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Integer Representation of Decimal Numbers for Exact Computations.

Javier Bernal1, Christoph Witzgall1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.

Journal of Research of the National Institute of Standards and Technology
|June 9, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a method to convert decimal numbers stored as floating-point values into integers for exact arithmetic operations. This approach ensures precision for calculations involving specific decimal number formats.

Keywords:
Delaunay triangulationVoronoi diagramcomputational geometryexact integer arithmeticpower diagramregular triangulationrobustness

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Area of Science:

  • Computer Science
  • Numerical Analysis

Background:

  • Double precision floating-point numbers are commonly used in computing but can introduce precision errors in decimal arithmetic.
  • Exact computation with decimal numbers is crucial in financial and scientific applications.

Purpose of the Study:

  • To present a scheme and software for exact decimal number arithmetic.
  • To enable precise calculations with decimal numbers stored as floating-point values.

Main Methods:

  • Representing decimal numbers as integers by rounding their floating-point representations.
  • Implementing multiplication, addition, and subtraction operations on these integer representations.
  • Applying constraints on the number of digits to the left of the decimal point and the total number of significant digits.

Main Results:

  • The developed scheme allows for exact arithmetic operations on decimal numbers.
  • The software facilitates the conversion and manipulation of these numbers with guaranteed precision.
  • The method is applicable to decimal numbers with up to nine digits before the decimal point, with specific rounding rules.

Conclusions:

  • The presented integer-based scheme effectively overcomes precision limitations of standard floating-point arithmetic for decimal numbers.
  • This method provides a reliable approach for exact decimal computations within defined numerical constraints.