Accuracy-Guaranteed Bit-Width Optimization

Abstract

Abstract-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.Index Terms-Field-programmable gate arrays (FPGAs), finite word-length effects, fixed-point arithmetic, optimization methods, simulated annealing (SA).

Fine Grain Precision Scaling for Datapath Approximations in Digital Signal Processing Systems

“…In [15], the authors adopt affine arithmetic (AA) to model the min/max error propagation of quantization noise. However, static min/max approaches are not appropriate for fine-grain precision scaling.…”

Fast Fixed-Point Optimization of DSP Algorithms

“…Its main feature is that it automatically cancels the linear dependencies of the included uncertainties along the computation path, thus avoiding the oversizing produced by Interval Arithmetic (IA) approaches [15]. Regarding fixed-point optimization, it has been applied to both scaling computation [16,17,10], and word-length selection [5,16,10,18]. Also, a modification, called Quantized Affine Arithmetic (QAA), has been applied to the computation of limit cycles [19] and dynamic range analysis of quantized LTI algorithms [17].…”

“…and it is formed by a collection of affine forms at each time step n. This expression of the error can be used to estimate the error peak-value, using the traditional interpretation of AA [20,10], and, also, to obtain the PDF of the error [5,20]. However, in the next subsection we focus on obtaining the value of the power of the error considering the actual PDF of each error term (i.e.…”

“…These approaches can be applied to Linear TimeInvariant (LTI) systems [5,2,6] and to differentiable non-linear systems [7][8][9][10]. As for the noise metric used, they are based on the peak value [10] and on the computation of SQNR [2,7,5,9,8]. Since SQNR is a very popular error metric within DSP systems and because LTI systems have been extensively studied, our work aims at fast SQNR estimation techniques for differentiable non-linear systems.…”

Reconfigurable design with clock gating

“…This can be achieved by various approaches; below we present one based on a method that combines word-length optimization with an accuracyguaranteed technique to reduce power consumption while maintaining error constraints for the outputs [10].…”