Research on the Accuracy of Single Precision on Graphics Processing Unit

Abstract

The single precision in the computer is composed of two parts: the mantissa and the exponent. which are expressed by the limited binary bits. During adding on the single precision, the smaller one should shift to line up the decimal points, If the mantissa of the smaller one exceeds the range of registers, truncating or rounding off will be executed and cause losing precision. As far as the serials of GTX200 is concerned, the length of the register storing intermediate results is the same as the one for the final results. The accuracy problem is very prominent while the length of the mantissa exceeds the range of register after lining up the decimal points during the single precision adding. In this paper, we use the partial sum algorithm to improve the accuracy of single precision adding, and verify the correctness of the algorithm from the perspective of experiment by means of the matrix multiplication. Finally, we analyze the effect of partial sum algorithm on compute peak of the GPU and come to the conclusion that the partial sum algorithm has little influence on the compute peak of the GPU.