# Googology
Googlogy is the [study and nomenclature of large numbers.](https://googology.wikia.org/wiki/Googology)
This crate is focused on the latter component of that description,
and provides utilities for converting numbers of arbitrarily large size
to some natural-language description.

Currently, this crate supports two systems for naming large numbers. 

The first is the [Conway-Wechsler]((http://www.mrob.com/pub/math/largenum.html#conway-wechsler))
system, which uses names that may be familiar to English speakers, such as
million, billion, and so on... By chaining latin prefixes together (such as in
the number "one millitrillion"), it is possible it is possible to use this
system to generate a name for any number, provided one has enough memory to
store both the digits in the input, as well as the string output.

This system supports three different "scale" parameters:
* `Scale::Short` uses a modern English naming convention where each new "illion"
is scaled by powers of 1,000. The value of 10^9 is called `"one billion"`.
* `Scale::LongBritish` uses an older convention used in the UK prior to 1974.
Each new "illion" is scaled by powers of 1,000,000, and powers of 1,000 that
lie in between "illions" are prefixed with "thousand". Thus, the value of 10^9
is called `"one thousand million"`.
* `Scale::LongPeletier` uses a naming convention still in use in many European
languages. Similar to `Scale::LongBritish`, "illions" are scaled by powers of
1,000,000. However, instead of prefixing the in betweens with "thousand", they
are instead suffixed with "ard" instead of "on". Thus, the value of 10^9 is
called `"one milliard"`. 

An alternative system called the Knuth-Yllion system is also provided. Here,
rather than scaling by powers of 1,000 or powers of 1,000,000, the scaling is
instead exponential. A new name is given for each n in 10^(2^n). For example,
10^2 is one hundred, 10^4 is one myriad, and 10^8 is one myllion. For values
in between, we describe an "yllion" number with those of lesser magnitude. For
example, 10^14 would be called "one hundred myriad myllion".

Two functions are provided in each module:
* `full_name` gives a name to any arbitrary number, given a base-10 string
representation of its digits.
* `power_of_ten` gives a name to a power of ten. This can be useful for numbers
that may be so large that storing them in memory would be impossible or
otherwise impractical.