/* specfunc/expint3.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"

static double expint3_data[24] = {

  1.269198414221126014,

 -0.248846446384140982,

  0.80526220717231041e-01,

 -0.25772733251968330e-01,

  0.7599878873073774e-02,

 -0.2030695581940405e-02,

  0.490834586699330e-03,

 -0.107682239142021e-03,

  0.21551726264290e-04,

 -0.3956705137384e-05,

  0.6699240933896e-06,

 -0.105132180807e-06,

  0.15362580199e-07,

 -0.20990960364e-08,

  0.2692109538e-09,

 -0.325195242e-10,

  0.37114816e-11,

 -0.4013652e-12,

  0.412334e-13,

 -0.40338e-14,

  0.3766e-15,

 -0.336e-16,

  0.29e-17,

 -0.2e-18

};

static cheb_series expint3_cs = {

  expint3_data,

  23,

  -1.0, 1.0,

  15

};

static double expint3a_data[23] = {

   1.9270464955068273729,

  -0.349293565204813805e-01,

   0.14503383718983009e-02,

  -0.8925336718327903e-04,

   0.70542392191184e-05,

  -0.6671727454761e-06,

   0.724267589982e-07,

  -0.87825825606e-08,

   0.11672234428e-08,

  -0.1676631281e-09,

   0.257550158e-10,

  -0.41957888e-11,

   0.7201041e-12,

  -0.1294906e-12,

   0.24287e-13,

  -0.47331e-14,

   0.95531e-15,

  -0.1991e-15,

   0.428e-16,

  -0.94e-17,

   0.21e-17,

  -0.5e-18,

   0.1e-18

};

static cheb_series expint3a_cs = {

  expint3a_data,

  22,

  -1.0, 1.0,

  10

};

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

int gsl_sf_expint_3_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 0.892979511569249211;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 1.6*GSL_ROOT3_DBL_EPSILON) {

    result->val = x;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if(x <= 2.0) {

    const double t = x*x*x/4.0 - 1.0;

    gsl_sf_result result_c;

    cheb_eval_e(&expint3_cs, t, &result_c);

    result->val = x * result_c.val;

    result->err = x * result_c.err;

    return GSL_SUCCESS;

  }

  else if(x < pow(-GSL_LOG_DBL_EPSILON, 1.0/3.0)) {

    const double t = 16.0/(x*x*x) - 1.0;

    const double s = exp(-x*x*x)/(3.0*x*x);

    gsl_sf_result result_c;

    cheb_eval_e(&expint3a_cs, t, &result_c);

    result->val = val_infinity - result_c.val * s;

    result->err = val_infinity * GSL_DBL_EPSILON + s * result_c.err;

    return GSL_SUCCESS;

  }

  else {

    result->val = val_infinity;

    result->err = val_infinity * GSL_DBL_EPSILON;

    return GSL_SUCCESS;

  }

}

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

#include "eval.h"

double gsl_sf_expint_3(double x)

{

  EVAL_RESULT(gsl_sf_expint_3_e(x, &result));

}