  Several techniques for analysis and transformations are used in compilers.
Among them, the peeling of loops for hoisting quasi-invariants can be used to
optimize generated code, or simply ease developers' lives. In this paper, we
introduce a new concept of dependency analysis borrowed from the field of
Implicit Computational Complexity (ICC), allowing to work with composed
statements called Chunks to detect more quasi-invariants. Based on an
optimization idea given on a WHILE language, we provide a transformation method
- reusing ICC concepts and techniques - to compilers. This new analysis
computes an invariance degree for each statement or chunks of statements by
building a new kind of dependency graph, finds the maximum or worst dependency
graph for loops, and recognizes if an entire block is Quasi-Invariant or not.
This block could be an inner loop, and in that case the computational
complexity of the overall program can be decreased. We already implemented a
proof of concept on a toy C parser 1 analysing and transforming the AST
representation. In this paper, we introduce the theory around this concept and
present a prototype analysis pass implemented on LLVM. In a very near future,
we will implement the corresponding transformation and provide benchmarks
comparisons.
