Crate quickersort

This crate implements the introsort sorting algorithm.

Interface

The interface is similar to the standard library sort and sort_by functions.

An example:

extern crate quickersort;

fn main() {
    let mut ss = vec!["Introsort", "or", "introspective", "sort", "is",
                      "a", "hybrid", "sorting", "algorithm", "that",
                      "provides", "both", "fast", "average",
                      "performance", "and", "(asymptotically)", "optimal",
                      "worst-case", "performance"];
    quickersort::sort(&mut ss[..]);
    println!("alphabetically");
    for s in ss.iter() { println!("\t{}", s); }
    quickersort::sort_by(&mut ss[..], &|a, b| a.len().cmp(&b.len()));
    println!("\nby length");
    for s in ss.iter() { println!("\t{}", s); }
}

Unlike the standard library sort function, introsort is not a stable sort.

Details

At its heart, it is a dual-pivot quicksort. For partition with many equal elements, it will instead use a single-pivot quicksort optimized for this case. It detects excessive recursion during quicksort and switches to heapsort if need be, guaranteeing O(n log(n)) runtime on all inputs. For small partitions it uses insertion sort instead of quicksort.

Unlike the std sort, it does not allocate.

Performance

It is quite fast, outperforming the standard sort on all data sets I have tried. The performance difference varies depending on the characteristics of the data. On large, completely random arrays, introsort is only 5-10% faster than the standard sort. However, introsort's performance is greatly improved if the data has few unique values or is (partially) sorted (including reversed data). For sorted data, introsort is ~4-5 times faster, and for data with few unique values it can be more than 20 times faster.

Floating point

The crate, if built with the "float" feature (which is the default), also includes a sort_floats function. Floating point numbers are not Ord, only PartialOrd, so sort can not be used on them. The ordering used by sort_floats is

| -inf | < 0 | -0 | +0 | > 0 | +inf | NaN |

sort_floats is much more efficient than passing a comparator function implementing this ordering to sort_by.

Functions

heapsort	Perform a heapsort using a comparison function.
insertion_sort	Perform an insertion sort using a comparison function.
sort	Sort using the default comparison function.
sort_by	Sort using a comparison function.
sort_by_key	Sort using a conversion function.
sort_floats	Sorts floating point number. The ordering used is | -inf | < 0 | -0 | +0 | > 0 | +inf | NaN |