const double x, gsl_sf_result * result)

{

  const double xsml = GSL_SQRT_DBL_EPSILON;  /* sqrt (r1mach(3)) */

  const double ax   = fabs(x);

  if(ax < xsml) {

    result->val = x;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if(ax <= 0.375) {

    gsl_sf_result result_c;

    cheb_eval_e(&shi_cs, 128.0*x*x/9.0-1.0, &result_c);

    result->val  = x * (1.0 + result_c.val);

    result->err  = x * result_c.err;

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

    return GSL_SUCCESS;

  }

  else {

    gsl_sf_result result_Ei;

    gsl_sf_result result_E1;

    int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei);

    int status_E1 = gsl_sf_expint_E1_e(x, &result_E1);

    result->val  = 0.5*(result_Ei.val + result_E1.val);

    result->err  = 0.5*(result_Ei.err + result_E1.err);

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

    if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) {

      GSL_ERROR ("underflow", GSL_EUNDRFLW);

    }

    else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) {

      GSL_ERROR ("overflow", GSL_EOVRFLW);

    }

    else {

      return GSL_SUCCESS;

    }

  }

}

int gsl_sf_Chi_e(const double x, gsl_sf_result * result)

{

  gsl_sf_result result_Ei;

  gsl_sf_result result_E1;

  int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei);

  int status_E1 = gsl_sf_expint_E1_e(x, &result_E1);

  if(status_Ei == GSL_EDOM || status_E1 == GSL_EDOM) {

    DOMAIN_ERROR(result);

  }

  else if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) {

    UNDERFLOW_ERROR(result);

  }

  else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) {

    OVERFLOW_ERROR(result);

  }

  else {

    result->val  = 0.5 * (result_Ei.val - result_E1.val);

    result->err  = 0.5 * (result_Ei.err + result_E1.err);

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

    return GSL_SUCCESS;

  }

}

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

#include "eval.h"

double gsl_sf_Shi(const double x)

{

  EVAL_RESULT(gsl_sf_Shi_e(x, &result));

}

double gsl_sf_Chi(const double x)

{

  EVAL_RESULT(gsl_sf_Chi_e(x, &result));

}