GLORE: generalized loop redundancy elimination upon LER-notation

Abstract

This paper presents GLORE, a novel approach to enabling the detection and removal of large-scope redundant computations in nested loops. GLORE works on LER-notation, a new representation of computations in both regular and irregular loops. Together with a set of novel algorithms, it makes GLORE able to systematically consider computation reordering at both the expression level and the loop level in a unified manner. GLORE shows an applicability much broader than prior methods have, and frequently lowers the computational complexities of some nested loops that are elusive to prior optimization techniques, producing significantly larger speedups. CCS Concepts: • Software and its engineering → General programming languages;

Coarsening optimization for differentiable programming

“…Gated SSA (GSA) proposes to explicitly specify the conditions in the 𝜙 functions, and introduces notations to distinguish loop entry, loop exit, and normal 𝜙functions [Ottenstein et al 1990], which share some similarities with part of the 𝜙-notations in this work. The loop notations in 𝜙-calculus is inspired by the notations in Glore [Ding and Shen 2017], a work that detects large-scoped loop invariants. In 1990s and early 2000s, there were a number of papers on recognizing and substituting inductive variables in loops based on SSA through symbolic analysis [Tu and Padua 1995].…”

Coarsening Optimization for Differentiable Programming

“…Gated SSA (GSA) proposes to explicitly specify the conditions in the φ functions, and introduces notations to distinguish loop entry, loop exit, and normal φ-functions [24], which share some similarities with part of the φ-notations in this work. The loop notations in φ-calculus is inspired by the notations in Glore [16], a work that detects large-scoped loop invariants. In 1990s and early 2000s, there were a number of papers on recognizing and substituting inductive variables in loops based on SSA through symbolic analysis [31].…”

Tensor Algebra Compilation with Workspaces

“…Loop invariant code motion has a long history in compilers, going back to the first FORTRAN compiler in 1957 [Backus 1978]. Recently, researchers have found new opportunities for removing redundancy in loops by taking advantage of high-level algebraic knowledge [Ding and Shen 2017]. Our workspace optimization applies to sparse tensor algebra and can remove loop reduncancies from sparse code with indirect-access loop bounds and many conditional branches.…”