Friday, 4 May 2012

Does F# have any advantages over C# for mathematical programs?


F# has many enormous benefits over C# in the context of mathematical programs:
  • F# interactive sessions let you run code on-the-fly to obtain results immediately and even visualize them, without having to build and execute a complete application.
  • F# supports some features that can provide massive performance improvements in the context of mathematics. Most notably, the combination of inline and higher-order functions allow mathematical code to be elegantly factored without adversely affecting performance. C# cannot express this.
  • F# supports some features that make it possible to implement mathematical concepts far more naturally than can be obtained in C#. For example, tail calls make it much easier to implement recurrence relations simply and reliably. C# cannot express this either.
  • Mathematical problems often require the use of more sophisticated data structures and algorithms. Expressing complicated solutions is vastly easier with F# compared to C#.
If you would like a case study, I converted an implementation of QR decomposition overSystem.Double from 2kLOC of C#. The F# was only 100 lines of code, runs over 10× faster and is generalized over the type of number so it works not only on float32float andSystem.Numerics.Complex but can even be applied to symbolic matrices to obtain symbolic results!

No comments: