/* specfunc/bessel_I1.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"
#define ROOT_EIGHT (2.0*M_SQRT2)
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC besi1(), besi1e() */
/* chebyshev expansions
series for bi1 on the interval 0. to 9.00000d+00
with weighted error 2.40e-17
log weighted error 16.62
significant figures required 16.23
decimal places required 17.14
series for ai1 on the interval 1.25000d-01 to 3.33333d-01
with weighted error 6.98e-17
log weighted error 16.16
significant figures required 14.53
decimal places required 16.82
series for ai12 on the interval 0. to 1.25000d-01
with weighted error 3.55e-17
log weighted error 16.45
significant figures required 14.69
decimal places required 17.12
*/
static double bi1_data[11] = {
-0.001971713261099859,
0.407348876675464810,
0.034838994299959456,
0.001545394556300123,
0.000041888521098377,
0.000000764902676483,
0.000000010042493924,
0.000000000099322077,
0.000000000000766380,
0.000000000000004741,
0.000000000000000024
};
static cheb_series bi1_cs = {
bi1_data,
10,
-1, 1,
10
};
static double ai1_data[21] = {
-0.02846744181881479,
-0.01922953231443221,
-0.00061151858579437,
-0.00002069971253350,
0.00000858561914581,
0.00000104949824671,
-0.00000029183389184,
-0.00000001559378146,
0.00000001318012367,
-0.00000000144842341,
-0.00000000029085122,
0.00000000012663889,
-0.00000000001664947,
-0.00000000000166665,
0.00000000000124260,
-0.00000000000027315,
0.00000000000002023,
0.00000000000000730,
-0.00000000000000333,
0.00000000000000071,
-0.00000000000000006
};
static cheb_series ai1_cs = {
ai1_data,
20,
-1, 1,
11
};
static double ai12_data[22] = {
0.02857623501828014,
-0.00976109749136147,
-0.00011058893876263,
-0.00000388256480887,
-0.00000025122362377,
-0.00000002631468847,
-0.00000000383538039,
-0.00000000055897433,
-0.00000000001897495,
0.00000000003252602,
0.00000000001412580,
0.00000000000203564,
-0.00000000000071985,
-0.00000000000040836,
-0.00000000000002101,
0.00000000000004273,
0.00000000000001041,
-0.00000000000000382,
-0.00000000000000186,
0.00000000000000033,
0.00000000000000028,
-0.00000000000000003
};
static cheb_series ai12_cs = {
ai12_data,
21,
-1, 1,
9
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_I1_scaled_e(const double x, gsl_sf_result * result)
{
const double xmin = 2.0 * GSL_DBL_MIN;
const double x_small = ROOT_EIGHT * GSL_SQRT_DBL_EPSILON;
const double y = fabs(x);
/* CHECK_POINTER(result) */
if(y == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(y < xmin) {
UNDERFLOW_ERROR(result);
}
else if(y < x_small) {
result->val = 0.5*x;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(y <= 3.0) {
const double ey = exp(-y);
gsl_sf_result c;
cheb_eval_e(&bi1_cs, y*y/4.5-1.0, &c);
result->val = x * ey * (0.875 + c.val);
result->err = ey * c.err + y * GSL_DBL_EPSILON * fabs(result->val);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else if(y <= 8.0) {
const double sy = sqrt(y);
gsl_sf_result c;
double b;
double s;
cheb_eval_e(&ai1_cs, (48.0/y-11.0)/5.0, &c);
b = (0.375 + c.val) / sy;
s = (x > 0.0 ? 1.0 : -1.0);
result->val = s * b;
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;
double b;
double s;
cheb_eval_e(&ai12_cs, 16.0/y-1.0, &c);
b = (0.375 + c.val) / sy;
s = (x > 0.0 ? 1.0 : -1.0);
result->val = s * b;
result->err = c.err / sy;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int gsl_sf_bessel_I1_e(const double x, gsl_sf_result * result)
{
const double xmin = 2.0 * GSL_DBL_MIN;
const double x_small = ROOT_EIGHT * GSL_SQRT_DBL_EPSILON;
const double y = fabs(x);
/* CHECK_POINTER(result) */
if(y == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(y < xmin) {
UNDERFLOW_ERROR(result);
}
else if(y < x_small) {
result->val = 0.5*x;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(y <= 3.0) {
gsl_sf_result c;
cheb_eval_e(&bi1_cs, y*y/4.5-1.0, &c);
result->val = x * (0.875 + c.val);
result->err = y * c.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else if(y < GSL_LOG_DBL_MAX) {
const double ey = exp(y);
gsl_sf_result I1_scaled;
gsl_sf_bessel_I1_scaled_e(x, &I1_scaled);
result->val = ey * I1_scaled.val;
result->err = ey * I1_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_I1_scaled(const double x)
{
EVAL_RESULT(gsl_sf_bessel_I1_scaled_e(x, &result));
}
double gsl_sf_bessel_I1(const double x)
{
EVAL_RESULT(gsl_sf_bessel_I1_e(x, &result));
}