Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

Placement-Driven Technology Mapping for LUT-Based FPGAs

In this paper, we study the problem of placement-driven technology mapping for table-lookup based FPGA architectures to optimize circuit performance. Early work on technology mapping for FPGAs such as Chortle-d[14] and Flowmap[3] aim to optimize the depth of the mapped solution without consideration of interconnect delay. Later works such as Flowmap-d[7], Bias-Clus[4] and EdgeMap consider interconnect delays during mapping, but do not take into consideration the effects of their mapping solution on the final placement. Our work focuses on the interaction between the mapping and placement stages. First, the interconnect delay information is estimated from the placement, and used during the labeling process. A placement-based mapping solution which considers both global cell congestion and local cell congestion is then developed. Finally, a legalization step and detailed placement is performed to realize the design. We have implemented our algorithm in a LUT based FPGA technology mapping package named PDM (Placement-Driven Mapping) and tested the implementation on a set of MCNC benchmarks. We use the tool VPR[1][2] for placement and routing of the mapped netlist. Experimental results show the longest path delay on a set of large MCNC benchmarks decreased by 12.3 % on the average

LUT Mapping and Optimization for Majority-Inverter Graphs

A Majority-Inverter Graph (MIG) is a directed acyclic graph in which every vertex represents a three-input majority operation and edges may be complemented to indicate operand inversion. MIGs have algebraic and Boolean properties that enable efficient logic optimization. They have been shown to obtain superior synthesis results as compared to state-of-the- art And-Inverter Graph (AIG) based algorithms. In this paper, we extend MIGs to Functionally Reduced MIGs (FRMIGs), analogous to the extension of AIGs to Functionally Reduced AIGs (FRAIGs). This enables the use of MIGs in a lossless synthesis design flow. We present an FRMIG based technology mapper for lookup tables (LUTs). Any MIG may be mapped to a k- LUT network. Using exact synthesis we may decompose the k- LUT network back into an equivalent MIG. We show how LUT mapping and exact k-LUT decomposition can be used to create an MIG optimization method. Finally, we present the results of applying our new optimization method and LUT mapper to both logic optimization and technology mapping

Beyond the arithmetic constraint: depth-optimal mapping of logic chains in reconfigurable fabrics

Look-up table based FPGAs have migrated from a niche technology for design prototyping to a valuable end-product component and, in some cases, a replacement for general purpose processors and ASICs alike. One way architects have bridged the performance gap between FPGAs and ASICs is through the inclusion of specialized components such as multipliers, RAM modules, and microcontrollers. Another dedicated structure that has become standard in reconfigurable fabrics is the arithmetic carry chain. Currently, it is only used to map arithmetic operations as identified by HDL macros. For non-arithmetic operations, it is an idle but potentially powerful resource.;Obstacles to using the carry chain for generic logic operations include lack of architectural and computer-aided design support. Current carry-select architectures facilitate carry chain reuse, although they do so only for (K-1)-input operations. Additionally, hardware description language (HDL) macros are the only recourse for a designer wishing to map generic logic chains in a carry-select architecture. A novel architecture that allows the full K-input operational capacity of the carry chain to be harnessed is presented as a solution to current architectural limitations. It is shown to have negligible impact on logic element area and delay. Using only two additional 2:1 pass transistor multiplexers, it enables the transmission of a K-input operation to the carry chain and general routing simultaneously. To successfully identify logic chains in an arbitrary Boolean network, ChainMap is presented as a novel technology mapping algorithm. ChainMap creates delay-optimal generic logic chains in polynomial time without HDL macros. It maps both arithmetic and non-arithmetic logic chains whenever depth increasing nodes, which increase logic depth but not routing depth, are encountered. Use of the chain is not reserved for arithmetic, but rather any set of gates exhibiting similar characteristics. By using the carry chain as a generic, near zero-delay adjacent cell interconnection structure a potential average optimal speedup of 1.4x is revealed. Post place and route experiments indicate that ChainMap solutions perform similarly to HDL chains when cluster resources are abundant and significantly better in cluster-constrained arrays

