Reproducible and Accurate Matrix Multiplication for GPU Accelerators

Roman Iakymchuk (1, 2) , David Defour (3, 4) , Caroline Collange (5) , Stef Graillat (2)

1 ISCD - Institut des Sciences du Calcul et des Données
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
3 UPVD - Université de Perpignan Via Domitia
4 DALI - Digits, Architectures et Logiciels Informatiques
5 ALF - Amdahl's Law is Forever

Due to non-associativity of floating-point operations and dynamic scheduling on parallel architectures, getting a bitwise reproducible floating-point result for multiple executions of the same code on different or even similar parallel architectures is challenging. In this paper, we address the problem of reproducibility in the context of matrix multiplication and propose an algorithm that yields both reproducible and accurate results. This algorithm is composed of two main stages: a filtering stage that uses fast vectorized floating-point expansions in con-junction with error-free transformations; an accumulation stage based on Kulisch long accumulators in a high-radix carry-save representation. Finally, we provide implementations and performance results in parallel environments like GPUs.

Mots clés: floating-point expansion; rounding-to-nearest; GPU accularators; Matrix multiplication; reproducibility; accuracy; Kulisch long accumulator; error-free transformation

Domaines: Arithmétique des ordinateurs; Calcul parallèle, distribué et partagé [cs.DC]

Roman Iakymchuk, David Defour, Caroline Collange, Stef Graillat. Reproducible and Accurate Matrix Multiplication for GPU Accelerators. 2015. ⟨hal-01102877⟩