The Fundamental Operations

Abstract

The fundamental building blocks of any software package for computer arithmetic are the functions that carry out the basic operations of addition, subtraction, multiplication, and division. The efficiency of the entire package hangs on the last two of these, and for that reason great care must be taken in the selection and implementation of the associated algorithms. Fortunately, volume 2 of Donald Knuth’s classic The Art of Computer Programming contains most of what we need for this portion of the FLINT/C functions.

Thus calculation can be seen as the basis and foundation of all the arts.

—Adam Ries, Book of Calculation

And you, poor creature, you are completely useless. Look at me. Everyone needs me.

—Aesop, “The Fir and the Blackberry Bush”

There is one small prerequisite for mastering the mathemagic tricks in this chapter—you need to know the multiplication tables through 10... backward and forward.

—Arthur Benjamin, Michael B. Shermer, Mathemagics