IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division

被引：1

作者：

Wei, Jianglin ^{[1
]}

Kuwana, Anna ^{[1
]}

Kobayashi, Haruo ^{[1
]}

Kubo, Kazuyoshi ^{[2
]}

机构：

[1] Gunma Univ, Div Elect & Informat, Kiryu, Gumma 3768515, Japan

[2] Oyama Natl Coll Technol, Oyama 3230806, Japan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2022年 / E105A卷 / 07期

关键词：

floating-point; logarithm; Taylor-series expansion; digital arithmetic;

D O I：

10.1587/transfun.2021EAP1076

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log(2)x) 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) = log(2)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-o ffs 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.

引用

页码：1020 / 1027

页数：8

共 3 条

[1] Floating-Point Square Root Calculation Algorithm Based on Taylor-Series Expansion and Region Division
Wei, Jianglin
Kuwana, Anna
Kobayashi, Haruo
Kubo, Kazuyoshi
Tanaka, Yuuki
2021 IEEE INTERNATIONAL MIDWEST SYMPOSIUM ON CIRCUITS AND SYSTEMS (MWSCAS), 2021, : 774 - 778
[2] Revisit to Floating-Point Division Algorithm Based on Taylor-Series Expansion
Wei, Jianglin
Kuwana, Anna
Kobayashi, Haruo
Kubo, Kazuyoshi
APCCAS 2020: PROCEEDINGS OF THE 2020 IEEE ASIA PACIFIC CONFERENCE ON CIRCUITS AND SYSTEMS (APCCAS 2020), 2020, : 240 - 243
[3] Floating-Point Inverse Square Root Algorithm Based on Taylor-Series Expansion
Wei, Jianglin
Kuwana, Anna
Kobayashi, Haruo
Kubo, Kazuyoshi
Tanaka, Yuuki
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2021, 68 (07) : 2640 - 2644

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