A distribution format for communication-free reshape in distributed memory computers

Data parallel languages designed for distributed memory computing environments provide a single global address space to the programmer. The mapping from this global address space to the distributed local address space is performed by a compiler, which does this mapping based on the array distribution format. Thus, each array in a data parallel language program has its own distribution format. The Reshape function changes the array distribution format as well as the array shape. However, the changed distribution format cannot be represented by any distribution format supported in current languages. Because there is no suitable distribution format, it is necessary to change the reshaped distribution format to an existing distribution format, with heavy overhead due to the redistribution function. To eliminate the redistribution step in Reshape function, we have proposed a new distribution format, HIER-CYCLIC, which can represent the reshaped distribution format. We have also proposed a language syntax to use HIER-CYCLIC and a compiling mechanism. Finally, we performed an experiment on an IBM-SP2 machine using a shift function.