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use core::mem;
use crate::invoke_macro_for_types;
pub trait RadixType: Clone + Copy + Default {
// RadixTypes are sortable by rdx_sort(.)
const IS_SIGNED: bool;
// signed data requires special handling in the last round
fn key(&self, round: usize) -> u8;
// the key is the radix of size u8, i.e. one byte
}
macro_rules! is_signed {
// convenience macro to derive which built-in number types are signed since
// they require special case handling in the final sorting round.
(i8) => {
true
};
(i16) => {
true
};
(i32) => {
true
};
(i64) => {
true
};
(i128) => {
true
};
(f32) => {
true
};
(f64) => {
true
};
($_t:ty) => {
false
};
}
macro_rules! radix_type {
// short-hand to add a default RadixType implementation for the
// given input type. Works with built-in types like integers.
($a:ident) => {
// forward to the general implementation below
radix_type!($a, $a);
};
($a:ident, $b:ident) => {
impl RadixType for $a {
const IS_SIGNED: bool = is_signed!($a);
fn key(&self, round: usize) -> u8 {
(*self as $b >> (round << 3)) as u8
}
}
};
}
// define built-in number types (integers, floats, bool) as RadixType
invoke_macro_for_types!(
radix_type, u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize
);
radix_type!(bool, u8);
impl RadixType for f32 {
const IS_SIGNED: bool = is_signed!(f32);
fn key(&self, round: usize) -> u8 {
// Interpret the bits of a float as if they were an integer.
// This relies on the floats being in IEEE-754 format to work.
(self.to_bits() >> (round << 3)) as u8
}
}
impl RadixType for f64 {
const IS_SIGNED: bool = is_signed!(f64);
fn key(&self, round: usize) -> u8 {
// Interpret the bits of a float as if they were an integer.
// This relies on the floats being in IEEE-754 format to work.
(self.to_bits() >> (round << 3)) as u8
}
}
pub trait Sort {
fn rdx_sort(&mut self);
}
impl<T: 'static + RadixType> Sort for Vec<T> {
fn rdx_sort(&mut self) {
// TODO(dl): Add an explanation of how radix sort works
let mut output = vec![T::default(); self.len()];
let rounds = mem::size_of::<T>();
// implementation of Friend's optimization: Compute all frequencies at once
let mut histogram_table = Vec::<Vec<usize>>::new();
histogram_table.resize(rounds, Vec::with_capacity(256));
for histogram in &mut histogram_table {
histogram.resize(256, 0);
}
self.iter().for_each(|num| {
for k in 0..rounds {
let radix = num.key(k);
unsafe {
*histogram_table
.get_unchecked_mut(k)
.get_unchecked_mut(radix as usize) += 1;
}
}
});
let mut skip_table = Vec::with_capacity(rounds);
skip_table.resize(rounds, false);
for k in 0..rounds {
// TODO: there must be a more elegant way to do this!
let mut prev = match T::IS_SIGNED && k == rounds - 1 {
// add offset to non-negative entries making room for negative ones
true => histogram_table[k].iter().skip(128).sum(),
false => 0,
};
if T::IS_SIGNED && k == rounds - 1 {
// last round for signed numbers needs to handle negatives
// note that the sign-bit is in the MSB
(0..128).for_each(|i| unsafe {
skip_table[k] = skip_table[k]
|| *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i) == self.len();
let temp = *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i);
*histogram_table.get_unchecked_mut(k).get_unchecked_mut(i) = prev;
prev += temp;
});
prev = 0;
for i in (128..256).rev() {
// build prefix sums for negative numbers from the right
unsafe {
skip_table[k] = skip_table[k]
|| *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i)
== self.len();
let temp = *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i);
*histogram_table.get_unchecked_mut(k).get_unchecked_mut(i) = prev;
prev += temp;
}
}
} else {
// a round can be skipped if all entries fall into the same bucket
skip_table[k] = histogram_table[k][0] == self.len();
// let mut prev = 0;
(0..256).for_each(|i| unsafe {
skip_table[k] = skip_table[k]
|| *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i) == self.len();
let temp = *histogram_table.get_unchecked_mut(k).get_unchecked_mut(i);
*histogram_table.get_unchecked_mut(k).get_unchecked_mut(i) = prev;
prev += temp;
});
}
}
// permutation rounds
for (k, skip_round) in skip_table.iter().enumerate().take(rounds) {
if *skip_round {
// skipping round {k} since all of input falls into exactly one bucket
continue;
}
// place values into their slot
self.iter().for_each(|num| {
let radix = num.key(k);
unsafe {
// performance optimization
let target = *histogram_table
.get_unchecked(k)
.get_unchecked(radix as usize);
*output.get_unchecked_mut(target) = *num;
*histogram_table
.get_unchecked_mut(k)
.get_unchecked_mut(radix as usize) += 1;
}
});
core::mem::swap(self, &mut output);
}
}
}
#[cfg(test)]
mod tests {
use rand::Rng;
use super::Sort;
#[test]
fn tenknumbers() {
let mut rng = rand::rng();
let mut list = Vec::new();
(0..10_000).for_each(|_| {
list.push(rng.random::<u64>());
});
list.rdx_sort();
list.windows(2).for_each(|i| {
// now verify numbers are in ascending order
assert!(i[0] <= i[1]);
});
}
#[test]
fn invertedrun() {
let mut list: Vec<i32> = (0..10_000).rev().collect();
list.windows(2).for_each(|i| {
// verify numbers are in descending order
assert!(i[0] > i[1]);
});
list.rdx_sort();
// Note: is_sorted has not been stabilized at the time of writing.
// assert!(list.is_sorted());
list.windows(2).for_each(|i| {
// now verify numbers are in ascending order
assert!(i[0] < i[1]);
});
}
#[test]
fn sort_bools() {
// assumes false < true
let mut bits: Vec<bool> = vec![false, false, false, false, false, true, false, true];
bits.rdx_sort();
assert_eq!(
bits,
vec![false, false, false, false, false, false, true, true]
)
}
#[test]
fn sort_f32() {
let mut bits: Vec<f32> = vec![1.0, 4.0, 3.2415, 0.0, 26.6, 14.32, 1.23, 0.12];
bits.rdx_sort();
assert_eq!(bits, vec![0.0, 0.12, 1.0, 1.23, 3.2415, 4.0, 14.32, 26.6])
}
#[test]
fn sort_f64() {
let mut bits = vec![1.0, 4.0, 3.2415, 0.0, 26.6, 14.32, 1.23, 0.12];
bits.rdx_sort();
assert_eq!(bits, vec![0.0, 0.12, 1.0, 1.23, 3.2415, 4.0, 14.32, 26.6])
}
#[test]
fn sort_i32() {
let mut input = vec![0, 128, -1, 170, 45, 75, 90, -127, 280, -4, 24, 1, 2, 66];
input.rdx_sort();
assert_eq!(
input,
vec![-127, -4, -1, 0, 1, 2, 24, 45, 66, 75, 90, 128, 170, 280]
);
}
#[test]
fn sort_i64() {
let mut input: Vec<i64> = vec![0, 128, -1, 170, 45, 75, 90, -127, 280, -4, 24, 1, 2, 66];
input.rdx_sort();
assert_eq!(
input,
vec![-127, -4, -1, 0, 1, 2, 24, 45, 66, 75, 90, 128, 170, 280]
);
}
}