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- /* specfunc/bessel_K0.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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_exp.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__chebyshev.h"
- #include "gsl_specfunc__cheb_eval.c"
- /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
- /* based on SLATEC bk0(), bk0e() */
- /* chebyshev expansions
- series for bk0 on the interval 0. to 4.00000d+00
- with weighted error 3.57e-19
- log weighted error 18.45
- significant figures required 17.99
- decimal places required 18.97
- series for ak0 on the interval 1.25000d-01 to 5.00000d-01
- with weighted error 5.34e-17
- log weighted error 16.27
- significant figures required 14.92
- decimal places required 16.89
- series for ak02 on the interval 0. to 1.25000d-01
- with weighted error 2.34e-17
- log weighted error 16.63
- significant figures required 14.67
- decimal places required 17.20
- */
- static double bk0_data[11] = {
- -0.03532739323390276872,
- 0.3442898999246284869,
- 0.03597993651536150163,
- 0.00126461541144692592,
- 0.00002286212103119451,
- 0.00000025347910790261,
- 0.00000000190451637722,
- 0.00000000001034969525,
- 0.00000000000004259816,
- 0.00000000000000013744,
- 0.00000000000000000035
- };
- static cheb_series bk0_cs = {
- bk0_data,
- 10,
- -1, 1,
- 10
- };
- static double ak0_data[17] = {
- -0.07643947903327941,
- -0.02235652605699819,
- 0.00077341811546938,
- -0.00004281006688886,
- 0.00000308170017386,
- -0.00000026393672220,
- 0.00000002563713036,
- -0.00000000274270554,
- 0.00000000031694296,
- -0.00000000003902353,
- 0.00000000000506804,
- -0.00000000000068895,
- 0.00000000000009744,
- -0.00000000000001427,
- 0.00000000000000215,
- -0.00000000000000033,
- 0.00000000000000005
- };
- static cheb_series ak0_cs = {
- ak0_data,
- 16,
- -1, 1,
- 10
- };
- static double ak02_data[14] = {
- -0.01201869826307592,
- -0.00917485269102569,
- 0.00014445509317750,
- -0.00000401361417543,
- 0.00000015678318108,
- -0.00000000777011043,
- 0.00000000046111825,
- -0.00000000003158592,
- 0.00000000000243501,
- -0.00000000000020743,
- 0.00000000000001925,
- -0.00000000000000192,
- 0.00000000000000020,
- -0.00000000000000002
- };
- static cheb_series ak02_cs = {
- ak02_data,
- 13,
- -1, 1,
- 8
- };
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int gsl_sf_bessel_K0_scaled_e(const double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(x <= 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x <= 2.0) {
- const double lx = log(x);
- const double ex = exp(x);
- int stat_I0;
- gsl_sf_result I0;
- gsl_sf_result c;
- cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
- stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
- result->val = ex * ((-lx+M_LN2)*I0.val - 0.25 + c.val);
- result->err = ex * ((M_LN2+fabs(lx))*I0.err + c.err);
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return stat_I0;
- }
- else if(x <= 8.0) {
- const double sx = sqrt(x);
- gsl_sf_result c;
- cheb_eval_e(&ak0_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(&ak02_cs, 16.0/x-1.0, &c);
- result->val = (1.25 + c.val) / sx;
- result->err = (c.err + GSL_DBL_EPSILON) / sx;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- }
- int gsl_sf_bessel_K0_e(const double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(x <= 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x <= 2.0) {
- const double lx = log(x);
- int stat_I0;
- gsl_sf_result I0;
- gsl_sf_result c;
- cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
- stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
- result->val = (-lx+M_LN2)*I0.val - 0.25 + c.val;
- result->err = (fabs(lx) + M_LN2) * I0.err + c.err;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return stat_I0;
- }
- else {
- gsl_sf_result K0_scaled;
- int stat_K0 = gsl_sf_bessel_K0_scaled_e(x, &K0_scaled);
- int stat_e = gsl_sf_exp_mult_err_e(-x, GSL_DBL_EPSILON*fabs(x),
- K0_scaled.val, K0_scaled.err,
- result);
- return GSL_ERROR_SELECT_2(stat_e, stat_K0);
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_bessel_K0_scaled(const double x)
- {
- EVAL_RESULT(gsl_sf_bessel_K0_scaled_e(x, &result));
- }
- double gsl_sf_bessel_K0(const double x)
- {
- EVAL_RESULT(gsl_sf_bessel_K0_e(x, &result));
- }
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