Probabilistic data flow analysis: a linear equational approach

TL;DR

This paper introduces a probabilistic extension to classical data-flow analysis using linear equations, enabling more accurate estimation of branch probabilities for speculative optimizations.

Contribution

It presents a novel linear equational approach to probabilistic data flow analysis that incorporates branch prediction probabilities for improved program analysis.

Findings

Linear equations can accurately model probabilistic control flow.

Method computes correct numerical solutions for probabilistic data flow.

Enhances speculative optimization techniques with probabilistic analysis.

Abstract

Speculative optimisation relies on the estimation of the probabilities that certain properties of the control flow are fulfilled. Concrete or estimated branch probabilities can be used for searching and constructing advantageous speculative and bookkeeping transformations. We present a probabilistic extension of the classical equational approach to data-flow analysis that can be used to this purpose. More precisely, we show how the probabilistic information introduced in a control flow graph by branch prediction can be used to extract a system of linear equations from a program and present a method for calculating correct (numerical) solutions.