Almost optimal column-wise prefix-sum computation on the GPU

• Published in: The Journal of supercomputing Vol. 74; no. 4; pp. 1510 - 1521
• Main Authors: Tokura, Hiroki, Fujita, Toru, Nakano, Koji, Ito, Yasuaki, Bordim, Jacir L.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-04-2018; Springer Nature B.V
• Subjects: Algorithms; Compilers; Computation; Computer memory; Computer Science; Euclidean geometry; Image processing; Interpreters; Matrices (mathematics); Processor Architectures; Programming Languages; Sums; CUDA; Parallel algorithm; Prefix computation; GPU
• ISSN: 0920-8542; 1573-0484
• DOI: 10.1007/s11227-018-2242-8

Row-wise and column-wise prefix-sum computation of a matrix has many applications in the area of image processing such as computation of the summed area table and the Euclidean distance map. It is known that the prefix-sums of a one-dimensional array can be computed efficiently on the GPU. Hence, row-wise prefix-sums of a matrix can also be computed efficiently on the GPU by executing this prefix-sum algorithm for every row in parallel. However, the same approach does not work well for computing column-wise prefix-sums due to inefficient stride memory access to the global memory is performed. The main contribution of this paper is to present an almost optimal column-wise prefix-sum algorithm on the GPU. Quite surprisingly, experimental results using NVIDIA TITAN X show that our column-wise prefix-sum algorithm runs only 2–6% slower than matrix duplication. Thus, our column-wise prefix-sum algorithm is almost optimal.