bint

Arbitrary-precision signed integer library for Luau.

bint stores integers as little-endian base-2^24 limbs, so values can grow without fixed-width overflow. It supports idiomatic operators (+, -, *, //, %, ^, comparisons), plus a lower-level core API with mutating and non-mutating functions.

v0.3.0 renames all conversion helpers to a uniform to_*/from_* convention, adds lossy scientific-notation decomposition (to_sci), and fixes several Burnikel-Ziegler division edge cases.

Latest release: 0.3.0.

Features

• Arbitrary-precision signed integers.
• Constructors from Lua numbers, strings (base 2-36), and raw limb arrays.
• Conversion to/from strings and byte strings (little/big endian).
• Floor and truncated division APIs.
• Integer exponentiation and integer square root.
• Multiple multiplication/division algorithms chosen by operand size.
• Luau + TypeScript declaration file support (src/index.d.ts).

Usage

local mod = require(path.to.bint)
local bint = mod.bint
local core = mod.core

local a = bint("123456789012345678901234567890")
local b = bint.from_int(42)

local sum = a + b
local prod = a * b
local q, r = core.divmod(a, b) -- floor division

print(sum:to_string()) -- method form
print(bint.to_string(prod)) -- function form
print(q, r)

bint(v) is an alias for bint.new(v).

For roblox-ts / TypeScript users, the standard non-mutating arithmetic/comparison operations are also available as instance methods (for example a:add(b), a:mul(b), a:divmod(b)), which avoids relying on Luau operator metamethod syntax in typed code. Mutating operations remain on core.

API summary

Constructors

• bint.from_int(n: number): Bint (converts the current Luau number value)
• bint.from_string(s: string, base?: number): Bint
• bint.from_limbs(limbs: {number}, signum?: -1 | 0 | 1): Bint
• bint.zero(): Bint
• bint.one(): Bint
• bint.new(v: Bint | number | string): Bint
• bint(v) (callable module alias)

Conversion helpers

• bint.to_string(a: Bint, base?: number): string
• bint.to_number(a: Bint): number
• bint.to_sci(a: Bint): (number, number) — lossy scientific notation (coefficient, exponent)
• bint.to_le(a: Bint, trim?: boolean): string
• bint.to_be(a: Bint, trim?: boolean): string
• bint.from_le(s: string): Bint
• bint.from_be(s: string): Bint

core operations

core provides low-level signed arithmetic on canonical Bint values. No input coercion or validation is performed — arguments must already be Bint instances. Reach for core when you need mutating operations (_mut variants) or want to avoid repeated allocation; use the bint class for everyday ergonomic use.

• Comparison: cmp, eq, lt, le
• Sign: abs, abs_mut, neg, neg_mut
• Arithmetic: add, add_mut, sub, sub_mut, mul, mul_mut
• Division (floor): divmod, idiv, mod
• Division (truncated): tdivmod, tdiv, tmod
• Other: pow, sqrt, lshift, rshift, lshift_words, rshift_words

algorithms entry points

Direct algorithm entry points that bypass automatic threshold dispatch at the top-level call. Each function has the same contract as its core counterpart and forces the named top-level algorithm regardless of operand size; recursive subproblems may still dispatch/fallback internally. Useful for benchmarking threshold crossover points and validating specific algorithm entry paths.

• Multiplication: algorithms.mul_basecase, algorithms.mul_karatsuba, algorithms.mul_toom3
• Division: algorithms.div_knuth, algorithms.div_burnikel
• Square root: algorithms.sqrt_newton, algorithms.sqrt_karatsuba

Operator behavior

Supported metamethods:

• +, -, *, //, %, ^, unary -
• ==, <, <=
• tostring(x) and x:to_string()
• #x returns decimal digit count of magnitude

/ is intentionally unsupported and throws an error. Use // for integer division.

Semantics and caveats

• bint.from_int(n) converts the already-represented Luau number exactly; Luau numbers are IEEE-754 doubles, so integer literals above 2^53 may already be rounded. Use bint.from_string(...) for exact large integer literals.
• bint.from_string / bint.to_string support bases 2..36.
• core.divmod and // use floor division semantics.
• core.tdivmod uses truncated (toward zero) semantics.
• core.rshift(a, n) uses arithmetic (sign-preserving) semantics, equivalent to floor(a / 2^n).
• core.lshift_words / core.rshift_words are limb-count shifts (base-2^24 words), not bit shifts.
• core.sqrt(a) returns 0 for a <= 0.
• bint.to_le/bint.to_be serialize magnitude only (sign is not encoded).
• bint.to_number is exact only up to magnitude 2^53.
• bint.to_sci is lossy by design; useful for display/formatting, not exact arithmetic.

Running tests

lune run libs/specs                       # full suite (all tags)
lune run libs/specs --tag fast            # quick local validation
lune run libs/specs --tag full            # CI-style: fast + full tests
lune run libs/specs --tag stress          # everything including slow/deep checks
lune run libs/specs --list-tags           # show available tags and counts

Changelog format

This repository uses the Keep a Changelog structure.