Energy-Efficient Digital Circuit Design using Threshold Logic Gates

abstract: Improving energy efficiency has always been the prime objective of the custom and automated digital circuit design techniques. As a result, a multitude of methods to reduce power without sacrificing performance have been proposed. However, as the field of design automation has matured over the last few decades, there have been no new automated design techniques, that can provide considerable improvements in circuit power, leakage and area. Although emerging nano-devices are expected to replace the existing MOSFET devices, they are far from being as mature as semiconductor devices and their full potential and promises are many years away from being practical. The research described in this dissertation consists of four main parts. First is a new circuit architecture of a differential threshold logic flipflop called PNAND. The PNAND gate is an edge-triggered multi-input sequential cell whose next state function is a threshold function of its inputs. Second a new approach, called hybridization, that replaces flipflops and parts of their logic cones with PNAND cells is described. The resulting \hybrid circuit, which consists of conventional logic cells and PNANDs, is shown to have significantly less power consumption, smaller area, less standby power and less power variation. Third, a new architecture of a field programmable array, called field programmable threshold logic array (FPTLA), in which the standard lookup table (LUT) is replaced by a PNAND is described. The FPTLA is shown to have as much as 50% lower energy-delay product compared to conventional FPGA using well known FPGA modeling tool called VPR. Fourth, a novel clock skewing technique that makes use of the completion detection feature of the differential mode flipflops is described. This clock skewing method improves the area and power of the ASIC circuits by increasing slack on timing paths. An additional advantage of this method is the elimination of hold time violation on given short paths. Several circuit design methodologies such as retiming and asynchronous circuit design can use the proposed threshold logic gate effectively. Therefore, the use of threshold logic flipflops in conventional design methodologies opens new avenues of research towards more energy-efficient circuits.Dissertation/ThesisDoctoral Dissertation Computer Science 201

The effect of an optical network on-chip on the performance of chip multiprocessors

Optical networks on-chip (ONoC) have been proposed to reduce power consumption and increase bandwidth density in high performance chip multiprocessors (CMP), compared to electrical NoCs. However, as buffering in an ONoC is not viable, the end-to-end message path needs to be acquired in advance during which the message is buffered at the network ingress. This waiting latency is therefore a combination of path setup latency and contention and forms a significant part of the total message latency. Many proposed ONoCs, such as Single Writer, Multiple Reader (SWMR), avoid path setup latency at the expense of increased optical components. In contrast, this thesis investigates a simple circuit-switched ONoC with lower component count where nodes need to request a channel before transmission. To hide the path setup latency, a coherence-based message predictor is proposed, to setup circuits before message arrival. Firstly, the effect of latency and bandwidth on application performance is thoroughly investigated using full-system simulations of shared memory CMPs. It is shown that the latency of an ideal NoC affects the CMP performance more than the NoC bandwidth. Increasing the number of wavelengths per channel decreases the serialisation latency and improves the performance of both ONoC types. With 2 or more wavelengths modulating at 25 Gbit=s , the ONoCs will outperform a conventional electrical mesh (maximal speedup of 20%). The SWMR ONoC outperforms the circuit-switched ONoC. Next coherence-based prediction techniques are proposed to reduce the waiting latency. The ideal coherence-based predictor reduces the waiting latency by 42%. A more streamlined predictor (smaller than a L1 cache) reduces the waiting latency by 31%. Without prediction, the message latency in the circuit-switched ONoC is 11% larger than in the SWMR ONoC. Applying the realistic predictor reverses this: the message latency in the SWMR ONoC is now 18% larger than the predictive circuitswitched ONoC

Is a 4-bit synaptic weight resolution enough? - Constraints on enabling spike-timing dependent plasticity in neuromorphic hardware

Large-scale neuromorphic hardware systems typically bear the trade-off between detail level and required chip resources. Especially when implementing spike-timing-dependent plasticity, reduction in resources leads to limitations as compared to floating point precision. By design, a natural modification that saves resources would be reducing synaptic weight resolution. In this study, we give an estimate for the impact of synaptic weight discretization on different levels, ranging from random walks of individual weights to computer simulations of spiking neural networks. The FACETS wafer-scale hardware system offers a 4-bit resolution of synaptic weights, which is shown to be sufficient within the scope of our network benchmark. Our findings indicate that increasing the resolution may not even be useful in light of further restrictions of customized mixed-signal synapses. In addition, variations due to production imperfections are investigated and shown to be uncritical in the context of the presented study. Our results represent a general framework for setting up and configuring hardware-constrained synapses. We suggest how weight discretization could be considered for other backends dedicated to large-scale simulations. Thus, our proposition of a good hardware verification practice may rise synergy effects between hardware developers and neuroscientists