Equivalence checking of retimed circuits

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 25).This thesis addresses the problem of verifying the equivalence of two circuits, one or both of which have undergone register retiming as well as logic resynthesis. The aim of the thesis is to improve the ability of Formality, an equivalence checking tool written at Synopsys, to handle retimed circuits. At the beginning of this project Formality already had an implementation of peripheral retiming, an algorithm that can handle a large set of retimed circuits. In this thesis, I explain the performance, usability and special case coverage problems found in the original implementation. I review other retiming verification algorithms and conclude that none of them would perform satisfactorily in Formality. Finally, I explain the modifications made to peripheral retiming in order to solve some of the identified issues and propose partial solutions for the problems that have not been solved yet.by Karolína Netolická.M.Eng

Fast algorithms for retiming large digital circuits

The increasing complexity of VLSI systems and shrinking time to market requirements demand good optimization tools capable of handling large circuits. Retiming is a powerful transformation that preserves functionality, and can be used to optimize sequential circuits for a wide range of objective functions by judiciously relocating the memory elements. Leiserson and Saxe, who introduced the concept, presented algorithms for period optimization (minperiod retiming) and area optimization (minarea retiming). The ASTRA algorithm proposed an alternative view of retiming using the equivalence between retiming and clock skew optimization;The first part of this thesis defines the relationship between the Leiserson-Saxe and the ASTRA approaches and utilizes it for efficient minarea retiming of large circuits. The new algorithm, Minaret, uses the same linear program formulation as the Leiserson-Saxe approach. The underlying philosophy of the ASTRA approach is incorporated to reduce the number of variables and constraints in this linear program. This allows minarea retiming of circuits with over 56,000 gates in under fifteen minutes;The movement of flip-flops in control logic changes the state encoding of finite state machines, requiring the preservation of initial (reset) states. In the next part of this work the problem of minimizing the number of flip-flops in control logic subject to a specified clock period and with the guarantee of an equivalent initial state, is formulated as a mixed integer linear program. Bounds on the retiming variables are used to guarantee an equivalent initial state in the retimed circuit. These bounds lead to a simple method for calculating an equivalent initial state for the retimed circuit;The transparent nature of level sensitive latches enables level-clocked circuits to operate faster and require less area. However, this transparency makes the operation of level-clocked circuits very complex, and optimization of level-clocked circuits is a difficult task. This thesis also presents efficient algorithms for retiming large level-clocked circuits. The relationship between retiming and clock skew optimization for level-clocked circuits is defined and utilized to develop efficient retiming algorithms for period and area optimization. Using these algorithms a circuit with 56,000 gates could be retimed for minimum period in under twenty seconds and for minimum area in under 1.5 hours

Elasticity and Petri nets

Digital electronic systems typically use synchronous clocks and primarily assume fixed duration of their operations to simplify the design process. Time elastic systems can be constructed either by replacing the clock with communication handshakes (asynchronous version) or by augmenting the clock with a synchronous version of a handshake (synchronous version). Time elastic systems can tolerate static and dynamic changes in delays (asynchronous case) or latencies (synchronous case) of operations that can be used for modularity, ease of reuse and better power-delay trade-off. This paper describes methods for the modeling, performance analysis and optimization of elastic systems using Marked Graphs and their extensions capable of describing behavior with early evaluation. The paper uses synchronous elastic systems (aka latency-tolerant systems) for illustrating the use of Petri nets, however, most of the methods can be applied without changes (except changing the delay model associated with events of the system) to asynchronous elastic systems.Peer ReviewedPostprint (author's final draft

End-to-End Industrial Study of Retiming

Sequential circuits are combinational circuits that are separated by registers. Retiming is considered as the most promising technique for optimizing sequential circuits, that involves moving the edge-triggered registers across the combinational logic without changing the functionality. Despite significant efforts spent on sequential optimization since 1980's, there are few works discussed its performance in an end to-end design flow. The retiming algorithms were mostly evaluated at the logic level. However, it turns out that the retiming results at logic level could be significantly different than evaluating the physical level.This paper provides the findings of how retiming algorithms perform in an end-to-end industrial design flow, with seven industry designs taken from a recent 14nm microprocessor. Experiments are conducted with several complete industrial design flows. The evaluations are made at the end of the physical design flow. The experimental results show that the performance (design quality) of the retiming algorithms vary on the designs. Based these experimental results, we discover a feature that describes the retiming potentials of sequential designs. This model successfully forecast whether the given industrial designs could be significantly improved by retiming in an end-to-end design flow, regarding timing, area, and power

High Level Synthesis for Packet Processing Pipelines

Packet processing is an essential function of state-of-the-art network routers and switches. Implementing packet processors in pipelined architectures is a well-known, established technique, albeit different approaches have been proposed. The design of packet processing pipelines is a delicate trade-off between the desire for abstract specifications, short development time, and design maintainability on one hand and very aggressive performance requirements on the other. This thesis proposes a coherent design flow for packet processing pipelines. Like the design process itself, I start by introducing a novel domain-specific language that provides a high-level specification of the pipeline. Next, I address synthesizing this model and calculating its worst-case throughput. Finally, I address some specific circuit optimization issues. I claim, based on experimental results, that my proposed technique can dramatically improve the design process of these pipelines, while the resulting performance matches the expectations of hand-crafted design. The considered pipelines exhibit a pseudo-linear topology, which can be too restrictive in the general case. However, especially due to its high performance, such an architecture may be suitable for applications outside packet processing, in which case some of my proposed techniques could be easily adapted. Since I ran my experiments on FPGAs, this work has an inherent bias towards that technology; however, most results are technology-independent

A low-power quadrature digital modulator in 0.18um CMOS

Quadrature digital modulation techniques are widely used in modern communication systems because of their high performance and flexibility. However, these advantages come at the cost of high power consumption. As a result, power consumption has to be taken into account as a main design factor of the modulator.In this thesis, a low-power quadrature digital modulator in 0.18um CMOS is presented with the target system clock speed of 150 MHz. The quadrature digital modulator consists of several key blocks: quadrature direct digital synthesizer (QDDS), pulse shaping filter, interpolation filter and inverse sinc filter. The design strategy is to investigate different implementations for each block and compare the power consumption of these implementations. Based on the comparison results, the implementation that consumes the lowest power will be chosen for each block. First of all, a novel low-power QDDS is proposed in the thesis. Power consumption estimation shows that it can save up to 60% of the power consumption at 150 MHz system clock frequency compared with one conventional design. Power consumption estimation results also show that using two pulse shaping blocks to process I/Q data, cascaded integrator comb (CIC) interpolation structure, and inverse sinc filter with modified canonic signed digit (MCSD) multiplication consume less power than alternative design choices. These low-power blocks are integrated together to achieve a low-power modulator. The power consumption estimation after layout shows that it only consumes about 95 mW at 150 MHz system clock rate, which is much lower than similar commercial products. The designed modulator can provide a low-power solution for various quadrature modulators. It also has an output bandwidth from 0 to 75 MHz, configurable pulse shaping filters and interpolation filters, and an internal sin(x)/x correction filter