| /* specfunc/bessel_Y1.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_trig.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "error.h" |
| |
| #include "bessel.h" |
| #include "bessel_amp_phase.h" |
| #include "cheb_eval.c" |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| /* based on SLATEC besy1, 1977 version, w. fullerton */ |
| |
| /* chebyshev expansions |
| |
| series for by1 on the interval 0. to 1.60000d+01 |
| with weighted error 1.87e-18 |
| log weighted error 17.73 |
| significant figures required 17.83 |
| decimal places required 18.30 |
| */ |
| |
| static double by1_data[14] = { |
| 0.03208047100611908629, |
| 1.262707897433500450, |
| 0.00649996189992317500, |
| -0.08936164528860504117, |
| 0.01325088122175709545, |
| -0.00089790591196483523, |
| 0.00003647361487958306, |
| -0.00000100137438166600, |
| 0.00000001994539657390, |
| -0.00000000030230656018, |
| 0.00000000000360987815, |
| -0.00000000000003487488, |
| 0.00000000000000027838, |
| -0.00000000000000000186 |
| }; |
| static cheb_series by1_cs = { |
| by1_data, |
| 13, |
| -1, 1, |
| 10 |
| }; |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result) |
| { |
| const double two_over_pi = 2.0/M_PI; |
| const double xmin = 1.571*GSL_DBL_MIN; /*exp ( amax1(alog(r1mach(1)), -alog(r1mach(2)))+.01) */ |
| const double x_small = 2.0 * GSL_SQRT_DBL_EPSILON; |
| const double xmax = 1.0/GSL_DBL_EPSILON; |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(x <= 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| else if(x < xmin) { |
| OVERFLOW_ERROR(result); |
| } |
| else if(x < x_small) { |
| const double lnterm = log(0.5*x); |
| gsl_sf_result J1; |
| gsl_sf_result c; |
| int status = gsl_sf_bessel_J1_e(x, &J1); |
| cheb_eval_e(&by1_cs, -1.0, &c); |
| result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x; |
| result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x; |
| return status; |
| } |
| else if(x < 4.0) { |
| const double lnterm = log(0.5*x); |
| int status; |
| gsl_sf_result J1; |
| gsl_sf_result c; |
| cheb_eval_e(&by1_cs, 0.125*x*x-1.0, &c); |
| status = gsl_sf_bessel_J1_e(x, &J1); |
| result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x; |
| result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x; |
| return status; |
| } |
| else if(x < xmax) { |
| const double z = 32.0/(x*x) - 1.0; |
| gsl_sf_result ca; |
| gsl_sf_result ct; |
| gsl_sf_result cp; |
| const int stat_ca = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm1_cs, z, &ca); |
| const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth1_cs, z, &ct); |
| const int stat_cp = gsl_sf_bessel_cos_pi4_e(x, ct.val/x, &cp); |
| const double sqrtx = sqrt(x); |
| const double ampl = (0.75 + ca.val) / sqrtx; |
| result->val = -ampl * cp.val; |
| result->err = fabs(cp.val) * ca.err/sqrtx + fabs(ampl) * cp.err; |
| result->err += GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp); |
| } |
| else { |
| UNDERFLOW_ERROR(result); |
| } |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_Y1(const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Y1_e(x, &result)); |
| } |