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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 <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 += 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 "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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