Pumma: Parallel universal matrix multiplication algorithms on distributed memory concurrent computers

The paper describes Parallel Universal Matrix Multiplication Algorithms (PUMMA) on distributed memory concurrent computers. The PUMMA package includes not only the non‐transposed matrix multiplication routine C = A ⋅ B, but also transposed multiplication routines C = A^T ⋅ B, C = A ⋅ B^T, and C = A^T ⋅ B^T, for a block cyclic data distribution. The routines perform efficiently for a wide range of processor configurations and block sizes. The PUMMA together provide the same functionality as the Level 3 BLAS routine xGEMM. Details of the parallel implementation of the routines are given, and results are presented for runs on the Intel Touchstone Delta computer.