Automatic Generation of High-Order Finite-Difference Code with Temporal Blocking for Extreme-Scale Many-Core Systems

摘要

In this paper we describe the basic idea, implementation and achieved performance of our DSL for stencil computation, Formura, on systems based on PEZY-SC2 manycore processor. Formura generates, from high-level description of the differential equation and simple description of finitedifference stencil, the entire simulation code with MPI parallelization with overlapped communication and calculation, advanced temporal blocking and parallelization for many-core processors. Achieved performance is 4.78 PF, or 21.5% of the theoretical peak performance for an explicit scheme for compressive CFD, with the accuracy of fourth-order in space and third-order in time. For a slightly modified implementation of the same scheme, efficiency was slightly lower (17.5%) but actual calculation time per one timestep was faster by 25%. Temporal blocking improved the performance by up to 70%. Even though the B/F number of PEZY-SC2 is low, around 0.02, we have achieved the efficiency comparable to those of highly optimized CFD codes on machines with much higher memory bandwidth such as K computer. We have demonstrated that automatic generation of the code with temporal blocking is a quite effective way to make use of very large-scale machines with low memory bandwidth for large-scale CFD calculations.