src/nmath/plogis.c

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1995, 1996	Robert Gentleman and Ross Ihaka
 *  Copyright (C) 2000		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"

/* Compute  log(1 + exp(x))  without overflow (and fast for x > 18)
   For the two cutoffs, consider in R
   curve(log1p(exp(x)) - x,       33.1, 33.5, n=2^10)
   curve(x+exp(-x) - log1p(exp(x)), 15, 25,   n=2^11)
*/
double Rf_log1pexp(double x) {
    if(x <= 18.) return log1p(exp(x));
    if(x > 33.3) return x;
    // else: 18.0 < x <= 33.3 :
    return x + exp(-x);
}

double plogis(double x, double location, double scale,
	      int lower_tail, int log_p)
{
#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(location) || ISNAN(scale))
	return x + location + scale;
#endif
    if (scale <= 0.0)	ML_ERR_return_NAN;

    x = (x - location) / scale;
    if (ISNAN(x))	ML_ERR_return_NAN;
    R_P_bounds_Inf_01(x);

    if(log_p) {
	// log(1 / (1 + exp( +- x ))) = -log(1 + exp( +- x))
	return -Rf_log1pexp(lower_tail ? -x : x);
    } else {
	return 1 / (1 + exp(lower_tail ? -x : x));
    }
}