scholarly journals Floating-point profiling of ACTS using Verrou

2019 ◽  
Vol 214 ◽  
pp. 05025
Author(s):  
Hadrien Grasland ◽  
François Févotte ◽  
Bruno Lathuilière ◽  
David Chamont
Keyword(s):  
Iterative Methods ◽  
Numerical Stability ◽  
Scientific Computing ◽  
Floating Point ◽  
Track Reconstruction ◽  
Dual Purpose ◽  
Dynamic Instrumentation

Floating-point computations play a central role in scientific computing. Achieving high numerical stability in these computations affects not just correctness, but also computing efficiency, by accelerating the convergence of iterative methods and expanding the available choices of precision. The ACTS project aims at establishing an experiment-agnostic track reconstruction toolkit. It originates from the ATLAS Run2 tracking software and has already received strong adoption by FCC-hh. It is also being evaluated for possible use by the CLICdp and Belle 2 experiments. In this study, Verrou, a Valgrind-based tool for dynamic instrumentation of floating-point computations, was applied to the ACTS codebase for the dual purpose of evaluating its numerical stability and investigating possible avenues for use of reduced-precision arithmetic.

scholarly journals Confidence Intervals for Stochastic Arithmetic

2021 ◽  
Vol 47 (2) ◽  
pp. 1-33
Author(s):  
Devan Sohier ◽  
Pablo De Oliveira Castro ◽  
François Févotte ◽  
Bruno Lathuilière ◽  
Eric Petit ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Uncertainty Quantification ◽  
Case Studies ◽  
Confidence Intervals ◽  
Scientific Computing ◽  
Floating Point ◽  
Stochastic Arithmetic ◽  
Quantity Of Interest ◽  
Normally Distributed

Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results. In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and code_aster.

Quantum algorithms and circuits for scientific computing

2016 ◽  
Vol 16 (3&4) ◽  
pp. 197-236
Author(s):  
Mihir K. Bhaskar ◽  
Stuart Hadfield ◽  
Anargyros Papageorgiou ◽  
Iasonas Petras
Keyword(s):  
Scientific Computing ◽  
Quantum Algorithms ◽  
Numerical Error ◽  
Floating Point ◽  
Square Root ◽  
Fractional Powers ◽  
Worst Case ◽  
Natural Logarithm ◽  
Performance Guarantees ◽  
Numerical Software

Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. We present quantum algorithms and circuits for computing the square root, the natural logarithm, and arbitrary fractional powers. We provide performance guarantees in terms of their worst-case accuracy and cost. We further illustrate their performance by providing tests comparing them to the respective floating point implementations found in widely used numerical software.

scholarly journals Improving Accuracy for Matrix Multiplications on GPUs

2011 ◽  
Vol 19 (1) ◽  
pp. 3-11
Author(s):  
Matthew Badin ◽  
Lubomir Bic ◽  
Michael Dillencourt ◽  
Alexandru Nicolau
Keyword(s):  
Numerical Computation ◽  
Scientific Computing ◽  
Matrix Multiplication ◽  
Floating Point ◽  
Double Precision ◽  
Rounding Errors ◽  
Current Generation ◽  
Original Algorithm ◽  
Improving Accuracy

Reproducibility of an experiment is a commonly used metric to determine its validity. Within scientific computing, this can become difficult due to the accumulation of floating point rounding errors in the numerical computation, greatly reducing the accuracy of the computation. Matrix multiplication is particularly susceptible to these rounding errors which is why there exist so many solutions, ranging from simulating extra precision to compensated summation algorithms. These solutions however all suffer from the same problem, abysmal performance when compared against the performance of the original algorithm. Graphics cards are particularly susceptible due to a lack of double precision on all but the most recent generation graphics cards, therefore increasing the accuracy of the precision that is offered becomes paramount. By using our method of selectively applying compensated summation algorithms, we are able to return a whole digit of accuracy on current generation graphics cards and potentially two digits of accuracy on the newly released “fermi” architecture. This is all possible with only a 2% drop in performance.

scholarly journals What Can Students Learn While Solving Colebrook’s Flow Friction Equation?

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 114 ◽  
Author(s):  
Dejan Brkić ◽  
Pavel Praks
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Iterative Methods ◽  
Special Functions ◽  
Floating Point ◽  
Numerical Examples ◽  
Flow Friction ◽  
Newton Raphson ◽  
The Difference ◽  
Fixed Point Iterative Method

Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton–Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Padé polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers.

scholarly journals Use cases of lossy compression for floating-point data in scientific data sets

2019 ◽  
Vol 33 (6) ◽  
pp. 1201-1220 ◽  
Author(s):  
Franck Cappello ◽  
Sheng Di ◽  
Sihuan Li ◽  
Xin Liang ◽  
Ali Murat Gok ◽  
...  
Keyword(s):  
High Performance ◽  
Scientific Computing ◽  
Lossy Compression ◽  
Scientific Data ◽  
Use Cases ◽  
Floating Point ◽  
Data Sets ◽  
Use Case ◽  
Computing Systems ◽  
Point Data

Architectural and technological trends of systems used for scientific computing call for a significant reduction of scientific data sets that are composed mainly of floating-point data. This article surveys and presents experimental results of currently identified use cases of generic lossy compression to address the different limitations of scientific computing systems. The article shows from a collection of experiments run on parallel systems of a leadership facility that lossy data compression not only can reduce the footprint of scientific data sets on storage but also can reduce I/O and checkpoint/restart times, accelerate computation, and even allow significantly larger problems to be run than without lossy compression. These results suggest that lossy compression will become an important technology in many aspects of high performance scientific computing. Because the constraints for each use case are different and often conflicting, this collection of results also indicates the need for more specialization of the compression pipelines.

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