Floating-point dynamic-variable-range multiple-precision operators

1972 ◽  
Vol 8 (8) ◽  
pp. 191
Author(s):  
L. Frecon ◽  
L. Claire
Keyword(s):  
Floating Point ◽  
Dynamic Variable ◽  
Variable Range ◽  
Multiple Precision

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.

Low-Power Multiple-Precision Iterative Floating-Point Multiplier with SIMD Support

2009 ◽  
Vol 58 (2) ◽  
pp. 175-187 ◽  
Author(s):  
Dimitri Tan ◽  
Carl E. Lemonds ◽  
Michael J. Schulte
Keyword(s):  
Low Power ◽  
Floating Point ◽  
Multiple Precision

scholarly journals Test of the Accuracy of Approximate Methods to Handle Distant Binary-Single Star Encounters

2007 ◽  
Vol 3 (S246) ◽  
pp. 469-470
Author(s):  
Yoko Funato ◽  
D.C. Heggie ◽  
P. Hut ◽  
Jun Makino
Keyword(s):  
Numerical Experiments ◽  
Star Clusters ◽  
Floating Point ◽  
Direct Integration ◽  
Single Particles ◽  
Approximate Methods ◽  
Single Star ◽  
Distant Interactions ◽  
Weak Perturbation ◽  
Multiple Precision

AbstractIn the numerical simulations of evolution of star clusters, binary-single star interactions frequently take place. Since the direct integration of them is time consuming, distant interactions between binaries and field stars are often integrated by using some approximations. Traditionally the effect of the error caused by the approximated treatment is regarded as small enough to be ignored. However, if we have a binary-dominated core, the energy drift is large. In this study, we perform numerical experiments to evaluate the effect of neglecting the weak perturbation from distant single particles. We developed an N-body integrator which can manipulate multiple precision floating point numbers.

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