Using a prime number p of memory banks on a vector processor allows a conflict-free access for any slice of p consecutive elements of a vector stored with a stride not multiple of p. To reject the use of a prime number of memory banks, it is generally advanced that address computation for such a memory system would require systematic Euclidean division by the number p. The Chinese Remainder The...

Recently, the residue number system (RNS) has been intensively studied. The Chinese remainder theorem (CRT) is a solution to the conversion problem of a number to RNS with a general moduli set. This paper introduces the generalized CRT (GCRT) with parallel algorithms used for the conversion. The GCRT differs from the CRT because it has the advantage of having more applications than does the CRT...

Based on two isomorphisms of Hopf algebras, we provide a bound in the optimal order remainder truncated Taylor expansion for controlled differential equations driven by branched rough paths.

This paper presents a novel secret sharing system that is based on Chinese remainder theorem. This scheme deals with a concept of multiple secrets to be shared to different groups, such that each group receives shares of secret intended for it. The sharing is a threshold scheme, that is more than a fixed number of members from any particular group, will be able to reconstruct the secret and any...

In this paper, with respect to multichannel synthetic aperture radars (SAR), we first formulate the problems of Doppler ambiguities on the radial velocity (RV) estimation of a ground moving target in range-compressed domain, range-Doppler domain and image domain, respectively. It is revealed that in these problems, a cascaded time-space Doppler ambiguity (CTSDA) may encounter, i.e., time domain...

In this paper, a novel 3-moduli set { 2 − 1, 2, 2 − 1 } , which has larger dynamic range when compared to other existing 3-moduli sets is proposed. After providing a proof that this moduli set always results in legitimate RNS, we subsequently propose an associated reverse converter based on the New Chinese Remainder Theorem. The proposed reverse converter has a delay of (4n + 6)tFA with an area...

For three positive integers ai, aj , ak pairwise coprime, we present an algorithm that find the least multiple of ai that is a positive linear combination of aj , ak. The average running time of this algorithm is O(Loga1). Using this algorithm and the chinese remainder theorem leads to a direct computation of the Frobenius number f(a1, a2, a3).