ZFP浮点数据压缩的误差分析
Error Analysis of ZFP Compression for Floating-Point Data
AI总结：
本文研究了ZFP压缩算法在存储查找表、模拟结果或计算过程中的解状态时的误差界，通过分析ZFP引入的舍入误差，建立了三种压缩模式下的误差界，并通过数值测试验证了结果的准确性。
摘要：
浮点数据压缩在高性能计算中将扮演重要角色，因为数据带宽和存储成本成为主导成本。虽然有损压缩在浮点数据中很强大，但需要理论结果来限制其在存储查找表、模拟结果或计算过程中的解状态时的误差。本文分析了ZFP，一种最先进的有损压缩算法所引入的舍入误差。ZFP的停止标准取决于用户指定的压缩模式；固定速率、固定精度或固定精度。虽然我们大部分讨论集中在ZFP的固定精度模式上，但我们为所有三种压缩模式建立了误差界。为了紧密捕捉误差，我们首先引入一个向量空间，允许我们处理组件的二进制表示。在此向量空间中，我们定义了实现ZFP压缩和解压每个步骤的算子，以建立ZFP引起的误差界。最后，提供了数值测试以证明所建立的界限的准确性。
英文摘要：
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.
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