  Numerous code optimization techniques, including loop nest optimizations,
have been developed over the last four decades. Loop optimization techniques
transform loop nests to improve the performance of the code on a target
architecture, including exposing parallelism. Finding and evaluating an
optimal, semantic-preserving sequence of transformations is a complex problem.
The sequence is guided using heuristics and/or analytical models and there is
no way of knowing how close it gets to optimal performance or if there is any
headroom for improvement. This paper makes two contributions. First, it uses a
comparative analysis of loop optimizations/transformations across multiple
compilers to determine how much headroom may exist for each compiler. And
second, it presents an approach to characterize the loop nests based on their
hardware performance counter values and a Machine Learning approach that
predicts which compiler will generate the fastest code for a loop nest. The
prediction is made for both auto-vectorized, serial compilation and for
auto-parallelization. The results show that the headroom for state-of-the-art
compilers ranges from 1.10x to 1.42x for the serial code and from 1.30x to
1.71x for the auto-parallelized code. These results are based on the Machine
Learning predictions.
