An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs
An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs
复制标题
浮点程序舍入误差分析的抽象解释框架
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C. Muñoz
中科院分区：
文献类型：
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作者：
Laura Titolo;Marco A. Feliú;Mariano M. Moscato;C. Muñoz
本文为浮点程序的圆形错误分析提供了一个抽象的解释框架。该框架定义了一个参数摘要分析，该分析计算程序的理想和浮点执行路径的每种组合，这是对可能发生的累积浮点圆形误差的声音过度交通。另外，还计算出导致误差近似的输入值的布尔表达式。提出了对程序控制流的抽象，以减轻分析产生的元素数量的爆炸。此外，定义了扩大的操作员以确保递归功能和循环的收敛性。该框架的实例化在原型工具Precisa中实现，该工具生成了正式的证明证书，以说明计算的圆形错误的正确性。
This paper presents an abstract interpretation framework for the round-off error analysis of floating-point programs. This framework defines a parametric abstract analysis that computes, for each combination of ideal and floating-point execution path of the program, a sound over-approximation of the accumulated floating-point round-off error that may occur. In addition, a Boolean expression that characterizes the input values leading to the computed error approximation is also computed. An abstraction on the control flow of the program is proposed to mitigate the explosion of the number of elements generated by the analysis. Additionally, a widening operator is defined to ensure the convergence of recursive functions and loops. An instantiation of this framework is implemented in the prototype tool PRECiSA that generates formal proof certificates stating the correctness of the computed round-off errors.
DOI：
10.29007/f4f3
发表时间：
2018
期刊：
Kalpa Publications in Computing
影响因子：
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作者：
Baranowski, Marek;Briggs, Ian;Chiang, Wei-Fan;Gopalakrishnan, Ganesh;Rakamaric, Zvonimir;Solovyev, Alexey
通讯作者：
Solovyev, Alexey