Any static, global analysis of the expression and data relationships in a program requires a knowledge of the control flow of the program. Since one of the primary reasons for doing such a global analysis in a compiler is to produce optimized programs, control flow analysis has been embedded in many compilers and has been described in several papers. An early paper by Prosser [5] described the use of Boolean matrices (or, more particularly, connectivity matrices) in flow analysis. The use of “dominance” relationships in flow analysis was first introduced by Prosser and much expanded by Lowry and Medlock [6]. References [6,8,9] describe compilers which use various forms of control flow analysis for optimization. Some recent developments in the area are reported in [4] and in [7]. The underlying motivation in all the different types of control flow analysis is the need to codify the flow relationships in the program. The codification may be in connectivity matrices, in predecessor-successor tables, in dominance lists, etc. Whatever the form, the purpose is to facilitate determining what the flow relationships are; in other words to facilitate answering such questions as: is this an inner loop?, if an expression is removed from the loop where can it be correctly and profitably placed?, which variable definitions can affect this use? In this paper the basic control flow relationships are expressed in a directed graph. Various graph constructs are then found and shown to codify interesting global relationships.

Control flow analysis

Many applications in DSP, telecommunications, graphics, and control have computations that either involve a large number of multiplications of one variable with several constants, or can easily be transformed to that form. A proper optimization of this part of the computation, which we call the multiple constant multiplication (MCM) problem, often results in a significant improvement in several key design metrics, such as throughput, area, and power. However, until now little attention has been paid to the MCM problem. After defining the MCM problem, we introduce an effective problem formulation for solving it where first the minimum number of shifts that are needed is computed, and then the number of additions is minimized using common subexpression elimination. The algorithm for common subexpression elimination is based on an iterative pairwise matching heuristic. The power of the MCM approach is augmented by preprocessing the computation structure with a new scaling transformation that reduces the number of shifts and additions. An efficient branch and bound algorithm for applying the scaling transformation has also been developed. The flexibility of the MCM problem formulation enables the application of the iterative pairwise matching algorithm to several other important and common high level synthesis tasks, such as the minimization of the number of operations in constant matrix-vector multiplications, linear transforms, and single and multiple polynomial evaluations. All applications are illustrated by a number of benchmarks.

Multiple constant multiplication : Efficient and versatile framework and algorithms for exploring common subexpression elimination

The search for efficient algorithms for register allocation dates back to the time of the first Fortran compiler for the IBM 704. Since then, many variants of the problem have been considered; depending on two factors: (1) the particular model for registers, and (2) the definition of the term “computation of a program” e.g. whether values may be computed more than once. We will show that several variants of the register allocation problem for straight line programs are polynomial complete. In particular we consider, (1) the case when each value is computed exactly once, and (2) the case when values may be recomputed as necessary. The completeness of the third problem considered is surprising. A straight line program starts with a set of initial values, and computes intermediate and final values. Suppose, for each value, the register that value must be computed into is preassigned. Then, (3) the problem of determining if there is a computation of the straight line program, that computes values into the assigned registers, is polynomial complete.

/pdf/complete-register-allocation-problems-2p5ar0ozlo.pdf

Complete register allocation problems

This paper introduces the notion of usage counts, shows how usage counts can be developed by algorithms that eliminate redundant computations, and describes how usage counts can provide the basis for register allocation. The paper compares register allocation based on usage counts to other commonly used register allocation techniques, and presents evidence which shows that the usage count technique is significantly better than these other techniques.

Register allocation via usage counts

In contrast to the predominant use of low-level intermediate text, high-level data flow analysis deals with programs essentially at source level and exploits the control flow information implicit in the parse tree. The need for high-level flow analysis arises from several aspects of recent work on advanced methods of program certification and optimization. This paper proposes a simple general method of high-level data flow analysis that allows free use of escape and jump statements, avoids large graphs when compiling large programs, facilitates updating of data flow information to reflect program changes, and derives new global information helpful in solving many familiar global flow analysis problems. An illustrative application to live variable analysis is presented. Many of the graphs involved are constructed and analyzed before any programs are compiled, thus avoiding certain costs that low-level methods incur repeatedly at compile time.

High-level data flow analysis

A method of optimizing the computation of arithmetic and indexing expressions of a Fortran program is presented. The method is based on a linear analysis of the definition points of the variables and the branching and DO loop structure of the program.The objectives of the processing are (1) to eliminate redundant calculations when references are made to common sub-expression values, (2) to remove invariant calculations from DO loops, (3) to efficiently compute subscripts containing DO iteration variables, and (4) to provide efficient index register usage.The method presented requires at least a three-pass compiler, the second of which is scanned backward. It has been used in the development of several FORTRAN compilers that have proved to produce excellent object code without significantly reducing the compilation speed.

Optimization of expressions in Fortran

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Optimization of expressions in Fortran