scholarly journals Numerical validation in quadruple precision using stochastic arithmetic

10.29007/5c91 ◽  
2018 ◽  
Author(s):  
Stef Graillat ◽  
Fabienne Jézéquel ◽  
Romain Picot ◽  
François Févotte ◽  
Bruno Lathuilière
Keyword(s):  
Double Precision ◽  
Rounding Errors ◽  
Numerical Validation ◽  
Stochastic Arithmetic ◽  
Quadruple Precision ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Significant Performance ◽  
Arbitrary Precision

Discrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been successfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision.

scholarly journals Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1370
Author(s):  
Eisa Zarei ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equation ◽  
Taylor Expansion ◽  
Expansion Method ◽  
Absolute Error ◽  
Optimal Error ◽  
Cestac Method ◽  
Stochastic Arithmetic ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Termination Criterion

The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA.

Design of quadruple precision multiplier architectures with SIMD single and double precision support

Integration ◽  
2019 ◽  
Vol 65 ◽  
pp. 163-174 ◽  
Author(s):  
Manish Kumar Jaiswal ◽  
Hayden K.-H. So
Keyword(s):  
Double Precision ◽  
Quadruple Precision

scholarly journals Research on IEEE 754 Standard Single Precision Floating Point Multipliers Designed using Urdhva Triyagbhyam Sutra of Vedic Mathematics

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2990-2993
Keyword(s):  
Floating Point ◽  
Double Precision ◽  
Single Precision ◽  
Vedic Mathematics ◽  
Quadruple Precision

Duplication of the coasting element numbers is the big activity in automated signal handling. So the exhibition of drifting problem multipliers count on a primary undertaking in any computerized plan. Coasting factor numbers are spoken to utilizing IEEE 754 modern day in single precision(32-bits), Double precision(sixty four-bits) and Quadruple precision(128-bits) organizations. Augmentation of those coasting component numbers can be completed via using Vedic generation. Vedic arithmetic encompass sixteen wonderful calculations or Sutras. Urdhva Triyagbhyam Sutra is most usually applied for growth of twofold numbers. This paper indicates the compare of tough work finished via exceptional specialists in the direction of the plan of IEEE 754 ultra-modern-day unmarried accuracy skimming thing multiplier the usage of Vedic technological statistics.

End-to-End Quality of Service in Evolved Packet Systems

2010 ◽  
pp. 361-376
Author(s):  
Wei Wu ◽  
Noun Choi
Keyword(s):  
Quality Of Service ◽  
Application Performance ◽  
Video Sharing ◽  
Short Period ◽  
Recent Emergence ◽  
Significant Performance ◽  
High Bandwidth ◽  
End To End ◽  
Mail Service

The recent emergence of new IP-based services that require high bandwidth and low service latency such as voice over IP (VoIP), video sharing, and music streaming have motivated the 3rd Generation Partnership Project (3GPP) to work on the all IP-based cellular networks called Evolved Packet System (EPS). It is challenging for EPS not only to meet the Quality of Service (QoS) requirements of new services but also to make sure the QoS of existing services not impacted. In this chapter, the authors will first present an overview of EPS, and then focus on the aspects of QoS principles and mechanisms in EPS. End-to-end QoS models have been developed to analyze the application performance in EPS. Simulation results have shown that VoIP service requires resource reservation to guarantee its QoS requirement, and e-mail service does not experience significant performance degradation even when assigned a low service priority and the system experiences short period congestion. However, web browsing performance may not be improved proportionally to the network bandwidth increase due to the inherent network probing procedure of the transport protocol.

scholarly journals Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic

2015 ◽  
Vol 317 ◽  
pp. 55-69 ◽  
Author(s):  
S. Graillat ◽  
F. Jézéquel ◽  
R. Picot
Keyword(s):  
Numerical Validation ◽  
Stochastic Arithmetic

scholarly journals Improving Weather Forecast Skill through Reduced-Precision Data Assimilation

2017 ◽  
Vol 146 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Sam Hatfield ◽  
Aneesh Subramanian ◽  
Tim Palmer ◽  
Peter Düben
Keyword(s):  
Data Assimilation ◽  
Observation Error ◽  
Double Precision ◽  
Ensemble Size ◽  
Error Statistics ◽  
Rounding Errors ◽  
Precision Data ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Computational Resources

Abstract A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain because of the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower-precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed toward, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double-, single-, and half-precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double-precision assimilation.

scholarly journals Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length

2020 ◽  
Vol 493 (3) ◽  
pp. 3932-3937 ◽  
Author(s):  
T C N Boekholt ◽  
S F Portegies Zwart ◽  
M Valtonen
Keyword(s):  
Dynamical Systems ◽  
Free Fall ◽  
Quantitative Relation ◽  
Double Precision ◽  
Planck Length ◽  
Rounding Errors ◽  
Massive Black Holes ◽  
System A ◽  
N Body Problem ◽  
Three Body

