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100 lines
2.5 KiB
C++
100 lines
2.5 KiB
C++
/*
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* This file is part of OpenTTD.
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* 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.
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* 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.
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* 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/>.
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*/
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/** @file math_func.cpp Math functions. */
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#include "../stdafx.h"
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#include "math_func.hpp"
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#include "../safeguards.h"
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/**
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* Compute least common multiple (lcm) of arguments \a a and \a b, the smallest
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* integer value that is a multiple of both \a a and \a b.
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* @param a First number.
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* @param b second number.
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* @return Least common multiple of values \a a and \a b.
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*
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* @note This function only works for non-negative values of \a a and \a b.
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*/
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int LeastCommonMultiple(int a, int b)
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{
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if (a == 0 || b == 0) return 0; // By definition.
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if (a == 1 || a == b) return b;
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if (b == 1) return a;
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return a * b / GreatestCommonDivisor(a, b);
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}
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/**
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* Compute greatest common divisor (gcd) of \a a and \a b.
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* @param a First number.
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* @param b second number.
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* @return Greatest common divisor of \a a and \a b.
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*/
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int GreatestCommonDivisor(int a, int b)
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{
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while (b != 0) {
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int t = b;
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b = a % b;
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a = t;
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}
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return a;
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}
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/**
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* Deterministic approximate division.
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* Cancels out division errors stemming from the integer nature of the division over multiple runs.
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* @param a Dividend.
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* @param b Divisor.
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* @return a/b or (a/b)+1.
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*/
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int DivideApprox(int a, int b)
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{
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int random_like = ((a + b) * (a - b)) % b;
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int remainder = a % b;
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int ret = a / b;
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if (abs(random_like) < abs(remainder)) {
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ret += ((a < 0) ^ (b < 0)) ? -1 : 1;
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}
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return ret;
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}
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/**
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* Compute the integer square root.
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* @param num Radicand.
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* @return Rounded integer square root.
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* @note Algorithm taken from http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
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*/
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uint32_t IntSqrt(uint32_t num)
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{
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uint32_t res = 0;
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uint32_t bit = 1UL << 30; // Second to top bit number.
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/* 'bit' starts at the highest power of four <= the argument. */
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while (bit > num) bit >>= 2;
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while (bit != 0) {
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if (num >= res + bit) {
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num -= res + bit;
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res = (res >> 1) + bit;
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} else {
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res >>= 1;
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}
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bit >>= 2;
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}
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/* Arithmetic rounding to nearest integer. */
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if (num > res) res++;
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return res;
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}
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