Mechanizing conventional SSA for a verified destruction with coalescing

Abstract

Modern optimizing compilers rely on the Static Single Assignment (SSA) form to make optimizations fast and simpler to implement. From a semantic perspective, the SSA form is nowadays fairly well understood, as witnessed by recent advances in the field of formally verified compilers. The destruction of the SSA form, however, remains a difficult problem, even in a non-verified environment. In fact, the out-of-SSA transformation has been revisited, for correctness and performance issues, up until recently. Unsurprisingly, state-of-the-art compiler formalizations thus either completely ignore, only partially handle, or implement naively the SSA destruction. This paper reports on the implementation of such a destruction within a verified compiler. We formally define and prove the properties of the generation of Conventional SSA (CSSA) which make its destruction simple to implement and prove. Second, we implement and prove correct a coalescing destruction of CSSA,à la Boissinot et al., where variables can be coalesced according to a refined notion of interference. This formalization work extends the CompCertSSA compiler, whose correctness proof is mechanized in the Coq proof assistant. Our CSSA-based, coalescing destruction removes, on average, more than 99% of introduced copies, and leads to encouraging results concerning spilling during post-SSA register allocation.

Semantic reasoning about the sea of nodes

“…In the third phase, it would remain to implement ϕ-nodes, i.e., destructing the SSA form. Here, we could possibly make use of some previous work done within the CompCertSSA project [10]. We are confident the work presented here is a solid base to attack these future works, and paves the way to an intregration of Sea of Nodes in formally verified compilers.…”

A Fast Verified Liveness Analysis in SSA Form

“…Indeed, Boissinot et al detail in yet another work [6] an SSA destruction pass that uses liveness checking. We could take advantage of [9] that already formalized most of [6] in CompCertSSA, but used a traditional data-flow-based liveness analysis. However, [6] describes an approach with a linear number of queries, while, for the sake of simplicity, [9] makes a quadratic number of them.…”

“…We could take advantage of [9] that already formalized most of [6] in CompCertSSA, but used a traditional data-flow-based liveness analysis. However, [6] describes an approach with a linear number of queries, while, for the sake of simplicity, [9] makes a quadratic number of them. As the "liveness checking" approach is interesting only if the number of queries is low, we would need to implement the clever approach of [6] first.…”

“…2 [2,11] 3 [3,11] 4 [5,11] 5 [6,9] 6 [9,9] 7 [7,7] 8 [8,8] 9 [10,11] 10 [11,11] 11 [4,4] (b) Dominance tree computation part that captures information about the CFG structure and an online part that answers the liveness queries based on this information. This architecture has two main advantages compared to the classic one.…”

Static optimization in PHP 7

“…A focus of recent research has been on the formal verification of SSA-based optimizations [15][16][17], as well as SSA construction [18], and destruction [19].…”