mirror of https://github.com/OpenTTD/OpenTTD.git
307 lines
8.6 KiB
C++
307 lines
8.6 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.hpp Integer math functions */
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#ifndef MATH_FUNC_HPP
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#define MATH_FUNC_HPP
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/**
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* Returns the absolute value of (scalar) variable.
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*
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* @note assumes variable to be signed
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* @param a The value we want to unsign
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* @return The unsigned value
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*/
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template <typename T>
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static inline T abs(const T a)
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{
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return (a < (T)0) ? -a : a;
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}
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/**
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* Return the smallest multiple of n equal or greater than x
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*
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* @note n must be a power of 2
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* @param x The min value
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* @param n The base of the number we are searching
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* @return The smallest multiple of n equal or greater than x
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*/
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template <typename T>
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static inline T Align(const T x, uint n)
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{
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assert((n & (n - 1)) == 0 && n != 0);
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n--;
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return (T)((x + n) & ~((T)n));
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}
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/**
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* Return the smallest multiple of n equal or greater than x
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* Applies to pointers only
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*
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* @note n must be a power of 2
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* @param x The min value
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* @param n The base of the number we are searching
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* @return The smallest multiple of n equal or greater than x
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* @see Align()
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*/
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template <typename T>
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static inline T *AlignPtr(T *x, uint n)
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{
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static_assert(sizeof(size_t) == sizeof(void *));
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return reinterpret_cast<T *>(Align((size_t)x, n));
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}
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/**
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* Clamp a value between an interval.
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*
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* This function returns a value which is between the given interval of
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* min and max. If the given value is in this interval the value itself
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* is returned otherwise the border of the interval is returned, according
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* which side of the interval was 'left'.
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*
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* @note The min value must be less or equal of max or you get some
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* unexpected results.
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* @param a The value to clamp/truncate.
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* @param min The minimum of the interval.
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* @param max the maximum of the interval.
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* @returns A value between min and max which is closest to a.
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* @see ClampU(uint, uint, uint)
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* @see Clamp(int, int, int)
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*/
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template <typename T>
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static inline T Clamp(const T a, const T min, const T max)
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{
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assert(min <= max);
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if (a <= min) return min;
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if (a >= max) return max;
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return a;
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}
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/**
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* Clamp an integer between an interval.
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*
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* This function returns a value which is between the given interval of
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* min and max. If the given value is in this interval the value itself
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* is returned otherwise the border of the interval is returned, according
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* which side of the interval was 'left'.
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*
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* @note The min value must be less or equal of max or you get some
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* unexpected results.
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* @param a The value to clamp/truncate.
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* @param min The minimum of the interval.
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* @param max the maximum of the interval.
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* @returns A value between min and max which is closest to a.
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* @see ClampU(uint, uint, uint)
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*/
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static inline int Clamp(const int a, const int min, const int max)
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{
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return Clamp<int>(a, min, max);
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}
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/**
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* Clamp an unsigned integer between an interval.
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*
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* This function returns a value which is between the given interval of
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* min and max. If the given value is in this interval the value itself
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* is returned otherwise the border of the interval is returned, according
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* which side of the interval was 'left'.
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*
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* @note The min value must be less or equal of max or you get some
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* unexpected results.
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* @param a The value to clamp/truncate.
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* @param min The minimum of the interval.
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* @param max the maximum of the interval.
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* @returns A value between min and max which is closest to a.
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* @see Clamp(int, int, int)
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*/
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static inline uint ClampU(const uint a, const uint min, const uint max)
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{
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return Clamp<uint>(a, min, max);
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}
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/**
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* Reduce a signed 64-bit int to a signed 32-bit one
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*
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* This function clamps a 64-bit integer to a 32-bit integer.
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* If the 64-bit value is smaller than the smallest 32-bit integer
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* value 0x80000000 this value is returned (the left one bit is the sign bit).
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* If the 64-bit value is greater than the greatest 32-bit integer value 0x7FFFFFFF
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* this value is returned. In all other cases the 64-bit value 'fits' in a
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* 32-bits integer field and so the value is casted to int32 and returned.
