Minisymposium Presentation

We introduce a new algorithm for high-precision computations of matrix multiplication. While hardware-supported floating-point operations are fast, they suffer from rounding errors due to their finite precision. When the accuracy of computed results is not satisfactory, high-precision computation may be considered. One option is to use multi-precision arithmetic, such as MPFR. However, if extending the range of the exponent part is unnecessary, an alternative is to represent numbers as the sum of floating-point numbers and perform operations on those sums. Examples include pair arithmetic by Lange and Rump and double-word arithmetic by Bailey.In this talk, we introduce an algorithm that leverages this structure for fused multiply-add operations and applies it to matrix multiplication. As a result, we have designed a computational method that is less costly than pair arithmetic or double-word arithmetic, allowing for a slight degradation in accuracy. Finally, we demonstrate the performance of the proposed method through numerical experiments. Additionally, we compare the performance of the proposed method with the GEMM-based emulation method known as the Ozaki scheme.