HyFM: function merging for free

Abstract

Function merging is an important optimization for reducing code size. The existing state-of-the-art relies on a wellknown sequence alignment algorithm to identify duplicate code across whole functions. However, this algorithm is quadratic in time and space on the number of instructions. This leads to very high time overheads and prohibitive levels of memory usage even for medium-sized benchmarks. For larger programs, it becomes impractical. This is made worse by an overly eager merging approach. All selected pairs of functions will be merged. Only then will this approach estimate the potential benefit from merging and decide whether to replace the original functions with the merged one. Given that most pairs are unprofitable, a significant amount of time is wasted producing merged functions that are simply thrown away.In this paper, we propose HyFM, a novel function merging technique that delivers similar levels of code size reduction for significantly lower time overhead and memory usage. Our alignment strategy works at the block level. Since basic blocks are usually much shorter than functions, even a quadratic alignment is acceptable. However, we also propose a linear algorithm for aligning blocks at a much lower cost. We extend this strategy with a multi-tier profitability analysis that bails out early from unprofitable merging attempts. By aligning individual pairs of blocks, we are able to decide their alignment's profitability before actually generating code.Experimental results on SPEC 2006 and 2017 show that HyFM needs orders of magnitude less memory, using up to 48 MB or 5.6 MB, depending on the variant used, while

F3M: Fast Focused Function Merging

“…In the last few years, there has been a flurry of function merging techniques that rely on Sequence Alignment [6]- [8]. They have significant differences but they all work following these key stages: a) select pairs of similar functions for merging, b) merge each pair of functions by using sequence alignment to identify equivalent code that can be reused by both functions, and c) if deemed profitable, replace the two original functions with the merged function that combines the functionality of both.…”

“…The execution of mismatched subsequences in the merged function is guarded by an original function identifier but matching subsequences are not guarded and are executed regardless of the function identifier. Figure 1 illustrates the function merging workflow in HyFM [8], which is the stateof-the-art used throughout this paper. Its code alignment strategy works on the basic block level, with a linear alignment algorithm applied on pairs of similar blocks.…”

“…At its most straightforward [3], [4], the idea is to identify identical functions, redirect all their calls to only one of them, and remove all the redundant copies of these identical functions. More sophisticated implementations are able to merge non-identical functions as long as they are similar in some way, for example having isomorphic control flow graphs [5] or overlapping instruction subsequences [6]- [8]. The latter approach, known as function merging by sequence alignment, is very flexible as it can merge even functions with little structural or algorithmic similarities.…”

“…For sequence alignment on the other hand, there is no accurate way to find functions that align well, apart from attempting to align every function with every other function. The state-of-the-art technique uses a heuristic to find somewhat acceptable function pairs [6], [8]. It computes a fingerprint for each function, a fixed size vector of instruction opcode frequencies in the function.…”

“…While comparing all fingerprints against all other fingerprints is faster than actually aligning all possible function pairs, this is still an expensive quadratic process. When we used the publicly available code on a range of applications, it worked sufficiently well for the small and medium sized programs of traditional benchmark suites but on Google Chrome matching fingerprints took almost two days, a very high overhead for an approach claiming to deliver function merging for free [8]. Unless we overcome this limitation, sequence alignment based function merging is unlikely to leave the confines of academic research.…”