A new algorithm, SSAPRE, for performing partial redundancy elimination based entirely on SSA form is presented. It achieves optimal code motion similar to lazy code motion [KRS94a, DS93], but is formulated independently and does not involve iterative data flow analysis and bit vectors in its solution. It not only exhibits the characteristics common to other sparse approaches, but also inherits the advantages shared by other SSA-based optimization techniques. SSAPRE also maintains its output in the same SSA form as its input. In describing the algorithm, we state theorems with proofs giving our claims about SSAPRE. We also give additional description about our practical implementation of SSAPRE, and analyze and compare its performance with a bit-vector-based implementation of PRE. We conclude with some discussion of the implications of this work. 1 Introduction The Static Single Assignment Form (SSA) has become a popular program representation in optimizing compilers, because it provid...

: Although code transformations are routinely applied to improve the performance of programs for both scalar and parallel machines, the properties of code improving transformations are not well understood. In this paper we present a framework that enables the exploration, both analytically and experimentally, of properties of code improving transformations. The major component of the framework is a specification language, Gospel, for expressing the conditions needed to safely apply a transformation and the actions required to change the code to implement the transformation. The framework includes a technique that facilitates an analytical investigation of code improving transformations using the Gospel specifications. It also contains a tool, Genesis, that automatically produces a transformer that implements the transformations specified in Gospel. We demonstrate the usefulness of the framework by exploring the enabling and disabling properties of transformations. We first present ana...

Reducing communication cost is crucial to achieving good performance on scalable parallel machines. This paper presents a new compiler algorithm for global analysis and optimization of communication in data-parallel programs. Our algorithm is distinct from existing approaches in that rather than handling loop-nests and array references one by one, it considers all communication in a procedure and their interactions under different placements before making a final decision on the placement of any communication. It exploits the flexibility resulting from this advanced analysis to eliminate redundancy, reduce the number of messages, and reduce contention for cache and communication buffers, all in a unified framework. In contrast, single loop-nest analysis often retains redundant communication, and more aggressive dataflow analysis on array sections can generate too many messages or cache and buffer contention. The algorithm has been implemented in the IBM pHPF compiler for High Performan...

. This paper addresses the problems of representing aliases and indirect memory operations in SSA form. We propose a method that prevents explosion in the number of SSA variable versions in the presence of aliases. We also present a technique that allows indirect memory operations to be globally commonized. The result is a precise and compact SSA representation based on global value numbering, called HSSA, that uniformly handles both scalar variables and indirect memory operations. We discuss the capabilities of the HSSA representation and present measurements that show the effects of implementing our techniques in a production global optimizer. Keywords. Aliasing, Factoring dependences, Hash tables, Indirect memory operations, Program representation, Static single assignment, Value numbering. 1 Introduction The Static Single Assignment (SSA) form [CFR+91] is a popular and efficient representation for performing analyses and optimizations involving scalar variables. Effecti...

This paper presents a new approach called SSAPRE [Chow et al. 1997] that shares the optimality properties of the best prior work [Knoop et al. 1992; Knoop et al. 1994; Drechsler and Stadel 1993] and that is based on static single assignment form. Static single assignment form (SSA) is a popular program representation in modern optimizing compilers. Its versatility stems from the fact that, in addition to representing the program, it provides accurate use-definition (use-def) relationships among the program variables in a concise form [Cytron et al. 1991; Wolfe 1996; Chow et al. 1996]. Many efficient global optimization algorithms have been developed based on SSA. Among these optimizations are dead store elimination [Cytron et al. 1991], constant propagation [Wegman and Zadeck 1991], value numbering [Alpern et al. 1988; Rosen et al. 1988; Briggs et al. 1997], induction variable analysis [Gerlek et al. 1995; Liu et al. 1996], live range computation [Gerlek et al. 1994] and global code motion [Click 1995]. Until recently, most uses of SSA have been restricted to solving problems based essentially on program variables. SSA could not readily be applied to solving expression-based problems because the concept of use-def for expressions is less obvious than for variables. This difficulty was mentioned by Dhamdhere et al. in the conclusion of [Dhamdhere et al. 1992]. They state, essentially, that there is no clear connection between the use-def information for variables represented by SSA form and the redundancy properties for expressions. By demonstrating such a connection and exploiting it, our work shows that an SSA-based approach to PRE and other expression-based problems is not only plausible, but also enlightening and practical. Although this paper addresses only the PRE ...

Abstract. Programs represented in Static Single Assignment (SSA) form contain phi instructions (or functions) whose operational semantics are to merge values coming from distinct control flow paths. However, translating phi instructions into native instructions is nontrivial when transformations such as copy propagation and code motion have been performed. In this paper we present a new framework for translating out of SSA form. By appropriately placing copy instructions, we ensure that none of the resources in a phi congruence class interfere. Within our framework, we propose three methods for copy placement. The first method pessimistically places copies for all operands of phi instructions. The second method uses an interference graph to guide copy placement. The third method uses both data flow liveness sets and an interference graph to guide copy placement. We also present a new SSAbased coalescing method that can selectively remove redundant copy instructions with interfering operands. Our experimental results indicate that the third method results in 35 % fewer copy instructions than the second method. Compared to the first method, the third method, on average, inserts 89.9% fewer copies during copy placement and runs 15 % faster, which are significant reductions in compilation time and space. 1.

. In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIM t , under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starti...

. Redundancy elimination optimizations avoid repeated computation of the same value by computing the value once, saving it in a temporary, and reusing the value from the temporary when it is needed again. Examples of redundancy elimination optimizations include common subexpression elimination, loop invariant code motion and partial redundancy elimination. We demonstrate that the introduction of temporaries to save computed values can result in a significant increase in register pressure. An increase in register pressure may in turn trigger generation of spill code which can more than offset the gains derived from redundancy elimination. While current techniques minimize increases in register pressure, to avoid spill code generation it is instead necessary to ensure that register pressure does not exceed the number of available registers. In this paper we develop a redundancy elimination algorithm that is sensitive to register pressure: our novel technique first sets upper limits on al...

We present a graph-based intermediate representation (IR) with simple semantics and a low-memory-cost C++ implementation. The IR uses a directed graph with labeled vertices and ordered inputs but unordered outputs. Vertices are labeled with opcodes, edges are unlabeled. We represent the CFG and basic blocks with the same vertex and edge structures. Each opcode is defined by a C++ class that encapsulates opcode-specific data and behavior. We use inheritance to abstract common opcode behavior, allowing new opcodes to be easily defined from old ones. The resulting IR is simple, fast and easy to use.

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