Analysis and application of Fourier-Motzkin variable elimination to program optimization : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science at Massey University, Albany, New Zealand - Niedzielski, David (Massey University, 2019)
This thesis examines four of the most influential dependence analysis techniques in use by optimizing compilers: Fourier-Motzkin Variable Elimination, the Banerjee Bounds Test, the Omega Test, and the I-Test. Although the performance and effectiveness of these tests have previously been documented empirically, no in-depth analysis of how these techniques are related from a purely analytical perspective has been done. The analysis given here clarifies important aspects of the empirical results that were noted but never fully explained. A tighter bound on the performance of one of the Omega Test algorithms than was known previously is proved and a link is shown between the integer refinement technique used in the Omega Test and the well-known Frobenius Coin Problem. The application of a Fourier-Motzkin based algorithm to the elimination of redundant bound checks in Java bytecode is described. A system which incorporated this technique improved performance on the Java Grande Forum Benchmark Suite by up to 10 percent.
Keywords: Compilers (Computer programs); Algorithms