Search for: All records

Proving the equivalence between SQL queries is a fundamental problem in database research. Existing solvers model queries using algebraic representations and convert such representations into first-order logic formulas so that query equivalence can be verified by solving a satisfiability problem. The main challenge lies in unbounded summations, which appear commonly in a query's algebraic representation in order to model common SQL features, such as projection and aggregate functions. Unfortunately, existing solvers handle unbounded summations in an ad-hoc manner based on heuristics or syntax comparison, which severely limits the set of queries that can be supported. This paper develops a new SQL equivalence prover called SQLSolver, which can handle unbounded summations in a principled way. Our key insight is to use the theory of LIA^*, which extends linear integer arithmetic formulas with unbounded sums and provides algorithms to translate a LIA^* formula to a LIA formula that can be decided using existing SMT solvers. We augment the basic LIA^* theory to handle several complex scenarios (such as nested unbounded summations) that arise from modeling real-world queries. We evaluate SQLSolver with 359 equivalent query pairs derived from the SQL rewrite rules in Calcite and Spark SQL. SQLSolver successfully proves 346 pairs of them, which significantly outperforms existing provers. 

Modern data center applications exhibit deep software stacks, resulting in large instruction footprints that frequently cause instruction cache misses degrading performance, cost, and energy efficiency. Although numerous mechanisms have been proposed to mitigate instruction cache misses, they still fall short of ideal cache behavior, and furthermore, introduce significant hardware overheads. We first investigate why existing I-cache miss mitigation mechanisms achieve sub-optimal performance for data center applications. We find that widely-studied instruction prefetchers fall short due to wasteful prefetch-induced cache line evictions that are not handled by existing replacement policies. Existing replacement policies are unable to mitigate wasteful evictions since they lack complete knowledge of a data center application’s complex program behavior. To make existing replacement policies aware of these eviction-inducing program behaviors, we propose Ripple, a novel software-only technique that profiles programs and uses program context to inform the underlying replacement policy about efficient replacement decisions. Ripple carefully identifies program contexts that lead to I-cache misses and sparingly injects “cache line eviction” instructions in suitable program locations at link time. We evaluate Ripple using nine popular data center applications and demonstrate that Ripple enables any replacement policy to achieve speedup that is closer to that of an ideal I-cache. Specifically, Ripple achieves an average performance improvement of 1.6% (up to 2.13%) over prior work due to a mean 19% (up to 28.6%) I-cache miss reduction. 

Modern data center applications exhibit deep software stacks, resulting in large instruction footprints that frequently cause instruction cache misses degrading performance, cost, and energy efficiency. Although numerous mechanisms have been proposed to mitigate instruction cache misses, they still fall short of ideal cache behavior, and furthermore, introduce significant hardware overheads. We first investigate why existing I-cache miss mitigation mechanisms achieve sub-optimal performance for data center applications. We find that widely-studied instruction prefetchers fall short due to wasteful prefetch-induced cache line evictions that are not handled by existing replacement policies. Existing replacement policies are unable to mitigate wasteful evictions since they lack complete knowledge of a data center application’s complex program behavior. To make existing replacement policies aware of these eviction inducing program behaviors, we propose Ripple, a novel software-only technique that profiles programs and uses program context to inform the underlying replacement policy about efficient replacement decisions. Ripple carefully identifies program contexts that lead to I-cache misses and sparingly injects “cache line eviction” instructions in suitable program locations at link time. We evaluate Ripple using nine popular data center applications and demonstrate that Ripple enables any replacement policy to achieve speedup that is closer to that of an ideal I-cache. Specifically, Ripple achieves an average performance improvement of 1.6% (up to 2.13%) over prior work due to a mean 19% (up to 28.6%) I-cache miss reduction.