C# has several built-in algorithms for sorting arrays, lists and other containers. Array.Sort and List.Sort have many variations for sorting full or partial containers, using an algorithm that runs on a single CPU core. The Linq library can also sort containers, using a single CPU core or multiple cores in parallel. These are powerful, flexible, high performance capabilities. If you need to sort even faster in C# (.NET) using the CPU, this blog describes high performance sorting algorithms provided in a free, open source library called HPCsharp – high performance computing in C#, or high performance C#, or or whatever else.

## HPCsharp Sorting

HPCsharp library is a NuGet package, available on nuget.org, with source code on GitHub. Currently, it provides Insertion Sort, Merge Sort, and Radix Sort. Merge Sort has a parallel and a serial implementation. Parallel implementation perform substantially faster than sorting using parallel Linq. Radix Sort runs on a single core, at the moment, and competitive versus Array.Sort, List.Sort and even parallel Linq.

These sorting algorithms in HPCsharp provide the same familiar interfaces of the standard C# sorting, making it simple to check these out.

## Parallel Merge Sort

The above graph compares performance of parallel Linq sorting versus HPCsharp Parallel Merge Sort. The x-axis is the size of the UInt32 array being sorted. The y-axis is time in seconds it takes to sort that array. For example, parallel Linq takes 28 seconds to sort a 150 million element array, while HPCsharp parallel Merge Sort takes 1.4 seconds. This is a speedup of about 20 times, not 20%, but 20 times faster.

The benchmarks in the above graph were run on a 36-core machine in AWS – c5.18xlarge node. The graph shows that the parallel Merge Sort scales much better. On a quad-core CPU parallel Merge Sort is at least 4X faster than parallel Linq.

Parallel Merge Sort is not limited to only sorting arrays of integers, but can sort arrays and lists of user defined classes – in general any type that can be compared. You can provide your own comparison method. The sort is also stable, whereas C# built-in sort for arrays and lists is not. Linq sort can be stable when .AsStable is used.

Serial implementation of Merge Sort is also provided, which is slower than C# Array.Sort and List.Sort, but is faster than Linq sort, serial and parallel. In this case, Merge Sort is using a single core, while parallel Linq is using all cores on a quad-core CPU, and serial Merge Sort is faster.

The above graph shows speedup of Parallel Merge Sort versus Parallel Linq. The x-axis is the array size of UInt32’s. The y-axis is the speedup provided by the Parallel Merge Sort. Most of the points land in the 15X to 30X range, showing that the Parallel Merge Sort is that many times faster.

## Radix Sort

## Parallel Merge

At the heart of the parallel Merge Sort is a parallel Merge algorithm. This algorithm is O(N) linear and parallelizes well.

## C# Built-in Sorting Algorithms Details

C# Array.Sort and List.Sort uses a hybrid sorting algoritm called introspective sort, which is a mixture of Insertion Sort, Heap Sort and Quicksort. “This implementation performs an unstable sort; that is, if two elements are equal, their order might not be preserved. In contrast, a stable sort preserves the order of elements that are equal. On average, this method is an O(*n* log *n*) operation, where *n* is Count; in the worst case it is an O(*n* ^ 2) operation” (msdn).

I’ll describe a library of sorting algorithms that has been developed over the last few years, which can sort faster while using a single CPU core, or multiple cores.