Code instruction selection based on SSA-graphs

Instruction selection for embedded processors is a challenging problem. Embedded system architectures feature highly irregular instruction sets and complex data paths. Traditional code generation techniques have difficulties to fully utilize the features of such architectures and typically result in inefficient code. In this paper we describe an instruction selection technique that uses static single assignment graphs (SSA-graphs) as underlying data structure for selection. Patterns defined as graph grammar guide the instruction selection to find (nearly) optimal results. We present an approach which maps the pattern matching problem to a partitioned boolean quadratic optimization problem (PBQP). A linear PBQP solver computes optimal solutions for almost all nodes of a SSA-graph. We have implemented our approach in a production DSP compiler. Our experiments show that our approach achieves significant better results compared to classical tree matching

Induction Variable Analysis with Delayed Abstractions

envelopes. In some cases, it is natural to map uncertain values to an abstract value. We have experimented instantiations of TREC with intervals, in which case we obtain a set of possible evolutions that we call an envelope. Allowing the coe#cients of TREC to contain abstract scalar values is a more natural extension than the use of maximum and minimum functions over MCR as proposed by [van Engelen et al. 2004] because it is then possible to define other kinds of envelopes using classic scalar abstract domains, such as polyhedra, octagons [Mine 2001], or congruences [Granger 1991]

Symbolic Analysis of Imperative Programming Languages

Abstract. We present a generic symbolic analysis framework for imperative programming languages. Our framework is capable of computing all valid variable bindings of a program at given program points. This information is invaluable for domain-specific static program analyses such as memory leak detection, program parallelisation, and the detection of superfluous bound checks, variable aliases and task deadlocks. We employ path expression algebra to model the control flow information of programs. A homomorphism maps path expressions into the symbolic domain. At the center of the symbolic domain is a compact algebraic structure called supercontext. A supercontext contains the complete control and data flow analysis information valid at a given program point. Our approach to compute supercontexts is based purely on algebra and is fully automated. This novel representation of program semantics closes the gap between program analysis and computer algebra systems, which makes supercontexts an ideal intermediate representation for all domainspecific static program analyses. Our approach is more general than existing methods because it can derive solutions for arbitrary (even intra-loop) nodes of reducible and irreducible control flow graphs. We prove the correctness of our symbolic analysis method. Our experimental results show that the problem sizes arising from real-world applications such as the SPEC95 benchmark suite are tractable for our symbolic analysis framework.