Arbitrary precision integer library for AutoHotkey v2 (alpha)

• Be easy to use, straightforward, consistent, accurate, and fast
• Ensure accuracy and validity through unit tests
• Any base as input and output (given char list of course)
• Include as many functions as possible & reasonable for an integer lib
• Pure AHK(2) solution. Not rely on third-party extensions, binaries, dll, or web requests to Wolfram|Alpha.

These are the requirements for all changes.

• A user function may NOT modify this or any args passed. Use obj.clone() or new BigInt(...) instead, and return a different BigInt object
• Any additions or changes to the library must pass all current unit tests, include unit tests relevant to the change, AND prove that it does not modify the original objects. (see BigIntUnitTest.ahk2 for examples)
• If possible, accept arguments that can be either BigInt instances OR normal ahk numbers.
• User functions should have short names consisting only of lower-case characters, and be at least mildly self-descriptive. Internal functions, including functions that may modify this and other args, should be prefixed with one or more underscores.

• I'm considering changing it so all functions have a counterpart that does modify this. They would be prefixed with one underscore, and of course have a non-this-modifying version that acts exactly like the current functions.

Regular Math:

x := new BigInt(55)

MsgBox % x.div(new BigInt(5)).__string()  ; integer division

MsgBox % x.mult(33).__string()  ; multiplication

y := new BigInt(0x800)

MsgBox % y.shl(400).__string()  ; left shift by 400 bits

MsgBox % y.shr().__string()  ; right shift (1 is default)

Take a really big number, and square it a bunch of times:

x := new BigInt("abcdef123456789", "hex")

loop 10
    x := x.pow(2)
    
msgbox % x.__string()  ; this is a really really huge number