💿🐜 Antkeeper source code
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331 lines
7.6 KiB
331 lines
7.6 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_BIT_MATH_HPP
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#define ANTKEEPER_BIT_MATH_HPP
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/// Bitwise math
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namespace bit {
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/**
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* Compresses the even bits of a value into the lower half, then clears the upper half.
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*
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* @param x Value to compress.
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* @return Compressed value.
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*/
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template <class T>
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constexpr T compress(T x) noexcept;
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/**
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* Returns the number of set bits in a value, known as a *population count* or *Hamming weight*.
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*
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* @param x Value to count.
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* @return Number of set bits in @p x.
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*/
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template <class T>
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constexpr int count(T x) noexcept;
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/**
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* Performs a single-point crossover between two values.
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*
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* @param a First value.
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* @param b Second value.
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* @param i Index of the crossover point.
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* @return Crossed over value.
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*/
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template <class T>
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constexpr T crossover(T a, T b, int i) noexcept;
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/**
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* Performs an n-point crossover between two values.
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*
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* @param a First value.
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* @param b Second value.
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* @param mask Bit mask with set bits marking crossover points.
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* @return Crossed over value.
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*/
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template <class T>
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constexpr T crossover_n(T a, T b, T mask) noexcept;
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/**
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* Reads bits from the least significant bits of a value and returns them in the positions marked by a mask.
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*
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* @param x Value from which bits should be read.
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* @param mask Bit mask indicating where bits should be deposited.
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* @return Bits from the least significant bits of @p x in the positions marked by @p mask.
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*/
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template <class T>
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constexpr T deposit(T x, T mask) noexcept;
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/**
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* Interleaves bits of the lower and upper halves of a value.
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*
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* @param x Value to desegregate.
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* @return Value with bits from the upper half of @p x interleaved with bits from the lower half.
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*/
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template <class T>
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constexpr T desegregate(T x) noexcept;
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/**
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* Returns the number of differing bits between two values, known as *Hamming distance*.
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*
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* @param x First value.
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* @param y Second value.
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* @return Hamming distance between @px and @p y.
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*/
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template <class T>
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constexpr int difference(T x, T y) noexcept;
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/**
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* Moves bits from the lower half of a value to occupy all even bits, and clears all odd bits.
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*
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* @param x Value to expand.
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* @return Expanded value.
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*/
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template <class T>
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constexpr T expand(T x) noexcept;
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/**
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* Reads bits from a value in the positions marked by a mask and returns them in the least significant bits.
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*
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* @param x Value from which bits should be read.
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* @param mask Bit mask indicating which bits to extract.
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* @return Bits of @p x from the positions marked by @p mask in the least significant bits.
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*/
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template <class T>
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constexpr T extract(T x, T mask) noexcept;
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/**
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* Flips a single bit in a value.
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*
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* @param x Value to modify.
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* @param i Index of the bit to flip.
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* @return Copy of @p x with one bit flipped.
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*/
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template <class T>
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constexpr T flip(T x, int i) noexcept;
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/**
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* Returns a value with even bits containing the first value's lower half, and odd bits containing the second value's lower half.
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*
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* @param a First value.
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* @param b Second value.
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* @return Value with bits from the lower halves of @p a and @p b interleaved.
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*/
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template <class T, class U = T>
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constexpr U interleave(T a, T b) noexcept;
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/**
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* Merges the bits of two values using a bit mask.
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*
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* @param a First value.
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* @param b Second value.
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* @param mask Bit mask with zeros where bits from @p a should be used, and ones where bits from @p b should be used.
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* @return Merged value.
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*/
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template <class T>
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constexpr T merge(T a, T b, T mask) noexcept;
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/**
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* Returns the parity of a value.
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*
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* @param x Value to test.
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* @return `1` if an odd number of bits are set, `0` otherwise.
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*/
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template <class T>
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constexpr T parity(T x) noexcept;
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/**
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* Segregates the odd and even bits of a value.
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*
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* @param x Value to segregate.
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* @return Value with even bits of @p x in the lower half, and odd bits in the upper half.
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*/
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template <class T>
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constexpr T segregate(T x) noexcept;
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/**
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* Swaps the each odd bit with its following even bit.
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*
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* @param x Value in which adjacent bits should be swap.
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* @return Copy of @p x with adjacent bits swapped.
