Summary

Add an unstable sort to libcore.

Motivation

At the moment, the only sort function we have in libstd is slice::sort. It is stable, allocates additional memory, and is unavailable in #![no_std] environments.

The sort function is stable, which is a good but conservative default. However, stability is rarely a required property in practice, and some other characteristics of sort algorithms like higher performance or lower memory overhead are often more desirable.

Having a performant, non-allocating unstable sort function in libcore would cover those needs. At the moment Rust is not offering this solution as a built-in (only crates), which is unusual for a systems programming language.

Q: What is stability?
A: A sort function is stable if it doesn't reorder equal elements. For example:


# #![allow(unused_variables)]
#fn main() {
let mut orig = vec![(0, 5), (0, 4)];
let mut v = orig.clone();

// Stable sort preserves the original order of equal elements.
v.sort_by_key(|p| p.0);
assert!(orig == v); // OK!

/// Unstable sort may or may not preserve the original order.
v.sort_unstable_by_key(|p| p.0);
assert!(orig == v); // MAY FAIL!
#}

Q: When is stability useful?
A: Not very often. A typical example is sorting columns in interactive GUI tables. E.g. you want to have rows sorted by column X while breaking ties by column Y, so you first click on column Y and then click on column X. This is a use case where stability is important.

Q: Can stable sort be performed using unstable sort?
A: Yes. If we transform [T] into [(T, usize)] by pairing every element with it's index, then perform unstable sort, and finally remove indices, the result will be equivalent to stable sort.

Q: Why is slice::sort stable?
A: Because stability is a good default. A programmer might call a sort function without checking in the documentation whether it is stable or unstable. It is very intuitive to assume stability, so having slice::sort perform unstable sorting might cause unpleasant surprises. See this story for an example.

Q: Why does slice::sort allocate?
A: It is possible to implement a non-allocating stable sort, but it would be considerably slower.

Q: Why is slice::sort not compatible with #![no_std]?
A: Because it allocates additional memory.

Q: How much faster can unstable sort be?
A: Sorting 10M 64-bit integers using pdqsort (an unstable sort implementation) is 45% faster than using slice::sort. Detailed benchmarks are here.

Q: Can unstable sort benefit from allocation?
A: Generally, no. There is no fundamental property in computer science saying so, but this has always been true in practice. Zero-allocation and instability go hand in hand.

Detailed design

The API will consist of three functions that mirror the current sort in libstd:

  1. core::slice::sort_unstable
  2. core::slice::sort_unstable_by
  3. core::slice::sort_unstable_by_key

By contrast, C++ has functions std::sort and std::stable_sort, where the defaults are set up the other way around.

Interface


# #![allow(unused_variables)]
#fn main() {
pub trait SliceExt {
    type Item;

    // ...

    fn sort_unstable(&mut self)
        where Self::Item: Ord;

    fn sort_unstable_by<F>(&mut self, compare: F)
        where F: FnMut(&Self::Item, &Self::Item) -> Ordering;

    fn sort_unstable_by_key<B, F>(&mut self, mut f: F)
        where F: FnMut(&Self::Item) -> B,
              B: Ord;
}
#}

Examples


# #![allow(unused_variables)]
#fn main() {
let mut v = [-5i32, 4, 1, -3, 2];

v.sort_unstable();
assert!(v == [-5, -3, 1, 2, 4]);

v.sort_unstable_by(|a, b| b.cmp(a));
assert!(v == [4, 2, 1, -3, -5]);

v.sort_unstable_by_key(|k| k.abs());
assert!(v == [1, 2, -3, 4, -5]);
#}

Implementation

Proposed implementaton is available in the pdqsort crate.

Q: Why choose this particular sort algorithm?
A: First, let's analyse what unstable sort algorithms other languages use:

  • C: quicksort
  • C++: introsort
  • D: introsort
  • Swift: introsort
  • Go: introsort
  • Crystal: introsort
  • Java: dual-pivot quicksort

The most popular sort is definitely introsort. Introsort is an implementation of quicksort that limits recursion depth. As soon as depth exceeds 2 * log(n), it switches to heapsort in order to guarantee O(n log n) worst-case. This method combines the best of both worlds: great average performance of quicksort with great worst-case performance of heapsort.

Java (talking about Arrays.sort, not Collections.sort) uses dual-pivot quicksort. It is an improvement of quicksort that chooses two pivots for finer grained partitioning, offering better performance in practice.

A recent improvement of introsort is pattern-defeating quicksort, which is substantially faster in common cases. One of the key tricks pdqsort uses is block partitioning described in the BlockQuicksort paper. This algorithm still hasn't been built into in any programming language's standard library, but there are plans to include it into some C++ implementations.

Among all these, pdqsort is the clear winner. Some benchmarks are available here.

Q: Is slice::sort ever faster than pdqsort?
A: Yes, there are a few cases where it is faster. For example, if the slice consists of several pre-sorted sequences concatenated one after another, then slice::sort will most probably be faster. Another case is when using costly comparison functions, e.g. when sorting strings. slice::sort optimizes the number of comparisons very well, while pdqsort optimizes for fewer writes to memory at expense of slightly larger number of comparisons. But other than that, slice::sort should be generally slower than pdqsort.

Q: What about radix sort?
A: Radix sort is usually blind to patterns in slices. It treats totally random and partially sorted the same way. It is probably possible to improve it by combining it with some other techniques, but it's not trivial. Moreover, radix sort is incompatible with comparison-based sorting, which makes it an awkward choice for a general-purpose API. On top of all this, it's not even that much faster than pdqsort anyway.

How We Teach This

Stability is a confusing and loaded term. Function slice::sort_unstable might be misunderstood as a function that has unstable API. That said, there is no less confusing alternative to "unstable sorting". Documentation should clearly state what "stable" and "unstable" mean.

slice::sort_unstable will be mentioned in the documentation for slice::sort as a faster non-allocating alternative. The documentation for slice::sort_unstable must also clearly state that it guarantees no allocation.

Drawbacks

The amount of code for sort algorithms will grow, and there will be more code to review.

It might be surprising to discover cases where slice::sort is faster than slice::sort_unstable. However, these peculiarities can be explained in documentation.

Alternatives

Unstable sorting is indistinguishable from stable sorting when sorting primitive integers. It's possible to specialize slice::sort to fall back to slice::sort_unstable. This would improve performance for primitive integers in most cases, but patching cases type by type with different algorithms makes performance more inconsistent and less predictable.

Unstable sort guarantees no allocation. Instead of naming it slice::sort_unstable, it could also be named slice::sort_noalloc or slice::sort_unstable_noalloc. This may slightly improve clarity, but feels much more awkward.

Unstable sort can also be provided as a standalone crate instead of within the standard library. However, every other systems programming language has a fast unstable sort in standard library, so why shouldn't Rust, too?

Unresolved questions

None.