Sequential decomposition of operations and compilers optimization

Code optimization is an important area of research that has remarkable contributions in addressing the challenges of information technology. It has introduced a new trend in hardware as well as in software. Efforts that have been made in this context led to introduce a new foundation, both for compilers and processors. In this report we study different techniques used for sequential decomposition of mappings without using extra variables. We focus on finding and improving these techniques of computations. Especially, we are interested in developing methods and efficient heuristic algorithms to find the decompositions and implementing these methods in particular cases. We want to implement these methods in a compiler with an aim of optimizing code in machine language. It is always possible to calculate an operation related to K registers by a sequence of assignments using only these K registers. We verified the results and introduced new methods. We described In Situ computation of linear mapping by a sequence of linear assignments over the set of integers and investigated bound for the algorithm. We introduced a method for the case of boolean bijective mappings via algebraic operations over polynomials in GF(2). We implemented these methods using Mapl

In Situ Design of Register Operations

International audienceWe present methods to design programs or electronic circuits, for performing any operation on K registers of any sizes in a processor, in such a way that one uses no other working memory (such as other registers or external memories). In this way, any operation is performed with at most 4K-3 assignments of these registers, or 2K-1 when the operation is linear or bijective