Effectiveness of abstract interpretation in automatic parallelization: a case study in logic programming

We report on a detailed study of the application and effectiveness of program analysis based on abstract interpretation to automatic program parallelization. We study the case of parallelizing logic programs using the notion of strict independence. We first propose and prove correct a methodology for the application in the parallelization task of the information inferred by abstract interpretation, using a parametric domain. The methodology is generic in the sense of allowing the use of different analysis domains. A number of well-known approximation domains are then studied and the transformation into the parametric domain defined. The transformation directly illustrates the relevance and applicability of each abstract domain for the application. Both local and global analyzers are then built using these domains and embedded in a complete parallelizing compiler. Then, the performance of the domains in this context is assessed through a number of experiments. A comparatively wide range of aspects is studied, from the resources needed by the analyzers in terms of time and memory to the actual benefits obtained from the information inferred. Such benefits are evaluated both in terms of the characteristics of the parallelized code and of the actual speedups obtained from it. The results show that data flow analysis plays an important role in achieving efficient parallelizations, and that the cost of such analysis can be reasonable even for quite sophisticated abstract domains. Furthermore, the results also offer significant insight into the characteristics of the domains, the demands of the application, and the trade-offs involved.

Optimization of multidimensional cross-section tables for few-group core calculations

Multigroup diffusion codes for three dimensional LWR core analysis use as input data pre-generated homogenized few group cross sections and discontinuity factors for certain combinations of state variables, such as temperatures or densities. The simplest way of compiling those data are tabulated libraries, where a grid covering the domain of state variables is defined and the homogenized cross sections are computed at the grid points. Then, during the core calculation, an interpolation algorithm is used to compute the cross sections from the table values. Since interpolation errors depend on the distance between the grid points, a determined refinement of the mesh is required to reach a target accuracy, which could lead to large data storage volume and a large number of lattice transport calculations. In this paper, a simple and effective procedure to optimize the distribution of grid points for tabulated libraries is presented. Optimality is considered in the sense of building a non-uniform point distribution with the minimum number of grid points for each state variable satisfying a given target accuracy in k-effective. The procedure consists of determining the sensitivity coefficients of k-effective to cross sections using perturbation theory; and estimating the interpolation errors committed with different mesh steps for each state variable. These results allow evaluating the influence of interpolation errors of each cross section on k-effective for any combination of state variables, and estimating the optimal distance between grid points.