Computer Algebra for Automated Performance Modeling of Fortran Programs

Time complexity of sequential programs or segments of parallel programs can be estimated using the dynamic frequency of statements and their execution time. The execution time of single statements can be estimated by counting basic operations. The present paper deals with a method of determining the global dynamic frequency of statements by transient analysis of a Markov model. For defining the model automatically and solving the related equations, we use AUGUR which is a research tool for performance modeling of Fortran programs. While static program analysis and model generation are implemented by routine compile techniques, AUGUR uses MAPLE for evaluating expressions, defining transition matrices, and transient analysis. Routines of LAPACK are considered to demonstrate the achievable results.