/* 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 #include #include #include #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)); }