Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes.It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution.Our main contribution is a novel method for calculating the required quasi-polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized enumerators in polynomial time (for fixed dimensions).

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VMAD (Virtual Machine for Advanced Dynamic analysis) is a platform for advanced profiling and analysis of programs, consisting in a static component and a runtime system. The runtime system is organized as a set of decoupled modules, dedicated to specific instrumenting or optimizing operations, dynamically loaded when required. The program binary files handled by VMAD are previously processed at compile time to include all necessary data, instrumentation instructions and callbacks to the runtime system. For this purpose, the LLVM compiler has been extended to automatically generate multiple versions of the code, each of them tailored for the targeted instrumentation or optimization strategies. The compiler chooses the most suitable intermediate representation for each version, depending on the information to be acquired and on the optimizations to be applied. The control flow graph is adapted to include the new versions and to transfer the control to and from the runtime system, which is in charge of the execution flow orchestration. The strength of our system resides in its extensibility, as one can add support for various new profiling or optimization strategies, independently of the existing modules. VMAD's potential is illustrated by presenting several analysis and optimization applications dedicated to loop nests: instrumentation by sampling, dynamic dependence analysis, adaptive version selection.