In range analysis (RA), suitable integer bit-widths are assigned to the variables so that no overflow occurs. Although the accuracy in RA rather than error analysis has more impact on hardware cost and efficiency, there are few works that offer new approaches to improve RA. Arithmetic functions, mostly represented by polynomials, are normally suitable for both optimization and verification purposes. In this paper, a safe and more accurate RA of feed-forward fixed-point polynomial data-flow graphs is proposed. The method employs particular features of RA and maps it to a specific class of polynomial optimization problems. The proposed method provides tighter ranges while taking less runtime in comparison with satisfiability-modulo theory-based method. Furthermore, the improved ranges lead to enhance the area and delay efficiency more than 50% and 24%, respectively, when the circuits are implementing the functions in comparison with the state-of-the-art techniques.

In this brief, we propose three efficient three-input XOR/XNOR circuits as the most significant blocks of digital systems with a new systematic cell design methodology (SCDM) in hybrid-CMOS logic style. SCDM, which is an extension of CDM, plays the essential role in designing efficient circuits. At first, it is deliberately given priority to general design goals in a base structure of circuits. This structure is generated systematically by employing binary decision diagram. After that, concerning high flexibility in design targets, SCDM aims to specific ones in the remaining three steps, which are wise selections of basic cells and amend mechanisms, as well as transistor sizing. In the end, the resultant three-input XOR/XNORs enjoy full-swing and fairly balanced outputs. They perform well with supply voltage scaling, and their critical path contains only two transistors. They also outperform their counterparts exhibiting 27%-77% reduction in average energy-delay product in HSPICE simulation based on TSMC 0.13-μm technology. The symmetric schematic topologies significantly simplify and minimize the layout, as 26%-32% improvement in area is demonstrated.