beta.c

/* 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));
}