Static Versus Dynamic Task Scheduling of the Lu Factorization on ARM big. LITTLE Architectures

We investigate several parallel algorithmic variants of the LU factorization with partial pivoting (LUpp) that trade off the exploitation of increasing levels of task-parallelism in exchange for a more cache-oblivious execution. In particular, our first variant corresponds to the classical implementation of LUpp in the legacy version of LAPACK, which constrains the concurrency exploited to that intrinsic to the basic linear algebra kernels that appear during the factorization, but exerts an strict control of the cache memory and a static mapping of kernels to cores. A second variant relaxes this task-constrained scenario by introducing a look-ahead of depth one to increase task-parallelism, increasing the pressure on the cache system in terms of cache misses. Finally, the third variant orchestrates an execution where the degree of concurrency is only limited by the actual data dependencies in LUpp, potentially yielding to a higher volume of conflicts due to competition for the cache memory resources. The target platform for our implementations and experiments is a specific asymmetric multicore processor (AMP) from ARM, which introduces the additional scheduling complexity of having to deal with two distinct types of cores; and an L2-shared cache per cluster of the AMP, which results in more conflictivity in the access to this key cache level.