Delay-optimized implementation of IEEE floating-point addition

Abstract—We present an IEEE floating-point adder (FP-adder) design. The adder accepts normalized numbers, supports all four IEEE rounding modes, and outputs the correctly normalized rounded sum/difference in the format required by the IEEE Standard. The FP-adder design achieves a low latency by combining various optimization techniques such as: A nonstandard separation into two paths, a simple rounding algorithm, unification of rounding cases for addition and subtraction, sign-magnitude computation of a difference based on one’s complement subtraction, compound adders, and fast circuits for approximate counting of leading zeros from borrow-save representation. We present technology-independent analysis and optimization of our implementation based on the Logical Effort hardware model and we determine optimal gate sizes and optimal buffer insertion. We estimate the delay of our optimized design at 30.6 FO4 delays for double precision operands (15.3 FO4 delays per stage between latches). We overview other IEEE FP addition algorithms from the literature and compare these algorithms with our algorithm. We conclude that our algorithm has shorter latency (-13 percent) and cycle time (-22 percent) compared to the next fastest algorithm. Index Terms—Floating-point addition, IEEE rounding, delay optimization, dual path algorithm, logical effort, optimized gate sizing, buffer insertion.