/* specfunc/atanint.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_mode.h>

#include <gsl/gsl_sf_expint.h>

#include "chebyshev.h"

#include "cheb_eval.c"

static double atanint_data[21] = {

  1.91040361296235937512,

 -0.4176351437656746940e-01,

  0.275392550786367434e-02,

 -0.25051809526248881e-03,

  0.2666981285121171e-04,

 -0.311890514107001e-05,

  0.38833853132249e-06,

 -0.5057274584964e-07,

  0.681225282949e-08,

 -0.94212561654e-09,

  0.13307878816e-09,

 -0.1912678075e-10,

  0.278912620e-11,

 -0.41174820e-12,

  0.6142987e-13,

 -0.924929e-14,

  0.140387e-14,

 -0.21460e-15,

  0.3301e-16,

 -0.511e-17,

  0.79e-18,

};

static cheb_series atanint_cs = {

  atanint_data,

  20,

  -1, 1,

  10

};

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

int

gsl_sf_atanint_e(const double x, gsl_sf_result * result)

{

  const double ax  = fabs(x);

  const double sgn = GSL_SIGN(x);

  /* CHECK_POINTER(result) */

  if(ax == 0.0) {

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if(ax < 0.5*GSL_SQRT_DBL_EPSILON) {

    result->val = x;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if(ax <= 1.0) {

    const double t = 2.0 * (x*x - 0.5);

    gsl_sf_result result_c;

    cheb_eval_e(&atanint_cs, t, &result_c);

    result->val  = x * result_c.val;

    result->err  = x * result_c.err;

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

    return GSL_SUCCESS;

  }

  else if(ax < 1.0/GSL_SQRT_DBL_EPSILON) {

    const double t = 2.0 * (1.0/(x*x) - 0.5);

    gsl_sf_result result_c;

    cheb_eval_e(&atanint_cs, t, &result_c);

    result->val  = sgn * (0.5*M_PI*log(ax) + result_c.val/ax);

    result->err  = result_c.err/ax + fabs(result->val*GSL_DBL_EPSILON);

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

    return GSL_SUCCESS;

  }

  else {

    result->val = sgn * (0.5*M_PI*log(ax) + 1.0 / ax);

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

    return GSL_SUCCESS;

  }

}

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

#include "eval.h"

double gsl_sf_atanint(const double x)

{

  EVAL_RESULT(gsl_sf_atanint_e(x, &result));

}