Error Analysis of ZFP Compression for Floating-Point Data
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. In this paper, we analyze the round-off error introduced by ZFP, a lossy compression algorithm. Here, the stopping criteria for ZFP depends on the compression mode specified by the user: fixed rate, fixed accuracy, or fixed precision [P. Lindstrom, ZFP 0.5.3 Documentation, 2018]. 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, first we 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.
- Authors:
-
[2];
[2];
- The Univ. of Florida, Gainesville, FL (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1572236
- Report Number(s):
- LLNL-JRNL-744818
Journal ID: ISSN 1064-8275; 900098
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Scientific Computing
- Additional Journal Information:
- Journal Volume: 41; Journal Issue: 3; Journal ID: ISSN 1064-8275
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; lossy compression; floating-point representation; error bounds
Citation Formats
Diffenderfer, James D., Fox, Alyson L., Hittinger, Jeffrey A., Sanders, Geoffrey D., and Lindstrom, Peter G. Error Analysis of ZFP Compression for Floating-Point Data. United States: N. p., 2019.
Web. doi:10.1137/18M1168832.
Diffenderfer, James D., Fox, Alyson L., Hittinger, Jeffrey A., Sanders, Geoffrey D., & Lindstrom, Peter G. Error Analysis of ZFP Compression for Floating-Point Data. United States. https://doi.org/10.1137/18M1168832
Diffenderfer, James D., Fox, Alyson L., Hittinger, Jeffrey A., Sanders, Geoffrey D., and Lindstrom, Peter G. Thu .
"Error Analysis of ZFP Compression for Floating-Point Data". United States. https://doi.org/10.1137/18M1168832. https://www.osti.gov/servlets/purl/1572236.
@article{osti_1572236,
title = {Error Analysis of ZFP Compression for Floating-Point Data},
author = {Diffenderfer, James D. and Fox, Alyson L. and Hittinger, Jeffrey A. and Sanders, Geoffrey D. and Lindstrom, Peter G.},
abstractNote = {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. In this paper, we analyze the round-off error introduced by ZFP, a lossy compression algorithm. Here, the stopping criteria for ZFP depends on the compression mode specified by the user: fixed rate, fixed accuracy, or fixed precision [P. Lindstrom, ZFP 0.5.3 Documentation, 2018]. 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, first we 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.},
doi = {10.1137/18M1168832},
journal = {SIAM Journal on Scientific Computing},
number = 3,
volume = 41,
place = {United States},
year = {Thu Jun 13 00:00:00 EDT 2019},
month = {Thu Jun 13 00:00:00 EDT 2019}
}
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