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A VLSI structure forX(modm) operation

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Abstract

High-computing speed and modularity have made RNS-based arithmetic processors attractive for a long time, especially in signal processing, where additions and multiplications are very frequent. The VLSI technology renewed this interest because RNS-based circuits are becoming more feasible; however, intermodular operations degradate their performance and a great effort results on this topic. In this paper, we deal with the problem of performing the basic operationX(modm), that is the remainder of the integer divisionX/m, for large values of the integerX, following an approximating and correcting approach, which guarantees the correctness of the result.

We also define a structure to computeX(modm) by means of few fast VLSI binary multipliers, which is exemplified for 32-bit long numbers, obtaining a total response time lower than 200 nsec. Furthermore, such a structure is evaluated in terms of VLSI complexity and area and time figuresA=ϑ(n 2 T 2 m ) andT=ϑ(T M ) for the parameterT M in\([\log n,\sqrt n ]\) are derived. A simple positional-to-residue converter is finally presented, based on this structure; it improves some complexity results previously obtained by authors.

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Authors and Affiliations

  1. Instituto di Elettronic e Telecomunicazioni, Facoltá di Ingegneria, Universitá di Pisa, Via Diotisalvi, 2, 56100, Pisa, Italy

    Giuseppe Alia

  2. Istituto di Elaborazione dell'Informazione del Consiglio Nazionale delle Ricerche, Via S. Maria, 46, 56100, Pisa, Italy

    Enrico Martinelli

Authors
  1. Giuseppe Alia
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  2. Enrico Martinelli
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Additional information

This work has been supported by the National Program on Solid-State Electronics and Devices of the Italian National Research Council.

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Alia, G., Martinelli, E. A VLSI structure forX(modm) operation. J VLSI Sign Process Syst Sign Image Video Technol 1, 257–264 (1990). https://doi.org/10.1007/BF00929920

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  • DOI: https://doi.org/10.1007/BF00929920

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