gosper

Continued Fraction Arithmetic

This library implements several methods for arbitrary precision continued fraction arithmetic based on Bill Gosper's inspired preprint work in the 2nd appendix of the MIT HAKMEM publication[^1], where he writes:

Abstract: Contrary to everybody, [...] continued fractions are not only perfectly amenable to arithmetic, they are amenable to perfect arithmetic.

He then goes on to describe an algorithm for producing a continued fraction representing arithmetic operations (+, -, *, /) between arbitrary continued fractions.

The main benefit of this approach is that even if the operands are non-terminating continued fractions (such as representations of transcendental numbers, e.g π), consuming enough terms of the operands can bound the next term of the result to within the range of a single integer.

In this way, the terms of the result can be read off one at a time, and computation can be discontinued when the desired accuracy is attained.