Detecting overflow detection

Fixed-point saturating arithmetic is widely used in media and digital signal processing applications. A number of processor architectures provide instructions that implement saturating operations. However, standard high-level languages, such as ANSI C, provide no direct support for saturating arithmetic. Applications written in standard languages have to implement saturating operations in terms of basic two's complement operations. In order to provide fast execution of such programs it is important to have an optimizing compiler automatically detect and convert appropriate code fragments to hardware instructions. We present a set of techniques for automatic recognition of saturating arithmetic operations. We show that in most cases the recognition problem is simply one of Boolean circuit equivalence. Given the expense of solving circuit equivalence, we develop a set of practical approximations based on abstract interpretation. Experiments show that our techniques, while reliably recognizing saturating arithmetic, have small compile-time overhead. We also demonstrate that our approach is not limited to saturating arithmetic, but is directly applicable to recognizing other idioms, such as add-with-carry and absolute value.