Research and Optimization on Rounding Algorithms for Floating-Point Multiplier

Floating point multiplier is one of the most important floating-point calculations. The difficulty of high performance multiplier is the rounding operation after multiplying of the mantissa. After an in-depth study of the rounding algorithm based on Injection-based algorithm [1] proposed by Guy. Even and Peter-Michael. Seidel and the fast sticky bit generation algorithm [2] proposed by Robert K. Yu and Gregory B. Zyner, an efficient rounding algorithm optimization program which can meet any precision in rounding algorithm is proposed in this paper. The optimization has been verified in circuit design. In this paper, the principles and formulas of two algorithms are derived from the perspective of circuit design and the latter is proved by mathematical induction. The speed of multiplier is increased effectively.