A summer of code and mathematics

Background

Since a few years I've been contributing code to the open-source project SymPy. SymPy is a so-called "computer algebra system", which lets you manipulate mathematical expressions symbolically. I've used this software package extensively in my own doctoral studies and it has been really useful.

My research involves formulating mathematical models to: rationalize experimental observations, fit parameters or aid in design of experiments. Traditionally one sits down and derive equations, often using pen & paper, then one writes computer code which implements said model, and finally one writes a paper with the same formulas as LaTeX code (or something similar). Note how this procedure involves writing the same equations essentially three times, during derivation, coding and finally the article.

By using SymPy I can, from a single source:

1. Do the derivations (fewer hard-to-find mistakes)
2. Generate the numerical code (a blazing fast computer program)
3. Output LaTeX formatted equations (pretty formulas for the report)

A very attractive side-effect of this is that one truly get reproducible research (reproducibility is one of the pillars in science). Every step of the process is self-documented, and because SymPy is free software: anyone can redo them. I can't stress enough how big this truly is. It is also the main motivation why I haven't used proprietary software in place of SymPy, even though that software may be considerably more feature complete than SymPy, any code I wrote for it would be inaccessible to people without a license (possibly even including myself if I leave academia).

For this work-flow to work in practice the capabilities of the computer algebra system need to be quite extensive, and it is here my current project with SymPy comes in. I have had several ideas on how to improve capability number two listed above: generating the numerical code, and now I get the chance to realize some of them and work with the community to improve SymPy.

First week

The majority of the first week has been spent on introducing type-awareness into the code-printers. SymPy has printer-classes which specialize printing of e.g. strings, C code, Fortran code etc. Up to now there has been no way to indicate what precision the generated code should be for. The default floating point type in python is for example "double precision" (i.e. 64-bit binary IEEE 754 floating point). This is also the default precision targeted by the code printers.

However, there are occasions where one want to use another precision. For example, consumer class graphics cards which are ubiquitous often have excellent single precision performance, but are intentionally capped with respect to double precision arithmetic (due to marketing reasons). At other times, one want just a bit of extra precision and extended precision (80-bit floating point, usually the data type of C's long double) is just what's needed to compute some values with the required precision. In C, the corresponding math functions are standardized since C99.

I have started the work to enable the code printers to print this in a pull-request to the SymPy source repository. I have also started experimenting with a class representing arrays. Arrays

The first weekly meeting with Aaron Meurer went well and we also briefly discussed how to reach out to the SymPy community for wishes on what code-generation functions to provide, I've set up a wiki-page for it under the SymPy projects wiki:

https://github.com/sympy/sympy/wiki/codegen-gsoc17

I'll be sending out an email to the mailing list for SymPy asking for feedback.

We also discussed the upcoming SciPy 2017 conference where Aaron Meurer and Jason Moore will be giving a tutorial on code-generation with SymPy. They've asked me to join forces with them and I've happily accepted that offer and am looking forward to working on the tutorial material and teaching fellow developers and researchers in the scientific python community about how to leverage SymPy for code generation.

Next blog post will most likely be a bit more technical, but I thought it was important to give some background on what motivates this effort and what the goal is.