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Truncated Squarers with Constant and Variable Correction

机译:带有恒定和可变校正的截尾平方器

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This paper describes truncated squarers, which are specialized squarers with a portion of the squaring matrix eliminated. Rounding error and errors due to matrix reduction are quantified and analyzed. Constant and variable correction techniques are presented that minimize either the mean error or the maximum absolute error as required by the application. Area and delay estimates are presented for a number of designs, as well as error statistics obtained both analytically and numerically by exhaustive simulation. As an example, one design of a 16-bit truncated squarer using constant correction is 10.1 % faster and requires 27.9 % less area than a comparable standard squarer with true rounding. The range of error for this truncated squarer is — 0.892 to + 0.625 ulps, compared to ± 0.5 ulps for the standard squarer.
机译:本文介绍了截短的平方器,它们是专门的平方器,其中部分平方矩阵被消除。舍入误差和由于矩阵归约引起的误差被量化和分析。提出了恒定和可变校正技术,可将平均误差或最大绝对误差减至最小,这是应用程序所需的。提出了许多设计的面积和延迟估计,以及通过详尽的仿真以解析方式和数值方式获得的误差统计信息。例如,采用恒定校正的16位截断平方器的一种设计比具有真正舍入的标准平方器要快10.1%,所需面积减少27.9%。该截短的平方器的误差范围为-0.892至+ 0.625 ulps,而标准平方器的误差范围为±0.5 ulps。

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