. Symbolic analysis is of paramount importance for parallelizing compilers and performance estimators to examine symbolic expressions with program unknowns such as machine and problem sizes and to solve queries based on systems of constraints (equalities and inequalities) . This paper describes novel techniques for counting the number of solutions to a system of constraints, simplifying systems of constraints, computing lower and upper bounds of symbolic expressions, and determining the relationship between symbolic expressions. All techniques target wide classes of linear and non-linear symbolic expressions and systems of constraints. Our techniques have been implemented and are used as part of a parallelizing compiler and a performance estimator to support analysis and optimization of parallel programs. Various examples and experiments demonstrate the effectiveness of our symbolic analysis techniques. Keywords: Program analysis, symbolic expressions, comparing symbolic expressions, ...

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Fortran D is a version of Fortran extended with data decomposition specifications. It is designed to provide a machine-independent programming model for data-parallel applications and has heavily influenced the design of High Performance Fortran (HPF). In previous work we described Fortran D compilation algorithms for individual procedures. This paper presents an interprocedural approach to analyze data & computation partitions, optimize communication, support dynamic data decomposition, and perform other tasks required to compile Fortran D programs. Our algorithms are designed to make interprocedural compilation efficient. First, we collect summary information after edits to solve important data-flow problems in a separate interprocedural propagation phase. Second, for non-recursive programs we compile procedures in reverse topological order to propagate additional interprocedural information during code generation. We thus limit compilation to a single pass over each procedure body. ...

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This paper presents a new intermediate format called Static Single Information (SSI) form. SSI form generalizes the traditional concept of a variable de nition to include all information de nition points, or points where the analysis may obtain information about the value in a variable. Information de nition points include conditional branches as well as assignments. Because SSI form provides a new name for each variable at each information de nition point, it provides excellent support for both predicated analyses, which exploit information gained from conditionals, and backwards dataow analyses.

Due to the growing disparity between processor speed and main memory speed, techniques that improve cache utilization and hide memory latency are often needed to help applications achieve peak performance. Compiler-directed software prefetching is a hybrid software/hardware strategy that addresses this need. In this form of prefetching, the compiler inserts cache prefetch instructions into a program during the compilation process. During the program's execution, the hardware executes the prefetch instructions in parallel with other operations, bringing data items into the cache prior to the point where they are actually used, eliminating processor stalls due to cache misses. In this dissertation, we focus on the compiler's role in software prefetching. In a set of experimental studies, we evaluate the performance of current software prefetching strategies, first for sequential benchmark programs running on a simulated uniprocessor machine, and then for a set of parallel benchmarks on a...

This paper presents techniques for compiling loops with complex, indirect array accesses into loops whose array references have at most one level of indirection. The transformation allows prefetching of array indices for more efficient structuring of communication on distributed-memory machines. It can also improve performance on other architectures by enabling prefetching of data between levels of the memory hierarchy or exploitation of hardware support for vectorized gather/scatter. Our techniques are implemented in a compiler for Fortran D and execution speed improvements are given for multiprocessor and vector machines. 1

This paper presents a unified approach for generalized induction variable recognition and substitution, pointer analysis, analysis of conditionally updated variables, value range analysis, array region analysis, and nonlinear dependence testing. The analysis techniques share a well-defined uniform approach based on the chains of recurrences algebra. The uniform algebraic approach provides a powerful unified framework for developing analysis algorithms for restructuring compilers. The paper introduces a new set of analysis algorithms that accurately handle conditional control flow, pointer arithmetic, and nonlinear symbolic expressions in loops, which are known to be problematic for conventional restructuring compilers.

this paper, we describe techniques developed in the Rice dHPF compiler to address key code generation challenges that arise in achieving high performance for regular applications on message-passing systems. We focus on techniques required to implement advanced optimizations and to achieve consistently high performance with existing optimizations. Many of the core communication analysis and code generation algorithms in dHPF are expressed in terms of abstract equations manipulating integer sets. This approach enables general and yet simple implementations of sophisticated optimizations, making it more practical to include a comprehensive set of optimizations in data-parallel compilers. It also enables the compiler to support much more aggressive computation partitioning algorithms than in previous compilers. We therefore believe this approach can provide higher and more consistent levels of performance than are available today. 1. Introduction

The quality of many optimizations and analyses of parallelizing compilers depends significantly on the ability to evaluate symbolic expressions and on the amount of information available about program variables at arbitrary program points. In this paper, we describe an effective and unified symbolic evaluation framework that statically determines the values of variables and symbolic expressions, assumptions about and constraints between variable values and the condition under which control flow reaches a program statement. We introduce program context, a novel representation for comprehensive and compact control and data flow analysis information. Program contexts are described as first order logic formulas which enable us to use public domain software for standard symbolic manipulation. Computations are represented as algebraic expressions defined over a program's problem size. Our symbolic evaluation techniques comprise accurate modeling of assignment and input/output statements, bra...