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*/
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template <class T>
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constexpr T swap_adjacent(T x) noexcept;
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template <class T>
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constexpr T compress(T x) noexcept
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{
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x &= T(0x5555555555555555);
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x = (x ^ (x >> 1)) & T(0x3333333333333333);
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x = (x ^ (x >> 2)) & T(0x0f0f0f0f0f0f0f0f);
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if constexpr(sizeof(T) >= 2)
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x = (x ^ (x >> 4)) & T(0x00ff00ff00ff00ff);
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if constexpr(sizeof(T) >= 4)
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x = (x ^ (x >> 8)) & T(0x0000ffff0000ffff);
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if constexpr(sizeof(T) >= 8)
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x = (x ^ (x >> 16)) & T(0x00000000ffffffff);
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return x;
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}
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template <class T>
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constexpr int count(T x) noexcept
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{
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int n = 0;
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for (; x; ++n)
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x &= x - 1;
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return n;
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}
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template <class T>
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inline constexpr T crossover(T a, T b, int i) noexcept
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{
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T mask = (T(1) << i) - 1;
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return merge(b, a, mask);
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}
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template <class T>
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constexpr T crossover_n(T a, T b, T mask) noexcept
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{
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T merge = ~T(0) * parity(mask);
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while (mask)
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{
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merge ^= (mask ^ (mask - 1)) >> 1;
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mask &= mask - 1;
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}
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return merge(a, b, merge);
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}
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template <class T>
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inline constexpr T desegregate(T x) noexcept
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{
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return interleave<T>(x, x >> (sizeof(T) << 2));
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}
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template <class T>
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constexpr T expand(T x) noexcept
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{
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x &= (1 << (sizeof(T) << 2)) - 1;
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if constexpr(sizeof(T) >= 8)
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x = (x ^ (x << 16)) & T(0x0000ffff0000ffff);
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if constexpr(sizeof(T) >= 4)
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x = (x ^ (x << 8)) & T(0x00ff00ff00ff00ff);
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if constexpr(sizeof(T) >= 2)
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x = (x ^ (x << 4)) & T(0x0f0f0f0f0f0f0f0f);
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x = (x ^ (x << 2)) & T(0x3333333333333333);
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x = (x ^ (x << 1)) & T(0x5555555555555555);
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return x;
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}
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template <class T>
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constexpr T deposit(T x, T mask) noexcept
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{
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T result = 0;
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for (T i = 1; mask; i <<= 1)
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{
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if (x & i)
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result |= mask & -mask;
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mask &= mask - 1;
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}
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return result;
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}
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template <class T>
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inline constexpr int difference(T x, T y) noexcept
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{
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return count(x ^ y);
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}
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template <class T>
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constexpr T extract(T x, T mask) noexcept
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{
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T result = 0;
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for (T i = 1; mask; i <<= 1)
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{
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if (x & mask & -mask)
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result |= i;
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mask &= mask - 1;
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}
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return result;
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}
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template <class T>
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inline constexpr T flip(T x, int i) noexcept
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{
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return x ^ (T(1) << i);
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}
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template <class T, class U>
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inline constexpr U interleave(T a, T b) noexcept
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{
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return expand<U>(a) | (expand<U>(b) << 1);
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}
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template <class T>
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inline constexpr T merge(T a, T b, T mask) noexcept
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{
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return a ^ ((a ^ b) & mask);
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}
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template <class T>
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constexpr T parity(T x) noexcept
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{
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if constexpr(sizeof(T) >= 8)
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x ^= x >> 32;
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if constexpr(sizeof(T) >= 4)
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x ^= x >> 16;
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if constexpr(sizeof(T) >= 2)
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x ^= x >> 8;
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x ^= x >> 4;
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return (0x6996 >> (x & 0xf)) & 1;
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}
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template <class T>
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constexpr T segregate(T x) noexcept
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{
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T odd = compress(x);
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T even = compress(x >> 1);
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return odd | (even << (sizeof(T) << 2));
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}
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template <class T>
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constexpr T swap_adjacent(T x) noexcept
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{
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return ((x & T(0xaaaaaaaaaaaaaaaa)) >> 1) | ((x & T(0x5555555555555555)) << 1);
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}
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} // namespace bit
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#endif // ANTKEEPER_BIT_MATH_HPP
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