Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

Brice Boyer (1) , Jean-Guillaume Dumas (1) , Clément Pernet (2) , Wei Zhou (3)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation
3 SCG - Symbolic Computation Group

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.

Domaines: Logiciel mathématique [cs.MS]

Brice Boyer, Jean-Guillaume Dumas, Clément Pernet, Wei Zhou. Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm. ISSAC 2009 - International Symposium on Symbolic and Algebraic Computation, Jul 2009, Séoul, South Korea. pp.55-62, ⟨10.1145/1576702.1576713⟩. ⟨hal-00163141v5⟩