Speaker
Description
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297–313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors $A$ and $B$ are split into integer slices, the product of these slices is computed exactly, and $AB$ is approximated by accumulating these integer products in floating-point arithmetic. This technique is particularly well suited to mixed-precision matrix multiply–accumulate units with integer support, such as the NVIDIA tensor cores or the AMD matrix cores The number of slices allows for performance-accuracy tradeoffs: more slices yield better accuracy but require more multiplications, which in turn reduce performance. We propose an inexpensive way to estimate the minimum number of multiplications needed to achieve a prescribed level of accuracy. Our error analysis shows that the algorithm may become inaccurate (or inefficient) if rows of $A$ or columns of $B$ are badly scaled. We perform a range of numerical experiments, both in simulation and on the latest NVIDIA GPUs, that confirm the analysis and illustrate strengths and weaknesses of the algorithm.