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/* specfunc/bessel_K1.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_exp.h>
#include <gsl/gsl_sf_bessel.h>
#include "error.h"
#include "chebyshev.h"
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC besk1(), besk1e() */
/* chebyshev expansions
series for bk1 on the interval 0. to 4.00000d+00
with weighted error 7.02e-18
log weighted error 17.15
significant figures required 16.73
decimal places required 17.67
series for ak1 on the interval 1.25000d-01 to 5.00000d-01
with weighted error 6.06e-17
log weighted error 16.22
significant figures required 15.41
decimal places required 16.83
series for ak12 on the interval 0. to 1.25000d-01
with weighted error 2.58e-17
log weighted error 16.59
significant figures required 15.22
decimal places required 17.16
*/
static double bk1_data[11] = {
0.0253002273389477705,
-0.3531559607765448760,
-0.1226111808226571480,
-0.0069757238596398643,
-0.0001730288957513052,
-0.0000024334061415659,
-0.0000000221338763073,
-0.0000000001411488392,
-0.0000000000006666901,
-0.0000000000000024274,
-0.0000000000000000070
};
static cheb_series bk1_cs = {
bk1_data,
10,
-1, 1,
8
};
static double ak1_data[17] = {
0.27443134069738830,
0.07571989953199368,
-0.00144105155647540,
0.00006650116955125,
-0.00000436998470952,
0.00000035402774997,
-0.00000003311163779,
0.00000000344597758,
-0.00000000038989323,
0.00000000004720819,
-0.00000000000604783,
0.00000000000081284,
-0.00000000000011386,
0.00000000000001654,
-0.00000000000000248,
0.00000000000000038,
-0.00000000000000006
};
static cheb_series ak1_cs = {
ak1_data,
16,
-1, 1,
9
};
static double ak12_data[14] = {
0.06379308343739001,
0.02832887813049721,
-0.00024753706739052,
0.00000577197245160,
-0.00000020689392195,
0.00000000973998344,
-0.00000000055853361,
0.00000000003732996,
-0.00000000000282505,
0.00000000000023720,
-0.00000000000002176,
0.00000000000000215,
-0.00000000000000022,
0.00000000000000002
};
static cheb_series ak12_cs = {
ak12_data,
13,
-1, 1,
7
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_K1_scaled_e(const double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(x < 2.0*GSL_DBL_MIN) {
OVERFLOW_ERROR(result);
}
else if(x <= 2.0) {
const double lx = log(x);
const double ex = exp(x);
int stat_I1;
gsl_sf_result I1;
gsl_sf_result c;
cheb_eval_e(&bk1_cs, 0.5*x*x-1.0, &c);
stat_I1 = gsl_sf_bessel_I1_e(x, &I1);
result->val = ex * ((lx-M_LN2)*I1.val + (0.75 + c.val)/x);
result->err = ex * (c.err/x + fabs(lx)*I1.err);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_I1;
}
else if(x <= 8.0) {
const double sx = sqrt(x);
gsl_sf_result c;
cheb_eval_e(&ak1_cs, (16.0/x-5.0)/3.0, &c);
result->val = (1.25 + c.val) / sx;
result->err = c.err / sx;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double sx = sqrt(x);
gsl_sf_result c;
cheb_eval_e(&ak12_cs, 16.0/x-1.0, &c);
result->val = (1.25 + c.val) / sx;
result->err = c.err / sx;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int gsl_sf_bessel_K1_e(const double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(x < 2.0*GSL_DBL_MIN) {
OVERFLOW_ERROR(result);
}
else if(x <= 2.0) {
const double lx = log(x);
int stat_I1;
gsl_sf_result I1;
gsl_sf_result c;
cheb_eval_e(&bk1_cs, 0.5*x*x-1.0, &c);
stat_I1 = gsl_sf_bessel_I1_e(x, &I1);
result->val = (lx-M_LN2)*I1.val + (0.75 + c.val)/x;
result->err = c.err/x + fabs(lx)*I1.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_I1;
}
else {
gsl_sf_result K1_scaled;
int stat_K1 = gsl_sf_bessel_K1_scaled_e(x, &K1_scaled);
int stat_e = gsl_sf_exp_mult_err_e(-x, 0.0,
K1_scaled.val, K1_scaled.err,
result);
result->err = fabs(result->val) * (GSL_DBL_EPSILON*fabs(x) + K1_scaled.err/K1_scaled.val);
return GSL_ERROR_SELECT_2(stat_e, stat_K1);
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_K1_scaled(const double x)
{
EVAL_RESULT(gsl_sf_bessel_K1_scaled_e(x, &result));
}
double gsl_sf_bessel_K1(const double x)
{
EVAL_RESULT(gsl_sf_bessel_K1_e(x, &result));
}
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