Abstract: The reproducibility of floating-point programs refers to the fact that the same floating-point program exactly obtains the same numerical results in bits in multiple different runs. This is of great significance for program debugging or correctness verification of numerical results, and is widely used in numerical simulation. However, the results of floating-point calculations are often influenced by the order of calculations, so the dynamic scheduling & disordered execution of instructions makes the reproducibility a challenge. Matrix decomposition algorithms are widely used in numerical simulation applications. Reproducible matrix decomposition algorithms can effectively improve the efficiency of debugging and result analysis in precision sensitive numerical simulation applications. Based on error free transformation technology, three reproducible matrix decomposition algorithms are implemented based on the reproducible BLAS library, including block LU decomposition, Cholesky decomposition, and QR decomposition, and verified on domestic processor. The experimental results show that reproducible matrix decomposition algorithms are numerical accurate and reproducible. 

Key words: reproducibility, LU decomposition, Cholesky decomposition, QR decomposition