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Efficient implementation of elementary functions in the medium-precision range [article]

Fredrik Johansson
2015 arXiv   pre-print
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

Fredrik Johansson
2015 2015 IEEE 22nd Symposium on Computer Arithmetic  
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

Eduard Kuriscak, Zdenek Wunsch, Petr Marsalek
2015 BMC Neuroscience  
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

Dmitrii Kouznetsov
2013 Optical Review  
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]

Farah Benmouhoub, Pierre-Loic Garoche, Matthieu Martel
2022 Lecture Notes in Computer Science  
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

Rihards Novickis, Daniels Jānis Justs, Kaspars Ozols, Modris Greitāns
2020 Electronics  
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

Nicolas Brunie, Florent de Dinechin, Olga Kupriianova, Christoph Lauter
2015 2015 IEEE 22nd Symposium on Computer Arithmetic  
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

Tibor Busznyák, István Lakatos
2020 Hungarian Journal of Industry and Chemistry  
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

Masoud Sadeghian, James Stine, E. Walters
2016 Electronics  
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

Hossein Vafaeenezhad, Seyed Mojtaba Zebarjad, Jalil Vahdati Khaki
2011 Advanced Materials Research  
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]

Markus Grimmer, Knut Petras, Nathalie Revol
2004 Lecture Notes in Computer Science  
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]

Benjamin Apffel, Emmanuel Fort
2021 arXiv   pre-print
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

Mohanaprasad Kothandaraman, Jeet Pawani, Arulmozhivarman Pachaiyappan, Sankar Sankaran
2017 International Journal of Intelligent Engineering and Systems  
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?

N. Facchi, F. Gringoli, D. Malone, P. Patras
2016 2016 IEEE 17th International Symposium on A World of Wireless, Mobile and Multimedia Networks (WoWMoM)  
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

Eero Sormunen
2000 Proceedings of the 23rd annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR '00  
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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