Today real numbers are most often represented by applying (elementary) functions to (decimal) integers. Throughout history, though, arithmetic and propositions involving (positive) real numbers were often considered from a purely geometrical point of view. Real numbers were identified by the length of some line segment and, e.g., the product of two numbers was identified by [...]
Posts tagged arithmetic
Implementing Multiple-Precision Arithmetic, Part 2
Introduction This article is a follow-up to part 1 where multiple-precision addition, subtraction, and multiplication for non-negative integers was discussed. This article deals with division. Again, the theoretic foundation is based on Section 4.3.1, The Classical Algorithms, of The Art of Computer Programming, Volume 2, by Donald E. Knuth.
Implementing Multiple-Precision Arithmetic, Part 1
This article is the first in a series dealing with algorithms for multiple-precision arithmetic. The goal is to present both a theoretical foundation with high-level algorithm descriptions (based on Section 4.3.1, The Classical Algorithms, of The Art of Computer Programming, Volume 2, by Donald E. Knuth) and a portable C++ implementation of the algorithms. The theory and high-level algorithms will be quite universal and generic, whereas the presented code will be just one way to implement the algorithms in a specific programming language.
)
