/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1995, 1996  Robert Gentleman and Ross Ihaka
 *  Copyright (C) 2000-2006   The R Development Core Team
 *
 *  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.
 */

#include "nmath.h"
#include "dpq.h"

double pt(double x, double n, int lower_tail, int log_p)
{
/* return  P[ T <= x ]	where
 * T ~ t_{n}  (t distrib. with n degrees of freedom).

 *	--> ./pnt.c for NON-central
 */
    double val, nx;
#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(n))
	return x + n;
#endif
    if (n <= 0.0) ML_ERR_return_NAN;

    if(!R_FINITE(x))
	return (x < 0) ? R_DT_0 : R_DT_1;
    if(!R_FINITE(n))
	return pnorm(x, 0.0, 1.0, lower_tail, log_p);
    if (n > 4e5) { /*-- Fixme(?): test should depend on `n' AND `x' ! */
	/* Approx. from	 Abramowitz & Stegun 26.7.8 (p.949) */
	val = 1./(4.*n);
	return pnorm(x*(1. - val)/sqrt(1. + x*x*2.*val), 0.0, 1.0,
		     lower_tail, log_p);
    }

    nx = (1 + (x/n)*x);
    if(fabs(x) > 1e30) {
	/* Danger of underflow. So use Abramowitz & Stegun 26.5.4
	   pbeta(z, a, b) ~ z^a(1-z)^b/aB(a,b)
	   ~ nx^(-n/2)/[n/2, B(n/2, 1/2)]
	*/
	double lval;
	lval = -0.5*n*(2*log(fabs(x)) - log(n));
	lval -= lbeta(0.5*n, 0.5) + log(0.5*n);
	val = log_p ? lval : exp(lval);
    } else {
	val = pbeta(1.0/nx, n / 2.0, 0.5, /*lower_tail*/1, log_p);
    }
    

    /* Use "1 - v"  if	lower_tail  and	 x > 0 (but not both):*/
    if(x <= 0.)
	lower_tail = !lower_tail;

    if(log_p) {
	if(lower_tail) return log1p(-0.5*exp(val));
	else return val - M_LN2; /* = log(.5* pbeta(....)) */
    }
    else {
	val /= 2.;
	return R_D_Cval(val);
    }
}
