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Efficient implementation of elementary functions in the medium-precision range
[article]
2015
arXiv
pre-print
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We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. ...
We collect denominators to reduce the number of divisions in the Taylor series, and avoid overhead by doing all multiprecision arithmetic using the mpn layer of the GMP library. ...
The author thanks the anonymous referees for valuable feedback. ...
arXiv:1410.7176v2
fatcat:uvp6iayr7fad5behodm564uhs4
Efficient Implementation of Elementary Functions in the Medium-Precision Range
2015
2015 IEEE 22nd Symposium on Computer Arithmetic
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We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. ...
We collect denominators to reduce the number of divisions in the Taylor series, and avoid overhead by doing all multiprecision arithmetic using the mpn layer of the GMP library. ...
The author thanks the anonymous referees for valuable feedback. ...
doi:10.1109/arith.2015.16
dblp:conf/arith/Johansson15
fatcat:4rsdu7w3qnhbfcvenhkncs3a2e
Voltage sensitive currents and information processing by single neurons
2015
BMC Neuroscience
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In order to abstract the implementation details, we theoretically estimate and recommend the useful range of time step sizes, number of compartments and computational complexity. ...
We study selected neurons in neural circuits, which have different precision of spike timing under reproducible experimental conditions. ...
Acknowledgements This work is funded by the Institutional Support for Long-term Development of Research Organizations (PRVOUK) P 24 to P. M. at the Charles University in Prague. ...
doi:10.1186/1471-2202-16-s1-p158
pmcid:PMC4697532
fatcat:4e2ljejocfcttbcvz7pwank23q
Superfunctions for amplifiers
2013
Optical Review
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In these examples, the transfer function and the distribution of the signal along the amplifier can be expressed in terms of special functions. ...
(For simplicity, distances are measured in units of the length of the amplifier.) ...
/TORI, where the high-resolution versions of the figures are presented, the C++ generators of these figures are loaded, the numerical implementations of these functions are supplied, and the algorithms ...
doi:10.1007/s10043-013-0058-6
fatcat:w6urd2qvk5d2vc6pfp7ns6jrxq
An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods
[chapter]
2022
Lecture Notes in Computer Science
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2022 pre-print arXiv:2205.05339v1 fatcat:p2vbbhivonhe5ap6y7ijog2edm
In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. ...
In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. ...
We integrated the following functions C × cos(x), C × (1/x 2 + 1) and C × tanh(x) with C = 10 6 , and b ranging in [2; 5] . The number of processors P ranges in [2; 8] . ...
doi:10.1007/978-3-030-95561-8_10
fatcat:wrldcje3kjcibdtepmnpxct2xu
An Approach of Feed-Forward Neural Network Throughput-Optimized Implementation in FPGA
2020
Electronics
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Various topologies are implemented and benchmarked, and a comparison with related work is provided. The proposed methodology is applied for the implementation of high-throughput virtual sensor. ...
Artificial Neural Networks (ANNs) have become an accepted approach for a wide range of challenges. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/electronics9122193
fatcat:kv7lzpqhrfhohjawuxq4mpwq7a
Code Generators for Mathematical Functions
2015
2015 IEEE 22nd Symposium on Computer Arithmetic
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These functions are provided by mathematical software libraries (libm), typically in IEEE754 single, double and quad precision. ...
This article discusses, with examples, the new challenges of this paradigm shift, and presents the current state of open-source function code generators. ...
Standard Mathematical Libraries The standard mathematical library (libm) provides, in a small set of precisions (simple and double precision), a small set of mathematical functions: • elementary functions ...
doi:10.1109/arith.2015.22
dblp:conf/arith/BrunieDKL15
fatcat:5dainnds2fblnkbara4lneoora
Examination of fuel consumption factors, basics of precision and on-board diagnostic measurements
2020
Hungarian Journal of Industry and Chemistry
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For the purposes of visibility, it was implemented using MAT-LAB. In statistical works, fuel consumption data require that the energy consumption of vehicles be analyzed correctly. ...
In this paper, different factors of fuel consumption are examined. Driveload equitation is used as a basis and the parts that handle energy consumption in particular are analyzed. ...
Acknowledgements This research was carried out as part of the EFOP-3.6.2-16-2017-00016 project within the framework of the New Széchenyi Plan. ...
doi:10.33927/hjic-2020-14
fatcat:qw2pavy6zbcpxd6qs3h3n7smo4
Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations
2016
Electronics
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The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). ...
