/* $Id: math_func.cpp 26482 2014-04-23 20:13:33Z rubidium $ */

/*
 * This file is part of OpenTTD.
 * OpenTTD 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, version 2.
 * OpenTTD 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 OpenTTD. If not, see <http://www.gnu.org/licenses/>.
 */

/** @file math_func.cpp Math functions. */

#include "../stdafx.h"
#include "math_func.hpp"

#include "../safeguards.h"

/**
 * Compute least common multiple (lcm) of arguments \a a and \a b, the smallest
 * integer value that is a multiple of both \a a and \a b.
 * @param a First number.
 * @param b second number.
 * @return Least common multiple of values \a a and \a b.
 *
 * @note This function only works for non-negative values of \a a and \a b.
 */
int LeastCommonMultiple(int a, int b)
{
	if (a == 0 || b == 0) return 0; // By definition.
	if (a == 1 || a == b) return b;
	if (b == 1) return a;

	return a * b / GreatestCommonDivisor(a, b);
}

/**
 * Compute greatest common divisor (gcd) of \a a and \a b.
 * @param a First number.
 * @param b second number.
 * @return Greatest common divisor of \a a and \a b.
 */
int GreatestCommonDivisor(int a, int b)
{
	while (b != 0) {
		int t = b;
		b = a % b;
		a = t;
	}
	return a;

}

/**
 * Deterministic approximate division.
 * Cancels out division errors stemming from the integer nature of the division over multiple runs.
 * @param a Dividend.
 * @param b Divisor.
 * @return a/b or (a/b)+1.
 */
int DivideApprox(int a, int b)
{
	int random_like = ((a + b) * (a - b)) % b;

	int remainder = a % b;

	int ret = a / b;
	if (abs(random_like) < abs(remainder)) {
		ret += ((a < 0) ^ (b < 0)) ? -1 : 1;
	}

	return ret;
}

/**
 * Compute the integer square root.
 * @param num Radicand.
 * @return Rounded integer square root.
 * @note Algorithm taken from http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
 */
uint32 IntSqrt(uint32 num)
{
	uint32 res = 0;
	uint32 bit = 1UL << 30; // Second to top bit number.

	/* 'bit' starts at the highest power of four <= the argument. */
	while (bit > num) bit >>= 2;

	while (bit != 0) {
		if (num >= res + bit) {
			num -= res + bit;
			res = (res >> 1) + bit;
		} else {
			res >>= 1;
		}
		bit >>= 2;
	}

	/* Arithmetic rounding to nearest integer. */
	if (num > res) res++;

	return res;
}
