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/*
* 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;
}
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