TreeFuser: a framework for analyzing and fusing general recursive tree traversals

Abstract

Series of traversals of tree structures arise in numerous contexts: abstract syntax tree traversals in compiler passes, rendering traversals of the DOM in web browsers, kd-tree traversals in computational simulation codes. In each of these settings, a tree is traversed multiple times to compute various values and modify various portions of the tree. While it is relatively easy to write these traversals as separate small updates to the tree, for efficiency reasons, traversals are often manually fused to reduce the number of times that each portion of the tree is traversed: by performing multiple operations on the tree simultaneously, each node of the tree can be visited fewer times, increasing opportunities for optimization and decreasing cache pressure and other overheads. This fusion process is often done manually, requiring careful understanding of how each of the traversals of on tree interact. This paper presents an automatic approach to traversal fusion: tree traversals can be written independently, and then our framework analyzes the dependences between the traversals to determine how they can be fused to reduce the number of visits to each node in the tree. A critical aspect of our framework is that it exploits two opportunities to increase the amount of fusion: i) it automatically integrates code motion, and ii) it supports partial fusion, where portions of one traversal can be fused with another, allowing for a reduction in node visits without requiring that two traversals be fully fused. We implement our framework as Clang tool, and show across several case studies that we can successfully fuse complex tree traversals, reducing the overall number of traversals and substantially improving locality and performance. CCS Concepts: • Software and its engineering → Automated static analysis; Compilers;

Sound, fine-grained traversal fusion for heterogeneous trees

“…Overall runtime. Fusion improves locality, but potentially at the cost of increased instruction overhead (as reported by Sakka et al [25]). The final effectiveness of fusion is hence determined by runtime.…”

“…The primary representation that Grafter uses to drive its fusion process is the dependence graph [25]. As described in Section 2, this graph has one vertex for each top level statement 4 and edges between statements if there are dependences between them.…”

“…Grafter computes the set of access paths for each top level simple statement in each traversal function. We do not elaborate further on this process, as this analysis is standard (and is similar to TreeFuser [25]).…”

“…In an attempt to balance these competing concerns, there has been prior work on compiler and software-engineering techniques for writing simple, fine-grained tree traversal passes that are then automatically fused into coarse-grained passes for performance reasons [19][20][21][23][24][25]. In the world of functional programs, deforestation techniques rewrite data structure operations to avoid materializing intermediate data structures, either through syntactic rewrites [5,29] or through the use of special combinators that promote fusion [7].…”

“…Previous approaches rely on programmers using specialpurpose languages or programming styles to express tree traversals, limiting generality, TreeFuser, by Sakka et al, offers an alternative [25]. Programmers write generic tree traversals in an imperative language-a subset of C-with no restrictions on how trees are traversed (unlike Rajbhandari et al who limit computations to binary trees traversed in pre-or post-order [23,24], or Petrashko et al who require very specific traversal structures in miniphases [21]).…”