Xabclib:A Fully Auto-tuned Sparse Iterative Solver

TL;DR

This paper introduces Xabclib, a fully auto-tuned sparse iterative solver leveraging a new auto-tuning framework, OpenATLib, achieving significant speedups and memory savings through novel run-time functions and policies.

Contribution

The paper presents a novel auto-tuning framework, OpenATLib, and a fully auto-tuned sparse solver, Xabclib, with new run-time functions and memory optimization policies.

Findings

14x speedup for symmetric SpMV operations

4.62x speedup using branchless segmented scan

1/45 reduction in memory space usage

Abstract

In this paper, we propose a general application programming interface named OpenATLib for auto-tuning (AT). OpenATLib is designed to establish the reusability of AT functions. By using OpenATLib, we develop a fully auto-tuned sparse iterative solver named Xabclib. Xabclib has several novel run-time AT functions. First, the following new implementations of sparse matrix-vector multiplication (SpMV) for thread processing are implemented:(1) non-zero elements; (2) omission of zero-elements computation for vector reduction; (3) branchless segmented scan (BSS). According to the performance evaluation and the comparison with conventional implementations, the following results are obtained: (1) 14x speedup for non-zero elements and zero-elements computation omission for symmetric SpMV; (2) 4.62x speedup by using BSS. We also develop a "numerical computation policy" that can optimize memory space and computational accuracy. Using the policy, we obtain the following: (1) an averaged 1/45 memory space reduction; (2) avoidance of the "fault convergence" situation, which is a problem of conventional solvers.