Previous table-driven methods have had some success in dealing with the total hardware complexity in terms of the size of the lookup tables and the complexity of the computational units. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/electronics5020017
fatcat:irxajddll5detesx3zrlwdvbey
Fuzzy Logic Modeling of Porous Carbon Body Fabrication from Cellulose Based Materials
2011
Advanced Materials Research
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A fuzzy logic (FL) method was implemented as a powerful and accurate way for predicting the bulk density change in special tree wood samples during carbonization process. ...
The interpretation of how carbonization parameters such as heat treatment temperature, carbonization time and initial density of wood affects the final solid carbon characteristics is a fundamental step ...
It has three member functions: low, medium and high. It ranged from 350 to 550 O C. Carbonization time period, input 2, has three membership functions which are short, medium and long. ...
doi:10.4028/www.scientific.net/amr.413.122
fatcat:spo6mejbzraodmi6bukdn3udhm
Multiple Precision Interval Packages: Comparing Different Approaches
[chapter]
2004
Lecture Notes in Computer Science
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Although multiple precision interval arithmetic might help, one should be aware of the fact that this often means an increase in the computational time and memory usage, cf. section 3. ...
Before classifying softwares that implement multiple precision interval arithmetic, let us first point out the possibility to vary or not the computing precision. ...
Furthermore, the integrand contains special functions. One of them as well as elementary functions had to be evaluated in the complex plane. ...
doi:10.1007/978-3-540-24738-8_4
fatcat:cn7cdo46pbbmfjevnfkgqx7tl4
Frequency conversion cascade by crossing multiple space and time interfaces
[article]
2021
arXiv
pre-print
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As an example, we implement this concept with water waves controlled by electrostriction and achieve frequency conversion cascades over a range of 4 octaves. ...
These cycles use an intermediate medium in which wave packets enter and exit through non-commutative space and time interfaces. ...
Due to the limited efficiency of water waves reflection an amplification loop must be used to send the wave packet back into the active medium (Fig. 4b) . ...
arXiv:2105.10482v3
fatcat:upl3epbl6negfc2mknoi365dre
Acoustic Echo Cancellation Using PEVD Based Adaptive Kalman Filter
2017
International Journal of Intelligent Engineering and Systems
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Existing AEC system implemented adaptive kalman filter which results in less output efficiency in the noisy environment. ...
If the ERLE lies in the range of 30-40 dB indicates the good echo cancellation. The simulations show that the proposed PEVD based adaptive kalman method provides higher cancellation of echo. ...
Acknowledgments I thank my guide and my students who helped in all aspects for successful completion of this paper. I thank my family for support me to submit this paper. ...
doi:10.22266/ijies2017.1031.25
fatcat:i7u6w3nnozgudhrxwh7kd6hvyu
When is the right time to transmit in multi-hop White-Fi?
2016
2016 IEEE 17th International Symposium on A World of Wireless, Mobile and Multimedia Networks (WoWMoM)
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Using a small test bed, we demonstrate a prototype implementation of a medium access protocol that learns appropriate transmission opportunities in such settings, achieving pseudo-scheduled behaviour ex ...
Potential exists for the TV white-space (TVWS) wireless technology to bridge this digital divide, though efficient channel access mechanisms suited to multi-hop networks that operate in sub-gigahertz bands ...
The University of Edinburgh is authorised to reproduce and distribute reprints and online copies for their purposes notwithstanding any copyright annotation hereon. ...
doi:10.1109/wowmom.2016.7523539
dblp:conf/wowmom/FacchiGMP16
fatcat:g3qzcqvf7vh5fbdya4jrwwsex4
A novel method for the evaluation of Boolean query effectiveness across a wide operational range
2000
Proceedings of the 23rd annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR '00
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Major results of a large case experiment are reported. The validity, reliability, and efficiency of the method are considered in the light of empirical and analytical test data. ...
It is based on a controlled formulation of inclusive query plans, on an automatic conversion of query plans into elementary queries, and on combining elementary queries into optimal queries at standard ...
Calculate the efficiency list using precision values r i /n i for remaining m elementary queries and sort elementary queries in order of descending efficiency. ...
doi:10.1145/345508.345541
dblp:conf/sigir/Sormunen00
fatcat:g5tgw4ealba5ncbfxe7oifnclu
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