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...

Abstract. Recently, pushdown systems (PDSs) have been extended to weighted PDSs, in which each transition is labeled with a value, and the goal is to determine the meet-over-allpaths value (for paths that meet a certain criterion). This paper shows how weighted PDSs yield new algorithms for certain classes of interprocedural dataflow-analysis problems. 1

We present Rhodium, a new language for writing compiler optimizations that can be automatically proved sound. Unlike our previous work on Cobalt, Rhodium expresses optimizations using explicit dataflow facts manipulated by local propagation and transformation rules. This new style allows Rhodium optimizations to be mutually recursively defined, to be automatically composed, to be interpreted in both flow-sensitive and-insensitive ways, and to be applied interprocedurally given a separate context-sensitivity strategy, all while retaining soundness. Rhodium also supports infinite analysis domains while guaranteeing termination of analysis. We have implemented a soundness checker for Rhodium and have specified and automatically proven the soundness of all of Cobalt’s optimizations plus a variety of optimizations not expressible in Cobalt, including Andersen’s points-to analysis, arithmetic-invariant detection, loop-induction-variable strength reduction, and redundant array load elimination. Categories and Subject Descriptors: D.2.4 [Software

While programs contain a large number of paths, a very small fraction of these paths are typically exercised during program execution. Thus, optimization algorithms should be designed to trade off the performance of less frequently executed paths in favor of more frequently executed paths. However, traditional formulations to code optimizations are incapable of performing such a trade-off. We present a path profile guided partial redundancy elimination algorithm that uses speculation to enable the removal of redundancy along more frequently executed paths at the expense of introducing additional expression evaluations along less frequently executed paths. We describe cost-benefit data flow analysis that uses path profiling information to determine the profitability of using speculation. The cost of enabling speculation of an expression at a conditional is determined by identifying paths along which an additional evaluation of the expression is introduced. The benefit of enabling specul...

We present a path profile guided partial dead code elimination algorithm that uses predication to enable sinking for the removal of deadness along frequently executed paths at the expense of adding additional instructions along infrequently executed paths. Our approach to optimization is particularly suitable for VLIW architectures since it directs the efforts of the optimizer towards aggressively enabling generation of fast schedules along frequently executed paths by reducing their critical path lengths. The paper presents a cost-benefit data flow analysis that uses path profiling information to determine the profitability of using predication enabled sinking. The cost of predication enabled sinking of a statement past a merge point is determined by identifying paths along which an additional statement is introduced. The benefit of predication enabled sinking is determined by identifying paths along which additional dead code elimination is achieved due to predication. The results...

Abstract. We present a method of specifying standard imperative program optimisations as a rewrite system. To achieve this we have extended the idea of matching sub-terms in expressions with simple patterns to matching blocks in a control flow graph. In order to express the complex restrictions on the applicability of these rewrites we add temporal logic side conditions. The combination of these features allows a flexible, high level, yet executable specification of many of the transformations found in optimising compilers. 1

In abstract model-checking, the semantics of an infinite transition system is abstracted to get a finite approximation on which temporal-logic/mu-calculus model-checking can be directly applied. The paper proposes two improvements of abstract model-checking which can be applied to infinite abstract transition systems: -- A new combination of forwards and backwards abstract fixed-point model-checking computations for universal safety. It computes a more precise result than that computed by conjunction of the forward and backward analyses alone, without needing to refine the abstraction; -- When abstraction is unsound (as can happen in minimum/maximum path-length problems), it is proposed to use the partial results of a classical combination of forward and backward abstract interpretation analyses for universal safety in order to reduce, on-the-fly, the concrete state space to be searched by model-checking.

In this paper we consider a strict generalization of context-free processes, the pushdown processes, and show that this class of processes is 1) closed under parallel composition with finite state systems, and can 2) be model checked by means of an elegant adaptation of the higher order model checker introduced in [BS92]. This shows the advantages of pushdown processes over context-free processes, which are not sufficiently general in order to support parallel composition.

We present an incremental algorithm for model checking in the alternation -free fragment of the modal mu-calculus, the first incremental algorithm for model checking of which we are aware. The basis for our algorithm, which we call MCI (for Model Checking Incrementally), is a linear-time algorithm due to Cleaveland and Steffen that performs global (non-incremental) computation of fixed points. MCI takes as input a set \Delta of changes to the labeled transition system under investigation, where a change constitutes an inserted or deleted transition; with virtually no additional cost, inserted and deleted states can also be accommodated. Like the Cleaveland-Steffen algorithm, MCI requires time linear in the size of the LTS in the worst case, but only time linear in \Delta in the best case. We give several examples to illustrate MCI in action, and discuss its implementation in the Concurrency Factory, an interactive design environment for concurrent systems.