The Impact of Address Arithmetic on the GPU Implementation of Fast Algorithms for the Vilenkin-Chrestenson Transform

This paper considers the impact of address arithmetic in the Cooley-Tukey and the constant geometry fast algorithms for the Vilenkin-Chrestenson transform on their implementation for the graphics processing unit (GPU). We consider issues such as using different transform radices and analyze the number of GPU instructions and register usage in the OpenCL implementations of the considered algorithms. Further, we compare the program running times on the GPU and on the central processing unit (CPU). Experiments show that the GPU implementations are from 10 to 22 times faster than the C/C++ CPU implementations, depending on the transform radix and the number of variables in the processed function. The OpenCL implementation of the constant geometry algorithm translates into a lower number of GPU arithmetic and fetch instructions and uses less registers. This implementation requires up to 21% shorter processing times than the corresponding Cooley-Tukey algorithm implementation.