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/* specfunc/bessel_I0.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_bessel.h>
#include "error.h"
#include "chebyshev.h"
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC besi0 */
/* chebyshev expansions
series for bi0 on the interval 0. to 9.00000d+00
with weighted error 2.46e-18
log weighted error 17.61
significant figures required 17.90
decimal places required 18.15
series for ai0 on the interval 1.25000d-01 to 3.33333d-01
with weighted error 7.87e-17
log weighted error 16.10
significant figures required 14.69
decimal places required 16.76
series for ai02 on the interval 0. to 1.25000d-01
with weighted error 3.79e-17
log weighted error 16.42
significant figures required 14.86
decimal places required 17.09
*/
static double bi0_data[12] = {
-.07660547252839144951,
1.92733795399380827000,
.22826445869203013390,
.01304891466707290428,
.00043442709008164874,
.00000942265768600193,
.00000014340062895106,
.00000000161384906966,
.00000000001396650044,
.00000000000009579451,
.00000000000000053339,
.00000000000000000245
};
static cheb_series bi0_cs = {
bi0_data,
11,
-1, 1,
11
};
static double ai0_data[21] = {
.07575994494023796,
.00759138081082334,
.00041531313389237,
.00001070076463439,
-.00000790117997921,
-.00000078261435014,
.00000027838499429,
.00000000825247260,
-.00000001204463945,
.00000000155964859,
.00000000022925563,
-.00000000011916228,
.00000000001757854,
.00000000000112822,
-.00000000000114684,
.00000000000027155,
-.00000000000002415,
-.00000000000000608,
.00000000000000314,
-.00000000000000071,
.00000000000000007
};
static cheb_series ai0_cs = {
ai0_data,
20,
-1, 1,
13
};
static double ai02_data[22] = {
.05449041101410882,
.00336911647825569,
.00006889758346918,
.00000289137052082,
.00000020489185893,
.00000002266668991,
.00000000339623203,
.00000000049406022,
.00000000001188914,
-.00000000003149915,
-.00000000001321580,
-.00000000000179419,
.00000000000071801,
.00000000000038529,
.00000000000001539,
-.00000000000004151,
-.00000000000000954,
.00000000000000382,
.00000000000000176,
-.00000000000000034,
-.00000000000000027,
.00000000000000003
};
static cheb_series ai02_cs = {
ai02_data,
21,
-1, 1,
11
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_I0_scaled_e(const double x, gsl_sf_result * result)
{
double y = fabs(x);
/* CHECK_POINTER(result) */
if(y < 2.0 * GSL_SQRT_DBL_EPSILON) {
result->val = 1.0 - y;
result->err = 0.5*y*y;
return GSL_SUCCESS;
}
else if(y <= 3.0) {
const double ey = exp(-y);
gsl_sf_result c;
cheb_eval_e(&bi0_cs, y*y/4.5-1.0, &c);
result->val = ey * (2.75 + c.val);
result->err = GSL_DBL_EPSILON * fabs(result->val) + ey * c.err;
return GSL_SUCCESS;
}
else if(y <= 8.0) {
const double sy = sqrt(y);
gsl_sf_result c;
cheb_eval_e(&ai0_cs, (48.0/y-11.0)/5.0, &c);
result->val = (0.375 + c.val) / sy;
result->err = 2.0 * GSL_DBL_EPSILON * (0.375 + fabs(c.val)) / sy;
result->err += c.err / sy;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double sy = sqrt(y);
gsl_sf_result c;
cheb_eval_e(&ai02_cs, 16.0/y-1.0, &c);
result->val = (0.375 + c.val) / sy;
result->err = 2.0 * GSL_DBL_EPSILON * (0.375 + fabs(c.val)) / sy;
result->err += c.err / sy;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int gsl_sf_bessel_I0_e(const double x, gsl_sf_result * result)
{
double y = fabs(x);
/* CHECK_POINTER(result) */
if(y < 2.0 * GSL_SQRT_DBL_EPSILON) {
result->val = 1.0;
result->err = 0.5*y*y;
return GSL_SUCCESS;
}
else if(y <= 3.0) {
gsl_sf_result c;
cheb_eval_e(&bi0_cs, y*y/4.5-1.0, &c);
result->val = 2.75 + c.val;
result->err = GSL_DBL_EPSILON * (2.75 + fabs(c.val));
result->err += c.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else if(y < GSL_LOG_DBL_MAX - 1.0) {
const double ey = exp(y);
gsl_sf_result b_scaled;
gsl_sf_bessel_I0_scaled_e(x, &b_scaled);
result->val = ey * b_scaled.val;
result->err = ey * b_scaled.err + y*GSL_DBL_EPSILON*fabs(result->val);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
OVERFLOW_ERROR(result);
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_I0_scaled(const double x)
{
EVAL_RESULT(gsl_sf_bessel_I0_scaled_e(x, &result); )
}
double gsl_sf_bessel_I0(const double x)
{
EVAL_RESULT(gsl_sf_bessel_I0_e(x, &result); )
}
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