Numbers and Computers by Ronald T. Kneusel

Author:Ronald T. Kneusel
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

With this separation of A and B into super digits we can examine the D 2n∕1n algorithm,

Algorithm D 2n∕1n

1. [Given]

A < β n B, β∕2 ≤ B < β n , n even, β is the base. Find and remainder R = A − QB.

2. [High Part]

Compute Q 1 as with remainder R 1 = [R 1, 1, R 1, 2] using algorithm D 3n∕2n .

3. [Low Part]

Compute Q 2 as with remainder R using algorithm D 3n∕2n .

4. [Return]

Return Q = [Q 1, Q 2] as the quotient and R as the remainder.

This algorithm is deceptively simple. The recursive nature of it becomes clear when we look at algorithm D 3n∕2n which in turn calls D 2n∕1n again. First we present D 3n∕2n and then we discuss them together,

Algorithm D 3n∕2n

1. [Givens]

A = [A 1, A 2, A 3] and B = [B 1, B 2] from D 2n∕1n . Find and remainder R = A − QB.

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