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/* specfunc/beta.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman */
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#include <config.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_sf_exp.h>
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#include <gsl/gsl_sf_log.h>
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#include <gsl/gsl_sf_psi.h>
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#include <gsl/gsl_sf_gamma.h>
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#include "error.h"
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static double
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isnegint (const double x)
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{
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return (x < 0) && (x == floor(x));
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}
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int
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gsl_sf_lnbeta_e(const double x, const double y, gsl_sf_result * result)
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{
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double sgn;
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int status = gsl_sf_lnbeta_sgn_e(x,y,result,&sgn);
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if (sgn == -1) {
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DOMAIN_ERROR(result);
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}
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return status;
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}
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int
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gsl_sf_lnbeta_sgn_e(const double x, const double y, gsl_sf_result * result, double * sgn)
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{
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/* CHECK_POINTER(result) */
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if(x == 0.0 || y == 0.0) {
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*sgn = 0.0;
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DOMAIN_ERROR(result);
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} else if (isnegint(x) || isnegint(y)) {
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*sgn = 0.0;
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DOMAIN_ERROR(result); /* not defined for negative integers */
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}
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/* See if we can handle the postive case with min/max < 0.2 */
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if (x > 0 && y > 0) {
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const double max = GSL_MAX(x,y);
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const double min = GSL_MIN(x,y);
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const double rat = min/max;
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if(rat < 0.2) {
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/* min << max, so be careful
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* with the subtraction
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*/
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double lnpre_val;
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double lnpre_err;
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double lnpow_val;
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double lnpow_err;
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double t1, t2, t3;
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gsl_sf_result lnopr;
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gsl_sf_result gsx, gsy, gsxy;
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gsl_sf_gammastar_e(x, &gsx;;
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gsl_sf_gammastar_e(y, &gsy;;
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gsl_sf_gammastar_e(x+y, &gsxy);
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gsl_sf_log_1plusx_e(rat, &lnopr);
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lnpre_val = log(gsx.val*gsy.val/gsxy.val * M_SQRT2*M_SQRTPI);
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lnpre_err = gsx.err/gsx.val + gsy.err/gsy.val + gsxy.err/gsxy.val;
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t1 = min*log(rat);
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t2 = 0.5*log(min);
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t3 = (x+y-0.5)*lnopr.val;
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lnpow_val = t1 - t2 - t3;
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lnpow_err = GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3));
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lnpow_err += fabs(x+y-0.5) * lnopr.err;
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result->val = lnpre_val + lnpow_val;
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result->err = lnpre_err + lnpow_err;
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result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
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*sgn = 1.0;
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return GSL_SUCCESS;
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}
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}
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/* General case - Fallback */
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{
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gsl_sf_result lgx, lgy, lgxy;
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double sgx, sgy, sgxy, xy = x+y;
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int stat_gx = gsl_sf_lngamma_sgn_e(x, &lgx, &sgx);
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int stat_gy = gsl_sf_lngamma_sgn_e(y, &lgy, &sgy);
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int stat_gxy = gsl_sf_lngamma_sgn_e(xy, &lgxy, &sgxy);
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*sgn = sgx * sgy * sgxy;
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result->val = lgx.val + lgy.val - lgxy.val;
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result->err = lgx.err + lgy.err + lgxy.err;
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result->err += 2.0 * GSL_DBL_EPSILON * (fabs(lgx.val) + fabs(lgy.val) + fabs(lgxy.val));
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result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
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return GSL_ERROR_SELECT_3(stat_gx, stat_gy, stat_gxy);
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}
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}
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int
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gsl_sf_beta_e(const double x, const double y, gsl_sf_result * result)
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{
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if((x > 0 && y > 0) && x < 50.0 && y < 50.0) {
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/* Handle the easy case */
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gsl_sf_result gx, gy, gxy;
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gsl_sf_gamma_e(x, &gx;;
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gsl_sf_gamma_e(y, &gy;;
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gsl_sf_gamma_e(x+y, &gxy);
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result->val = (gx.val*gy.val)/gxy.val;
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result->err = gx.err * fabs(gy.val/gxy.val);
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result->err += gy.err * fabs(gx.val/gxy.val);
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result->err += fabs((gx.val*gy.val)/(gxy.val*gxy.val)) * gxy.err;
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result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
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return GSL_SUCCESS;
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}
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else if (isnegint(x) || isnegint(y)) {
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DOMAIN_ERROR(result);
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} else if (isnegint(x+y)) { /* infinity in the denominator */
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result->val = 0.0;
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result->err = 0.0;
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return GSL_SUCCESS;
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} else {
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gsl_sf_result lb;
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double sgn;
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int stat_lb = gsl_sf_lnbeta_sgn_e(x, y, &lb, &sgn);
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if(stat_lb == GSL_SUCCESS) {
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int status = gsl_sf_exp_err_e(lb.val, lb.err, result);
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result->val *= sgn;
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return status;
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}
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else {
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result->val = 0.0;
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result->err = 0.0;
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return stat_lb;
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}
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}
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}
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/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
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#include "eval.h"
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double gsl_sf_lnbeta(const double x, const double y)
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{
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EVAL_RESULT(gsl_sf_lnbeta_e(x, y, &result));
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}
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double gsl_sf_beta(const double x, const double y)
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{
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EVAL_RESULT(gsl_sf_beta_e(x, y, &result));
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}
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