<scp>BullsEye</scp> : Scalable and Accurate Approximation Framework for Cache Miss Calculation

For Affine Control Programs or Static (SCoP), symbolic counting of reuse distances could induce polynomials for each pair. These along with cache capacity constraints lead to non-affine (semi-algebraic) sets; and these sets is considered be a hard problem. The state-of-the-art methods use various exact enumeration techniques relying on existing cardinality algorithms that can efficiently count affine sets. We propose BullsEye , novel, scalable, accurate, problem-size independent approximation framework. It an analytical model fully associative caches LRU replacement policy focusing sampling linearization stack distance polynomials. First, we simple domain method improve the scalability enumeration. Second, Handelman’s theorem Bernstein’s representation . To technique, template (Interval Octagon) sub-polyhedral approximations. Our obtain significant compile-time improvements high-accuracy when compared HayStack important polyhedral compilation kernels such as nussinov cholesky adi from PolyBench harris gaussianblur LLVM -TestSuite. Overall, kernels, our show up 3.31× (geomean) speedup errors below ≈ 0.08% octagon approximation.