Online Alignment and Addition in Multi-Term Floating-Point Adders

TL;DR

This paper introduces a novel online algorithm for multi-term floating-point addition that enables parallel processing of alignment and addition, leading to significant improvements in delay, area, and power efficiency.

Contribution

It proposes a new online, associative operator-based algorithm for parallel multi-term floating-point addition, improving efficiency over traditional serial methods.

Findings

Area savings of up to 23%

Power savings of up to 26%

Delay improvements in multi-term adders

Abstract

Multi-term floating-point addition appears in vector dot-product computations, matrix multiplications, and other forms of floating-point data aggregation. A critical step in multi-term floating point addition is the alignment of fractions of the floating-point 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 multi-term floating point adders can improve delay or save significant area and power. The achieved area and power savings range between 3%-23% and 4%-26%, respectively.