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- /* 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__chebyshev.h"
- #include "gsl_specfunc__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 "gsl_specfunc__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));
- }
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