Generating communication sets of array assignment statements for block-cyclic distribution on distributed memory parallel computers

This paper is concerned with the design of efficient algorithms for generating global name-space communication sets based on execution of array assignment statements for arbitrary strides and block sizes on distributed-memory parallel computers. We will present a hybrid approach, which combines the advantages of the set-theoretic method and the integer lattice method for generating communication sets. When block sizes are extremely small or large, a cyclic-based or a row-wise set-theoretic method is used. For other cases when block sizes are medium, we propose a new integer lattice method, in which data in each local block are treated as a unit. The first virtual referenced element in each virtual referenced local block can be generated efficiently by using an integer lattice method, in which the left boundary of index domain in each processing element is extended for this purpose. Then, the physical referenced elements in each physical referenced local block can be determined by the intersection of two closed forms, whose result is also a closed form. Because the cost of generating indices for packing and unpacking messages at the sending and receiving ends may be expensive for certain cases, we also study the conventional communication model and the deposit communication model. As each of the proposed algorithms and the communication models has its special use for certain cases, we thus identify rules of thumb to decide the most suitable algorithm for dealing with general cases.