一种定点化平方根倒数运算的硬件实现

The Hardware Implement of Fixed-Point Reciprocal Square Root

针对平方根倒数运算电路中传统的多次迭代法占用较多运算单元,以及多项式逼近法占用大量存储单元的问题,提出一种基于分段二次项式逼近与牛顿迭代相结合的定点化平方根倒数运算的硬件实现方法。结合两种方法的优点,即运用少量存储单元存储二次多项式系数用于求解迭代初值;然后对迭代初值进行一次牛顿迭代使根快速收敛。其中,对系数及过程变量都进行定点化处理,避免复杂的浮点运算。实验结果表明,该现实方法仅需584bit存储单元及少量乘加运算单元,求解误差小。

In order to solve the problem that repeatedly iterative methods occupy more computing units and the polynomial approximation method occupies a large number of storage units, a hardware implement of fixed point reciprocal square root（RSR） based on segmented quadratic approximation formula with Newton iteration is proposed. Combining the advantages of the two methods, a quadratic polynomial coefficient is stored in a little memory cells to solve the iteration seed. Then, one time Newton iteration is performed on the iteration seed to make the root converge rapidly. In the mean time, the coefficient and process variables are fixed-point processing, to avoid complex floating-point operations. The results show that this method requires only 584 bit memory cells and a small number of multiply-add units, and the solution error is small.