Fast low energy RNS comparators for 4-moduli sets {2 ±1, 2 , m} with m∈{2+1±1, 2−1−1}

Sign Detection and Signed Integer Comparison for the 3-Moduli Set {2^n±1,2^(n+k)}

“…The absolute value of X equals M − X = 60 − 58 = 2; since X is negative, we have X = (1, 2, 3) = −2. Several approaches have attempted to develop RNS comparison methods (mostly for unsigned numbers) [3,5,10,12,[22][23][24]27]. Some other works compared signed numbers from a different perspective in which the dynamic range included both positive and negative numbers [13,20].…”

“…Such convertors are usually based on Chinese remainder theorem (CRT) [21] or mixed-radix conversion (MRC) [21]. Subsequently, there are some other comparators [2,12,24,27] that do not convert numbers completely and compare operands during the reverse-conversion process. In [10], a method for non-modular operations in RNS by summation sets of floatingpoint numbers is proposed; however, this method is efficient only on modern massively parallel general-purpose computing platforms such as GPU-based systems.…”

“…Difficult operations are often required for several nonlinear procedures, such as median and rank-order filtering [20]. Several RNS comparison [3,5,10,12,13,20,[22][23][24]27], sign-detection [9], and division [25] methods have been proposed over the past two decades. As regarding the role of comparison in other complicated operations such as division, sign, and overflow detection, it is expected that a cost-effective and high-speed implementation of the comparison will assist in improving other complicated operations.…”