/* 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));
}