Parallel matrix multiplication based on space-filling curves on shared memory multicore platforms

Abstract

We present a parallel implementation of a cache oblivious algorithm for matrix multiplication on multicore platforms. The algorithm is based on a storage scheme and a block-recursive approach for multiplication, which are both based on a Peano space-filling curve. The recursion is stopped on matrix blocks with a size that needs to perfectly match the size of the L1 cache of the underlying CPU. The respective block multiplications are implemented by multiplication kernels that are hand-optimised for the SIMD units of current x86 CPUs. The Peano storage scheme is used to partition the block multiplications to different cores. Performance tests on various multicore platforms with up to 16 cores and different memory architecture show that the resulting implementation leads to better parallel scalability than achieved by Intel's MKL or GotoBLAS, and can outperform both libraries in terms of absolute performance on eight or more cores.