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Studies on combined arithmetic circuits for high-speed digital signal processing

Research Project

Project/Area Number 08680358
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionNagoya University

Principal Investigator

TAKAGI Naofumi  Nagoya University, Graduate school of Engineering, Associete Professor, 工学研究科, 助教授 (10171422)

Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1996: ¥900,000 (Direct Cost: ¥900,000)
KeywordsComputer arithmetic / Multiplication / Division / Square rooting / Multiply-addition / Powering / Modular division / Hardware algorithm / べき乗計算 / ディジタル信号処理
Research Abstract

We have developed methods for designing combined arithmetic circuits which execute consecutive addition/subtractions and multiplications appearing in degital signal processing as one operation, and also developed high-speed computing method using these circuits. The main results are as follows :
1. We have designed an add-multiply-adder which executes consecutive addition, multipli-cation and addition appearing often in degital signal processing as one operation, and shown its applications.
2. We have developed a new high-speed square rooting algorithm using a multiply-adder which executes consecutive multiplication and addition as one operation.
3. We have developed a new method for generating powers of an operand, such as recirocal, square root, reciprocal square root, reciprocal square, reciprocal cube and so on, using a multiplier with operand modifier.
4. We have developed an adder which is optimal in theory and very efficient in practice, under the assumption of left-to-righ input arrival.
5. We have developed two hardware algorithms for modular division with very large modulus which is required in cryptosystems. One is based on the extended Euclidean algorithm and the other is based on the binay GCD algorithm.
6. We have developed massively parallel algorithms for executing arithmetic operations on a functional memory and have developed a method for motion vector detection using them.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] Naofumi Takagi: "A hardware algorithm for modular division based on the extended Euclidean algorithm" IEICE Transactions on Information and Systems. E79-D,11. 1518-1522 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Square rooting by iterative multiply-additions" Information Processing Letters. 60. 267-269 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Efficient intinitial approximation for multiplicative division and square root by a multiplication with operand modification" IEEE Transactions on Computers. 46,4. 495-498 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "O(n)-depth modular exponentiation circuit algorithm" IEEE Transactions on Comupters. 46,6. 701-704 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "A VLSI algorithm for modular division based on the binary GCD algorithm" IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences. E81・A,5(5月発行予定). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Generating a power of an operand by a table look-up and a multiplication" Proceedings of the IEEE 13th Symposium on Computer Arithmetic. 126-131 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "A hardware algorithm for modular division based on the extended Euclidean algorithm" IEICE Trans. Info. & Systems. Vol.E79-D,No.11. 1518-1522 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Square Rooting by Iterative Multiply-Additions" Information Processing Letters. no.60. 267-269 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Efficient Initial Approximation for Multiplicative Division and Square Root by a Multiplication with Operand Modification" IEEE Trans. Computers. Vol.46, No.4. 495-498 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "O (n) -Depth Modular Exponentiation Circuit Algorithm" IEEE Trans. Computers. Vol.46, No.6. 701-704 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "A VLSI Algorithm for Modular Division Based on the Binary GCD Algorithm" IEICE Trans. Fundamentals. Vol.E81-A,no.5 (to appear). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Generating a Power of an Operand by a Tabie Look-up and a Multiplication" Proc.13th IEEE Symp. Computer Arithmetic. 126-131 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "A motion vector detection algorithm for moving video compression using functional memory" IEICE Technical Report. COMP96-56. (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Efficient adder under left-to-right input arrival" IEICE Technical Report. COMP97-21. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "Generation of reciprocal, square root, and so forth by means of a multiplier with an operand modifier" IEICE Technical Report. COMD5P97-112. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "A redundant basis for fast iterative multiplication on GF (2^m) and a parallel multiplier based on it." IEICE Technical Report. COMP97-83. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Naofumi Takagi: "O(n)-depth modular exponentiation circuit algorithm" IEEE Transactions on Computers. 46・6. 701-704 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Naofumi Takagi: "A VLSI algorithm for modular division based on the binary GCD algorithm" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E81・A・5(5月発行予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Naofumi Takagi: "Generating a power of an operand by a table look-up and multiplication" Proceedings of the IEEE 13th Symposium on Computer Arithmetic. 126-131 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高木直史: "上位からの時差入力下での最適並列加算器" 電子情報通信学会技術研究報告. COMP97-21. (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高木直史: "乗数変形機能付き乗算器を用いた逆数や平方根等の生成" 電子情報通信学会技術研究報告. DSP97-112. (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高木直史: "GF(2^w)上の繰り返し乗算の高速化のための冗長基底とそれを用いた並列乗算器" 電子情報通信学会技術研究報告. COMP97-83. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Naofumi Takagi: "A hardware algorithm for modular division based on the extended Euclidean algorithm" IEICE Transactions on Information and Systems. E79・D・11. 1518-1522 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Naofumi Takagi: "Square rooting by iterative multiply-additons" Information Processing Letters. 60・5. (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Naofumi Takagi: "Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification" IEEE Transactions on Computers. 46・4. (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 高木直史: "機能メモリを用いた動画像圧縮のための動きベクトル検出アルゴリズム" 電子情報通信学会技術研究報告. COMP96-56. 61-68 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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