Simple multiple precision algorithms for exponential functions
Authors:
- Leonid Moroz,
- Volodymyr Samotyy,
- Zbigniew Kokosiński,
- Paweł Gepner
Abstract
Exponential functions are essential in many areas of science and engineering. Fast and efficient computing of such functions in multiple floatingpoint formats is a complex task for all classes of processing units—general purpose CPUs, digital signal processors, GPUs, intelligent processing units, and tensor processors (TPU)—developed recently for neural computing and deep machine learning. In this article, several numerical algorithms are presented that are relatively simple and highly accurate in computing exponential functions in floating-point (FP) representations half, single, or double varying in precision. The algorithms can be easily adapted for the required accuracy level by using either polynomials of the lowest possible degree or the technique called piecewise approximation. In most cases in approximation algorithms, only low-level polynomials like square functions are applied that are computationally efficient. The characteristic feature of the proposed algorithms is using exclusively fast low-level bithack operations [bit manipulation techniques (BMT)], FP addition and multiplication as well as fused multiply-add (FMA) operation.
- Record ID
- CUTa99d2e3b944345088596c1cb8d6fa78f
- Publication categories
- ;
- Author
- Journal series
- IEEE Signal Processing Magazine, ISSN 1053-5888, e-ISSN 1558-0792
- Issue year
- 2022
- Vol
- 39
- No
- 4
- Pages
- 130-137
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 136-137; Bibliografia (liczba pozycji) - 23; Oznaczenie streszczenia - Streszcz. ang.; Numeracja w czasopiśmie - Vol. 39, Iss. 4
- Substantive notes
- Sekcja: Tips & Tricks
- Keywords in English
- machine learning algorithms, program processors, tensors, software algorithms, signal processing algorithms, machine learning, approximation algorithms
- ASJC Classification
- ; ;
- DOI
- DOI:10.1109/MSP.2022.3157460 Opening in a new tab
- URL
- https://ieeexplore.ieee.org/document/9810030 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 200
- Score source
- journalList
- Score
- Publication indicators
- Citation count
- 2
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTa99d2e3b944345088596c1cb8d6fa78f/
- URN
urn:pkr-prod:CUTa99d2e3b944345088596c1cb8d6fa78f
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.