Quadruple-precision BLAS using Bailey's arithmetic with FMA instruction: its performance and applications

When a floating-point arithmetic is executed on a processor unit, round-off and truncation errors occur every calculation. These errors cause a precision issue in a large simulation which requires a great number of calculations. Therefore, we have developed the quadruple-precision basic linear algebra subprograms (QPBLAS) based on Bailey's double-double arithmetic. The multiplication operation of Bailey's arithmetic is realized by 24 double-precision operations. When using an FMA (fused multiply-add) instruction, we can reduce the number of operations in about half. Therefore, we develop QPBLAS using the FMA instruction and evaluate its performance. The result shows that the QPBLAS using FMA is basically faster than QPBLAS. Moreover, when we replace QPBLAS of the quadruple-precision eigenvalue solver QPEigenK with QPBLAS using FMA, we can obtain about 10~20% speedup.