We consider the problem of estimating the numerical accuracy of programs with operations in fixed-point arithmetic and variables of arbitrary, mixed precision and possibly non-deterministic value. By applying a set of parameterised rewrite rules, we transform the relevant fragments of the program under consideration into sequences of operations in integer arithmetic over vectors of bits, thereby reducing the problem as to whether the error enclosures in the initial program can ever exceed a given order of magnitude to simple reachability queries on the transformed program. We describe a possible verification flow and a prototype analyser that implements our technique.We present an experimental evaluation on a particularly complex industrial case study, including a preliminary comparison between bit-level and word-level decision procedures.

我们考虑估计具有定点算术运算和任意、混合精度和可能非确定性值的变量的程序的数值精度的问题。通过应用一组参数化的重写规则，我们将所考虑的程序的相关片段转换为对位向量进行整数运算的操作序列，从而减少初始程序中的错误封闭是否可能超过给定的问题数量级到对转换后的程序的简单可达性查询。我们描述了一个可能的验证流程和一个实现我们技术的原型分析器。我们对一个特别复杂的工业案例研究进行了实验评估，包括比特级和字级决策程序之间的初步比较。