jasondavies / radixsort.js

Sort numbers in O(kN) time using JavaScript's typed arrays.

radixsort.js

Radix sort has linear time complexity, O(kN), where k is the number of radices per value, and N is the number of values.

How is this possible? The theoretical lower bound of O(N log N) only applies to comparison-based sorting algorithms, whereas radix sort doesn't actually perform any comparisons on the input data.

Usage

var sort = radixsort(),
    data = new Float32Array([…]);

var sorted = sort(data);

// You can also preallocate the auxiliary array…
sorted = sort(data, new Float32Array(data.length));

Note that radix sort modifies the input array, even though it uses an auxiliary array too. In fact, the sorted result will be the input array when an even number of radixes are in use, which is currently always the case.

The sorter always returns a buffer representing the sorted result, so you can pass this to the appropriate typed array constructor, as in the example above.

Informal Benchmark

The most common usage scenario for this will probably be sorting 32-bit floats e.g. for geometry algorithms. My informal benchmark repeatedly sorts an array of 65,536 random 32-bit floats.

Of course, the comparison is not entirely fair as JavaScript's native sort will be sorting double-precision (64-bit) numbers, as this is all JavaScript supports. But 32 bits is sufficient for most geometry algorithms, so the comparison is reasonable.

• Radixsort.js: ~411 sorts per second.
• JavaScript native sort: ~25 sorts per second.

Radixsort.js is roughly 16x faster! The speed difference gets even larger as you increase the input size.

radixsort.js's Issues

Output is sorted but does not contain the correct elements

I have started writing a benchmark for sorting methods. I included your NPM package radixsort in this benchmark. After the benchmark has run, I do a sanity check on the output. I consistently get the wrong output with random inputs (I started by copying the approach you had taken in your tests) . The output is sorted, however, it does not correspond to the input. I have checked a bunch of other sorting functions that yield the correct output. Did I do something wrong?

Radix-sort numbers with associated data

@jasondavies thanks for the awesome module, its performance is mind-blowing! Still scratching my head over the following issue though:

In most algorithms, you don't just sort a set of numbers without context — usually you sort numbers associated with some additional data. For example, when sorting 2d points by x, you can't use radixSort in the current form because you also need to access y in addition to x in resulting x-sorted points.

What's the easiest way to modify this module to support this kind of use case? For example, could we additionally generate an array associating each sorted element wth original array through indices?