机载 RISC FPU 中基本算术运算算法研究与实现

Improved Algorithms for Basic Arithmetic Operations in Airborne RISC FPU

根据实际科研工作的需要 ,进行浮点部件 NRS FPU中基本算术运算算法的研究与实现。对完成指数和尾数加减的回绕进位加法器算法进行了详细的分析。同时 ,对尾数乘运算的改进BOOTH算法进行改造 ,改进了 BOOTH的译码表 ,在 BOOTH译码过程中省掉了数据符号位的保存和参与 ,简化了乘运算实现的逻辑复杂度。最后 ,提出了新的扩展 GOLDSCHMIDT算法 ,有效减少 GOLDSCHMIDT算法的乘运算次数 ,提高了运算速度。另外 ,对浮点的加、减、乘。

The performance of Airborne RISC FPU depends on the latency of basic arithmetic operations. The existing algorithms for basic arithmetic operations are too complicated in implementation. We present improved algorithms which are suitable for the fabrication process in China. Our main contribution lies in the improvement of Goldschmidt division algorithm which is discussed in detail in subsection 2.3. In Goldschmidt algorithm, the scaling factor is always 1+X , seeing the divisor as 1-X . But we provide choices of scaling factors. These factors are determined by a “trying principle” which is based on Theorem 1. The speed of Goldschmidt algorithm is determined by the scaling factor. So the converging speed of our improved algorithm is adjustable by selecting different scaling factors according to requirements for precision. Our improved algorithm has been implemented in an airborne RISC FPU. Simulation shows that our improved Goldschmidt algorithm is much faster than the conventional one.