We present a bit-vector algorithm for the optimal and economical placement of computations within flow graphs, which is as efficient as standard uni-directional analyses. The point of our algorithm is the decomposition of the bi-directional structure of the known placement algorithms into a sequence of a backward and a forward analysis, which directly implies the efficiency result. Moreover, the new compositional structure opens the algorithm for modification: two further uni-directional analysis components exclude any unnecessary code motion. This laziness of our algorithm minimizes the register pressure, which has drastic effects on the run-time behaviour of the optimized programs in practice, where an economical use of registers is essential. Topics: data flow analysis, program optimization, partial redundancy elimination, code motion, bit-vector data flow analyses. 1 Motivation Code motion is a technique to improve the efficiency of a program by avoiding unnecessary recomputati...

An implementation oriented algorithm for lazy code motion is presented that minimizes the number of computations in programs while suppressing any unnecessary code motion in order to avoid superfluous register pressure. In particular, this variant of the original algorithm for lazy code motion works on flowgraphs whose nodes are basic blocks rather than single statements, as this format is standard in optimizing compilers. The theoretical foundations of the modified algorithm are given in the first part, where t-refined flowgraphs are introduced for simplifying the treatment of flowgraphs whose nodes are basic blocks. The second part presents the `basic block' algorithm in standard notation, and gives directions for its implementation in standard compiler environments. Keywords Elimination of partial redundancies, code motion, data flow analysis (bit-vector, unidirectional, bidirectional), nondeterministic flowgraphs, t-refined flow graphs, critical edges, lifetimes of registers, com...

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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 ...

The paper develops a framework that is based on the idea that modal logic provides an appropriate framework for the specification of data flow analysis (DFA) algorithms as soon as programs are represented as models of the logic. This can be exploited to construct a DFA-generator that generates efficient implementations of DFA-algorithms from modal specifications by partially evaluating a specific model checker with respect to the specifying modal formula. Moreover, the use of a modal logic as specification language for DFA-algorithms supports the compositional development of specifications and structured proofs of properties of DFA-algorithms. -- The framework is illustrated by means of a real life example: the problem of determining optimal computation points within flow graphs.

We present a bit-vector algorithm that uniformly combines code motion and strength reduction, avoids superfluous register pressure due to unnecessary code motion, and is as efficient as standard unidirectional analyses. The point of this algorithm is to combine the concept of lazy code motion of [1] with the concept of unifying code motion and strength reduction of [2, 3, 4, 5]. This results in an algorithm for lazy strength reduction, which consists of a sequence of unidirectional analyses, and is unique in its transformational power. Keywords: Data flow analysis, program optimization, partial redundancy elimination, code motion, strength reduction, bit-vector data flow analyses. 1 Motivation Code motion improves the runtime efficiency of a program by avoiding unnecessary recomputations of a value at runtime. Strength reduction improves runtime efficiency by reducing "expensive" recomputations to less expensive ones, e.g., by reducing computations involving multiplication to computat...

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this paper we present a theory which handles unidirectional as well as bidirectional data ow problems uniformly. Apart from explaining the known results in unidirectional and bidirectional ows, it provides deeper insights into the process of data ow analysis. Though the exposition of the theory is based on the bit vector problems, the theory is applicable to all bounded monotone data ow problems which possess the property of separability of solution. Several proofs have been omitted from the paper for brevity; they can be found in [Khedker and Dhamdhere 1992]

GIVE-N-TAKE is a code placement framework which uses a general producer-consumer concept. An advantage of GIVE-N-TAKE over existing partial redundancy elimination techniques is its concept of production regions, instead of single locations, which can be beneficial for general latency hiding. GIVE-N-TaKE guarantees balanced production, that is, each production will be started and stopped once. The framework can also take advantage of production coming "for free," as induced by side effects, without disturbing balance. GIVE-N-TAKE can place production either before or after consumption, and it also provides the option to hoist code out of potentially zero-trip loop (nest) con- structs. GIVE-N-TAKE uses a fast elimination method based on Tarjan intervals, with a complexity linear in the program size in most cases. We have

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