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//! [Hamming space](https://en.wikipedia.org/wiki/Hamming_space).
use crate::distance::{Metric, Proximity};
use num_traits::PrimInt;
/// A point in Hamming space.
///
/// This wrapper equips any integer with the [Hamming distance] metric.
///
/// [Hamming distance]: https://en.wikipedia.org/wiki/Hamming_distance
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub struct Hamming<T>(pub T);
impl<T> Hamming<T> {
/// Wrap a point.
pub fn new(point: T) -> Self {
Self(point)
}
/// Unwrap a point.
pub fn into_inner(self) -> T {
self.0
}
}
/// Compute the Hamming distance between two integers.
///
/// ```math
/// \begin{aligned}
/// \mathrm{hamming\_distance}(x, y) &= |\{i \mid x_i \ne y_i\}| \\
/// &= \mathrm{popcount}(x \wedge y)
/// \end{aligned}
/// ```
pub fn hamming_distance<T: PrimInt>(x: T, y: T) -> i32 {
(x ^ y).count_ones() as i32
}
/// The hamming distance function.
impl<T: PrimInt> Proximity for Hamming<T> {
type Distance = i32;
fn distance(&self, other: &Self) -> Self::Distance {
hamming_distance(self.0, other.0)
}
}
impl<T: PrimInt> Proximity<T> for Hamming<T> {
type Distance = i32;
fn distance(&self, other: &T) -> Self::Distance {
hamming_distance(self.0, *other)
}
}
impl<T: PrimInt> Proximity<Hamming<T>> for T {
type Distance = i32;
fn distance(&self, other: &Hamming<T>) -> Self::Distance {
hamming_distance(*self, other.0)
}
}
/// Hamming distance is a metric.
impl<T: PrimInt> Metric for Hamming<T> {}
impl<T: PrimInt> Metric<T> for Hamming<T> {}
impl<T: PrimInt> Metric<Hamming<T>> for T {}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_distance() {
assert_eq!(hamming_distance(0, 0xFFFFFFFFu32), 32);
assert_eq!(Hamming(0xFFFFFFFFu32).distance(&Hamming(0xAAAAAAAAu32)), 16);
assert_eq!(Hamming(0x55555555u32).distance(&0xAAAAAAAAu32), 32);
assert_eq!(0xDEADBEEFu32.distance(&Hamming(0xACABACABu32)), 10);
}
}
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