IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

The main characteristic of Reconfigurable Computing is the presence of hardware that can be reconfigured to implement specific functionality more suitable for specially tailored hardware than on a simple uniprocessor. Reconfigurable computing systems join microprocessors and programmable hardware in order to take advantage of the combined strengths of hardware and software and have been used in applications ranging from embedded systems to high performance computing. Many of the fundamental theories have been identified and used by the Hardware/Software Co-Design research field. Although the same background ideas are shared in both areas, they have different goals and use different approaches.This book is intended as an introduction to the entire range of issues important to reconfigurable computing, using FPGAs as the context, or "computing vehicles" to implement this powerful technology. It will take a reader with a background in the basics of digital design and software programming and provide them with the knowledge needed to be an effective designer or researcher in this rapidly evolving field.

· Treatment of FPGAs as computing vehicles rather than glue-logic or ASIC substitutes
· Views of FPGA programming beyond Verilog/VHDL
· Broad set of case studies demonstrating how to use FPGAs in novel and efficient ways

Reconfigurable Computing: The Theory and Practice of FPGA-Based Computation

Reconfigurable computing is becoming increasingly attractive for many applications. This survey covers two aspects of reconfigurable computing: architectures and design methods. The paper includes recent advances in reconfigurable architectures, such as the Alters Stratix II and Xilinx Virtex 4 FPGA devices. The authors identify major trends in general-purpose and special-purpose design methods. It is shown that reconfigurable computing designs are capable of achieving up to 500 times speedup and 70% energy savings over microprocessor implementations for specific applications.

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Reconfigurable computing: architectures and design methods

Moore's Law states that the number of transistors on a device doubles every two years; however, it is often (mis)quoted based on its impact on CPU performance. This important corollary of Moore's Law states that improved clock frequency plus improved architecture yields a doubling of CPU performance every 18 months. This paper examines the impact of Moore's Law on the peak floating-point performance of FPGAs. Performance trends for individual operations are analyzed as well as the performance trend of a common instruction mix (multiply accumulate). The important result is that peak FPGA floating-point performance is growing significantly faster than peak floating-point performance for a CPU.

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FPGAs vs. CPUs: trends in peak floating-point performance

A unified algorithm for elementary functions

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

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Accuracy-Guaranteed Bit-Width Optimization

This paper presents a method that offers a uniform treatment for bit-width optimisation of both fixed-point and floating-point designs. Our work utilises automatic differentiation to compute the sensitivities of outputs to the bit-width of the various operands in the design. This sensitivity analysis enables us to explore and compare fixed-point and floating-point implementation for a particular design. As a result, we can automate the selection of the optimal number representation for each variable in a design to optimize area and performance. We implement our method in the BitSize tool targeting reconfigurable architectures, which takes user-defined constraints to direct the optimisation procedure. We illustrate our approach using applications such as ray-tracing and function approximation.

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Unifying bit-width optimisation for fixed-point and floating-point designs

Automatic bitwidth analysis is a key ingredient for highlevel programming of FPGAs and high-level synthesis of VLSI circuits. The objective is to find the minimal number of bits to represent a value in order to minimise the circuit area and to improve efficiency of the respective arithmetic operations, while satisfying user-defined numerical constraints. We present a novel approach to bitwidth- or precision-analysis for floating-point designs. The approach involves analysing the dataflow graph representation of a design to see how sensitive the output of a node is to changes in the outputs of other nodes: higher sensitivity requires higher precision and hence more output bits. We automate such sensitivity analysis by a mathematical method called automatic differentiation, which involves differentiating variables in a design with respect to other variables. We illustrate our approach by optimising the bitwidth for two examples, a discrete Fourier transform (DFT) implementation and a Finite Impulse Response (FIR) filter implementation.

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Floating-point bitwidth analysis via automatic differentiation

We present a methodology and an automated system for function evaluation unit generation. Our system selects the best function evaluation hardware for a given function, accuracy requirements, technology mapping, and optimization metrics, such as area, throughput, and latency. Function evaluation f(x) typically consists of range reduction and the actual evaluation on a small convenient interval such as [0, /spl pi//2) for sin(x). We investigate the impact of hardware function evaluation with range reduction for a given range and precision of x and f(x) on area and speed. An automated bit-width optimization technique for minimizing the sizes of the operators in the data paths is also proposed. We explore a vast design space for fixed-point sin(x), log(x), and /spl radic/x accurate to one unit in the last place using MATLAB and ASC, a stream compiler for field-programmable gate arrays (FPGAs). In this study, we implement over 2,000 placed-and-routed FPGA designs, resulting in over 100 million application-specific integrated circuit (ASIC) equivalent gates. We provide optimal function evaluation results for range and precision combinations between 8 and 48 bits.

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Optimizing hardware function evaluation

MiniBit, our automated approach for optimizing bit-widths of fixed-point designs is based on static analysis via affine arithmetic. We describe methods to minimize both the integer and fraction parts of fixed-point signals with the aim of minimizing circuit area. Our range analysis technique identifies the number of integer bits required. For precision analysis, we employ a semi-analytical approach with analytical error models in conjunction with adaptive simulated annealing to find the optimum number of fraction bits. Improvements for a given design reduce area and latency by up to 20% and 12% respectively, over optimum uniform fraction bit-widths on a Xilinx Virtex-4 FPGA.

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A.A. Gaffar

Papers

Accuracy-Guaranteed Bit-Width Optimization

Unifying bit-width optimisation for fixed-point and floating-point designs

Floating-point bitwidth analysis via automatic differentiation

Optimizing hardware function evaluation

MiniBit: bit-width optimization via affine arithmetic