Zero-dependency collection of advanced mathematical functions using BigInts.
This is my personal zero-dependency collection of various mathematical functions using BigInts,
completely written from scratch.
Functions should be optimized for performance and accuracy, and should be safe for large numbers.
But I can give zero guarentees. If you're using this, you're on your own.
I do write tests for every single function implemented, but I can't guarentee, that the tests are sane either...
All functions are documented - and I tried to comment the code as well as the tests as good as possible.
This is not a fully fledge mathematical library like mathjs.
It's a collection of functions I re-use occasionally. And it's BigInt only!
- abs - Absolute value of a BigInt
- floorLog2 - Calculate the floor of the base-2 logarithm of a number
- clamp - Clamp a BigInt to a given range
- bitLength - Bit length of a BigInt
- hammingWeight - Population count (number of set bits) of a BigInt
- prodOdd - Calculate the product of all odd numbers in a given range
- pow - Power of a BigInt (x^y)
- nthRoot - nth root of a BigInt (x^(1/n))
- sqrt - Square root of a BigInt
- manhattanDist - Manhattan distance between two BigInts
- euclideanDist - Euclidean distance between two BigInts
- gcd - Greatest common divisor (2 inputs)
- gcdMulti - Greatest common divisor of multiple numbers (variadic)
- gcdExt - Extended Euclidean gcd algorithm for Bézout coefficients
- lcm - Least common multiple (2 inputs)
- lcmMulti - Least common multiple of multiple numbers (variadic)
- mod - True modulo operation for BigInt (not remainder)
- modPow - Modular exponentiation of a base raised to an exponent modulo a number
- modInv - Modular inverse of a number using the Extended Euclidean algorithm
- modDiv - Modular division of two numbers
- modSqrt - Tonelli-Shanks square root mod an odd prime p
- modNthRoot - Tonelli-Shanks nth root mod an odd prime p
- isPrime - Miller-Rabin primality test on 64-bit-size BigInts with deterministic base set
- eulerCriterion - Euler's criterion for quadratic residues modulo a prime p
- randomBigInt - Cryptographically-strong (hopefully) random bigint in given range
- quadraticPoly - Quadratic polynomial f(x) = x² + c modulo n
- pollardRho - Pollard's ρ algorithm for integer factorization using Brent's cycle detection
- factor - Prime factorization using Pollard's rho
- highestSetBit - Position of the highest set bit in a BigInt
- fibPair - Calculate the nth Fibonacci number modulo m using iterative fast-doubling
- fib - Calculate the nth Fibonacci number Fₙ for any integer n
- primePisano - Pisano period π(p) for a prime p
- pisanoPeriod - Pisano period π(n) for any positive integer n ≥ 1
- totient - Euler's totient function φ(n)
- jacobi - Calculate the Jacobi symbol (a | n) for any positive integer n ≥ 1
- mobius - Möbius function μ(n) for positive integer n ≥ 1
- factorial - Calculate the exact factorial n! of a number for bigint n ≥ 0
- crt - Chinese Remainder Theorem solver for a system of congruences
... more to come
- Test coverage overview / reporting
- Build step & minification for browser
- Better test setup (still figuring out bun:test)
- Add more functions (only with tests)
- NPM package maybe
- Maybe split up mathlib into smaller related chunks
ContributingDon't really expect anyone to contribute but...
- Bun is needed to run the tests
- TypeScript only
- Adhere to style guide (eslint)
- Every function should have a test
- Every function should be documented