Numeria

The rust_physics_engine library, from Python.

4,086 functions, 2,254 methods, 416 classes and 106 constants across 71 domains, from Newtonian mechanics to Reed–Solomon codes, with no runtime dependencies on either side.

$ pip install numeria

Wheels are published for Linux, macOS (universal2, so both Apple Silicon and Intel) and Windows, and need no Rust toolchain. Anywhere else, pip falls back to the source distribution, which carries the library with it and builds against that copy — a Rust toolchain is the only requirement.

To build from a checkout instead:

$ pip install ./bindings/python

To work on the bindings themselves, from an activated virtualenv:

$ pip install maturin
$ maturin develop --release -m bindings/python/Cargo.toml

>>> import math
>>> import numeria as nm
>>> nm.classical.projectile_range(speed=20.0, angle_rad=math.pi / 4, g=9.80665)
40.78864851911713

Every Python module mirrors a Rust module of the same name, and every function keeps the name, the argument order and the units it has in Rust, so rust_physics_engine::linalg::lu::solve is numeria.linalg.lu.solve. If you can read docs/MODULE_MAP.md, you can find your way around here.

What the bindings add

The Rust API is not changed, but five things are translated so that it reads as Python rather than as Rust seen through glass.

Errors are exceptions. Result<T, SolveError> becomes a return value and a raise; the variants that carry data carry it onto the exception.

>>> try:
...     nm.linalg.lu.solve([[1.0, 2.0], [2.0, 4.0]], [1.0, 2.0])
... except nm.SingularMatrixError as e:
...     print(e)
matrix is singular or pivot below threshold

Everything raised derives from PhysicsError, so except PhysicsError catches all of it and nothing else:

PhysicsError
├── InvalidArgumentError      a documented precondition was violated
├── SolverError
│   ├── SingularMatrixError
│   ├── NotPositiveDefiniteError
│   ├── ConvergenceError          .iterations, .residual
│   └── DimensionMismatchError    .expected, .got
├── GeometryError
│   ├── DegenerateGeometryError
│   ├── NotManifoldError
│   └── EmptyInputError
└── UnitsError

The library also validates arguments with assert!, which in Rust is the right call — a negative mass is a programming error, not a runtime condition. Those become InvalidArgumentError carrying the assertion's own message, rather than aborting the interpreter:

>>> nm.classical.acceleration(force=10.0, mass=-1.0)
Traceback (most recent call last):
numeria.InvalidArgumentError: mass must be positive

Small value types accept literals. Anywhere a Vec2, Vec3, Vec4, Mat3 or Quaternion is expected, a sequence of the right length will do; anywhere a Matrix is expected, a list of rows will do. The wrapper classes still exist, with their methods, their operators and their tolist().

>>> nm.classical.position_3d((0, 0, 100), (5, 0, 0), (0, 0, -9.81), 2.0).tolist()
[10.0, 0.0, 80.38]
>>> v = nm.math.Vec3(1, 2, 2)
>>> v.magnitude(), (v + (1, 0, 0)).tolist(), v[0], list(v)
(3.0, [2.0, 2.0, 2.0], 1.0, [1.0, 2.0, 2.0])

Three Rust types are Python types. They have exact counterparts, so they are translated rather than wrapped, and the round trip loses nothing:

>>> nm.exact.bigint.factorial(30)
265252859812191058636308480000000
>>> nm.transforms.fft.fft([1, 0, 0, 0])
[(1+0j), (1+0j), (1+0j), (1+0j)]

Builders chain. A Rust method that takes &mut self and returns &mut Self hands the same Python object back, so a circuit reads the way it does in Rust:

>>> c = nm.quantum.circuit.Circuit(2)
>>> c.h(0).cx(0, 1)                                  # a Bell pair
>>> state = c.run(nm.quantum.circuit.QState.zero(2))
>>> [round(abs(z) ** 2, 3) for z in state.amps]
[0.5, 0.0, 0.0, 0.5]

Functions can be Python functions. Anywhere the library takes a &dyn Fn, pass a callable. An exception raised inside it comes back out of the call with its own traceback, rather than turning into a NaN:

>>> import math
>>> nm.numerical.integrate.simpson(math.sin, 0.0, math.pi, 1000)
2.0000000000010805
>>> nm.numerical.roots.newton_raphson(lambda x: x*x - 2, lambda x: 2*x, 1.0, 1e-12, 50)
1.414213562373095

Types, and your editor

The package ships py.typed and a .pyi stub for every module, so mypy, pyright and editor completion all work without importing the extension.

What is not bound

4,086 of the library's 4,149 free functions, 2,254 of its 2,277 methods, 416 of its 426 types and all 106 of its constants, across 296 modules.

The rest is mostly three things: functions generic over a type parameter, which cannot be monomorphised without knowing what to monomorphise to; &dyn Trait arguments for traits with no Python equivalent; and routines returning a closure. COVERAGE.md lists every unbound item by name with its reason, and is regenerated with the bindings, so it cannot drift from them.

How this is built

generate.py reads the library's source with rustscan.py and writes the wrapper for every item it can bind. The alternative — writing 6,000 wrappers by hand — fails quietly: the first commit that adds a function to the library leaves the binding stale, and nothing breaks to tell you. Here, regenerating is one command, and CI runs

$ python3 bindings/python/generate.py --check

which fails if what is committed differs from what the current source produces.

To work on the bindings:

$ python3 bindings/python/generate.py     # after changing the library
$ maturin develop --release -m bindings/python/Cargo.toml
$ python -m pytest bindings/python/tests

The hand-written half is small and lives in src/runtime/: the exception hierarchy and the panic guard (errors.rs), the literal coercions and the three type identifications (coerce.rs), and the callable adapter (callback.rs). Anything a generator cannot reach — a Python protocol like __getitem__, a method defined by a macro_rules! the scanner cannot see — is declared in a table at the top of generate.py and spliced in, so there is one place to look.

Releasing

.github/workflows/python-release.yml runs on a v* tag and nothing else, and publishes to PyPI by Trusted Publishing — there is no API token in the repository to leak or rotate.

$ # bump the version in Cargo.toml and bindings/python/Cargo.toml together
$ python3 bindings/python/check_version.py v0.2.0
$ git tag v0.2.0 && git push origin v0.2.0

The tag check runs first, before any runner minutes are spent, because PyPI will not let a version be re-uploaded even after it is deleted — so tagging v0.2.0 against a Cargo.toml that still says 0.1.0 is a mistake with no undo.

PyPI's trusted publisher for numeria is pinned to this repository, to the file name python-release.yml, and to the pypi environment. Renaming any of those three breaks the release until PyPI is told about it — the header of that workflow file spells them out. Putting a required reviewer on the pypi environment makes every publish wait for a human, which is worth doing for the same reason the version check exists.

Performance notes

The GIL is released around calls that do real work — those taking or returning arrays — so several threads can compute at once. It is held for scalar calls, where releasing it would cost more than the call, and for anything involving a Python callable, which needs it.