ABSTRACT Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work, we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to 5 per cent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.

scholarly journals Progress toward High-Resolution, Real-Time Radiosonde Reports

2016 ◽  
Vol 97 (11) ◽  
pp. 2149-2161 ◽  
Author(s):  
Bruce Ingleby ◽  
Patricia Pauley ◽  
Alexander Kats ◽  
Jeff Ator ◽  
Dennis Keyser ◽  
...  
Keyword(s):  
High Resolution ◽  
Real Time ◽  
Numerical Weather Prediction ◽  
Meteorological Data ◽  
Weather Prediction ◽  
Vertical Resolution ◽  
Not Given ◽  
Rounding Errors ◽  
Numerical Weather

Abstract Some real-time radiosonde reports are now available with higher vertical resolution and higher precision than the alphanumeric TEMP code. There are also extra metadata; for example, the software version may indicate whether humidity corrections have been applied at the station. Numerical weather prediction (NWP) centers and other users need to start using the new Binary Universal Form for Representation of Meteorological Data (BUFR) reports because the alphanumeric codes are being withdrawn. TEMP code has various restrictions and complexities introduced when telecommunication speed and costs were overriding concerns; one consequence is minor temperature rounding errors. In some ways BUFR reports are simpler: the whole ascent should be contained in a single report. BUFR reports can also include the time and location of each level; an ascent takes about 2 h and the balloon can drift 100 km or more laterally. This modernization is the largest and most complex change to the worldwide reporting of radiosonde observations for many years; international implementation is taking longer than planned and is very uneven. The change brings both opportunities and challenges. The biggest challenge is that the number and quality of the data from radiosonde ascents may suffer if the assessment of the BUFR reports and two-way communication between data producers and data users are not given the priority they require. It is possible that some countries will only attempt to replicate the old reports in the new format, not taking advantage of the benefits, which include easier treatment of radiosonde drift and a better understanding of instrument and processing details, as well as higher resolution.

scholarly journals NUMERICAL CALCULATION WITH ARBITRARY PRECISION

2007 ◽  
Vol 16 (09) ◽  
pp. 3045-3048
Author(s):  
B. O. RODRIGUES ◽  
L. A. C. P. DA MOTA ◽  
L. G. S. DUARTE
Keyword(s):  
Numerical Calculation ◽  
Numerical Computation ◽  
Rounding Errors ◽  
Limited Precision ◽  
Arbitrary Precision

The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect interpretation of his or her answer. In this work, we have developed a computational package to minimize this kind of error by offering arbitrary precision numbers and calculation. This is very important in Physics where we can work with numbers too small and too big simultaneously.

SOAP Notes During APPEs: Assessment of Student Performance

2019 ◽  
pp. 089719001988527
Author(s):  
Timothy Nguyen ◽  
Elaine Wong ◽  
Zhe Wang ◽  
Tamara Goldberg
Keyword(s):  
Student Performance ◽  
Objective Assessment ◽  
Pharmacy Practice ◽  
Pharmacy Students ◽  
Full Time ◽  
Institutional Review ◽  
Significant Performance ◽  
Academic Year ◽  
Time Faculty

Objectives: To evaluate and compare students’ ability to perform in each area of the subjective, objective, assessment, and plan (SOAP) note during advanced pharmacy practice experiences (APPEs) within an academic year. This study also aimed to compare the quality of SOAP notes between semesters: summer (1-3 rotation blocks), fall (4-6 rotation blocks), and spring (7-9 rotation blocks). Methods: During internal medicine and acute-care APPEs, students were required to submit a minimum of 2 SOAP notes. Each SOAP note was assessed by a full-time faculty member at a College of Pharmacy. Students were rated on the ability to perform in each area of the SOAP note using a rubric with a scale of 1 to 5 (1 = unacceptable/needs significant improvement, 5 = exemplary). This study was granted exempt approval by the Long Island University institutional review board. Results: Quality of the SOAP note summer versus fall versus spring rotations: Thirty-four SOAP notes were assessed during the summer, 48 SOAP notes were assessed during the fall, and 46 SOAP notes were assessed during the spring. Students performed similarly regardless of the semester they took for “subjective/objective, assess, and plan.” All P values were nonstatistically significant. Performance on SOAP note #1 versus SOAP note # 2: On overall rubrics for SOAP notes 1 versus SOAP notes 2, students did better on SOAP notes 2 after feedback, and an opportunity to improve was provided. There were statistically significant differences on all areas of SOAP note “subjective/objective, assess, and plan.” Conclusion: Overall, students performed adequately on the SOAP note activity during APPE rotations. Students performed similarly regardless of the semester/time when students took the APPEs during an academic year.

Sign in / Sign up

Export Citation Format

Share Document