RNS parity detection for the two-moduli set {2p - j,2p +j}

摘要

This paper presents a new parity detection technique over the type of two-moduli set T = {2p - j,2p+j} for some positive integer p satisfying gcd(p,j) = 1. Let t = (1/2P) mod j, where f is an odd number. Given an RNS number X = (x_0,x_1) on T, we show that the parity of X is (p+ 「|t| j mod 4/2 」mod 2)*(x_0+x_1) + 「(2j - |f|)x_(0⊕S(t)) + |f|x_(1⊕S(t))/2j」 mod 2, where S(t) denotes the sign bit of the number f, if x_0 ≥ x_1]. Otherwise, the parity of X is (p + 「|t| jmod 4/2」mod 2)*(x_0 + x_1) + 「(2j - |t|)x_(0⊕S(t)) + |t|x_(1⊕S(t))-1/2j」mod 2.