| /* |
| * R : A Computer Language for Statistical Data Analysis |
| * Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka |
| * Copyright (C) 2000-2007 The R 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, a copy is available at |
| * https://www.R-project.org/Licenses/ |
| */ |
| |
| #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); |
| |
| #ifdef R_version_le_260 |
| 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); |
| } |
| #endif |
| |
| nx = 1 + (x/n)*x; |
| /* FIXME: This test is probably losing rather than gaining precision, |
| * now that pbeta(*, log_p = TRUE) is much better. |
| * Note however that a version of this test *is* needed for x*x > D_MAX */ |
| if(nx > 1e100) { /* <==> x*x > 1e100 * n */ |
| /* Danger of underflow. So use Abramowitz & Stegun 26.5.4 |
| pbeta(z, a, b) ~ z^a(1-z)^b / aB(a,b) ~ z^a / aB(a,b), |
| with z = 1/nx, a = n/2, b= 1/2 : |
| */ |
| double lval; |
| lval = -0.5*n*(2*log(fabs(x)) - log(n)) |
| - lbeta(0.5*n, 0.5) - log(0.5*n); |
| val = log_p ? lval : exp(lval); |
| } else { |
| val = (n > x * x) |
| ? pbeta (x * x / (n + x * x), 0.5, n / 2., /*lower_tail*/0, log_p) |
| : pbeta (1. / nx, n / 2., 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); |
| } |
| } |