摘要： 提出一种基于分段二次插值的单精度浮点数初等函数逼近设计，以实现倒数、均方根、均方根倒数、指数、三角函数等多种函数运算。通过对二次多项式进行变换，将1次平方运算、2次乘法运算和3次加法运算，转化为2次乘累加运算，并且采用复用乘累加结构的方法完成运算。实验结果证明，尽管整个逼近运算需要2个时钟周期完成，但是运算部分面积能够减少56%，总的硬件设计成本能够降低17.5%。

关键词: 二次插值, 初等函数, 低成本, 单精度, 变换, 复用

Abstract: A low cost design for elementary function approximation based on piecewise quadratic interpolation to support single- precision floating-point data, that can be able to complete the approximation to the reciprocal, squarer root, squarer root reciprocal, exponential, trigonometric and other elementary functions is presented. The traditional computation of quadratic polynomial needs one squarer, two multiplications and three additions. But this design only needs two Multiply And Accumulate(MAC) operations by the deformation of quadratic polynomial, and can complete the computation by reusing the MAC architecture. In the result, the design can reduce 56% of the computing area and save 17.5% cost of hardware in total, though the entire approximation operation takes two clock cycles to complete.

Key words: quadratic interpolation, elementary function, low cost, single precision, deformation, reuse

中图分类号: 

• TP311