拡張した二重指数分割表現による数値表現法に関する研究  [in Japanese] A Study on Representation of Numbers Based on Extended Double Exponential Cut  [in Japanese]

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Author(s)

    • 富松 剛 TOMIMATSU Tsuyoshi
    • 東京大学大学院理学系研究化情報科学専攻 Department of Information Science, Faculty of Science, the University of Tokyo

Abstract

浜田の提案したURR(niversal Representation of Real number)は1から離れるに従って,急速に精度が悪化するという欠点がある.この欠点を改善するためにURRを一般化し,拡張した二重指数分割表現を提案する.URRは二重指数±2^<±2^m>で実数を大まかに近似するが,本表現では二重指数を±p^<±q^m>と一般化する.本表現により,pとqを大きくするとで,より大きな実数に対しては,より少ないビット数で近似できること,pとqを適切に選ぶことによって,URRに比べより広範囲にわたって,IEEE表現よりも精度の良い表現方法があることがわかった.さらに本表現はURRの欠点でもある急激な精度の悪化も抑えることがわかった.Precision of URR (Universal Representation of Real numbers) which was proposed by Hamada goes to the worse when the number is away from ±1. By generalizing from URR, we propose the floating point representation of the extended double exponential cut of URR. Our representation is based on the double exponential cut of ±p^<±q^m>. By selecting suitable values for p and q, we can represent numbers more precise than the IEEE representation. And our floating point representation cut can escape from the demerit in URR representation of getting worse in the precision when the number is away from ±1.

Precision of URR(Universal Representation of Real numbers) which was proposed by Hamada goes to the worse when the number is away from ±1. By generalizing from URR, we propose the floating point representation of the extended double exponential cut of URR. Our representation is based on the double exponential cut of ±p^<±q^m>. By selecting suitable values for p and q, we can represent numbers more precise than the IEEE representation. And our floating point representation cut can escape from the demerit in URR representation of getting worse in the precision when the number is away from ±1.

Journal

  • IPSJ SIG Notes

    IPSJ SIG Notes 1995(97(1995-HPC-058)), 57-62, 1995-10-18

    Information Processing Society of Japan (IPSJ)

References:  5

Cited by:  3

Codes

  • NII Article ID (NAID)
    110002932278
  • NII NACSIS-CAT ID (NCID)
    AN10463942
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • Data Source
    CJP  CJPref  NII-ELS  IPSJ 
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