Error Analysis of ZFP Compression for Floating-Point Data

TL;DR

This paper provides a theoretical analysis of the round-off errors introduced by the ZFP lossy compression algorithm for floating-point data, establishing bounds across different compression modes and validating them with numerical tests.

Contribution

It introduces a vector space framework to analyze ZFP's error bounds and extends the analysis to all compression modes, which was previously lacking.

Findings

Error bounds are established for ZFP in all compression modes.

Numerical tests confirm the tightness of the theoretical error bounds.

The analysis enhances understanding of lossy compression impacts on floating-point data accuracy.

Abstract

Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to bound its errors when used to store look-up tables, simulation results, or even the solution state during the computation. \black{In this paper, we analyze the round-off error introduced by ZFP, a %state-of-the-art lossy compression algorithm.} The stopping criteria for ZFP depends on the compression mode specified by the user; either fixed rate, fixed accuracy, or fixed precision [P. Lindstrom, Fixed-rate compressed floating-point arrays, IEEE Transactions on Visualization and Computer Graphics, 2014]. While most of our discussion is focused on the fixed precision mode of ZFP, we establish a bound on the error introduced by all three compression modes. In order to tightly capture the error, we first introduce a vector space that allows us to work with binary representations of components. Under this vector space, we define operators that implement each step of the ZFP compression and decompression to establish a bound on the error caused by ZFP. To conclude, numerical tests are provided to demonstrate the accuracy of the established bounds.