Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores

Massimiliano Fasi (1) , Nicholas J Higham (2) , Florent Lopez (3) , Théo Mary (4, 5) , Mantas Mikaitis (2)

1 department of Computer science, Durham University
2 School of Mathematics - Department of Mathematics [Manchester]
3 LSTC - Livermore Software Technology Corporation [Livermore]
4 CNRS - Centre National de la Recherche Scientifique
5 PEQUAN - Performance et Qualité des Algorithmes Numériques

Mots clés: multiword arithmetic; reduced precision; mixed precision; GPUs; NVIDIA V100; NVIDIA A100; tensor cores; rounding modes; blocked summation; FABsum; matrix multiplication; numerical linear algebra; rounding error analysis; floatingpoint arithmetic

Domaines: Informatique [cs]; Mathématiques [math]

Massimiliano Fasi, Nicholas J Higham, Florent Lopez, Théo Mary, Mantas Mikaitis. Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores. SIAM Journal on Scientific Computing, In press. ⟨hal-03543925v2⟩