Loop and data transformations for sparse matrix code

This paper introduces three new compiler transformations for representing and transforming sparse matrix computations and their data representations. In cooperation with run-time inspection, our compiler derives transformed matrix representations and associated transformed code to implement a variety of representations targeting different architecture platforms. This systematic approach to combining code and data transformations on sparse computations, which extends a polyhedral transformation and code generation framework, permits the compiler to compose these transformations with other transformations to generate code that is on average within 5% and often exceeds manually-tuned, high-performance sparse matrix libraries CUSP and OSKI. Additionally, the compiler-generated inspector codes are on average 1.5 faster than OSKI and perform comparably to CUSP, respectively.