Fast Runtime Block Cyclic Data Redistribution on Multiprocessors

Block cyclic distribution seems to suit well for most linear algebra algorithms and this type of data distribution was chosen for the ScaLAPACK library as well as for the HPF language. But one has to choose a good compromise for the size of the blocks (to achieve a good computation and communication eeciency and a good load balancing). This choice heavily depends on each operation, so it is essential to be able to go from one block cyclic distribution to another very quickly. Moreover, it is also essential to be able to choose the right number of processors and the best grid shape for a given operation. We present here the data redistribution algorithms we implemented in the ScaLAPACK library in order to go from one block cyclic distribution on a grid to another one on another grid. A complexity study is made that shows the eeciency of our solution. Timing results on the Intel Paragon and the Cray T3D corroborate our results.