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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 "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"
- /*-*-*-*-*-*-*-*-*-*-*-* 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 "gsl_specfunc__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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