The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cet article, un algorithme basé sur le développement en série de Taylor est proposé pour calculer le logarithme (enregistrer2x) d'un nombre à virgule flottante de précision binaire754 IEEE32 par une méthode de partitionnement multi-domaine. La mantisse générale (1≤x<2) est multiplié par 2, 4, 8,… (ou de manière équivalente décalée vers la gauche de 1, 2, 3,… bits), les régions de (2≤x<4), (4≤x<8), (8≤x<16),… sont pris en compte et le développement en série de Taylor est appliqué. Dans ces régions, la pente de f(x)=journal2 x par rapport à x est doux par rapport à la région de (1≤x<2), ce qui réduit le nombre de termes requis. Nous considérons également les compromis entre le nombre d'additions, de soustractions et de multiplications et la taille de la table de consultation (LUT) dans le matériel afin de sélectionner le meilleur algorithme pour la conception de l'ingénieur et de construire le meilleur périphérique matériel.
Jianglin WEI
Gunma University
Anna KUWANA
Gunma University
Haruo KOBAYASHI
Gunma University
Kazuyoshi KUBO
Oyama National College of Technology
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copier
Jianglin WEI, Anna KUWANA, Haruo KOBAYASHI, Kazuyoshi KUBO, "IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 7, pp. 1020-1027, July 2022, doi: 10.1587/transfun.2021EAP1076.
Abstract: In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1076/_p
Copier
@ARTICLE{e105-a_7_1020,
author={Jianglin WEI, Anna KUWANA, Haruo KOBAYASHI, Kazuyoshi KUBO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division},
year={2022},
volume={E105-A},
number={7},
pages={1020-1027},
abstract={In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.},
keywords={},
doi={10.1587/transfun.2021EAP1076},
ISSN={1745-1337},
month={July},}
Copier
TY - JOUR
TI - IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1020
EP - 1027
AU - Jianglin WEI
AU - Anna KUWANA
AU - Haruo KOBAYASHI
AU - Kazuyoshi KUBO
PY - 2022
DO - 10.1587/transfun.2021EAP1076
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2022
AB - In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.
ER -