OPTIMAL AREA AND PERFORMANCE MAPPING OF K-LUT BASED FPGAS

FPGA circuits are increasingly used in many fields: for rapid prototyping of new products (including fast ASIC implementation), for logic emulation, for producing a small number of a device, or if a device should be reconfigurable in use (reconfigurable computing). Determining if an arbitrary, given wide, function can be implemented by a programmable logic block, unfortunately, it is generally, a very difficult problem. This problem is called the Boolean matching problem. This paper introduces a new implemented algorithm able to map, both for area and performance, combinational networks using k-LUT based FPGAs.k-LUT based FPGAs, combinational circuits, performance-driven mapping.

Support-reducing decomposition for FPGA mapping

Decomposition is a technology-independent process, in which a large complex function is broken into smaller, less complex functions. The costs of two-level or factored-form representations (cubes and literals) are used in most decomposition methods, as they have a high correlation with the area of cell-based designs. However, this correlation is weaker for field-programmable gate arrays (FPGAs) based on look-up tables. Furthermore, local optimizations have limited power due to the structural bias of the circuit descriptions. This paper tries to reduce the structural biasing by remapping the LUT network and decomposing the derived functions using the support as cost function. The proposed method improves the FPGA mapping results of a commercial tool for the 20 largest MCNC benchmarks, with gains of 28% in delay plus 18% in area when targeting delay, and a reduction of 28% in area plus 14% in delay with area as cost function. Results with 23% less area and 6% less delay are obtained after physical synthesis (post place-and-route). Moreover, 12 of the best known results for delay (and 3 for area) of the EPFL benchmarks are improved.Peer ReviewedPostprint (author's final draft

A General Approach to Boolean Function Decomposition and its Application in FPGABased Synthesis

An effective logic synthesis procedure based on parallel and serial decomposition of a Boolean function is presented in this paper. The decomposition, carried out as the very first step of the .synthesis process, is based on an original representation of the function by a set of r-partitions over the set of minterms. Two different decomposition strategies, namely serial and parallel, are exploited by striking a balance between the two ideas. The presented procedure can be applied to completely or incompletely specified, single- or multiple-output functions and is suitable for different types of FPGAs including XILINX, ACTEL and ALGOTRONIX devices. The results of the benchmark experiments presented in the paper show that, in several cases, our method produces circuits of significantly reduced complexity compared to the solutions reported in the literature

Significance of Logic Synthesis in FPGA-Based Design of Image and Signal Processing Systems

This chapter, taking FIR filters as an example, presents the discussion on efficiency of different implementation methodologies of DSP algorithms targeting modern FPGA architectures. Nowadays, programmable technology provides the possibility to implement digital systems with the use of specialized embedded DSP blocks. However, this technology gives the designer the possibility to increase efficiency of designed systems by exploitation of parallelisms of implemented algorithms. Moreover, it is possible to apply special techniques, such as distributed arithmetic (DA). Since in this approach, general-purpose multipliers are replaced by combinational LUT blocks, it is possible to construct digital filters of very high performance. Additionally, application of the functional decomposition-based method to LUT blocks optimization, and mapping has been investigated. The chapter presents results of the comparison of various design approaches in these areas

Decomposition tool targeting FPGA architectures

The growing interest in the field of logic synthesis targeting Field Programmable Gate Arrays (FPGA) and the active research carried out by a number of research groups in the area of functional decomposition is the prime motivation for this thesis. Logic synthesis has been an area of interest in many universities all over the world. The work involves the study and implementation of techniques and methods in logic synthesis. In this work, a logic synthesis tool has been developed implementing the aspects of general and complete Decomposition method based on functional decomposition techniques [4]. The tool is aimed at producing outputs faster and more efficient than the available software. C++ Standard template library is used to develop this tool. The output of this tool is designed to be compatible with the available vendor software. The tool has been tested on MCNC benchmarks and those created keeping in mind the industry requirements

Division-based versus general decomposition-based multiple-level logic synthesis

During the last decade, many different approaches have been proposed to solve the multiple-level synthesis problem with different minimum functionally complete systems of primitive logic blocks. The most popular of them is the division-based approach. However, modem microelectronic technology provides a large variety of building blocks which considerably differ from those typically considered. The traditional methods are therefore not suitable for synthesis with many modem building blocks. Furthermore, they often fail to find global optima for complex designs and leave unconsidered some important design aspects. Some of their weaknesses can be eliminated without leaving the paradigm they are based on, other ones are more fundamental. A paradigm which enables efficient exploitation of the opportunities created by the microelectronic technology is the general decomposition paradigm. The aim of this paper is to analyze and compare the general decomposition approach and the division-based approach. The most important advantages of the general decomposition approach are its generality (any network of any building blocks can be considered) and totality (all important design aspects can be considered) as well as handling the incompletely specified functions in a natural way. In many cases, the general decomposition approach gives much better results than the traditional approaches

Post-mapping Topology Rewriting for FPGA Area Minimization

Circuit designers require Computer-Aided Design (CAD) tools when compiling designs into Field Programmable Gate Arrays (FPGAs) in order to achieve high quality results due to the complexity of the compilation tasks involved. Technology mapping is one critical step in the FPGA CAD flow. The final mapping result has significant impact on the subsequent steps of clustering, placement and routing, for the objectives of delay, area and power dissipation. While depth-optimal FPGA technology mapping can be solved in polynomial time, area minimization has proven to be NP-hard. Most modern state-of-the-art FPGA technology mappers are structural in nature; they are based on cut enumeration and use various heuristics to yield depth and area minimized solutions. However, the results produced by structural technology mappers rely strongly on the structure of the input netlists. Hence, it is common to apply additional heuristics after technology mapping to further optimize area and reduce the amount of structural bias while not harming depth. Recently, SAT-based Boolean matching has been used for post-mapping area minimization. However, SAT-based matching is computationally complex and too time consuming in practice. This thesis proposes an alternative Boolean matching approach based on NPN equivalence. Using a library of pre-computed topologies, the matching problem becomes as simple as performing NPN encoding followed by a hash lookup which is very efficient. In conjunction with Ashenhurst decomposition, the NPN-based Boolean matching is allowed to handle up to 10-input Boolean functions. When applied to a large set of designs, the proposed algorithm yields, on average, more than 3% reduction in circuit area without harming circuit depth. The priori generation of a library of topologies can be difficult; the potential difficulty in generating a library of topologies represents one limitation of the proposed algorithm

Boolean decomposition for AIG optimization

Restructuring techniques for And-Inverter Graphs (AIG), such as rewriting and refactoring, are powerful, scalable and fast, achieving highly optimized AIGs after few iterations. However, these techniques are biased by the original AIG structure and limited by single output optimizations. This paper investigates AIG optimization for area, exploring how far Boolean methods can reduce AIG nodes through local optimization.Boolean division is applied for multi-output functions using two-literal divisors and Boolean decomposition is introduced as a method for AIG optimization. Multi-output blocks are extracted from the AIG and optimized, achieving a further AIG node reduction of 7.76% on average for ITC99 and MCNC benchmarks.Peer ReviewedPostprint (author's final draft

Decomposition and encoding of finite state machines for FPGA implementation

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