高性能浮点除法

A. Liddicoat, M. Flynn
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引用次数: 27

摘要

在现代处理器中,浮点除法运算通常需要20到25个时钟周期,是乘法运算的5倍。高性能除法通常采用二次收敛的乘法算法。提出了一种基于乘法牛顿-拉夫森迭代的除法单元。该除法单元利用高阶牛顿-拉夫森倒数近似来快速、高效和高吞吐量地计算商。除法单元通过直接计算近似的平方、立方和更高次幂来实现快速执行,比传统的串行乘法方法快得多。此外,第二项、第三项和高阶项同时计算,进一步减少了除法延迟。已经确定了显著的硬件减少,从而大大减少了总体计算,从而减少了实现所需的面积和计算消耗的功率。所提出的硬件单元被设计为在一次迭代中实现期望的商精度,允许该单元完全流水线化以获得最大吞吐量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
High-performance floating point divide
In modern processors floating point divide operations often take 20 to 25 clock cycles, five times that of multiplication. Typically multiplicative algorithms with quadratic convergence are used for high-performance divide. A divide unit based on the multiplicative Newton-Raphson iteration is proposed. This divide unit utilizes the higher-order Newton-Raphson reciprocal approximation to compute the quotient fast, efficiently and with high throughput. The divide unit achieves fast execution by computing the square, cube and higher powers of the approximation directly and much faster than the traditional approach with serial multiplications. Additionally, the second, third and higher-order terms are computed simultaneously further reducing the divide latency. Significant hardware reductions have been identified that reduce the overall computation significantly and therefore, reduce the area required for implementation and the power consumed by the computation. The proposed hardware unit is designed to achieve the desired quotient precision in a single iteration allowing the unit to be fully pipelined for maximum throughput.
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