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A dynamic non-uniform segmentation method for first-order polynomial function evaluation

机译：一阶多项式函数评估的动态非均匀分割方法

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摘要

This paper presents a new dynamic non-uniform segmentation method for the first-order polynomial function evaluation. The proposed method can evaluate the elementary functions (e.g. log, exp, sin, cos, tan, etc.) and combinations of these functions by an optimized linear approximation with the fewest non-uniform segments. Compared with the previous evaluation method based on the static bit-width analysis, the proposed method is mainly based on a dynamic bit-width analysis and capable of reducing the number of segments, which in turn can significantly reduce the memory size occupied in hardware. The proposed dynamic method can evaluate the function to satisfy accuracy by the linear approximation in which the input, coefficients, and intermediate values are rounded to fewer bit-width, which cannot be achieved by previous static non-uniform segmentation methods. The hardware performance evaluation results on FPCA show that the proposed method consumes about 66% fewer hardware resources, 56% less actual memory usage, and performs 32% shorter delay on average in comparison with the non-uniform segmentation method based on static bit-width analysis.
机译：为一阶多项式函数估计提供了一种新的动态非均匀分割方法。所提出的方法可以通过具有最少非均匀段的优化线性逼近来评估基本函数（例如log，exp，sin，cos，tan等）以及这些函数的组合。与以前的基于静态位宽分析的评估方法相比，该方法主要基于动态位宽分析，并且能够减少段数，从而可以显着减少硬件占用的内存。所提出的动态方法可以通过将输入，系数和中间值四舍五入为较小的位宽的线性近似来评估功能是否满足精度，这是以前的静态非均匀分割方法无法实现的。 FPCA的硬件性能评估结果表明，与基于静态位宽的非均匀分段方法相比，该方法消耗的硬件资源减少了约66％，实际内存使用量减少了56％，平均延迟减少了32％。分析。

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