Fixed-point arithmetic

Abstract: Leakage power is a major concern in current and future microprocessor designs. In this paper, we explore the potential of architectural techniques to reduce leakage through power-gating of execution units. This paper first develops parameterized analytical equations that estimate the break-even point for application of power-gating techniques. The potential for power gating execution units is then evaluated, for the range of relevant break-even points determined by the analytical equations, using a state-of-the-art out-of-order superscalar processor model. The power gating potential of the floating-point and fixed-point units of this processor is then evaluated using three different techniques to detect opportunities for entering sleep mode; ideal, time-based, and branch-misprediction-guided. Our results show that using the time-based approach, floating-point units can be put to sleep for up to 28% of the execution cycles at a performance loss of 2%. For the more difficult to power-gate fixed-point units, the branch misprediction guided technique allows the fixed-point units to be put to sleep for up to 40% more of the execution cycles compared to the simpler time-based technique, with similar performance impact. Overall, our experiments demonstrate that architectural techniques can be used effectively in power-gating execution units.

Abstract: This paper presents a set of geometric signature features for offline automatic signature verification based on the description of the signature envelope and the interior stroke distribution in polar and Cartesian coordinates. The features have been calculated using 16 bits fixed-point arithmetic and tested with different classifiers, such as hidden Markov models, support vector machines, and Euclidean distance classifier. The experiments have shown promising results in the task of discriminating random and simple forgeries.

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

Abstract: Most of the literature dealing with overflow oscillation in fixed-point arithmetic digital filters has considered the direct form exclusively. It is possible to eliminate overflow oscillations, regardless of pole locations, by considering more general forms. A sufficient condition is given for a two's complement state variable realization of any order to be free of overflow oscillation. A simple characterization of the condition is given for second-order filters. Among those second-order forms which meet the condition are normal forms, and forms which minimize output roundoff noise.