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- /* 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 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_exp.h"
- #include "gsl_sf_log.h"
- #include "gsl_sf_psi.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_specfunc__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 += 2.0 * 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 "gsl_specfunc__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));
- }
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