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/* 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 2 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));
}
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