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 many asymptotically fast algorithms and dispatches between them based on input size. Alongside this, tables are recycled to their fullest potential, bringing the allocation count low. It also utilizes the full power of native code generation. This makes real use be very fast.

Benchmarks

Note that these were done on a Ryze 9 8940HX CPU @ 4.5GHz. The benchmark script can be found in /bench/.
The results are updated every time the performance gets improved.
For division, we do a 2NxN division. (2N = digit count)

Raw

Digit count	Addition	Subtraction	Multiplication	Division	Square root
1	27ns	20ns	158ns	105ns	9μs
50	400ns	600ns	476ns	846ns	27μs
100	500ns	700ns	1μs	2μs	73μs
500	2μs	1μs	23μs	14μs	143μs
1,000	3μs	3μs	111μs	47μs	299μs
5,000	11μs	18μs	1ms	195μs	796μs
10,000	21μs	24μs	3ms	1ms	2ms
50,000	102μs	222μs	46ms	38ms	28ms
100,000	387μs	310μs	122ms	114ms	87ms