Static Single Information Form

Fernando Magno Quintão Pereira, Fabrice Rastello

Abstract: Data-flow analyses usually associate information with control-flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include many such points, then we call it sparse. Sparse analyses have advantages over their dense versions: They tend to run faster and require less storage space. The Static Single Assignment form already lets us implement sparse versions of several static analyses, such as constant propagation. Additionally, it is possible to augment this representation to support sparse versions of many other analyses. Key to these extensions is the so-called Single Information Property. We say that a given superset of the SSA form representation bears this property for some data-flow analysis if the data-flow information associated with a variable remains invariant along the entire live range of that variable. This chapter explains which static analyses admit the single information property, and how the said property can be achieved via extensions of the SSA form. It also shows that these SSA extensions are equivalent to techniques originally conceived to support sparse data-flow analyses, such as the Static Single Information form or Sparse Evaluation Graphs.