Online Alignment and Addition in Multiterm Floating-Point Adders

Multiterm floating-point (FP) addition appears in vector dot-product computations, matrix multiplications, and other forms of FP data aggregation. A critical step in multiterm floating-point addition is the alignment of fractions of the FP terms before adding them. Alignment is executed serially by identifying first the maximum of all exponents and then shifting the fraction of each term according to the difference of its exponent from the maximum one. Contrary to common practice, this work proposes a new online algorithm that splits the identification of the maximum exponent, the alignment shift for each fraction, and their addition to multiple fused incremental steps that can be computed in parallel. Each fused step is implemented by a new associative operator that allows the incremental alignment and addition for arbitrary number of operands. Experimental results show that employing the proposed align-and-add operators for the implementation of multiterm floating-point adders can improve delay or save significant area and power. The achieved area and power savings range between 3% and 23% and between 4% and 26%, respectively.