Introsort

This is an implementation of the introsort sorting algorithm.

This crate does not depend on std, and can be used with #![no_std] crates. It does however depend on core, but has no other dependencies except for testing.

To use with cargo, add the following to your Cargo.toml:

[dependencies]
introsort = "0.5.1"

and in your crate root, add

extern crate introsort;

Interface

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

An example:

extern crate introsort;

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"];
    introsort::sort(&mut ss[..]);
    println!("alphabetically");
    for s in ss.iter() { println!("\t{}", s); }
    introsort::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. Due to the partitioning method(s) used, the heapsort will only be used in exceedingly rare circumstances. 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.

Detailed benchmark data (only for integers as of now) is available.

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.

Due to removal of the Float trait from the standard library, enabling float support will pull in std as a transitive dependency (#3). This problem should just be temporary while I figure out a good solution. Building without float support (add default-features = false under [dependencies.introsort]) still works with #![no_std].