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- /*
- * Copyright (C) 2021 Christopher J. Howard
- *
- * This file is part of Antkeeper source code.
- *
- * Antkeeper source code 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, either version 3 of the License, or
- * (at your option) any later version.
- *
- * Antkeeper source code 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. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
- */
-
- #ifndef ANTKEEPER_BIT_MATH_HPP
- #define ANTKEEPER_BIT_MATH_HPP
-
- /// Bitwise math
- namespace bit {
-
- /**
- * Compresses the even bits of a value into the lower half, then clears the upper half.
- *
- * @param x Value to compress.
- * @return Compressed value.
- */
- template <class T>
- constexpr T compress(T x) noexcept;
-
- /**
- * Returns the number of set bits in a value, known as a *population count* or *Hamming weight*.
- *
- * @param x Value to count.
- * @return Number of set bits in @p x.
- */
- template <class T>
- constexpr int count(T x) noexcept;
-
- /**
- * Performs a single-point crossover between two values.
- *
- * @param a First value.
- * @param b Second value.
- * @param i Index of the crossover point.
- * @return Crossed over value.
- */
- template <class T>
- constexpr T crossover(T a, T b, int i) noexcept;
-
- /**
- * Performs an n-point crossover between two values.
- *
- * @param a First value.
- * @param b Second value.
- * @param mask Bit mask with set bits marking crossover points.
- * @return Crossed over value.
- */
- template <class T>
- constexpr T crossover_n(T a, T b, T mask) noexcept;
-
- /**
- * Reads bits from the least significant bits of a value and returns them in the positions marked by a mask.
- *
- * @param x Value from which bits should be read.
- * @param mask Bit mask indicating where bits should be deposited.
- * @return Bits from the least significant bits of @p x in the positions marked by @p mask.
- */
- template <class T>
- constexpr T deposit(T x, T mask) noexcept;
-
- /**
- * Interleaves bits of the lower and upper halves of a value.
- *
- * @param x Value to desegregate.
- * @return Value with bits from the upper half of @p x interleaved with bits from the lower half.
- */
- template <class T>
- constexpr T desegregate(T x) noexcept;
-
- /**
- * Returns the number of differing bits between two values, known as *Hamming distance*.
- *
- * @param x First value.
- * @param y Second value.
- * @return Hamming distance between @px and @p y.
- */
- template <class T>
- constexpr int difference(T x, T y) noexcept;
-
- /**
- * Moves bits from the lower half of a value to occupy all even bits, and clears all odd bits.
- *
- * @param x Value to expand.
- * @return Expanded value.
- */
- template <class T>
- constexpr T expand(T x) noexcept;
-
- /**
- * Reads bits from a value in the positions marked by a mask and returns them in the least significant bits.
- *
- * @param x Value from which bits should be read.
- * @param mask Bit mask indicating which bits to extract.
- * @return Bits of @p x from the positions marked by @p mask in the least significant bits.
- */
- template <class T>
- constexpr T extract(T x, T mask) noexcept;
-
- /**
- * Flips a single bit in a value.
- *
- * @param x Value to modify.
- * @param i Index of the bit to flip.
- * @return Copy of @p x with one bit flipped.
- */
- template <class T>
- constexpr T flip(T x, int i) noexcept;
-
- /**
- * Returns a value with even bits containing the first value's lower half, and odd bits containing the second value's lower half.
- *
- * @param a First value.
- * @param b Second value.
- * @return Value with bits from the lower halves of @p a and @p b interleaved.
- */
- template <class T, class U = T>
- constexpr U interleave(T a, T b) noexcept;
-
- /**
- * Merges the bits of two values using a bit mask.
- *
- * @param a First value.
- * @param b Second value.
- * @param mask Bit mask with zeros where bits from @p a should be used, and ones where bits from @p b should be used.
- * @return Merged value.
- */
- template <class T>
- constexpr T merge(T a, T b, T mask) noexcept;
-
- /**
- * Returns the parity of a value.
- *
- * @param x Value to test.
- * @return `1` if an odd number of bits are set, `0` otherwise.
- */
- template <class T>
- constexpr T parity(T x) noexcept;
-
- /**
- * Segregates the odd and even bits of a value.
- *
- * @param x Value to segregate.
- * @return Value with even bits of @p x in the lower half, and odd bits in the upper half.
- */
- template <class T>
- constexpr T segregate(T x) noexcept;
-
- /**
- * Swaps the each odd bit with its following even bit.
- *
- * @param x Value in which adjacent bits should be swap.
