Efficient RNS-to-binary conversion using high-radix SRT division

Burgess, Neil

doi:10.1049/ip-cdt:20010202

Cited by 7 publications

(2 citation statements)

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“…As evident from Table I and discussion of the examples it contains, redundant residue sets have been applied in an ad hoc fashion as tools for speeding up or simplifying circuit realizations 3,8,11,12,16,19 . Only very recently have these been explicitly recognized as redundant residues and, thus, received a unified treatment 14 .…”

Section: Consider a Modulus M Satisfyingmentioning

confidence: 99%

“…At the end, either the redundant mixed-radix number is converted to nonredundant form or it is used directly to deduce the information of interest such as sign or relative magnitude through special lookahead circuits. Table II contains a numerical example in which u = (6 -2 -2 1) RNS is converted from a 4-modulus RNS (7,5,3,2) to (1 -2 -3 1) MR in the equivalent mixed-radix format The computation is easily checked by noting that the mixed-radix number has the value 30 -12 -6 + 1 = 13. Approximate CRT decoding, and consequently approximate sign detection, can be performed with pseudoresidues in virtually the same way as with residues.…”

Section: Example 2 (Rns To Mixed-radix Conversion): Consider An Rns Rmentioning

confidence: 99%

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Application of symmetric redundant residues for fast and reliable arithmetic

Parhami

2002

SPIE Proceedings

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Despite difficulties in general division, magnitude comparison, and sign detection, residue number system arithmetic has been used for many special-purpose systems in light of its parallelism and modularity for the most common arithmetic operations of addition/subtraction and multiplication. Computation in RNS requires modular reduction, both for the initial conversion from binary to RNS and after each operation to bring the result back to within a valid residue range. Use of redundant residues simplifies this critical operation, leading to even faster arithmetic. One type of redundant mod-m residue, that keeps the representational redundancy to the minimum of 1 bit per residue, has the nearly symmetric range [-m, m) and allows two values for each pseudoresidue: 〈x〉 m or 〈x〉 m -m. We study the extent of simplification and speed-up in the modular reduction process afforded by such redundant residues and discuss its potential implications to the design of RNS arithmetic circuits. In particular, we show that besides cost and performance benefits, introduction of error checking and fault tolerance in arithmetic computations is facilitated when such redundant residues are used.

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