Hacker’s Multiple-Precision Integer-Division Program in Close Scrutiny

2019 ◽  
pp. 376-391
Author(s):  
Jyrki Katajainen
Keyword(s):  
Multiple Precision ◽  
Integer Division

Efficient multiple-precision integer division algorithm

2014 ◽  
Vol 114 (3) ◽  
pp. 152-157
Author(s):  
Debapriyay Mukhopadhyay ◽  
Subhas C. Nandy
Keyword(s):  
Division Algorithm ◽  
Multiple Precision ◽  
Integer Division

NUMERICAL ANALYSIS OF CFRP STRENGTHENED STEEL MEMBER USING MULTIPLE PRECISION ARITHMETIC

2018 ◽  
Vol 74 (2) ◽  
pp. I_23-I_31
Author(s):  
Kensuke KASAYUKI ◽  
Hiroaki T-KANEKIYO ◽  
Toshiyuki ISHIKAWA ◽  
Hiroshige DAN
Keyword(s):  
Numerical Analysis ◽  
Multiple Precision ◽  
Multiple Precision Arithmetic

Synthesis of Single-Input and Multiple-Output Port Mechanisms with Springs for Specified Energy Absorption

1994 ◽  
Vol 116 (3) ◽  
pp. 937-943 ◽  
Author(s):  
J. G. Jenuwine ◽  
A. Midha
Keyword(s):  
Energy Absorption ◽  
Output Port ◽  
Constant Force ◽  
Plane Symmetry ◽  
Multiple Precision ◽  
Linear Spring ◽  
Single Input ◽  
Force Mechanism ◽  
Closure Method ◽  
Constant Force Mechanism

A means of synthesis of single-input and multiple-output port mechanisms for specified energy absorption is formulated for multiple precision points. The synthesis presented makes use of an extension of the loop closure method which includes expressions for energy absorption by linear spring elements. The configuration considered locates spring elements at two output ports of a multi-loop, planar mechanism. Economies realized for the symmetric mechanism are discussed for both one- and two-plane symmetry. Synthesis examples are included for both the general and symmetric mechanism. Special applications presented include synthesis of a constant force mechanism and synthesis of a mechanism suited to the energy absorption requirements of an automotive crashworthiness system.

scholarly journals Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon

2018 ◽  
Vol 10 (8) ◽  
pp. 2749
Author(s):  
Qi Wang ◽  
Fenzhen Su ◽  
Yu Zhang ◽  
Huiping Jiang ◽  
Fei Cheng
Keyword(s):  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Effective Means ◽  
Slope Aspect ◽  
Change Rate ◽  
Local Slope ◽  
Evaluation Approach ◽  
Multiple Precision ◽  
Surface Models ◽  
Reconstructed Surface

In addition to remote-sensing monitoring, reconstructing morphologic surface models through interpolation is an effective means to reflect the geomorphological evolution, especially for the lagoons of coral atolls, which are underwater. However, which interpolation method is optimal for lagoon geomorphological reconstruction and how to assess the morphological precision have been unclear. To address the aforementioned problems, this study proposed a morphological precision index system including the root mean square error (RMSE) of the elevation, the change rate of the local slope shape (CRLSS), and the change rate of the local slope aspect (CRLSA), and introduced the spatial appraisal and valuation approach of environment and ecosystems (SAVEE). In detail, ordinary kriging (OK), inverse distance weighting (IDW), radial basis function (RBF), and local polynomial interpolation (LPI) were used to reconstruct the lagoon surface models of a typical coral atoll in South China Sea and the morphological precision of them were assessed, respectively. The results are as follows: (i) OK, IDW, and RBF exhibit the best performance in terms of RMSE (0.3584 m), CRLSS (51.43%), and CRLSA (43.29%), respectively, while with insufficiently robust when considering all three aspects; (ii) IDW, LPI, and RBF are suitable for lagoon slopes, lagoon bottoms, and patch reefs, respectively; (iii) The geomorphic decomposition scale is an important factor that affects the precision of geomorphologic reconstructions; and, (iv) This system and evaluation approach can more comprehensively consider the differences in multiple precision indices.

scholarly journals Strength Reduction of Integer Division and Modulo Operations

2003 ◽  
pp. 254-273 ◽  
Author(s):  
Jeffrey Sheldon ◽  
Walter Lee ◽  
Ben Greenwald ◽  
Saman Amarasinghe
Keyword(s):  
Strength Reduction ◽  
Integer Division

scholarly journals Multiple-Precision BLAS Library for Graphics Processing Units

2020 ◽  
Author(s):  
Konstantin Isupov ◽  
Vladimir Knyazkov
Keyword(s):  
Graphics Processing Units ◽  
Arithmetic Operation ◽  
Number System ◽  
Residue Number System ◽  
Floating Point ◽  
Data Types ◽  
Rounding Errors ◽  
Multiple Precision ◽  
Graphics Processing ◽  
Point Arithmetic

The binary32 and binary64 floating-point formats provide good performance on current hardware, but also introduce a rounding error in almost every arithmetic operation. Consequently, the accumulation of rounding errors in large computations can cause accuracy issues. One way to prevent these issues is to use multiple-precision floating-point arithmetic. This preprint, submitted to Russian Supercomputing Days 2020, presents a new library of basic linear algebra operations with multiple precision for graphics processing units. The library is written in CUDA C/C++ and uses the residue number system to represent multiple-precision significands of floating-point numbers. The supported data types, memory layout, and main features of the library are considered. Experimental results are presented showing the performance of the library.

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