- * @return Copy of @p x with adjacent bits swapped.
- */
- template <class T>
- constexpr T swap_adjacent(T x) noexcept;
-
-
- template <class T>
- constexpr T compress(T x) noexcept
- {
- x &= T(0x5555555555555555);
-
- x = (x ^ (x >> 1)) & T(0x3333333333333333);
- x = (x ^ (x >> 2)) & T(0x0f0f0f0f0f0f0f0f);
-
- if constexpr(sizeof(T) >= 2)
- x = (x ^ (x >> 4)) & T(0x00ff00ff00ff00ff);
- if constexpr(sizeof(T) >= 4)
- x = (x ^ (x >> 8)) & T(0x0000ffff0000ffff);
- if constexpr(sizeof(T) >= 8)
- x = (x ^ (x >> 16)) & T(0x00000000ffffffff);
-
- return x;
- }
-
- template <class T>
- constexpr int count(T x) noexcept
- {
- int n = 0;
- for (; x; ++n)
- x &= x - 1;
- return n;
- }
-
- template <class T>
- inline constexpr T crossover(T a, T b, int i) noexcept
- {
- T mask = (T(1) << i) - 1;
- return merge(b, a, mask);
- }
-
- template <class T>
- constexpr T crossover_n(T a, T b, T mask) noexcept
- {
- T merge = ~T(0) * parity(mask);
-
- while (mask)
- {
- merge ^= (mask ^ (mask - 1)) >> 1;
- mask &= mask - 1;
- }
-
- return merge(a, b, merge);
- }
-
- template <class T>
- inline constexpr T desegregate(T x) noexcept
- {
- return interleave<T>(x, x >> (sizeof(T) << 2));
- }
-
- template <class T>
- constexpr T expand(T x) noexcept
- {
- x &= (1 << (sizeof(T) << 2)) - 1;
-
- if constexpr(sizeof(T) >= 8)
- x = (x ^ (x << 16)) & T(0x0000ffff0000ffff);
- if constexpr(sizeof(T) >= 4)
- x = (x ^ (x << 8)) & T(0x00ff00ff00ff00ff);
- if constexpr(sizeof(T) >= 2)
- x = (x ^ (x << 4)) & T(0x0f0f0f0f0f0f0f0f);
-
- x = (x ^ (x << 2)) & T(0x3333333333333333);
- x = (x ^ (x << 1)) & T(0x5555555555555555);
-
- return x;
- }
-
- template <class T>
- constexpr T deposit(T x, T mask) noexcept
- {
- T result = 0;
-
- for (T i = 1; mask; i <<= 1)
- {
- if (x & i)
- result |= mask & -mask;
- mask &= mask - 1;
- }
-
- return result;
- }
-
- template <class T>
- inline constexpr int difference(T x, T y) noexcept
- {
- return count(x ^ y);
- }
-
- template <class T>
- constexpr T extract(T x, T mask) noexcept
- {
- T result = 0;
-
- for (T i = 1; mask; i <<= 1)
- {
- if (x & mask & -mask)
- result |= i;
- mask &= mask - 1;
- }
-
- return result;
- }
-
- template <class T>
- inline constexpr T flip(T x, int i) noexcept
- {
- return x ^ (T(1) << i);
- }
-
- template <class T, class U>
- inline constexpr U interleave(T a, T b) noexcept
- {
- return expand<U>(a) | (expand<U>(b) << 1);
- }
-
- template <class T>
- inline constexpr T merge(T a, T b, T mask) noexcept
- {
- return a ^ ((a ^ b) & mask);
- }
-
- template <class T>
- constexpr T parity(T x) noexcept
- {
- if constexpr(sizeof(T) >= 8)
- x ^= x >> 32;
- if constexpr(sizeof(T) >= 4)
- x ^= x >> 16;
- if constexpr(sizeof(T) >= 2)
- x ^= x >> 8;
-
- x ^= x >> 4;
-
- return (0x6996 >> (x & 0xf)) & 1;
- }
-
- template <class T>
- constexpr T segregate(T x) noexcept
- {
- T odd = compress(x);
- T even = compress(x >> 1);
-
- return odd | (even << (sizeof(T) << 2));
- }
-
- template <class T>
- constexpr T swap_adjacent(T x) noexcept
- {
- return ((x & T(0xaaaaaaaaaaaaaaaa)) >> 1) | ((x & T(0x5555555555555555)) << 1);
- }
-
- } // namespace bit
-
- #endif // ANTKEEPER_BIT_MATH_HPP
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