On RNS with VLSI-friendly diagonal function

Chervyakov, Nikolay I.; Lyakhov, Pavel; Semyonova, Nataliya; Valueva, Maria

doi:10.1109/sibircon.2017.8109854

Cited by 1 publication

(3 citation statements)

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“…Step 2. Given a pair ( 1 , 2 ), find 1 , 2 , and as 7requires and check whether the conditions 2 > 1 (see (8)) and ( , ) = 1 are satisfied; otherwise consider next pair.…”

Section: B Two Odd and One Evenmentioning

confidence: 99%

“…One way to implement non-modular operations in RNS is to use a diagonal function from [7][8][9][10] requiring division with the remainder by the diagonal module SQ. Division with a remainder in the general case is the most complex arithmetic operation in computer technology.…”

Section: Introductionmentioning

confidence: 99%

“…Under the condition = 2 − 1 the remainder of the division by SQ is calculated as the sum of the k-bit parts of the dividend modulo SQ [11]. Algorithms for RNS constructing with special SQ forms based on number-theoretical properties are presented in [7] and [8]. The main drawbacks of those algorithms is the impossibility of RNS construction with predetermined dynamic ranges as well as obtaining unbalanced RNSs (with too much difference in modules bit-width) in most cases.…”

Section: Introductionmentioning

confidence: 99%

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Classification of Moduli Sets for Residue Number System With Special Diagonal Functions

et al. 2020

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The paper presents algorithms for the generation of Residue Number System (RNS) triples with = 2 − 1 and quadruples with = 2 for some k. Triples and quadruples allow us to design efficient hardware implementations of non-modular operations in RNS such as division, sign detection, comparison of numbers, reverse conversion with using of a diagonal function from requiring division with the remainder by the diagonal module SQ. Division with a remainder in the general case is the most complex arithmetic operation in computer technology. However, the consideration of special cases can significantly simplify this operation and increase the efficiency of hardware implementation. We show that there are 5573 good RNS triples (2301 even and 2372 odd) with elements less than 10 000, as the values of SQ vary from 2 5 − 1 to 2 27 − 1. In contrast, RNS quadruples with = 2 seem to be quite rare. Restricting our search to sums of the elements in a quadruple less than 4000 we find that exactly 31 such quadruples exist. Their values of SQ vary between 2 20 and 2 30 with always even exponent. We suggest the measure of RNS balance and find perfectly balanced RNS among triples according to this measure. We demonstrate the advantages of more balanced quadruples by means of hardware implementation.

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“…Step 2. Given a pair ( 1 , 2 ), find 1 , 2 , and as 7requires and check whether the conditions 2 > 1 (see (8)) and ( , ) = 1 are satisfied; otherwise consider next pair.…”

Section: B Two Odd and One Evenmentioning

confidence: 99%