K-calling context profiling

Calling context trees are one of the most fundamental data structures for representing the interprocedural control flow of a program, providing valuable information for program understanding and optimization. Nodes of a calling context tree associate performance metrics to whole distinct paths in the call graph starting from the root function. However, no explicit information is provided for detecting short hot sequences of activations, which may be a better optimization target in large modular programs where groups of related functions are reused in many different parts of the code. Furthermore, calling context trees can grow prohibitively large in some scenarios. Another classical approach, called edge profiling, collects performance metrics for caller-callee pairs in the call graph, allowing it to detect hot paths of fixed length one. We study a generalization of edge and context-sensitive profiles by introducing a novel data structure called k-calling context forest (k-CCF). Nodes in a k-CCF associate performance metrics to paths of length at most k that lead to each distinct routine of the program, providing edge profiles for k=1, full context-sensitive profiles for k equal to infinity, as well as any other intermediate point in the spectrum. We study the properties of the k-CCF both theoretically and experimentally on a large suite of prominent Linux applications, showing how to construct it efficiently and discussing its relationships with the calling context tree. Our experiments show that the k-CCF can provide effective space-accuracy tradeoffs for interprocedural contextual profiling, yielding useful clues to the hot spots of a program that may be hidden in a calling context tree and using less space for small values of k, which appear to be the most interesting in practice.