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/* specfunc/shint.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_expint.h>
#include "error.h"
#include "chebyshev.h"
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC shi.f, W. Fullerton
series for shi on the interval 0.00000e+00 to 1.40625e-01
with weighted error 4.67e-20
log weighted error 19.33
significant figures required 17.07
decimal places required 19.75
*/
static double shi_data[7] = {
0.0078372685688900950695,
0.0039227664934234563973,
0.0000041346787887617267,
0.0000000024707480372883,
0.0000000000009379295591,
0.0000000000000002451817,
0.0000000000000000000467
};
static cheb_series shi_cs = {
shi_data,
6,
-1, 1,
6
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_Shi_e(const double x, gsl_sf_result * result)
{
const double xsml = GSL_SQRT_DBL_EPSILON; /* sqrt (r1mach(3)) */
const double ax = fabs(x);
if(ax < xsml) {
result->val = x;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(ax <= 0.375) {
gsl_sf_result result_c;
cheb_eval_e(&shi_cs, 128.0*x*x/9.0-1.0, &result_c);
result->val = x * (1.0 + result_c.val);
result->err = x * result_c.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
gsl_sf_result result_Ei;
gsl_sf_result result_E1;
int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei);
int status_E1 = gsl_sf_expint_E1_e(x, &result_E1);
result->val = 0.5*(result_Ei.val + result_E1.val);
result->err = 0.5*(result_Ei.err + result_E1.err);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) {
GSL_ERROR ("underflow", GSL_EUNDRFLW);
}
else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) {
GSL_ERROR ("overflow", GSL_EOVRFLW);
}
else {
return GSL_SUCCESS;
}
}
}
int gsl_sf_Chi_e(const double x, gsl_sf_result * result)
{
gsl_sf_result result_Ei;
gsl_sf_result result_E1;
int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei);
int status_E1 = gsl_sf_expint_E1_e(x, &result_E1);
if(status_Ei == GSL_EDOM || status_E1 == GSL_EDOM) {
DOMAIN_ERROR(result);
}
else if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) {
UNDERFLOW_ERROR(result);
}
else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) {
OVERFLOW_ERROR(result);
}
else {
result->val = 0.5 * (result_Ei.val - result_E1.val);
result->err = 0.5 * (result_Ei.err + result_E1.err);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_Shi(const double x)
{
EVAL_RESULT(gsl_sf_Shi_e(x, &result));
}
double gsl_sf_Chi(const double x)
{
EVAL_RESULT(gsl_sf_Chi_e(x, &result));
}
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