In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single assignment form and the control dependence graph have been proposed to represent data flow and control flow propertiee of programs. Each of these previously unrelated techniques lends efficiency and power to a useful class of program optimization. Although both of these structures are attractive, the difficulty of their construction and their potential size have discouraged their use. We present new algorithms that efficiently compute these data structures for arbitrary control flow graphs. The algorithms use dominance frontiers, a new concept that may have other applications. We also give analytical and experimental evidence that all of these data structures are usually linear in the size of the original program. This paper thus presents strong evidence that these structures can be of practical use in optimization.

In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. Control dependence5 are introduced to analogously represent only the essential control flow relationships of a program. Control dependences are derived from the usual control flow graph. Many traditional optimizations operate more efficiently on the PDG. Since dependences in the PDG connect computationally related parts of the program, a single walk of these dependences is sufficient to perform many optimizations. The PDG allows transformations such as vectorization, that previ-ously required special treatment of control dependence, to be performed in a manner that is uniform for both control and data dependences. Program transformations that require interaction of the two dependence types can also be easily handled with our representation. As an example, an incremental approach to modifying data dependences resulting from branch deletion or loop unrolling is intro-duced. The PDG supports incremental optimization, permitting transformations to be triggered by one another and applied only to affected dependences.

The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0-Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worst-case exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...

This paper discusses the theoretical concepts underlying a project at Rice University to develop an automatic translator, called PFC (for Parallel FORTRAN Converter), from FORTRAN to FORTRAN 8x. The Rice project, based initially upon the research of Kuck and others at the University of Illinois [6, 17-21, 24, 32, 36], is a continuation of work begun while on leave at IBM Research in Yorktown Heights, N.Y. Our first implementation was based on the Illinois PARAFRASE compiler [20, 36], but the current version is a completely new program (although it performs many of the same transformations as PARAFRASE). Other projects that have influenced our work are the Texas Instruments ASC compiler [9, 33], the Cray-1 FORTRAN compiler [15], and the Massachusetts Computer Associates Vectorizer [22, 25]. The paper is organized into seven sections. Section 2 introduces FORTRAN 8x and gives examples of its use. Section 3 presents an overview of the translation process along with an extended translation example. Section 4 develops the concept of interstatement dependence and shows how it can be applied to the problem of vectorization. Loop carried dependence and loop independent dependence are introduced in this section to extend dependence to multiple statements and multiple loops. Section 5 develops dependence-based algorithms for code generation and transformations for enhancing the parallelism of a statement. Section 6 describes a method for extending the power of data dependence to control statements by the process of IF conversion. Finally, Section 7 details the current state of PFC and our plans for its continued development

The need to integrate several versions of a program into a common one arises frequently, but it is a tedious and time consuming task to integrate programs by hand. To date, the only available tools for assisting with program integration are variants of text-based differential file comparators; these are of limited utility because one has no guarantees about how the program that is the product of an integration behaves compared to the programs that were integrated. This paper concerns the design of a semantics-based tool for automatically integrating program versions. The main contribution of the paper is an algorithm that takes as input three programs A, B, and Base, where A and 8 are two variants of Base. Whenever the changes made to Base to create A and B do not “interfere ” (in a sense defined in the paper), the algorithm produces a program M that integrates A and B. The algorithm is predicated on the assumption that differences in the behavior of the variant programs from that of Base, rather than differences in the text, are significant and must be preserved in M. Although it is undecidable whether a program modification actually leads to such a difference, it is possible to determine a safe approximation by comparing each of the variants with Base. To determine this information, the integration algorithm employs a program representation that is similar (although not identical) to the dependence graphs that have been used

Precise and efficient dependence tests are essential to the effectiveness of a parallelizing compiler. This paper proposes a dependence testing scheme based on classifying pairs of subscripted variable references. Exact yet fast dependence tests are presented for certain classes of array references, as well as empirical results showing that these references dominate scientific Fortran codes. These dependence tests are being implemented at Rice University in both PFC, a parallelizing compiler, and ParaScope, a parallel programming environment.

The centerpiece of this thesis is a new processing paradigm for exploiting instruction level parallelism. This paradigm, called the multiscalar paradigm, splits the program into many smaller tasks, and exploits fine-grain parallelism by executing multiple, possibly (control and/or data) depen-dent tasks in parallel using multiple processing elements. Splitting the instruction stream at statically determined boundaries allows the compiler to pass substantial information about the tasks to the hardware. The processing paradigm can be viewed as extensions of the superscalar and multiprocess-ing paradigms, and shares a number of properties of the sequential processing model and the dataflow processing model. The multiscalar paradigm is easily realizable, and we describe an implementation of the multis-calar paradigm, called the multiscalar processor. The central idea here is to connect multiple sequen-tial processors, in a decoupled and decentralized manner, to achieve overall multiple issue. The mul-tiscalar processor supports speculative execution, allows arbitrary dynamic code motion (facilitated by an efficient hardware memory disambiguation mechanism), exploits communication localities, and does all of these with hardware that is fairly straightforward to build. Other desirable aspects of the

This paper addresses the problem of compiling perfectly nested loops for multicomputers (distributed memory machines). The relatively high communication startup costs in these machines renders frequent communication very expensive. Motivated by this, we present a method of aggregating a number of loop iterations into tiles where the tiles execute atomically -- a processor executing the iterations belonging to a tile receives all the data it needs before executing any one of the iterations in the tile, executes all the iterations in the tile and then sends the data needed by other processors. Since synchronization is not allowed during the execution of a tile, partitioning the iteration space into tiles must not result in deadlock. We first show the equivalence between the problem of finding partitions and the problem of determining the cone for a given set of dependence vectors. We then present an approach to partitioning the iteration space into deadlock-free tiles so that communicati...

Symbolic Domain The objects in our abstract symbolic domain are canonical symbolic expressions. A canonical symbolic expression is a lexicographically ordered sequence of symbolic terms. Each symbolic term is in turn a pair of an integer coefficient and a sequence of pairs of pointers to program variables in the program symbol table and their exponents. The latter sequence is also lexicographically ordered. For example, the abstract value of the symbolic expression 2ij+3jk in an environment that i is bound to (1; (( " i ; 1))), j is bound to (1; (( " j ; 1))), and k is bound to (1; (( " k ; 1))) is ((2; (( " i ; 1); ( " j ; 1))); (3; (( " j ; 1); ( " k ; 1)))). In our framework, environment is the abstract analogous of state concept; an environment is a function from program variables to abstract symbolic values. Each environment e associates a canonical symbolic value e x for each variable x 2 V ; it is said that x is bound to e x. An environment might be represented by...

This paper describes a language-independent program representation-the program dependence graph—and &mCusses how program dependence graphs, together with operations such as program slicing, can provide the basis for powerfid programming tools that address important software-engineering problems, such as understanding what an existing program does and how it works, understanding the differences between several versions of a program, and creating new programs by combining pieces of old programs. The paper primarily surveys work in this mea that has been czried out at the University of Wisconsin during the past five years.