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Although reliable long precision floating-point arithmetic libraries such asQD and MPFR/GMP are necessary to solve ill-conditioned problems in numericalsimulation, long precision BLAS-level computation such as matrix multiplicationhas not been fully optimized because tuning costs are very high compared toIEEE float and double precision arithmetic. In this study, we develop atechnique to shorten this tuning time by using prediction of computationaltimes in several block sizes for the blocking algorithm, and then selecting thefastest matrix multiplication method for tuning multiple precision dense realmatrix multiplication in various precisions, matrix sizes, and degrees ofparallelization.

Tuning Technique for Multiple Precision Dense Matrix Multiplication using Prediction of Computational Time