src/core/math_func.cpp

   1 /* $Id$ */
   2
   3 /*
   4  * This file is part of OpenTTD.
   5  * 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.
   6  * 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.
   7  * 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/>.
   8  */
   9
  10 /** @file math_func.cpp Math functions. */
  11
  12 #include "../stdafx.h"
  13 #include "math_func.hpp"
  14
  15 /**
  16  * Compute least common multiple (lcm) of arguments \a a and \a b, the smallest
  17  * integer value that is a multiple of both \a a and \a b.
  18  * @param a First number.
  19  * @param b second number.
  20  * @return Least common multiple of values \a a and \a b.
  21  *
  22  * @note This function only works for non-negative values of \a a and \a b.
  23  */
  24 int LeastCommonMultiple(int a, int b)
  25 {
  26         if (a == 0 || b == 0) return 0; // By definition.
  27         if (a == 1 || a == b) return b;
  28         if (b == 1) return a;
  29
  30         return a * b / GreatestCommonDivisor(a, b);
  31 }
  32
  33 /**
  34  * Compute greatest common divisor (gcd) of \a a and \a b.
  35  * @param a First number.
  36  * @param b second number.
  37  * @return Greatest common divisor of \a a and \a b.
  38  */
  39 int GreatestCommonDivisor(int a, int b)
  40 {
  41         while (b != 0) {
  42                 int t = b;
  43                 b = a % b;
  44                 a = t;
  45         }
  46         return a;
  47
  48 }
  49
  50 /**
  51  * Deterministic approximate division.
  52  * Cancels out division errors stemming from the integer nature of the division over multiple runs.
  53  * @param a Dividend.
  54  * @param b Divisor.
  55  * @return a/b or (a/b)+1.
  56  */
  57 int DivideApprox(int a, int b)
  58 {
  59         int random_like = ((a + b) * (a - b)) % b;
  60
  61         int remainder = a % b;
  62
  63         int ret = a / b;
  64         if (abs(random_like) < abs(remainder)) {
  65                 ret += ((a < 0) ^ (b < 0)) ? -1 : 1;
  66         }
  67
  68         return ret;
  69 }
  70
  71 /**
  72  * Compute the integer square root.
  73  * @param num Radicand.
  74  * @return Rounded integer square root.
  75  * @note Algorithm taken from http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
  76  */
  77 uint32 IntSqrt(uint32 num)
  78 {
  79         uint32 res = 0;
  80         uint32 bit = 1UL << 30; // Second to top bit number.
  81
  82         /* 'bit' starts at the highest power of four <= the argument. */
  83         while (bit > num) bit >>= 2;
  84
  85         while (bit != 0) {
  86                 if (num >= res + bit) {
  87                         num -= res + bit;
  88                         res = (res >> 1) + bit;
  89                 } else {
  90                         res >>= 1;
  91                 }
  92                 bit >>= 2;
  93         }
  94
  95         /* Arithmetic rounding to nearest integer. */
  96         if (num > res) res++;
  97
  98         return res;
  99 }