Why and How to Use Arbitrary Precision

@article{Ghazi2010WhyAH,
  title={Why and How to Use Arbitrary Precision},
  author={Kaveh R. Ghazi and Vincent Lef{\`e}vre and Philippe Th{\'e}veny and Paul Zimmermann},
  journal={Comput. Sci. Eng.},
  year={2010},
  volume={12},
  pages={5}
}
Although double precision is usually enough, arbitrary precision increases accuracy and the reproducibility of floating-point computations. 
Reliable Computing with GNU MPFR
This article presents a few applications where reliable computations are obtained using the GNU MPFR library.
Arbitrary Precision Complex Interval Computations in C-XSC
TLDR
The new package allows to code mathematical expressions for the complex interval data type in their usual mathematical notation yielding easy to read and self-documenting source code and more than 30 elementary mathematical functions have been realized.
Easing development of precision-sensitive applications with a beyond-quad-precision library
  • C. Lauter
  • Computer Science
    2015 49th Asilomar Conference on Signals, Systems and Computers
  • 2015
TLDR
The libwidefloat software is proposed, which offers precisions from 64 through 512 bits, and supports all basic operations (+, -, ×, /, FMA, comparisons etc.) It is fully implemented in header files for automatic optimization.
A Modular-Positional Computation Technique for Multiple-Precision Floating-Point Arithmetic
TLDR
This paper deals with a new technique of multiple-precision computations, based on the use of modular-positional floating-point format for representation of numbers, thus enabling high-speed processing of the significands with possible parallelization by RNS modules.
An Arbitrary Precision Integer Arithmetic Library for FPGA s
TLDR
The intent of this thesis work is to support application programmers using FPGAs with an arbitrary precision (integer) arithmetic logic so that a user can implement cryptographic algorithms like RSA, AES etc.
Extending Summation Precision for Network Reduction Operations
TLDR
Fixed-point representations of double precision variables that enable arbitrarily large summations without error and provide exact and reproducible results are proposed, which are called big integer (BigInt).
Automatic Generation of Code for the Evaluation of Constant Expressions at Any Precision with a Guaranteed Error Bound
  • S. Chevillard
  • Computer Science
    2011 IEEE 20th Symposium on Computer Arithmetic
  • 2011
TLDR
An algorithm is presented that takes as input a constant formula and that automatically produces code for evaluating it in arbitrary precision with a rigorous error bound and has been implemented in the Solly a free software tool.
Evaluating a constant expression in multiple precision with a guaranteed error bound
TLDR
An algorithm is presented that takes as input a constant formula and that automatically produces code for evaluating it in arbitrary precision with a rigorous error bound and has been implemented in the Sollya free software tool.
High-accuracy numerical integration methods for fractional order derivatives and integrals computations
. In this paper the authors present highly accurate and remarkably efficient computational methods for fractional order derivatives and integrals applying Riemann-Liouville and Caputo formulae: the
...
...

References

SHOWING 1-5 OF 5 REFERENCES
MPFR: A multiple-precision binary floating-point library with correct rounding
This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas
Revision of ANSI-IEEE Standard 754-1985
  • Revision of ANSI-IEEE Standard 754-1985
  • 2008
Test of mathematical functions of the standard C library
  • Test of mathematical functions of the standard C library
Constant folding
  • Constant folding