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Diffstat (limited to 'gsl-1.9/specfunc/beta.c')
| -rw-r--r-- | gsl-1.9/specfunc/beta.c | 169 |
1 files changed, 169 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/beta.c b/gsl-1.9/specfunc/beta.c new file mode 100644 index 0000000..47801a4 --- /dev/null +++ b/gsl-1.9/specfunc/beta.c @@ -0,0 +1,169 @@ +/* specfunc/beta.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_exp.h> +#include <gsl/gsl_sf_log.h> +#include <gsl/gsl_sf_psi.h> +#include <gsl/gsl_sf_gamma.h> + +#include "error.h" + +static double +isnegint (const double x) +{ + return (x < 0) && (x == floor(x)); +} + +int +gsl_sf_lnbeta_e(const double x, const double y, gsl_sf_result * result) +{ + double sgn; + int status = gsl_sf_lnbeta_sgn_e(x,y,result,&sgn); + if (sgn == -1) { + DOMAIN_ERROR(result); + } + return status; +} + +int +gsl_sf_lnbeta_sgn_e(const double x, const double y, gsl_sf_result * result, double * sgn) +{ + /* CHECK_POINTER(result) */ + + if(x == 0.0 || y == 0.0) { + *sgn = 0.0; + DOMAIN_ERROR(result); + } else if (isnegint(x) || isnegint(y)) { + *sgn = 0.0; + DOMAIN_ERROR(result); /* not defined for negative integers */ + } + + /* See if we can handle the postive case with min/max < 0.2 */ + + if (x > 0 && y > 0) { + const double max = GSL_MAX(x,y); + const double min = GSL_MIN(x,y); + const double rat = min/max; + + if(rat < 0.2) { + /* min << max, so be careful + * with the subtraction + */ + double lnpre_val; + double lnpre_err; + double lnpow_val; + double lnpow_err; + double t1, t2, t3; + gsl_sf_result lnopr; + gsl_sf_result gsx, gsy, gsxy; + gsl_sf_gammastar_e(x, &gsx); + gsl_sf_gammastar_e(y, &gsy); + gsl_sf_gammastar_e(x+y, &gsxy); + gsl_sf_log_1plusx_e(rat, &lnopr); + lnpre_val = log(gsx.val*gsy.val/gsxy.val * M_SQRT2*M_SQRTPI); + lnpre_err = gsx.err/gsx.val + gsy.err/gsy.val + gsxy.err/gsxy.val; + t1 = min*log(rat); + t2 = 0.5*log(min); + t3 = (x+y-0.5)*lnopr.val; + lnpow_val = t1 - t2 - t3; + lnpow_err = GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3)); + lnpow_err += fabs(x+y-0.5) * lnopr.err; + result->val = lnpre_val + lnpow_val; + result->err = lnpre_err + lnpow_err; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + *sgn = 1.0; + return GSL_SUCCESS; + } + } + + /* General case - Fallback */ + { + gsl_sf_result lgx, lgy, lgxy; + double sgx, sgy, sgxy, xy = x+y; + int stat_gx = gsl_sf_lngamma_sgn_e(x, &lgx, &sgx); + int stat_gy = gsl_sf_lngamma_sgn_e(y, &lgy, &sgy); + int stat_gxy = gsl_sf_lngamma_sgn_e(xy, &lgxy, &sgxy); + *sgn = sgx * sgy * sgxy; + result->val = lgx.val + lgy.val - lgxy.val; + result->err = lgx.err + lgy.err + lgxy.err; + result->err += GSL_DBL_EPSILON * (fabs(lgx.val) + fabs(lgy.val) + fabs(lgxy.val)); + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_ERROR_SELECT_3(stat_gx, stat_gy, stat_gxy); + } +} + + +int +gsl_sf_beta_e(const double x, const double y, gsl_sf_result * result) +{ + if((x > 0 && y > 0) && x < 50.0 && y < 50.0) { + /* Handle the easy case */ + gsl_sf_result gx, gy, gxy; + gsl_sf_gamma_e(x, &gx); + gsl_sf_gamma_e(y, &gy); + gsl_sf_gamma_e(x+y, &gxy); + result->val = (gx.val*gy.val)/gxy.val; + result->err = gx.err * fabs(gy.val/gxy.val); + result->err += gy.err * fabs(gx.val/gxy.val); + result->err += fabs((gx.val*gy.val)/(gxy.val*gxy.val)) * gxy.err; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else if (isnegint(x) || isnegint(y)) { + DOMAIN_ERROR(result); + } else if (isnegint(x+y)) { /* infinity in the denominator */ + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } else { + gsl_sf_result lb; + double sgn; + int stat_lb = gsl_sf_lnbeta_sgn_e(x, y, &lb, &sgn); + if(stat_lb == GSL_SUCCESS) { + int status = gsl_sf_exp_err_e(lb.val, lb.err, result); + result->val *= sgn; + return status; + } + else { + result->val = 0.0; + result->err = 0.0; + return stat_lb; + } + } +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_lnbeta(const double x, const double y) +{ + EVAL_RESULT(gsl_sf_lnbeta_e(x, y, &result)); +} + +double gsl_sf_beta(const double x, const double y) +{ + EVAL_RESULT(gsl_sf_beta_e(x, y, &result)); +} |