The automatic generation of sparse primitives

Primitives in mathematical software are usually written and optimized by hand. With the implementation of a "sparse compiler" that is capable of automatically converting a dense program into sparse code, however, a completely different approach to the generation of sparse primitives can be taken. A dense implementation of a particular primitive is supplied to the sparse compiler, after which it can be converted into many different sparse versions of this primitive. Each version is specifically tailored to a class of sparse matrices having a specific nonzero structure. In this article, we discuss some of our experiences with this new approach.