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@ -24,7 +24,10 @@ namespace bit |
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{ |
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/**
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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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* |
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* @param x Value to compress. |
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* @return Compressed value. |
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*/ |
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*/ |
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template <class T> |
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template <class T> |
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constexpr T compress(T x) noexcept; |
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constexpr T compress(T x) noexcept; |
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@ -70,6 +73,15 @@ constexpr T crossover_n(T a, T b, T mask) noexcept; |
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template <class T> |
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template <class T> |
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constexpr T deposit(T x, T mask) noexcept; |
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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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/**
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* Returns the number of differing bits between two values, known as *Hamming distance*. |
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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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* |
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@ -80,6 +92,15 @@ constexpr T deposit(T x, T mask) noexcept; |
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template <class T> |
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template <class T> |
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constexpr int difference(T x, T y) noexcept; |
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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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/**
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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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* 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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* |
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@ -101,13 +122,22 @@ template |
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constexpr T flip(T x, int i) noexcept; |
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constexpr T flip(T x, int i) noexcept; |
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/**
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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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* |
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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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*/ |
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template <class T, class U = T> |
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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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constexpr U interleave(T a, T b) noexcept; |
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/**
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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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* |
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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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*/ |
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template <class T> |
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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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constexpr T merge(T a, T b, T mask) noexcept; |
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@ -121,13 +151,6 @@ constexpr T merge(T a, T b, T mask) noexcept; |
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template <class T> |
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template <class T> |
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constexpr T parity(T x) noexcept; |
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constexpr T parity(T x) noexcept; |
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/**
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* |
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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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/**
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* Segregates the odd and even bits of a value. |
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* Segregates the odd and even bits of a value. |
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* |
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* |
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@ -135,66 +158,16 @@ constexpr T swap_adjacent(T x) noexcept; |
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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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* @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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*/ |
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template <class T> |
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template <class T> |
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T segregate(T x) |
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{ |
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T odd = bit::compress(x); |
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T even = bit::compress(x >> 1); |
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return odd | (even << (sizeof(T) << 2)); |
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} |
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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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T desegregate(T x) |
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{ |
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return bit::interleave<T>(x, x >> (sizeof(T) << 2)); |
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} |
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constexpr T segregate(T x) noexcept; |
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/**
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/**
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* Replicates each bit in the lower half of a value. |
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* Swaps the each odd bit with its following even bit. |
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* |
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* |
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* @param x Value to replicate. |
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* @return Value of @p x interleaved with itself. |
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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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*/ |
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template <class T> |
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template <class T> |
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T replicate(T x) |
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{ |
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x = bit::expand(x); |
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return x | (x << 1); |
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} |
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/**
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* Isolates a pair of bits and returns them in the two least significant bits. |
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* |
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* @param x Diploid chromosome with interleaved alleles. |
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* @param i Index of the pair to isolate. |
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* @return Isolated pair of bits in the two least significant bits. |
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*/ |
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template <class T> |
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T isolate(T x, int i) |
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{ |
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return (x >> (i << 1)) & 0b11; |
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} |
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/**
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* Isolates a sequence of genes and returns their alleles in the least significant bits. |
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* |
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* @param x Diploid chromosome with interleaed alleles. |
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* @param i Index of the first gene in the sequence. |
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* @param n Length of the sequence, in genes. |
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* @return Alleles of the sequeuence in the least significant bits. |
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*/ |
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template <class T> |
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T isolate_n(T x, int i, int n) |
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{ |
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T mask = (T(1) << (n << 1)) - 1; |
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return (x >> (i << 1)) & mask; |
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} |
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constexpr T swap_adjacent(T x) noexcept; |
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template <class T> |
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template <class T> |
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@ -228,13 +201,13 @@ template |
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inline constexpr T crossover(T a, T b, int i) noexcept |
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inline constexpr T crossover(T a, T b, int i) noexcept |
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{ |
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{ |
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T mask = (T(1) << i) - 1; |
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T mask = (T(1) << i) - 1; |
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return bit::merge(b, a, mask); |
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return merge(b, a, mask); |
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} |
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} |
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template <class T> |
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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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constexpr T crossover_n(T a, T b, T mask) noexcept |
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{ |
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{ |
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T merge = ~T(0) * bit::parity(mask); |
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T merge = ~T(0) * parity(mask); |
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while (mask) |
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while (mask) |
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{ |
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{ |
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@ -242,7 +215,13 @@ constexpr T crossover_n(T a, T b, T mask) noexcept |
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mask &= mask - 1; |
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mask &= mask - 1; |
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} |
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} |
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return bit::merge(a, b, merge); |
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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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} |
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template <class T> |
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template <class T> |
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@ -263,28 +242,6 @@ constexpr T expand(T x) noexcept |
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return x; |
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return x; |
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} |
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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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/**
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* For an n-bit number with r set bits, there are `n! / ((n - r)! * r!)` permutations. |
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*/ |
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template <class T> |
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constexpr T next_permutation(T x) noexcept |
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{ |
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T y = (x | (x - 1)) + 1; |
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return y | ((((y & -y) / (x & -x)) >> 1) - 1); |
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} |
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template <class T> |
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template <class T> |
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constexpr T deposit(T x, T mask) noexcept |
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constexpr T deposit(T x, T mask) noexcept |
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{ |
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{ |
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@ -300,6 +257,12 @@ constexpr T deposit(T x, T mask) noexcept |
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return result; |
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return result; |
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} |
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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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template <class T> |
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constexpr T extract(T x, T mask) noexcept |
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constexpr T extract(T x, T mask) noexcept |
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{ |
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{ |
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@ -316,13 +279,19 @@ constexpr T extract(T x, T mask) noexcept |
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} |
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} |
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template <class T> |
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template <class T> |
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inline constexpr int difference(T x, T y) noexcept |
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inline constexpr T flip(T x, int i) noexcept |
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{ |
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{ |
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return count(x ^ y); |
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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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} |
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template <class T> |
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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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inline constexpr T merge(T a, T b, T mask) noexcept |
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{ |
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{ |
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return a ^ ((a ^ b) & mask); |
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return a ^ ((a ^ b) & mask); |
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} |
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} |
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@ -342,6 +311,15 @@ constexpr T parity(T x) noexcept |
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return (0x6996 >> (x & 0xf)) & 1; |
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return (0x6996 >> (x & 0xf)) & 1; |
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} |
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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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template <class T> |
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constexpr T swap_adjacent(T x) noexcept |
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constexpr T swap_adjacent(T x) noexcept |
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{ |
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{ |
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