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.