A Simple, Verified Validator for Software Pipelining (verification pearl) Jean-Baptiste Tristan Xavier Leroy INRIA Paris-Rocquencourt INRIA Paris-Rocquencourt B.P. 105, 78153 Le Chesnay, France B.P. 105, 78153 Le Chesnay, France
[email protected] [email protected] Abstract unrolling the loop then performing acyclic scheduling. Software Software pipelining is a loop optimization that overlaps the execu- pipelining is implemented in many production compilers and de- tion of several iterations of a loop to expose more instruction-level scribed in several compiler textbooks [1, section 10.5] [2, chapter parallelism. It can result in first-class performance characteristics, 20] [16, section 17.4]. In the words of the rather dramatic quote but at the cost of significant obfuscation of the code, making this above, “truly desperate” programmers occasionally perform soft- optimization difficult to test and debug. In this paper, we present a ware pipelining by hand, especially on multimedia and signal pro- translation validation algorithm that uses symbolic evaluation to de- cessing kernels. tect semantics discrepancies between a loop and its pipelined ver- Starting in the 1980’s, many clever algorithms were designed sion. Our algorithm can be implemented simply and efficiently, is to produce efficient software pipelines and implement them either provably sound, and appears to be complete with respect to most on stock hardware or by taking advantage of special features such modulo scheduling algorithms. A conclusion of this case study is as those of the IA64 architecture. In this paper, we are not con- that it is possible and effective to use symbolic evaluation to reason cerned about the performance characteristics of these algorithms, about loop transformations.