Automatic Data and Computation Mapping for Distributed-Memory Machines.

Distributed memory parallel computers offer enormous computation power, scalability and flexibility. However, these machines are difficult to program and this limits their widespread use. An important characteristic of these machines is the difference in the access time for data in local versus non-local memory; non-local memory accesses are much slower than local memory accesses. This is also a characteristic of shared memory machines but to a less degree. Therefore it is essential that as far as possible, the data that needs to be accessed by a processor during the execution of the computation assigned to it reside in its local memory rather than in some other processor\u27s memory. Several research projects have concluded that proper mapping of data is key to realizing the performance potential of distributed memory machines. Current language design efforts such as Fortran D and High Performance Fortran (HPF) are based on this. It is our thesis that for many practical codes, it is possible to derive good mappings through a combination of algorithms and systematic procedures. We view mapping as consisting of wo phases, alignment followed by distribution. For the alignment phase we present three constraint-based methods--one based on a linear programming formulation of the problem; the second formulates the alignment problem as a constrained optimization problem using Lagrange multipliers; the third method uses a heuristic to decide which constraints to leave unsatisfied (based on the penalty of increased communication incurred in doing so) in order to find a mapping. In addressing the distribution phase, we have developed two methods that integrate the placement of computation--loop nests in our case--with the mapping of data. For one distributed dimension, our approach finds the best combination of data and computation mapping that results in low communication overhead; this is done by choosing a loop order that allows message vectorization. In the second method, we introduce the distribution preference graph and the operations on this graph allow us to integrate loop restructuring transformations and data mapping. These techniques produce mappings that have been used in efficient hand-coded implementations of several benchmark codes

Compiler Techniques for Optimizing Communication and Data Distribution for Distributed-Memory Computers

Advanced Research Projects Agency (ARPA)National Aeronautics and Space AdministrationOpe