George A. Constantinides

Accuracy-Guaranteed Bit-Width Optimization

An automated static approach for optimizing bit widths of fixed-point feedforward designs with guaranteed accuracy, called MiniBit, is presented. Methods to minimize both the integer and fraction parts of fixed-point signals with the aim of minimizing the circuit area are described. For range analysis, the technique in this paper identifies the number of integer bits necessary to meet range requirements. For precision analysis, a semianalytical approach with analytical error models in conjunction with adaptive simulated annealing is employed to optimize the number of fraction bits. The analytical models make it possible to guarantee overflow/underflow protection and numerical accuracy for all inputs over the user-specified input intervals. Using a stream compiler for field-programmable gate arrays (FPGAs), the approach in this paper is demonstrated with polynomial approximation, RGB-to-YCbCr conversion, matrix multiplication, B-splines, and discrete cosine transform placed and routed on a Xilinx Virtex-4 FPGA. Improvements for a given design reduce the area and the latency by up to 26% and 12%, respectively, over a design using optimum uniform fraction bit widths. Studies show that MiniBit-optimized designs are within 1% of the area produced from the integer linear programming approach

A Parallel Hardware Architecture for Scale and Rotation Invariant Feature Detection

This paper proposes a parallel hardware architecture for image feature detection based on the scale invariant feature transform algorithm and applied to the simultaneous localization and mapping problem. The work also proposes specific hardware optimizations considered fundamental to embed such a robotic control system on-a-chip. The proposed architecture is completely stand-alone; it reads the input data directly from a CMOS image sensor and provides the results via a field-programmable gate array coupled to an embedded processor. The results may either be used directly in an on-chip application or accessed through an Ethernet connection. The system is able to detect features up to 30 frames per second (320times240 pixels) and has accuracy similar to a PC-based implementation. The achieved system performance is at least one order of magnitude better than a PC-based solution, a result achieved by investigating the impact of several hardware-orientated optimizations on performance, area and accuracy.

Wordlength optimization for linear digital signal processing

This paper presents an approach to the wordlength allocation and optimization problem for linear digital signal processing systems implemented as custom parallel processing units. Two techniques are proposed, one which guarantees an optimum set of wordlengths for each internal variable, and one which is a heuristic approach. Both techniques allow the user to tradeoff implementation area for arithmetic error at system outputs. Optimality (with respect to the area and error estimates) is guaranteed through modeling as a mixed integer linear program. It is demonstrated that the proposed heuristic leads to area improvements of 6% to 45% combined with speed increases compared to the optimum uniform wordlength design. In addition, the heuristic reaches within 0.7% of the optimum multiple wordlength area over a range of benchmark problems.

Embedded Online Optimization for Model Predictive Control at Megahertz Rates

Faster, cheaper, and more power efficient optimization solvers than those currently possible using general-purpose techniques are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We provide analysis ensuring the reliable operation of the resulting controller under reduced precision fixed-point arithmetic. Implementation of the proposed architectures in FPGAs shows that satisfactory control performance at a sample rate beyond 1 MHz is achievable even on low-end devices, opening up new possibilities for the application of MPC on embedded systems.

Perturbation analysis for word-length optimization

This paper introduces a design tool and its associated procedures for determining the sensitivity of outputs in a digital signal processing design to small errors introduced by rounding or truncation of internal variables. The proposed approach can be applied to both linear and nonlinear designs. By analyzing the resulting sensitivity values, the proposed procedure is able to determine an appropriate distinct word-length for each internal variable. Also in this paper, the power optimizing capabilities of word-length optimization are studied for the first time. Application of the proposed procedure to adaptive filters realized in a Xilinx Virtex FPGA (field programmable gate array) has resulted in area reductions of up to 80% combined with power reductions of up to 98% and speed-up of up to 36% over common alternative design strategies.

The Multiple Wordlength Paradigm

This paper presents a paradigm for the design of multiple wordlength parallel processing systems for DSP applications based on varying the wordlength and scaling of each signal in a DSP block diagram. A technique for estimating the observable effects of truncation and roundoff error is illustrated, and used to form the basis of an optimization algorithm to automate the design of such multiple wordlength systems. Results from implementation on a reconfigurable computing platform show that significant logic usage savings and increased clock rates can be obtained by customizing the datapath precision to the algorithm according to the techniques described in this paper. On selected DSP benchmarks, we obtain up to 45% area reduction and up to 39% speed increase over standard design techniques.

The complexity of multiple wordlength assignment

This note discusses the multiple wordlength assignment problem for the design of custom digital signal processing (DSP) parallel processors. It is demonstrated that this assignment problem is NP-hard.

Optimum wordlength allocation

This paper presents an approach to the wordlength allocation and optimization problem for linear digital signal processing systems implemented in Field-Programmable Gate Arrays. The proposed technique guarantees an optimum set of wordlengths for each internal variable, allowing the user to trade-off implementation area for error at system outputs. Optimality is guaranteed through modelling as a mixed integer linear program, constructed through novel techniques for the linearization of error and area constraints. Optimum results in this field are valuable since they can be used to assess the effectiveness of heuristic wordlength optimization techniques. It is demonstrated that one such previously published heuristic reaches within 0.7% of the optimum area over a range of benchmark problems.

Combining data reuse exploitationwith data-level parallelization for FPGA targeted hardware compilation: A geometric programming framework

A nonlinear optimization framework is proposed in this paper to automate exploration of the design space consisting of data-reuse (buffering) decisions and loop-level parallelization, in the context of field-programmable-gate-array-targeted hardware compilation. Buffering frequently accessed data in on-chip memories can reduce off-chip memory accesses and open avenues for parallelization. However, the exploitation of both data reuse and parallelization is limited by the memory resources available on-chip. As a result, considering these two problems separately, e.g., first exploring data reuse and then exploring data-level parallelization, based on the data-reuse options determined in the first step, may not yield the performance-optimal designs for limited on-chip memory resources. We consider both problems at the same time, exposing the dependence between the two. We show that this combined problem can be formulated as a nonlinear program and further show that efficient solution techniques exist for this problem, based on recent advances in optimization of so-called geometric programming problems. The results from applying this framework to several real benchmarks implemented on a Xilinx device demonstrate that given different constraints on on-chip memory utilization, the corresponding performance-optimal designs are automatically determined by the framework. We have also implemented designs determined by a two-stage optimization method that first explores data reuse and then explores parallelization on the same platform, and by comparison, the performance-optimal designs proposed by our framework are faster than the designs determined by the two-stage method by up to 5.7 times.

Heuristic datapath allocation for multiple wordlength systems

This paper introduces a heuristic to solve the combined scheduling, resource building, and wordlength selection problem for multiple wordlength systems. The algorithm involves an iterative refinement of operator wordlength information, leading to a scheduled and bound data-flow graph. Scheduling is performed with incomplete wordlength information during the intermediate stages of this refinement process. Results show significant area savings over known alternative approaches.