hex-arith

Part of hex, a computer algebra library for Lean 4. The aim is fast executable code, fully verified, built with spec-driven development.

Low-level exact arithmetic for Hex, implemented in Lean 4 without Mathlib.

The package provides wide UInt64 operations, extended gcd, modular powers and inverses, primality helpers, and Barrett and Montgomery reduction. Its native wide-word implementation is part of the package build and is covered by the same theorem-facing API as the portable arithmetic layer.

Quickstart

[[require]]
name = "hex-arith"
git = "https://github.com/leanprover/hex-arith.git"
rev = "main"

import HexArith

Functionality

The umbrella exposes the Hex.Barrett and Hex.Montgomery contexts, Hex.extGcd, the Nat modular-arithmetic lemmas, and wide-word operations. Reduction contexts make their modulus and range invariants explicit; hot-loop clients can reuse a context rather than recomputing constants.

Verification

See the SPEC for contracts, edge cases, and performance policy. Benchmarks and conformance targets run in hex-dev.

Contributing

Development happens in the hex-dev monorepo, not in this published mirror. Contributions are welcome as pull requests to the SPEC/ directory: describe the behavior you want and leave the implementation to the maintainer.