Equivalence checking of arithmetic expressions using fast evaluation

Abstract

Arithmetic expressions are the fundamental building blocks of hardware and software systems.An important problem in computational theory is to decide if two arithmetic expressions are equivalent. However, the general problem of equivalence checking, in digital computers, belongs to the NP Hard class of problems. Moreover, existing general techniques for solving this decision problem are applicable to very simple expressions and impractical when applied to more complex expressions found in programs written in high-level languages. In this paper we propose a method for solving the arithmetic expression equivalence problem using partial evaluation. In particular, our technique is specifically designed to solve the problem of equivalence checking of arithmetic expressions obtained from high-level language descriptions of hardware/software systems, which consists of regular arithmetic operators (+, −, ×) and logical operators (and, or, not). In our method, we use interval analysis to substantially prune the domain space of arithmetic expressions and limit the evaluation effort to a sufficiently limited set of subspaces. Our results show that the proposed method is fast enough to be of use in practice.

Optimizing control flow in loops using interval and dependence analysis

“…Furthermore, it is acceptable for a compiler intended for embedded computing to take longer to compile but perform aggressive optimizations, such as the ones presented in [16]. In our case, the additional compiler execution time was of the order of 10 mili seconds per loop [3].…”

“…In this subsection we summarize the analysis technique developed in [3] and used for our transformation. Without loss of generality, the remaining discussions in the paper will use C/C++ notation.…”

“…As defined in [3], a conditional expression cond_expr is either a simple condition or a complex condition. A simple condition is in the form of (expr 1 ROP expr 2 ).…”

“…. , x k , the domain space partitioning problem [3] is to partition the domain space of cond_expr into a mini- …”

“…The control flow and data-dependences within the loop body are analyzed using a static interval analysis technique previously outlined in [3]. Interval analysis provides information on the true/false paths within the original loop body as a function of the loop indices.…”