Improve crossover function, add crossover_n, add more bit math utilities, add inherit function

src/game/genetics/bit-math.hpp

@@ -52,6 +52,93 @@ constexpr T bit_extract(T x, T mask) noexcept;
 template <typename T>
 constexpr int popcount(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 <typename T>
+constexpr int hamming_distance(T x, T y) noexcept;
+
+
+template <typename T>
+constexpr T bit_merge(T a, T b, T mask) noexcept
+{
+	return a ^ ((a ^ b) & mask);
+}
+
+template <class T>
+constexpr T bit_pad(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 <typename T>
+constexpr T bit_interleave(T a, T b) noexcept
+{
+	return (bit_pad(b) << 1) | bit_pad(a);
+}
+
+template <typename T>
+constexpr T bit_swap_adjacent(T x) noexcept
+{
+	return ((x & T(0xaaaaaaaaaaaaaaaa)) >> 1) | ((x & T(0x5555555555555555)) << 1);
+}
+
+template <typename T>
+constexpr T bit_shuffle_adjacent(T x, T mask) noexcept
+{
+	T y = bit_swap_adjacent(x);
+	return bit_merge(x, y, bit_interleave<T>(mask, mask));
+}
+
+/**
+ * Shuffles the adjacent bits of a value.
+ *
+ * @param x Value to shuffle.
+ * @param g Uniform random bit generator.
+ * @return Value with adjacent bits shuffled.
+ */
+/*
+template <class T, class URBG>
+constexpr T bit_shuffle_adjacent(T x, URBG&& g) noexcept
+{
+	return bit_swap_adjacent(x, static_cast<T>(g()));
+}*/
+
+/**
+ *
+ */
+template <class T, class U>
+U bit_splice(T a, T b, U mask)
+{
+	return bit_deposit(static_cast<U>(a), ~mask) | bit_deposit(static_cast<U>(b), mask);
+}
+
+/**
+ * For an n-bit number with r set bits, there are `n! / ((n - r)! * r!)` permutations.
+ */
+template <class T>
+T next_bit_permutation(T x)
+{
+	T y = (x | (x - 1)) + 1;
+	return y | ((((y & -y) / (x & -x)) >> 1) - 1);  
+}
+
 template <class T>
 constexpr T bit_deposit(T x, T mask) noexcept
 {
@@ -91,6 +178,24 @@ constexpr int popcount(T x) noexcept
 	return n;
 }
 
+template <typename T>
+inline constexpr int hamming_distance(T x, T y) noexcept
+{
+	return popcount(x ^ y);
+}
+
+/**
+ *
+ * @param mask Least significant bits indicate whether to inherit the first (0) or second (1) allele from @p a. Most significant bits indicate whether to inherit the first (0) or second (1) allele from @p b.
+ */
+template <class T>
+constexpr T inherit(T a, T b, T mask) noexcept
+{
+	a = bit_shuffle_adjacent<T>(a, mask);
+	b = bit_shuffle_adjacent<T>(b, mask >> (sizeof(T) << 2));
+	return bit_merge<T>(a, b, T(0x5555555555555555));
+}
+
 } // namespace dna
 
 #endif // ANTKEEPER_BIT_MATH_HPP

src/game/genetics/crossover.hpp

@@ -20,32 +20,53 @@
 #ifndef ANTKEEPER_CROSSOVER_HPP
 #define ANTKEEPER_CROSSOVER_HPP
 
+#include "bit-math.hpp"
+
 namespace dna
 {
 
 /**
- * Performs a genetic crossover between two chromosomes.
+ * Performs a single-point crossover between two values.
+ *
+ * @param a First value.
+ * @param b Second value.
+ * @parma pos Position of the crossover point.
+ */
+template <class T>
+constexpr T crossover(T a, T b, int pos) noexcept;
+
+/**
+ * Performs an n-point crossover between two values.
  *
- * @param a Chromosome of the first parent.
- * @param b Chromosome of the second parent.
- * @param g Uniform random bit generator.
- * @return Chromosome of the new offspring.
+ * @param a First value.
+ * @param b Second value.
+ * @param mask Bit mask with set bits marking crossover points.
  */
-template <class T, class URBG>
-T crossover(T a, T b, URBG&& g)
+template <class T>
+constexpr T crossover_n(T a, T b, T mask) noexcept;
+
+template <class T>
+inline constexpr T crossover(T a, T b, int pos) noexcept
 {
-	T c = 0, i = 1;
+	T mask = (T(1) << pos) - 1;
+	return bit_merge(b, a, mask);
+}
+
+template <class T>
+constexpr T crossover_n(T a, T b, T mask) noexcept
+{
+	T merge = 0, i = 0;
 	
-	do
+	while (mask)
 	{
-		c |= (a >> (g() % 2)) & i;
-		i <<= 1;
-		c |= (b << (g() % 2)) & i;
-		i <<= 1;
+		merge ^= (mask ^ (mask - 1)) >> 1;
+		mask &= mask - 1;
+		i = !i;
 	}
-	while (i);
 	
-	return c;
+	merge ^= ~T(0) * i;
+	
+	return bit_merge<T>(a, b, merge);
 }
 
 } // namespace dna

src/game/genetics/mutate.hpp

@@ -24,16 +24,16 @@ namespace dna
 {
 
 /**
- * Mutates a value by flipping a single random bit.
+ * Mutates a value by flipping a single bit.
  *
  * @param x Value to mutate.
- * @param g Uniform random bit generator.
+ * @param i Index of the bit to flip.
  * @return Mutated copy of @p x.
  */
-template <class T, class URBG>
-T mutate(T x, URBG&& g)
+template <class T>
+T mutate(T x, int i)
 {
-	return x ^ (T(1) << (g() % (sizeof(T) << 3)));
+	return x ^ (T(1) << i);
 }
 
 } // namespace dna

src/game/genetics/zygosity.hpp

@@ -24,33 +24,33 @@ namespace dna
 {
 
 /**
- * Tests a gene for heterozygosity.
+ * Tests the two least significant bits of a value for equality
  *
- * @param x Gene with alleles encoded in the two least significant bits.
- * @return `true` if the gene is heterozygous, `false` otherwise.
+ * @param x Value to test.
+ * @return `true` if the two least significant bits are equal, `false` otherwise.
  */
 template <class T>
-bool is_heterozygous(T x);
+constexpr bool homozygous(T x) noexcept;
 
 /**
- * Tests a gene for homozygosity.
+ * Tests the two least significant bits of a value for inequality.
  *
- * @param x Gene with alleles encoded in the two least significant bits.
- * @return `true` if the gene is homozygous, `false` otherwise.
+ * @param x Value to test.
+ * @return `true` if the two least significant bits are inequal, `false` otherwise.
  */
 template <class T>
-bool is_homozygous(T x);
+constexpr bool heterozygous(T x) noexcept;
 
 template <class T>
-inline bool is_heterozygous<T>(T x)
+inline constexpr bool homozygous<T>(T x) noexcept
 {
-	return (x & 1) != (x >> 1);
+	return (x & 1) == ((x >> 1) & 1);
 }
 
 template <class T>
-inline bool is_homozygous<T>(T x)
+inline constexpr bool heterozygous<T>(T x) noexcept
 {
-	return (x & 1) == (x >> 1);
+	return (x & 1) != ((x >> 1) & 1);
 }
 
 } // namespace dna