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/* 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 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_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));
}
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