high performance computing on graphics processing units: hgpu.org

The Discrete Memory Machine (DMM) is a theoretical parallel computing model that captures the essence of the shared memory access of GPUs. The bank conflicts should be avoided for maximizing the bandwidth of the shared memory access. Offline permutation of an array is a task to copy all elements in array $a$ into array $b$ along a permutation given in advance. The main goal of this paper is to implement a conflict-free permutation algorithm on the DMM in a GPU. We have also implemented straightforward permutation algorithms on the GPU. The experimental results for 1024 float numbers on NVIDIA GeForce GTX-680 show that a straightforward permutation algorithm takes 246ns and 877ns for random permutation and bit-reversal permutation, respectively. Quite surprisingly, our conflict-free permutation algorithm runs in 165ns both for random permutation and for bit-reversal permutation although it performs more memory access operations. It follows that our conflict-free permutation is 1.5 times faster for random permutation and 5.3 times faster for bit-reversal permutation.