Lightweight, highest performance BigInteger library for Luau

AptInt is THE fastest luau implementation of BigInteger, designed for working with numbers over 10,000 digits long.

Overview

This library provides arbitrary precision arithmetic capabilities implemented in just Luau. It uses a 2^24 word size to store numbers and can easily be configured to your liking.

This library provides:

• Functionality for all arithmetic operations (:AddRaw() :SubtractRaw() :MultiplyRaw() :DivideRaw() :PowRaw() :ModRaw() :sqrt())
• Comparison functions (:LowerThanRaw() :EqualsRaw() :LowerOrEqualToRaw())
• Metamethod support (+ - * / ^ % < <= == >= =)
• Limb-wise Left shift and right shift
• Conversion functions (:ToString() :ToNumber())
• Extra utilities such as (:Abs() :Min() :Max())

The implementations are as performant as possible, so they have no safety checks, with the exception of the metamethods.

Usage

Usage Documentation can be found here.
Algorithm choice can be found here.

What makes it so fast?

AptInt uses the Karatsuba and Toom-Cook3 algorithms for multiplication, Knuths algorithm D for division, Karatsuba sqrt for finding the square root and more. Alongside these algorithms, it uses many techniques to shave off hundreds of milliseconds of computing time.

It also utilizes the full power of native code generation to get even faster results.

Benchmarks

Note that these were done on an i7-10750H CPU. The benchmark script can be found in /bench/.
The results are updated every time the performance gets improved. They are also generally ~1.3x faster if running on the roblox server.
For division, we do a 2NxN division. (2N = digit count)

Raw

Digit count	Addition	Subtraction	Multiplication	Division	Square root
1	1μs	1μs	1μs	2μs	29μs
50	1μs	3μs	4μs	11μs	31μs
100	2μs	7μs	6μs	15μs	73μs
500	5μs	9μs	56μs	28μs	250μs
1,000	7μs	13μs	173μs	58μs	357μs
5,000	23μs	30μs	1ms	195μs	796μs
10,000	57μs	74μs	4ms	1ms	2ms
50,000	209μs	243μs	46ms	38ms	35ms
100,000	389μs	396μs	137ms	114ms	89ms