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*
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* @param a The 64-bit value to clamps
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* @return The 64-bit value reduced to a 32-bit value
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* @see Clamp(int, int, int)
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*/
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static inline int32 ClampToI32(const int64 a)
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{
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return static_cast<int32>(Clamp<int64>(a, INT32_MIN, INT32_MAX));
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}
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/**
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* Reduce an unsigned 64-bit int to an unsigned 16-bit one
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*
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* @param a The 64-bit value to clamp
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* @return The 64-bit value reduced to a 16-bit value
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* @see ClampU(uint, uint, uint)
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*/
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static inline uint16 ClampToU16(const uint64 a)
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{
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/* MSVC thinks, in its infinite wisdom, that int min(int, int) is a better
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* match for min(uint64, uint) than uint64 min(uint64, uint64). As such we
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* need to cast the UINT16_MAX to prevent MSVC from displaying its
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* infinite loads of warnings. */
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return static_cast<uint16>(std::min(a, static_cast<uint64>(UINT16_MAX)));
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}
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/**
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* Returns the (absolute) difference between two (scalar) variables
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*
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* @param a The first scalar
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* @param b The second scalar
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* @return The absolute difference between the given scalars
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*/
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template <typename T>
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static inline T Delta(const T a, const T b)
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{
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return (a < b) ? b - a : a - b;
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}
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/**
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* Checks if a value is between a window started at some base point.
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*
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* This function checks if the value x is between the value of base
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* and base+size. If x equals base this returns true. If x equals
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* base+size this returns false.
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*
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* @param x The value to check
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* @param base The base value of the interval
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* @param size The size of the interval
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* @return True if the value is in the interval, false else.
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*/
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template <typename T>
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static inline bool IsInsideBS(const T x, const size_t base, const size_t size)
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{
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return (size_t)(x - base) < size;
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}
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/**
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* Checks if a value is in an interval.
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*
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* Returns true if a value is in the interval of [min, max).
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*
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* @param x The value to check
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* @param min The minimum of the interval
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* @param max The maximum of the interval
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* @see IsInsideBS()
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*/
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template <typename T>
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static constexpr inline bool IsInsideMM(const T x, const size_t min, const size_t max) noexcept
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{
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return (size_t)(x - min) < (max - min);
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}
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/**
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* Type safe swap operation
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* @param a variable to swap with b
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* @param b variable to swap with a
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*/
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template <typename T>
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static inline void Swap(T &a, T &b)
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{
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T t = a;
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a = b;
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b = t;
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}
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/**
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* Converts a "fract" value 0..255 to "percent" value 0..100
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* @param i value to convert, range 0..255
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* @return value in range 0..100
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*/
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static inline uint ToPercent8(uint i)
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{
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assert(i < 256);
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return i * 101 >> 8;
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}
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/**
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* Converts a "fract" value 0..65535 to "percent" value 0..100
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* @param i value to convert, range 0..65535
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* @return value in range 0..100
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*/
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static inline uint ToPercent16(uint i)
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{
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assert(i < 65536);
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return i * 101 >> 16;
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}
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int LeastCommonMultiple(int a, int b);
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int GreatestCommonDivisor(int a, int b);
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int DivideApprox(int a, int b);
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/**
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* Computes ceil(a / b) for non-negative a and b.
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* @param a Numerator
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* @param b Denominator
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* @return Quotient, rounded up
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*/
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static inline uint CeilDiv(uint a, uint b)
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{
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return (a + b - 1) / b;
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}
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/**
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* Computes ceil(a / b) * b for non-negative a and b.
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* @param a Numerator
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* @param b Denominator
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* @return a rounded up to the nearest multiple of b.
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*/
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static inline uint Ceil(uint a, uint b)
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{
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return CeilDiv(a, b) * b;
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}
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/**
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* Computes round(a / b) for signed a and unsigned b.
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* @param a Numerator
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* @param b Denominator
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* @return Quotient, rounded to nearest
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*/
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static inline int RoundDivSU(int a, uint b)
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{
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if (a > 0) {
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/* 0.5 is rounded to 1 */
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return (a + static_cast<int>(b) / 2) / static_cast<int>(b);
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} else {
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/* -0.5 is rounded to 0 */
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return (a - (static_cast<int>(b) - 1) / 2) / static_cast<int>(b);
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}
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}
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/**
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* Computes (a / b) rounded away from zero.
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* @param a Numerator
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* @param b Denominator
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* @return Quotient, rounded away from zero
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*/
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static inline int DivAwayFromZero(int a, uint b)
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{
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const int _b = static_cast<int>(b);
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if (a > 0) {
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return (a + _b - 1) / _b;
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} else {
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/* Note: Behaviour of negative numerator division is truncation toward zero. */
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return (a - _b + 1) / _b;
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}
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}
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uint32 IntSqrt(uint32 num);
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#endif /* MATH_FUNC_HPP */
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