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150 lines
3.6 KiB
C++
150 lines
3.6 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 "bitmath_func.hpp"
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#include "../safeguards.h"
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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 = (((int64_t) (a + b)) * ((int64_t) (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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/**
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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 IntSqrt64(uint64_t num)
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{
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uint64_t res = 0;
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uint64_t bit = 1ULL << 62; // 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 (uint32_t)res;
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}
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/**
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* Compute the integer cube 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 https://stackoverflow.com/a/56738014
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*/
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uint32_t IntCbrt(uint64_t num)
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{
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uint64_t r0 = 1;
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uint64_t r1 = 0;
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if (num == 0) return 0;
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#ifdef WITH_BITMATH_BUILTINS
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int b = 64 - __builtin_clzll(num);
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#ifdef _DEBUG
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assert(b == FindLastBit(num) + 1);
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#endif
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#else
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int b = FindLastBit(num) + 1;
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#endif
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r0 <<= (b + 2) / 3; /* ceil(b / 3) */
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do /* quadratic convergence: */
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{
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r1 = r0;
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r0 = (2 * r1 + num / (r1 * r1)) / 3;
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}
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while (r0 < r1);
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return ((uint32_t) r1); /* floor(cbrt(x)); */
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}
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/**
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* Compress unsigned integer into 16 bits, in a way that increases dynamic range, at the expense of precision for large values
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*/
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uint16_t RXCompressUint(uint32_t num)
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{
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if (num <= 0x100) return num;
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if (num <= 0x7900) return 0x100 + ((num - 0x100) >> 3);
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return std::min<uint32_t>(UINT16_MAX, 0x1000 + ((num - 0x7900) >> 6));
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}
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/**
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* Inverse of RXCompressUint
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*/
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uint32_t RXDecompressUint(uint16_t num)
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{
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if (num > 0x1000) return ((num - 0x1000) << 6) + 0x7900;
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if (num > 0x100) return ((num - 0x100) << 3) + 0x100;
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return num;
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}
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