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....module is being implemented in JDBC. Its structure is shown in Figure 2.2. Java applications include the PDA, PVA, and GUI module implemented by Java. The JDBC provides a bridge between Java applications and performance database. Figure 2. 2 Relational Queries Module We use symbolic evaluation [2, 6] that combines both data and control flow analysis to determine variable values, assumptions about and constraints between variable values, and conditions under which control flow reaches a program statement. Computations are represented as symbolic expressions defined over the program s problem ....

M. Scheibl, A. Celic, and T. Fahringer, Interfacing Mathematica from the Vienna Fortran Compilation System, Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

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M. Scheibl, A. Pozgaj, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

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M. Scheibl, A. Celic, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

....as non linear expressions. Note that our algorithm for counting solutions to a system of constraints (see Section 4) is restricted to a sub class of these expressions. In order to provide a useful framework for manipulating symbolic expressions and constraints, we implemented standard techniques [19] which include multiplying out products and powers, reduce products of factors, put all terms over a common denominator, separate into terms with simple denominators, cancel common factors between numerators and denominators, etc. 3 Evaluate Symbolic Expressions In this section we present our ....

....we describe the computation of the algebraic sum E over a variable v 2 V, where l and u have been extracted (S4.3 in Figure 2) from constraints of I. E is a symbolic expression over V [ P, which has been simplified down to its simplest form by using our own symbolic manipulation package [19]. Computing the algebraic sum is then reduced to solving: E 0 E 1 v E 2 v : E q v Sigmaq (12) E i is a linear or non linear expression over P [ V Gamma fvg. Sigmaq (q is an integer constant) means that the sign of q can either be positive or negative. The problem, ....

M. Scheibl, A. Celic, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

....hold the name of the Fortran 90 compiler which is to be used in the profiling phase. The value of this variable is typically f90. A. 3 The Work Distribution Parameter In order to provide a useful framework for manipulating symbolic expressions and constraints, we implemented standard techniques [66] which include multiplying out products and powers, reducing products of factors, putting all terms over a common denominator, separating into terms with simple denominators, canceling common factors between numerators and denominators, etc. In this Section, we first describe the most important ....

....In what follows, we describe the computation of the algebraic sum u P v=l E over a variable v 2 V, where l and u have been extracted from constraints of I. E is a symbolic expression over V [P, which has been simplified down to its simplest form by using our own symbolic manipulation package [66]. Computing the algebraic sum is then reduced to solving: u X v=l E 0 E 1 v Sigma1 E 2 v Sigma2 : E q v Sigmaq (A.2) APPENDIX A. IMPLEMENTATION 84 typedef struct setexpr EXPR expr; struct setexpr next; SETEXPR; Figure A.8: SETEXPR data structure. E i is a ....

M. Scheibl, A. Pozgaj, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

....by pointers and EQUIVALENT statements in Fortran 90 which goes beyond the scope of this work. 2. 2 Manipulating and Simplifying Symbolic Expressions and Constraints In order to provide a useful framework for manipulating symbolic expressions and constraints, we have implemented an interface [45] to Mathematica TM 1 via MathLink TM [50] Our framework has been developed primarily based on Mathematica s support for pattern matching and transforming rules to rewrite expressions. Note that Mathematica does not provide explicit support for manipulating integer valued symbolic expressions. ....

....of linear and non linear symbolic expressions 1 Mathematica and MathLink are registered trademarks of Wolfram Research, Inc. 5 and constraints. For detailed information about our manipulation and simplification techniques, which goes beyond the scope of this paper, the reader may refer to [23, 24, 25, 45]. Furthermore, we have also integrated our framework with the Omega library [42] developed by Prof. W. Pugh at the University of Maryland, for simplifying first order logic expressions and constraints. 3 Symbolic Evaluation Symbolic evaluation statically analyses a program at compile time. Every ....

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M. Scheibl, A. Celic, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

.... is given by the boundary conditions (initial values for recurrence variables in the loop preheader) the recurrence relations (implied by the assignments to the recurrence variables in the loop body) and the recurrence condition (loop or exit condition) We have implemented a recurrence solver (Scheibl et al. 1996) written on top of Mathematica. The recurrence solver tries to determine closed forms for recurrence variables based on their recurrence system which is directly obtained from the program context. The implementation of our recurrence solver is largely based on methods described in (Gerlek et al. ....

Scheibl, M., A. Celic, and T. Fahringer: 1996, `Interfacing Mathematica from the Vienna Fortran Compilation System'. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna.

....as non linear expressions. Note that our algorithm for counting solutions to a system of constraints (see Section 4) is restricted to a sub class of these expressions. In order to provide a useful framework for manipulating symbolic expressions and constraints, we implemented standard techniques [20] which include multiplying out products and powers, reduce products of factors, put all terms over a common denominator, separate into terms with simple denominators, cancel common factors between numerators and denominators, etc. 3. Evaluate Symbolic Expressions In this section we present our ....

....we describe the computation of the algebraic sum u P v=l E over a variable v 2 V, where l and u have been extracted (S4.3 in Figure 2) from constraints of I. E is a symbolic expression over V [P, which has been simplified down to its simplest form by using our own symbolic manipulation package [20]. Computing the algebraic sum is then reduced to solving: u X v=l E0 E1 v Sigma1 E2 v Sigma2 : Eq v Sigmaq (12) E i is a linear or non linear expression over P [ V Gamma fvg. Sigmaq (q is an integer constant) means that the sign of q can either be positive or negative. ....

M. Scheibl, A. Celic, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

....2 ; C 2 ] Note that f(n 1) 2 f(n) has been rewritten to f(n) 2 f(n Gamma 1) Similar accounts for i(n) We use a program written under Mathematica [15] to solve recurrence systems. For this purpose we implemented an interface to Mathematica via MathLink [15] which is described in detail in [12]. By using this system we can automatically compute a solution (loop invariant) to the previous system of recurrences for n 0: f(n) y 2 n (1) i(n) b (n 1) 2) Based on (2) and i(n) m (loop condition) we can automatically determine the value of the loop variable at the exit of the ....

....of this code. 3 Experiments We are currently implementing the techniques described in this paper as part of VFCS (Vienna Fortran Compilation System [3] and P 3 T (a performance estimator for parallel programs [8] The interface to Mathematica for solving systems of recurrences [12] as well as the simplifier [9] for linear and non linear systems of constraints are already implemented. Nevertheless, in the following we show an experiment to demonstrate the potential benefits of the application of symbolic evaluation techniques for improving the performance of programs on ....

M. Scheibl, A. Celic, and T. Fahringer. Interfacing Mathematica from the Vienna Fortran Compilation System. Technical Report, Institute for Software Technology and Parallel Systems, Univ. of Vienna, December 1996.

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