Rational number reconstruction using Chinese remainder theorem on GPU

The purpose of this study is to make rational number arithmetic fast. For this purpose, we implemented a rational number reconstruction method, a kind of modular algorithms, in which we used Chinese remainder theorem in order to parallelize calculation. We implemented it on CPU and GPU. Then, we applied them to some examples of computing such as inner products, Frobenius normal forms of matrices and determinants of matrices to examine their efficiencies. As a result, we showed that our implementations calculated faster than the standard arithmetic by using GMP at least in the latter two cases (i.e., computing of Frobenius normal forms and determinants). We also showed that the GPU version calculated 8.3 times faster at most than the CPU version.