/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998   Ross Ihaka
 *  Copyright (C) 2000-9 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, a copy is available at
 *  http://www.r-project.org/Licenses/
 */
package jdistlib;

import static java.lang.Math.*;
import static jdistlib.math.MathFunctions.isInfinite;
import static jdistlib.math.MathFunctions.tanpi;
import jdistlib.generic.GenericDistribution;
import jdistlib.rng.RandomEngine;

public class Cauchy extends GenericDistribution {
	public static final double density(double x, double location, double scale, boolean give_log)
	{
		double y;
		/* NaNs propagated correctly */
		if (Double.isNaN(x) || Double.isNaN(location) || Double.isNaN(scale)) return x + location + scale;
		if (scale <= 0) return Double.NaN;

		y = (x - location) / scale;
		return give_log ?
			- log(PI * scale * (1. + y * y)) :
			1. / (PI * scale * (1. + y * y));
	}

	public static final double cumulative(double x, double location, double scale, boolean lower_tail, boolean log_p)
	{
		if (Double.isNaN(x) || Double.isNaN(location) || Double.isNaN(scale)) return x + location + scale;
		if (scale <= 0) return Double.NaN;

		x = (x - location) / scale;
		if (Double.isNaN(x)) return Double.NaN;
		if(isInfinite(x)) {
			if(x < 0) return (lower_tail ? (log_p ? Double.NEGATIVE_INFINITY : 0.) : (log_p ? 0. : 1.));
			else return (lower_tail ? (log_p ? 0. : 1.) : (log_p ? Double.NEGATIVE_INFINITY : 0.));
		}
		if (!lower_tail)
			x = -x;
		// for large x, the standard formula suffers from cancellation.
		// This is from Morten Welinder thanks to  Ian Smith's  atan(1/x) :
		if (abs(x) > 1) {
			double y = atan(1.0/x) / PI;
			//return (x > 0) ? R_D_Clog(y) : R_D_val(-y);
			return (x > 0) ? (log_p	? log1p(-(y)) : (0.5 - (y) + 0.5)) : (log_p	? log(-y) : (-y));
		}
		//return R_D_val(0.5 + atan(x) / M_PI);
		x = 0.5 + atan(x) / PI;
		return (log_p ? log(x) : (x));
	}

	public static final double quantile(double p, double location, double scale, boolean lower_tail, boolean log_p)
	{
		if (Double.isNaN(p) || Double.isNaN(location) || Double.isNaN(scale))
			return p + location + scale;
		//R_Q_P01_check(p);
		if ((log_p	&& p > 0) || (!log_p && (p < 0 || p > 1)) ) return Double.NaN;
		if (scale <= 0 || isInfinite(scale)) {
			if (scale == 0) return location;
			/* else */ return Double.NaN;
		}

		if (log_p) {
			if (p > -1) {
				/* when ep := exp(p),
				 * tan(pi*ep)= -tan(pi*(-ep))= -tan(pi*(-ep)+pi) = -tan(pi*(1-ep)) =
				 *		 = -tan(pi*(-expm1(p))
				 * for p ~ 0, exp(p) ~ 1, tan(~0) may be better than tan(~pi).
				 */
				if (p == 0.) /* needed, since 1/tan(-0) = -Inf  for some arch. */
					return location + (lower_tail ? scale : -scale) * Double.POSITIVE_INFINITY;
				lower_tail = !lower_tail;
				p = -expm1(p);
			} else
				p = exp(p);
		} else {
			if (p > 0.5) {
				if (p == 1.)
					return location + (lower_tail ? scale : -scale) * Double.POSITIVE_INFINITY;
				p = 1 - p;
				lower_tail = !lower_tail;
			}
		}

		if (p == 0.5) return location; // avoid 1/Inf below
		if (p == 0) return location + (lower_tail ? scale : -scale) * Double.NEGATIVE_INFINITY; // p = 1. is handled above
		return location + (lower_tail ? -scale : scale) / tanpi( p);
		/*	-1/tan(pi * p) = -cot(pi * p) = tan(pi * (p - 1/2))  */
	}

	public static final double random(double location, double scale, RandomEngine random)
	{
		if (Double.isNaN(location) || isInfinite(scale) || scale < 0) return Double.NaN;
		if (scale == 0. || isInfinite(location)) return location;
		return location + scale * tanpi(random.nextDouble());
	}

	public static final double[] random(int n, double location, double scale, RandomEngine random) {
		double[] rand = new double[n];
		for (int i = 0; i < n; i++)
			rand[i] = random(location, scale, random);
		return rand;
	}

	protected double location, scale;

	/**
	 * Standard constructor for Cauchy (location = 0, scale = 1)
	 */
	public Cauchy() {
		this(0, 1);
	}

	public Cauchy(double location, double scale) {
		this.location = location; this.scale = scale;
	}

	@Override
	public double density(double x, boolean log) {
		return density(x, location, scale, log);
	}

	@Override
	public double cumulative(double p, boolean lower_tail, boolean log_p) {
		return cumulative(p, location, scale, lower_tail, log_p);
	}

	@Override
	public double quantile(double q, boolean lower_tail, boolean log_p) {
		return quantile(q, location, scale, lower_tail, log_p);
	}

	@Override
	public double random() {
		return random(location, scale, random);
	}

	/*
	public static final void main(String[] args) {
		double x;
		x = 25.24006759446327;
		x = atan(1.0/((x - 12.0) / 2.0)) / M_PI ;
		System.out.println(String.format("%3.18g", x));
		// R's value    = 0.04772202611746988870634
		// Java's value = 0.0477220261174698900

		x = 0.04772202611746988870634;
		// R's value    = 25.24006759446326952911
		// Java's value = 25.240067594463270
		System.out.println(String.format("%3.18g", 12 + 2 / tan(M_PI * x)));
	}
	//*/
}