LIP6 2001/026
- Thesis
Optimisations des chemins de données arithmétiques par l'utilisation de plusieurs systèmes de numération - Y. Dumonteix
- 228 pages - 10/10/2001- document en - http://www.lip6.fr/lip6/reports/2001/lip6.2001.026.pdf - 1,771 Ko
- Contact : Yannick.Dumonteix (at) nulllip6.fr
- Ancien Thème : ASIM
- Keywords : Computer arithmetic, classical number systems, redundant number systems, arithmetic operators and algorithms, arithmetic optimization, arithmetic datapath synthesis
- Publisher : Francois.Dromard (at) nulllip6.fr
This thesis presents the integration of redundant number representations in arithmetic circuit design flow. The work is divided in three parts. The first part is dedicated to the introduction of the redundant number systems in addition to the classical number systems. For that purpose we have defined a new arithmetic, named __it mixed arithmetic_, which takes into account the problems of the simultaneous use of classic and redundant notations. We have also developed a set of new operators which ensure all the possible input / output combinations in redundant and classical notations. The three elementary operations : addition (two operands), sum (more than two operands) and multiplication, have been studied. For each one we have created a generator. The generation parameter list is composed of the size, the sign and the notation of all inputs/outputs, and of the computation algorithm to use. The aim of the second part is to study the impact of the mixed arithmetic in data path design. The analysis concerns the choice of the notations used between the different operators of an architecture. Combinatorial and sequential chains have been studied. The analysis also applies to the use of the addition tree properties (sum properties). This part allowed us to identify several generic rules of arithmetic optimizations in arithmetic circuit design. The third part is dedicated to the introduction of the mixed arithmetic in the architecture synthesis. We are essentially interested in the behavioral-to-structural conversion. The goal is to propose a mapping phase taking into account the arithmetic operators and our knowledge in their usage. Therefore, the mapping is not directly based on standard cells but on a generator set. These generators build the operator architectures ( standard cells based netlist ) depending on the context. For this last part, first we present a arithmetic data path synthesis methodology using basic function generators then we p!
ropose the specification of a data path synthesis aid tool. The defined tool input is a simplified data path description.
ropose the specification of a data path synthesis aid tool. The defined tool input is a simplified data path description.