Tight coupling of timing driven placement and retiming

Retiming is a widely investigated technique for performance optimization. In general, it performs extensive modifications on a circuit netlist, leaving it unclear, whether the achieved performance improvement will still be valid after placement has been performed. This paper presents an approach for integrating retiming into a timing-driven placement environment. The experimental results show the benefit of the proposed approach on circuit performance in comparison with design flows using retiming only as a pre- or postplacement optimization method

Placement driven retiming with a coupled edge timing model

Retiming is a widely investigated technique for performance optimization. It performs powerful modifications on a circuit netlist. However, often it is not clear, whether the predicted performance improvement will still be valid after placement has been performed. This paper presents a new retiming algorithm using a highly accurate timing model taking into account the effect of retiming on capacitive loads of single wires as well as fanout systems. We propose the integration of retiming into a timing-driven standard cell placement environment based on simulated annealing. Retiming is used as an optimization technique throughout the whole placement process. The experimental results show the benefit of the proposed approach. In comparison with the conventional design flow based on standard FEAS our approach achieved an improvement in cycle time of up to 34% and 17% on the average

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

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

Elastic systems

Elastic systems provide tolerance to the variations in computation and communication delays. The incorporation of elasticity opens new opportunities for optimization using new correct-by-construction transformations that cannot be applied to rigid non-elastic systems. The basics of synchronous and asynchronous elastic systems will be reviewed. A set of behavior-preserving transformations will be presented: retiming, recycling, early evaluation, variable-latency units and speculative execution. The application of these transformations for performance and power optimization will be discussed. Finally, a novel framework for microarchitectural exploration will be introduced, showing that the optimal pipelining of a circuit can be automatically obtained by using the previous transformations.Peer ReviewedPostprint (published version

High-Level Optimization by Combining Retiming and Shannon Decomposition

Applying Shannon decomposition can reshape sequential circuits and improve opportunities for retiming. Both Shannon decomposition and retiming only rely on limited information about combinational blocks (timing estimates), so both techniques are suitable for high-level synthesis. We describe an efficient algorithm to preprocess a circuit using Shannon decomposition to increase retiming efficacy. It assembles complex chains of Shannon decompositions while carefully avoiding parallel ones in order to limit the area overhead due to logic duplication. We compare a traditional retiming flow with the same flow augmented with our algorithm. Although our algorithm provides no improvement on half of our benchmarks, for the other half we obtain a 25% speed-up on average (7% to 61%), while only increasing area by 5% (3% to 12%)

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

Correct-by-construction microarchitectural pipelining

This paper presents a method for correct-by-construction microarchitectural pipelining that handles cyclic systems with dependencies between iterations. Our method combines previously known bypass and retiming transformations with a few transformations valid only for elastic systems with early evaluation (namely, empty FIFO insertion, FIFO capacity sizing, insertion of anti-tokens, and introducing early evaluation multiplexors). By converting the design to a synchronous elastic form and then applying this extended set of transformations, one can pipeline a functional specification with an automatically generated distributed controller that implements stalling logic resolving data hazards off the critical path of the design. We have developed an interactive toolkit for exploring elastic microarchitectural transformations. The method is illustrated by pipelining a few simple examples of instruction set architecture ISA specifications.Peer ReviewedPostprint (published version

On-Chip Transparent Wire Pipelining (invited paper)

Wire pipelining has been proposed as a viable mean to break the discrepancy between decreasing gate delays and increasing wire delays in deep-submicron technologies. Far from being a straightforwardly applicable technique, this methodology requires a number of design modifications in order to insert it seamlessly in the current design flow. In this paper we briefly survey the methods presented by other researchers in the field and then we thoroughly analyze the solutions we recently proposed, ranging from system-level wire pipelining to physical design aspects