We present a method for formal verification of transcendental hardware and software algorithms that scales to higher precision without suffering an exponential growth in runtimes. A class of implementations using piecewise polynomial approximation to compute the result is verified using MetiTarski, an automated theorem prover, which verifies a range of inputs for each call. The method was applied to commercial implementations from Cadence Design Systems with significant runtime gains over exhaustive testing methods and was successful in proving that the expected accuracy of one implementation was overly optimistic. Reproducing the verification of a sine implementation in software, previously done using an alternative theorem proving technique, demonstrates that the MetiTarski approach is a viable competitor. Verification of a 52 bit implementation of the square root function highlights the method’s high precision capabilities.

我们提出了一种对超越硬件和软件算法进行形式验证的方法，该算法可以扩展到更高的精度，而不会在运行时出现指数增长。使用分段多项式近似来计算结果的一类实现使用 MetiTarski 进行验证，MetiTarski 是一种自动定理证明器，它验证每个调用的输入范围。该方法被应用于 Cadence Design Systems 的商业实现，与详尽的测试方法相比具有显着的运行时间增益，并且成功地证明了一种实现的预期准确性过于乐观。在软件中重现对正弦实现的验证，以前使用另一种定理证明技术完成，这表明 MetiTarski 方法是一个可行的竞争对手。