Error Analysis of ZFP Compression for Floating-Point Data
Error Analysis of ZFP Compression for Floating-Point Data
复制标题
浮点数据ZFP压缩的误差分析
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
Peter Lindstrom
中科院分区：
文献类型：
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作者：
James Diffenderfer;Alyson Fox;J. Hittinger;G. Sanders;Peter Lindstrom
随着数据带宽和存储成为主要成本，浮点数据压缩将在高性能计算中发挥重要作用。浮点数据的有损压缩功能强大，但在用于存储查找表、仿真结果甚至计算期间的解状态时，需要理论结果来限制其误差。 lack{在本文中，我们分析了ZFP（一种最先进的有损压缩算法）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[P. Lindstrom，Fixed-rate compressed floating-point arrays，IEEE Transactions on Visualization and Computer Graphics，2014]。虽然我们的大部分讨论都集中在ZFP的固定精度模式上，但我们对所有三种压缩模式引入的误差建立了一个界限。为了紧密地捕获错误，我们首先引入一个向量空间，它允许我们使用组件的二进制表示。在这个向量空间下，我们定义了实现ZFP压缩和解压缩的每个步骤的运算符，以建立ZFP引起的错误的界限。最后，数值试验，以证明所建立的界限的准确性。
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. lack{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.