Data-Flow Transformations using Taylor Expansion Diagrams

Abstract

An original technique to transform functional representation of the design into a structural representation in form of a data flow graph (DFG) is described. A canonical, word-level data structure, Taylor Expansion Diagram (TED), is used as a vehicle to effect this transformation. The problem is formulated as that of applying a sequence of decomposition cuts to a TED that transforms it into a DFG optimized for a particular objective. A systematic approach to arrive at such a decomposition is described. Experimental results show that such constructed DFG provides a better starting point for architectural synthesis than those extracted directly from HDL specifications.

Optimizing data flow graphs to minimize hardware implementation

“…The goal of TED decomposition described in this work is to find a factored form that will produce DFG with minimum hardware cost of the final, scheduled implementation. This is different than a straightforward minimization of the number of operations in the unsched-uled DFG, which has been the subject of the known previous work [3,4,12]. The TED decomposition method described here extends the work of the original cut-based decomposition of Askar [4], which was based on the identification and selection of admissible cut sequences.…”

“…This is different than a straightforward minimization of the number of operations in the unsched-uled DFG, which has been the subject of the known previous work [3,4,12]. The TED decomposition method described here extends the work of the original cut-based decomposition of Askar [4], which was based on the identification and selection of admissible cut sequences. The cut-based method was applicable only to TED graphs characterized by the presence of simple cuts: additive and multiplicative edges whose removal would separate the graph into two disjoint subgraphs, and hence was limited only to the disjoint decomposition.…”

“…It has been shown that the TED structure allows for efficient factorization and decomposition of expressions modeled as linear multi-variate polynomials [3,4]. For example, a TED for expression F = ab + ac, for variable ordering (a, b, c) naturally represents the polynomial in its factored form, a(b + c).…”

“…TEDs have already been applied to functional optimization, such as factorization and common subexpression elimination (CSE). However, so far their scope was limited to linear expressions, such as linear DSP transforms and to the simplification of arithmetic expressions, without considering final scheduled implementation [3,4]. This paper describes how TEDs can be extended to handle the optimization of nonlinear polynomial expressions, using novel factorization and decomposition algorithms, to generate optimized data flow graphs (DFG), better suited for high-level synthesis.…”

Intelligent high level synthesis for customization on reconfigurable platforms

“…Pattern finding in CDFG has also been studied to identify oft repeated patterns and synthesize them as individual hardware blocks. In [84] where the authors propose an algorithm to find recurring patterns in an application through subgraph enumeration, pruning and matching techniques in compute intensive applications. These patterns are then mapped to FPGAs.…”