Ein Branch&Bound-Ansatz zur Verdrahtung von Field Programmable Gate-Arrays

Zur Verdrahtung der meisten FPGA-Architekturen können die aus dem ASIC-Entwurf stammenden Werkzeuge wie z.B. Kanalverdrahter nicht eingesetzt werden. Eine vollautomatische Verdrahtung mit optimalen Signallaufzeiten kann nur dann erreicht werden, wenn bei gegebener Plazierung die Leitungführung den technologischen Gegebenheiten angepaßt wird. Diese unterscheiden sich deutlich von denen in ASICs. Im Rahmen des von der Deutschen Forschungsgemeinschaft (DFG) geförderten Gemeinschafts-Projekts „FPGA Entwurfssystem“, an dem die Universität Leipzig, die Universität Tübingen und die Technischen Universität München beteiligt sind, wurden am Lehrstuhl für Computersysteme (Prof. W.G. Spruth) des Instituts für Informatik der Universität Leipzig Verfahren zur effizienten und qualitativ hochwertigen Verdrahtung von FPGA-Bausteinen entwickelt. Es wird eine Beschreibung des Verdrahtungsproblems für FPGAs gegeben und ein Lösungsansatz mit Hilfe des Branch&Bound – Verfahrens vorgestellt. Die Ergebnisse in Form von Programmlaufzeiten, Länge des kritischen Pfades und Anzahl der betrachteten Suchknoten in Abhängigkeit von einer Vielzahl von Schaltungsvarianten sind tabellarisch dargestellt und dokumentieren eine deutliche Verkürzung der längsten Pfade gegenüber dem Plazier- und Verdrahtungswerkzeug von Xilinx. Abschließend werden Probleme und weiterführende Arbeiten diskutiert

A Router for Symmetrical FPGAs based on Exact Routing Density Evaluation

Abstract This paper presents a new performance and routability driven routing algorithm for symmetrical array based field-programmable gate arrays (FPGAs). A key contribution of our work is to overcome one essential limitation of the previous routing algorithms: inaccurate estimations of routing density which were too general for symmetrical FPGAs. To this end, we derive an exact routing density calculation that is based on a precise analysis of the structure (switch block) of symmetrical FPGAs, and utilize it consistently in global and detailed routings. With an introduction of the proposed accurate routing metrics, we design a new routing algorithm called a cost-effective net-decomposition based routing which is fast, and yet produces remarkable routing results in terms of both routability and path/net delays. We performed an extensive experiment to show the effectiveness of our algorithm based on the proposed cost metrics

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

Routing, Driven Placement for ATMEL 6000 Architecture FPGAs

Based on the concept of Cell Binary Tree (CBT), a new technique for mapping combination circuits into ATMEL 6000 Architecture FPGAs is presented in this thesis. Cell Binary Tree (CBT) is a net-list representation of combinational circuits. For each node of CBT there is a distinguished variable associated with it, the node itself represents a certain logic function, which is selected according to target FPGA architecture. The proposed CBT placement algorithms preserve local connectivity and allow better mapping into ATMEL FPGA. Experiments reveal that the new mapping technique achieved reduction in a number buses used for routing comparing with previously proposed Modified Squashed Binary Tree (MSBT) approach and possibly reduction of area as well. In general, the new technique is realized through following four major steps: 1. Grouping and generating CBT: This is a step to read blifformat file, which is the result of logic synthesis, into a CBT data structure through grouping algorithm, which is a process of gathering logic functions into nodes for mapping based on a targeted FPGA architecture. The main objective of creating CBT is to generate a minimum number of nodes (or cells) to be mapped. 2. CBT placement: Upon getting the minimum number of nodes in CBT to be mapped, the next step is to map those nodes into cells in FPGA. The significance of the placement method in this thesis is to lineup the cells with the same variable into the same row in the FPGA. 3. Bus Assignment: The process of assigning variables to local buses, which run in two possible directions; horizontal and vertical. ATMEL 6000 has two horizontal buses and two vertical buses for each cell. The assignment is based on the number of times a variable appears in a row or column. 4. Routing: The last stage of the process is the connecting cells which have the same input variable. One of the important steps in the routing process is to choose connection bridge cells with the minimum impact on the area

A survey of DA techniques for PLD and FPGA based systems

Programmable logic devices (PLDs) are gaining in acceptance, of late, for designing systems of all complexities ranging from glue logic to special purpose parallel machines. Higher densities and integration levels are made possible by the new breed of complex PLDs and FPGAs. The added complexities of these devices make automatic computer aided tools indispensable for achieving good performance and a high usable gate-count. In this article, we attempt to present in an unified manner, the different tools and their underlying algorithms using an example of a vending machine controller as an illustrative example. Topics covered include logic synthesis for PLDs and FPGAs along with an in-depth survey of important technology mapping, partitioning and place and route algorithms for different FPGA architectures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31206/1/0000108.pd

Logic perturbation based circuit partitioning and optimum FPGA switch-box designs.

