| /* 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 2 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)); |
| } |
