/*
* 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 .
*/
#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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
constexpr T swap_adjacent(T x) noexcept;
template
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
constexpr int count(T x) noexcept
{
int n = 0;
for (; x; ++n)
x &= x - 1;
return n;
}
template
inline constexpr T crossover(T a, T b, int i) noexcept
{
T mask = (T(1) << i) - 1;
return merge(b, a, mask);
}
template
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
inline constexpr T desegregate(T x) noexcept
{
return interleave(x, x >> (sizeof(T) << 2));
}
template
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
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
inline constexpr int difference(T x, T y) noexcept
{
return count(x ^ y);
}
template
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
inline constexpr T flip(T x, int i) noexcept
{
return x ^ (T(1) << i);
}
template
inline constexpr U interleave(T a, T b) noexcept
{
return expand(a) | (expand(b) << 1);
}
template
inline constexpr T merge(T a, T b, T mask) noexcept
{
return a ^ ((a ^ b) & mask);
}
template
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
constexpr T segregate(T x) noexcept
{
T odd = compress(x);
T even = compress(x >> 1);
return odd | (even << (sizeof(T) << 2));
}
template
constexpr T swap_adjacent(T x) noexcept
{
return ((x & T(0xaaaaaaaaaaaaaaaa)) >> 1) | ((x & T(0x5555555555555555)) << 1);
}
} // namespace bit
#endif // ANTKEEPER_BIT_MATH_HPP