Cheung Chak Chung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 101-114).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiVita --- p.vTable of Contents --- p.viList of Figures --- p.xList of Tables --- p.xivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Aims and Contribution --- p.4Chapter 1.3 --- Thesis Overview --- p.5Chapter 2 --- VLSI Design Cycle --- p.6Chapter 2.1 --- Logic Synthesis --- p.7Chapter 2.1.1 --- Logic Minimization --- p.8Chapter 2.1.2 --- Technology Mapping --- p.8Chapter 2.1.3 --- Testability --- p.8Chapter 2.2 --- Physical Design Synthesis --- p.8Chapter 2.2.1 --- Partitioning --- p.9Chapter 2.2.2 --- Floorplanning & Placement --- p.10Chapter 2.2.3 --- Routing --- p.11Chapter 2.2.4 --- "Compaction, Extraction & Verification" --- p.12Chapter 2.2.5 --- Physical Design of FPGAs --- p.12Chapter 3 --- Alternative Wiring --- p.13Chapter 3.1 --- Introduction --- p.13Chapter 3.2 --- Notation and Definitions --- p.15Chapter 3.3 --- Application of Rewiring --- p.17Chapter 3.3.1 --- Logic Optimization --- p.17Chapter 3.3.2 --- Timing Optimization --- p.17Chapter 3.3.3 --- Circuit Partitioning and Routing --- p.18Chapter 3.4 --- Logic Optimization Analysis --- p.19Chapter 3.4.1 --- Global Flow Optimization --- p.19Chapter 3.4.2 --- OBDD Representation --- p.20Chapter 3.4.3 --- Automatic Test Pattern Generation (ATPG) --- p.22Chapter 3.4.4 --- Graph Based Alternative Wiring (GBAW) --- p.23Chapter 3.5 --- Augmented GBAW --- p.26Chapter 3.6 --- Logic Optimization by using GBAW --- p.28Chapter 3.7 --- Conclusions --- p.31Chapter 4 --- Multi-way Partitioning using Rewiring Techniques --- p.33Chapter 4.1 --- Introduction --- p.33Chapter 4.2 --- Circuit Partitioning Algorithm Analysis --- p.38Chapter 4.2.1 --- The Kernighan-Lin (KL) Algorithm --- p.39Chapter 4.2.2 --- The Fiduccia-Mattheyses (FM) Algorithm --- p.42Chapter 4.2.3 --- Geometric Representation Algorithm --- p.46Chapter 4.2.4 --- The Multi-level Partitioning Algorithm --- p.49Chapter 4.2.5 --- Hypergraph METIS - hMETIS --- p.51Chapter 4.3 --- The GBAW Partitioning Algorithm --- p.53Chapter 4.4 --- Experimental Results --- p.56Chapter 4.5 --- Conclusions --- p.58Chapter 5 --- Optimum FPGA Switch-Box Designs - HUSB --- p.62Chapter 5.1 --- Introduction --- p.62Chapter 5.2 --- Background and Definitions --- p.65Chapter 5.2.1 --- Routing Architectures --- p.65Chapter 5.2.2 --- Global Routing --- p.67Chapter 5.2.3 --- Detailed Routing --- p.67Chapter 5.3 --- FPGA Router Comparison --- p.69Chapter 5.3.1 --- CGE --- p.69Chapter 5.3.2 --- SEGA --- p.70Chapter 5.3.3 --- TRACER --- p.71Chapter 5.3.4 --- VPR --- p.72Chapter 5.4 --- Switch Box Design --- p.73Chapter 5.4.1 --- Disjoint type switch box (XC4000-type) --- p.73Chapter 5.4.2 --- Anti-symmetric switch box --- p.74Chapter 5.4.3 --- Universal Switch box --- p.74Chapter 5.4.4 --- Switch box Analysis --- p.75Chapter 5.5 --- Terminology --- p.77Chapter 5.6 --- "Hyper-universal (4, W)-design analysis" --- p.82Chapter 5.6.1 --- "H3 is an optimum (4, 3)-design" --- p.84Chapter 5.6.2 --- "H4 is an optimum (4,4)-design" --- p.88Chapter 5.6.3 --- "Hi is a hyper-universal (4, i)-design for i = 5,6,7" --- p.90Chapter 5.7 --- Experimental Results --- p.92Chapter 5.8 --- Conclusions --- p.95Chapter 6 --- Conclusions --- p.99Chapter 6.1 --- Thesis Summary --- p.99Chapter 6.2 --- Future work --- p.100Chapter 6.2.1 --- Alternative Wiring --- p.100Chapter 6.2.2 --- Partitioning Quality --- p.100Chapter 6.2.3 --- Routing Devices Studies --- p.100Bibliography --- p.101Chapter A --- 5xpl - Berkeley Logic Interchange Format (BLIF) --- p.115Chapter B --- Proof of some 2-local patterns --- p.122Chapter C --- Illustrations of FM algorithm --- p.124Chapter D --- HUSB Structures --- p.127Chapter E --- Primitive minimal 4-way global routing Structures --- p.13