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Lessons Learned on the Path to Guaranteeing the Error Bound in Lossy Quantizers

Alex Fallin, Martin Burtscher

TL;DR

The paper tackles why error-bounded lossy compressors sometimes violate bounds and presents LC’s approach to guarantee $ABS$, $REL$, and $NOA$ bounds across CPU and GPU. It identifies floating-point rounding, FMA-induced discrepancies, and library differences as primary sources of parity loss, and proposes double-check quantization, inline lossless outliers, and parity-preserving log2/pow2 implementations to close these gaps. The results show that LC preserves the error bound for all tested values with only a modest average reduction in compression ratio (about $5\%$ for REL) while maintaining throughputs comparable to non-guaranteed configurations. By exhaustively validating across billions of 32-bit values and delivering bit-for-bit identical cross-device outputs, LC provides a practical, open-source path toward robust, cross-architecture lossy compression in HPC workflows.

Abstract

Rapidly increasing data sizes in scientific computing are the driving force behind the need for lossy compression. The main drawback of lossy data compression is the introduction of error. This paper explains why many error-bounded compressors occasionally violate the error bound and presents the solutions we use in LC, a CPU/GPU compatible lossy compression framework, to guarantee the error bound for all supported types of quantizers. We show that our solutions maintain high compression ratios and cause no appreciable change in throughput.

Lessons Learned on the Path to Guaranteeing the Error Bound in Lossy Quantizers

TL;DR

The paper tackles why error-bounded lossy compressors sometimes violate bounds and presents LC’s approach to guarantee , , and bounds across CPU and GPU. It identifies floating-point rounding, FMA-induced discrepancies, and library differences as primary sources of parity loss, and proposes double-check quantization, inline lossless outliers, and parity-preserving log2/pow2 implementations to close these gaps. The results show that LC preserves the error bound for all tested values with only a modest average reduction in compression ratio (about for REL) while maintaining throughputs comparable to non-guaranteed configurations. By exhaustively validating across billions of 32-bit values and delivering bit-for-bit identical cross-device outputs, LC provides a practical, open-source path toward robust, cross-architecture lossy compression in HPC workflows.

Abstract

Rapidly increasing data sizes in scientific computing are the driving force behind the need for lossy compression. The main drawback of lossy data compression is the introduction of error. This paper explains why many error-bounded compressors occasionally violate the error bound and presents the solutions we use in LC, a CPU/GPU compatible lossy compression framework, to guarantee the error bound for all supported types of quantizers. We show that our solutions maintain high compression ratios and cause no appreciable change in throughput.
Paper Structure (17 sections, 4 figures, 9 tables)

This paper contains 17 sections, 4 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Common Error-bound Types
  4. Point-Wise Absolute Error (ABS)
  5. Point-Wise Relative Error (REL)
  6. Point-Wise Normalized Absolute Error (NOA)
  7. Floating-point Arithmetic
  8. Result Parity
  9. Edge Cases
  10. Approach
  11. Floating-point Arithmetic
  12. Result Parity
  13. Edge Case
  14. Related Work
  15. Experimental Methodology
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Compression ratios of the parity-ensured $pow()$ and $log()$ REL compressor normalized to the non-ensured ratios.
  • Figure 2: GPU throughput of the parity-ensured $pow()$ and $log()$ REL compressor normalized to the non-ensured throughputs. Blue bars are compression, red bars are decompression.
  • Figure 3: GPU compression throughput of the rounding-error protected ABS compressor normalized to the non-protected throughput.
  • Figure 4: GPU compression ratio of the rounding-error protected ABS compressor normalized to the non-protected compression ratio.