# 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](https://perl.plover.com/classes/cftalk/INFO/gosper.txt): 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.