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445 lines
13 KiB
C++
445 lines
13 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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#include "strong_typedef_type.hpp"
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#include <limits>
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#include <type_traits>
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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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constexpr 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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constexpr 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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constexpr 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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constexpr 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 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 If the min value is greater than the max, return value is the average of the min and max.
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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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*/
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template <typename T>
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constexpr T SoftClamp(const T a, const T min, const T max)
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{
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if (min > max) {
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using U = std::make_unsigned_t<T>;
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return min - (U(min) - max) / 2;
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}
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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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constexpr 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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constexpr 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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* Clamp the given value down to lie within the requested type.
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*
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* For example ClampTo<uint8_t> will return a value clamped to the range of 0
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* to 255. Anything smaller will become 0, anything larger will become 255.
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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 value within the given allowed range
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* for the return type.
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* @see Clamp(int, int, int)
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*/
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template <typename To, typename From, std::enable_if_t<std::is_integral<From>::value, int> = 0>
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constexpr To ClampTo(From value)
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{
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static_assert(std::numeric_limits<To>::is_integer, "Do not clamp from non-integer values");
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static_assert(std::numeric_limits<From>::is_integer, "Do not clamp to non-integer values");
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if constexpr (sizeof(To) >= sizeof(From) && std::numeric_limits<To>::is_signed == std::numeric_limits<From>::is_signed) {
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/* Same signedness and To type is larger or equal than From type, no clamping is required. */
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return static_cast<To>(value);
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}
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if constexpr (sizeof(To) > sizeof(From) && std::numeric_limits<To>::is_signed) {
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/* Signed destination and a larger To type, no clamping is required. */
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return static_cast<To>(value);
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}
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/* Get the bigger of the two types based on essentially the number of bits. */
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using BiggerType = typename std::conditional<sizeof(From) >= sizeof(To), From, To>::type;
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if constexpr (std::numeric_limits<To>::is_signed) {
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/* The output is a signed number. */
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if constexpr (std::numeric_limits<From>::is_signed) {
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/* Both input and output are signed. */
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return static_cast<To>(std::clamp<BiggerType>(value,
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std::numeric_limits<To>::lowest(), std::numeric_limits<To>::max()));
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}
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/* The input is unsigned, so skip the minimum check and use unsigned variant of the biggest type as intermediate type. */
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using BiggerUnsignedType = typename std::make_unsigned<BiggerType>::type;
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return static_cast<To>(std::min<BiggerUnsignedType>(std::numeric_limits<To>::max(), value));
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}
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/* The output is unsigned. */
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if constexpr (std::numeric_limits<From>::is_signed) {
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/* Input is signed; account for the negative numbers in the input. */
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if constexpr (sizeof(To) >= sizeof(From)) {
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/* If the output type is larger or equal to the input type, then only clamp the negative numbers. */
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return static_cast<To>(std::max<From>(value, 0));
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}
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/* The output type is smaller than the input type. */
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using BiggerSignedType = typename std::make_signed<BiggerType>::type;
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return static_cast<To>(std::clamp<BiggerSignedType>(value,
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std::numeric_limits<To>::lowest(), std::numeric_limits<To>::max()));
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}
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/* The input and output are unsigned, just clamp at the high side. */
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return static_cast<To>(std::min<BiggerType>(value, std::numeric_limits<To>::max()));
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}
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/**
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* Specialization of ClampTo for #StrongType::Typedef.
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*/
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template <typename To, typename From, std::enable_if_t<std::is_base_of<StrongTypedefBase, From>::value, int> = 0>
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constexpr To ClampTo(From value)
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{
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return ClampTo<To>(value.base());
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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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constexpr 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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constexpr 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, std::enable_if_t<std::disjunction_v<std::is_convertible<T, size_t>, std::is_base_of<StrongTypedefBase, T>>, int> = 0>
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constexpr bool IsInsideMM(const T x, const size_t min, const size_t max) noexcept
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{
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if constexpr (std::is_base_of_v<StrongTypedefBase, T>) {
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return (size_t)(x.base() - min) < (max - min);
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} else {
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return (size_t)(x - min) < (max - min);
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}
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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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constexpr 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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constexpr 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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constexpr 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 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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constexpr 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) for non-negative a and b (templated).
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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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template <typename T>
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constexpr inline T CeilDivT(T a, T 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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constexpr 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 ceil(a / b) * b for non-negative a and b (templated).
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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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template <typename T>
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constexpr inline T CeilT(T a, T b)
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{
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return CeilDivT<T>(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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constexpr 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 towards negative infinity for b > 0.
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* @param a Numerator
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* @param b Denominator
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* @return Quotient, rounded towards negative infinity
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*/
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template <typename T>
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constexpr inline T DivTowardsNegativeInf(T a, T b)
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{
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return (a / b) - (a % b < 0 ? 1 : 0);
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}
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/**
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* Computes a / b rounded towards positive infinity for b > 0.
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* @param a Numerator
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* @param b Denominator
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* @return Quotient, rounded towards positive infinity
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*/
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template <typename T>
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constexpr inline T DivTowardsPositiveInf(T a, T b)
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{
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return (a / b) + (a % b > 0 ? 1 : 0);
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}
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/**
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* Computes ten to the given power.
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* @param power The power of ten to get.
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* @return The power of ten.
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*/
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constexpr uint64_t PowerOfTen(int power)
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{
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assert(power >= 0 && power <= 20 /* digits in uint64_t */);
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uint64_t result = 1;
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for (int i = 0; i < power; i++) result *= 10;
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return result;
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}
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/**
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* Unsigned saturating add.
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*/
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template<typename T, std::enable_if_t<std::is_unsigned_v<T>, int> = 0>
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constexpr inline T SaturatingAdd(T a, T b)
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{
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#ifdef WITH_OVERFLOW_BUILTINS
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T c;
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if (unlikely(__builtin_add_overflow(a, b, &c))) {
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return std::numeric_limits<T>::max();
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}
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return c;
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#else
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T c = a + b;
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if (c < a) return std::numeric_limits<T>::max();
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return c;
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#endif
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}
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uint32_t IntSqrt(uint32_t num);
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uint32_t IntSqrt64(uint64_t num);
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uint32_t IntCbrt(uint64_t num);
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uint16_t RXCompressUint(uint32_t num);
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uint32_t RXDecompressUint(uint16_t num);
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#endif /* MATH_FUNC_HPP */
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