Anne Mignotte

Retiming DAGs [direct acyclic graph]

This paper is devoted to a low-complexity algorithm for retiming circuits without cycles, i.e., those whose network graph is a direct acyclic graph (DAG). On one hand, DAGs have a great practical importance, as shown by the on-line arithmetic circuits used as a target application in this paper. On the other hand, retiming is a costly design optimization technique, in particular when applied to large circuits. Hence the need to design a specialized retiming algorithm to handle DAGs more efficiently than general-purpose retiming algorithms. Our algorithm dramatically improves on current solutions in the literature. We gain an order of magnitude in the worst case complexity, and we show convincing experimental results at the end of this paper.

Reducing the complexity of ILP formulations for synthesis

Integer linear programming (ILP) is commonly used in high level and system level synthesis. It is an NP complete problem (in general cases). There exist some tools that give an optimal solution for small ILP formulations. Nevertheless, these tools may not give solutions for complex formulations. We present a solution to overcome the problem of complexity in ILP formulations. We propose a partitioning methodology based on a constraint graph representing all the constraints included in any ILP formulation. To direct the partitioning, the constraint graph nodes are grouped to represent data flow graph (DFG) nodes. This reduced constraint graph can be used to partition any ILP formulation based on DFG. We illustrate this method on ILP formulation for scheduling. Results on ILP scheduling formulations are promising.

Scheduling using mixed arithmetic: an ILP formulation

Summary form only given. We present a way to automatically select, within an architectural synthesis tool, the best operand and operator number systems, in order to find the best speed/area tradeoff. This implies the use of different number systems (redundant and non-redundant) for the same design: this is what we call mixed arithmetics. We present an integer linear programming (ILP) formulation to solve a scheduling problem.

The Influence on Synthesis of Modern Computer Arithmetic

Taking into account the various possibilities offered by computer arithmetic during high-level synthesis may help to design much powerfull architectures. The arithmetic operators (mainly in floating point arithmetic) may be carefully tuned up to exactly fit the time and accuracy requirements. This, of course, may have an influence on the synthesis process. In this paper, we mainly address two topics: first of all the problem of numerical error control; and then the possible use of redundant number systems — which allow some nice features such as carry free addition or digit-serial, most significant digit first arithmetic operations. We then propose some potential applications and we discuss the new synthesis problems they involve.