Commission of the European Communities

The performance modelling of complex programs is a tiresome and error prune process when done for a large program. Counting the number of instructions in the program, analyzing the program structure and combining them in a detailed time complexity function takes up a lot of human time and because it is a precise but often boring task is likely to be subject to errors. More important, numerical programs can be so large and complex that the one simply looses the overview over the program. Tens of thousands lines of code are not uncommon for numerical programs; tracking the variable usage and subroutine nestings has then become a difficult task and if we want to model the performance characteristics of a program we need to analyze the program structure. With such a large structure, which can be very unclear in dusty deck programs, the modelling task has become problematic. If this work is done only once, it is acceptable to put some effort into it to do it by hand, but in a research or development environment we want to experiment with the different factors that influence the performance. Changing these factors change the time complexity formula, and requires to redo some of the work. When this is the case, it is necessary to create an environment in which most of the mind boring tasks are automated and which assist the developer in the performance evaluation. Such a tool is described in this report. We describe the performance of a program using a SAD formula, which expresses the time complexity. The SAD formula (as described in [1]) consist of three layers. The first level of the SAD formula describes the execution cost of a basic block, which is simply a summation of the execution cost of the various instructions. The second level adds the control flow to the SAD formula. The execution time of a program is the execution time of each basic block times the number of times each block is executed. The second level SAD formula is therefor a summation of the product of the execution cost of a basic block and a certain factor. The factors are determined by the expressions in if and loop program constructs. The factors in this formula are however not independent, since in the real program the if constructs and loops are also nested and often depend on each other. Therefor we can …