High precision integer multiplication with a graphics processing unit

In this paper we evaluate the potential for using an NVIDIA graphics processing unit (GPU) to accelerate high precision integer multiplication. The reported peak vector performance for a typical GPU appears to offer considerable potential for accelerating such a regular computation. Because of limitations in the on-chip memory, the high cost of kernel launches, and the particular nature of the architecture's support for parallelism, we found it necessary to use a hybrid algorithmic approach to obtain good performance. On the GPU itself we use an adaptation of the Strassen FFT algorithm to multiply 32KB chunks, while on the CPU we adapt the Karatsuba divide-and-conquer approach to optimize the application of the GPU's partial multiplies, which are viewed as “digits” by our implementation of Karatsuba. Even with this approach, the result is at best a modest increase in performance, compared with executing the same multiplication using the GMP package on a CPU at a comparable technology node. We identify the sources of this lackluster performance and discuss the likely impact of planned advances in GPU architecture.