/* specfunc/clausen.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_trig.h>

#include <gsl/gsl_sf_clausen.h>

#include "chebyshev.h"

#include "cheb_eval.c"

static double aclaus_data[15] = {

  2.142694363766688447e+00,

  0.723324281221257925e-01,

  0.101642475021151164e-02,

  0.3245250328531645e-04,

  0.133315187571472e-05,

  0.6213240591653e-07,

  0.313004135337e-08,

  0.16635723056e-09,

  0.919659293e-11,

  0.52400462e-12,

  0.3058040e-13,

  0.18197e-14,

  0.1100e-15,

  0.68e-17,

  0.4e-18

};

static cheb_series aclaus_cs = {

  aclaus_data,

  14,

  -1, 1,

  8  /* FIXME:  this is a guess, correct value needed here BJG */

};

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

int gsl_sf_clausen_e(double x, gsl_sf_result *result)

{

  const double x_cut = M_PI * GSL_SQRT_DBL_EPSILON;

  double sgn = 1.0;

  int status_red;

  if(x < 0.0) {

    x   = -x;

    sgn = -1.0;

  }

  /* Argument reduction to [0, 2pi) */

  status_red = gsl_sf_angle_restrict_pos_e(&x);

  /* Further reduction to [0,pi) */

  if(x > M_PI) {

    /* simulated extra precision: 2PI = p0 + p1 */

    const double p0 = 6.28125;

    const double p1 = 0.19353071795864769253e-02;

    x = (p0 - x) + p1;

    sgn = -sgn;

  }

  if(x == 0.0) {

    result->val = 0.0;

    result->err = 0.0;

  }

  else if(x < x_cut) {

    result->val = x * (1.0 - log(x));

    result->err = x * GSL_DBL_EPSILON;

  }

  else {

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

    gsl_sf_result result_c;

    cheb_eval_e(&aclaus_cs, t, &result_c);

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

    result->err = x * (result_c.err + GSL_DBL_EPSILON);

  }

  result->val *= sgn;

  return status_red;

}

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

#include "eval.h"

double gsl_sf_clausen(const double x)

{

  EVAL_RESULT(gsl_sf_clausen_e(x, &result));

}