diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_Y1.c')
| -rw-r--r-- | gsl-1.9/specfunc/bessel_Y1.c | 137 |
1 files changed, 137 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_Y1.c b/gsl-1.9/specfunc/bessel_Y1.c new file mode 100644 index 0000000..205eed3 --- /dev/null +++ b/gsl-1.9/specfunc/bessel_Y1.c @@ -0,0 +1,137 @@ +/* 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)); +} |