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

Pipelining of register transfer netlists

This paper describes a method for pipelining of register-to-register netlists. We define algorithms for inserting latches in a data path, both inside each unit and between the units as well as between control logic and the data path and for readjusting the state transition table. Experimental results on several benchmarks show 30%-40% improvement in performance

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

Power and memory optimization techniques in embedded systems design

Embedded systems incur tight constraints on power consumption and memory (which impacts size) in addition to other constraints such as weight and cost. This dissertation addresses two key factors in embedded system design, namely minimization of power consumption and memory requirement. The first part of this dissertation considers the problem of optimizing power consumption (peak power as well as average power) in high-level synthesis (HLS). The second part deals with memory usage optimization mainly targeting a restricted class of computations expressed as loops accessing large data arrays that arises in scientific computing such as the coupled cluster and configuration interaction methods in quantum chemistry. First, a mixed-integer linear programming (MILP) formulation is presented for the scheduling problem in HLS using multiple supply-voltages in order to optimize peak power as well as average power and energy consumptions. For large designs, the MILP formulation may not be suitable; therefore, a two-phase iterative linear programming formulation and a power-resource-saving heuristic are presented to solve this problem. In addition, a new heuristic that uses an adaptation of the well-known force-directed scheduling heuristic is presented for the same problem. Next, this work considers the problem of module selection simultaneously with scheduling for minimizing peak and average power consumption. Then, the problem of power consumption (peak and average) in synchronous sequential designs is addressed. A solution integrating basic retiming and multiple-voltage scheduling (MVS) is proposed and evaluated. A two-stage algorithm namely power-oriented retiming followed by a MVS technique for peak and/or average power optimization is presented. Memory optimization is addressed next. Dynamic memory usage optimization during the evaluation of a special class of interdependent large data arrays is considered. Finally, this dissertation develops a novel integer-linear programming (ILP) formulation for static memory optimization using the well-known fusion technique by encoding of legality rules for loop fusion of a special class of loops using logical constraints over binary decision variables and a highly effective approximation of memory usage

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

FPGA Implementation of Data Flow Graphs for Digital Signal Processing Applications

A rapid growth in digital signal processing applications has increased the requirement for high-speed digital systems. Multiprocessor systems are the best choice for these applications. A prior sequence of operations should be applied to the operations that described the nature of these applications before hardware implementation is produced. These operations should be scheduled and hardware allocated. This paper proposes a new scheduling technique for digital signal processing (DSP) applications has been represented by data flow graphs (DFGs). In addition, hardware allocation is implemented in the form of embedded system. A proposed scheduling technique also achieves the optimal scheduling of a DFG at design time. The optimality criteria considered in this algorithm are the maximum throughput within the available hardware resources. The maximum throughput is achieved by arranging the DFG nodes according to their inter-related data dependencies. Then, two nodes can be clustered into one compound task to reduce the overall execution time by minimizing the number of tasks to be executed that minimizing the number of cycles to execute them. Then each task is presented in form of instruction to be executed in the hardware system. A hardware system is composed of one or multiple homogenous pipelined processing elements and it is designed to meet the maximum-rate schedule.  Two implementations are proposed of the system architecture according to the number of the processing elements, namely:  the serial system and the parallel system. The serial system comprises one processing element where all tasks are processed sequentially, whilst the parallel system has four processing elements to execute tasks concurrently. These systems consist mainly of seven units: central shared memory, state table, multiway function unit buffer, execution array, processing element/s, instruction buffer and the address generation unit. The hardware components were built on an FPGA chip using Verilog HDL. In synthesis results, the parallel system has better system performance by 25.5% than the serial system. While the serial system requires smaller area size, which described by the number of slice registers and the number of the slice lookup tables (LUTs) than the parallel one. The relationship between the number of instructions that are executed in both systems, and the system area and the system performance that presented by system frequency, are studied. By increasing memories size in both systems, the system performance isn’t affected as in a serial system, and it is slightly decreased as the parallel system by 1.5% to 4.5%. In terms of the systems area, both serial system area and parallel system area are increased and in some cases are doubled. The proposed scheduling technique is shown to outperform the retaining technique, which we have chosen to compare with.  The serial system has better performance by 19.3% higher system frequency than a retiming technique. And the parallel system also outperforms the retaining technique by 51.2% higher system frequency in synthesis results

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

Exploiting parallelism within multidimensional multirate digital signal processing systems

The intense requirements for high processing rates of multidimensional Digital Signal Processing systems in practical applications justify the Application Specific Integrated Circuits designs and parallel processing implementations. In this dissertation, we propose novel theories, methodologies and architectures in designing high-performance VLSI implementations for general multidimensional multirate Digital Signal Processing systems by exploiting the parallelism within those applications. To systematically exploit the parallelism within the multidimensional multirate DSP algorithms, we develop novel transformations including (1) nonlinear I/O data space transforms, (2) intercalation transforms, and (3) multidimensional multirate unfolding transforms. These transformations are applied to the algorithms leading to systematic methodologies in high-performance architectural designs. With the novel design methodologies, we develop several architectures with parallel and distributed processing features for implementing multidimensional multirate applications. Experimental results have shown that those architectures are much more efficient in terms of execution time and/or hardware cost compared with existing hardware implementations