Using single or mixed precision is a potential approach to increase the computational efficiency and reduce the computational cost. Because the single-precision (SP) floating point data form only takes 32 bits, as defined by the IEEE 754 standard, to represent a certain number. However, 64 bits are needed for double-precision (DP) data form. This difference means that the memory usage of same data is saved by 50% when single precision is applied comparing with the double precision. Additionally, the memory access speed will be doubled. On the CPU platform, when the vectorization instruction set, such as streaming SIMD extensions (SSE) or advanced vector extensions (AVX) is used, the computational speed is also be doubled, resulting in a theoretical speed-up of 2. In modern architecture of clusters and supercomputers, the accelerators, including the graphic processing unit (GPU) and the field-programmable gate array (FPGA), play a more and more important role for obtaining high computing performance. And these special devices have been widely applied in quantum chemistry methods, including the Hartree-Fock (HF) method the integral evaluation, and many post-HF methods. Because the different design of the GPU hardware architecture, the speed-up for single precision is even larger on some GPUs.