Address Sequence Generation for Data-Parallel Programs Using Integer Lattices

In data-parallel languages such as High Performance Fortran and Fortran D, arrays are mapped to processors through a two step process involving alignment followed by distribution. A compiler that generates code for each processor has to compute the sequence of local memory addresses accessed by each processor and the sequence of sends and receives for a given processor to access non-local data. In this paper, we present a novel approach to the address sequence generation problem based on integer lattices. The set of elements referenced can be generated by integer linear combinations of basis vectors. Using the basis vectors, we derive a loop nest that enumerates the addresses, which are points in the lattice generated by the basis vectors. The basis determination and lattice enumeration algorithms are linear time algorithms. Experimental results show that our solution to the address generation problem is faster than other solutions to this problem.