A mathematical formulation of the loop pipelining problem

This paper presents a mathematical model for the loop pipelining problem that considers several parameters for optimization and supports any combination of resource and timing constraints. The unrolling degree of the loop is one of the variables explored by the model. By using Farey’s series, an optimal exploration of the unrolling degree is performed and optimal solutions not considered by other methods are obtained. Finding an optimal schedule that minimizes resource and register requirements is solved by using an Integer linear programming (ILP) model. A novel paradigm called branch and prune is proposed to eficiently converge towards the optimal schedule and prune the search tree for integer solutions, thus drastically reducing the running time. This is the first formulation that combines the unrolling degree of the loop with timing and resource constraints in a mathematical model that guarantees optimal solutions.Peer ReviewedPostprint (author's final draft

Harmonic scheduling of linear recurrences in digital filter design

Linear difference equations involving recurrences are fundamental equations that describe many important signal processing applications. For many high sample rate digital filter applications, we need to effectively parallelize the linear difference equations used to describe digital filters - a difficult task due to the recurrences inherent in the data dependences. We present a novel approach, Harmonic Scheduling, that exploits parallelism in these recurrences beyond loop-carried dependencies, and which generates optimal schedules for parallel evaluation of linear difference equations with resource constraints. This approach also enables us to derive a parallel schedule with minimum control overhead, given an execution time with resource constraints. We also present a Harmonic Scheduling algorithm that generates optimal schedules for digital filters described by second-order difference equations with resource constraints

Multiple voltage scheme with frequency variation for power minimization of pipelined circuits at high-level synthesis

High-Level Synthesis (HLS) is defined as a translation process from a behavioral description into structural description. The high-level synthesis process consists of three interdependent phases: scheduling, allocation and binDing The order of the three phases varies depending on the design flow. There are three important quality measures used to support design decision, namely size, performance and power consumption. Recently, with the increase in portability, the power consumption has become a very dominant factor in the design of circuits. The aim of low-power high-level synthesis is to schedule operations to minimize switching activity and select low power modules while satisfying timing constraints. This thesis presents a heuristic that helps minimize power consumption by operating the functional units at multiple voltages and varied clock frequencies. The algorithm presented here deals with pipelined operations where multiple instance of the same operation are carried out. The algorithm was implemented using C++, on LINUX platform

Constraint analysis for DSP code generation

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Memory partitioning and scheduling co-optimization in behavioral synthesis

Abstract—Achieving optimal throughput by extracting parallel-ism in behavioral synthesis often exaggerates memory bottleneck issues. Data partitioning is an important technique for increasing memory bandwidth by scheduling multiple simultaneous memory accesses to different memory banks. In this paper we present a vertical memory partitioning and scheduling algorithm that can generate a valid partition scheme for arbitrary affine memory inputs. It does this by arranging non-conflicting memory accesses across the border of loop iterations. A mixed memory partitioning and scheduling algorithm is also proposed to com-bine the advantages of the vertical and other state-of-art algo-rithms. A set of theorems is provided as criteria for selecting a valid partitioning scheme. This is followed by an optimal and scalable memory scheduling algorithm. By utilizing the property of constant strides between memory addresses in successive loop iterations, an address translation optimization technique for an arbitrary partition factor is proposed to improve performance, area and energy efficiency. Experimental results show that on a set of real-world medical image processing kernels, the proposed mixed algorithm with address translation optimization can gain speed-up, area reduction and power savings of 15.8%, 36 % and 32.4 % respectively, compared to the state-of-art memory parti-tioning algorithm