autodiff

Luna-Flow/autodiff computes exact first derivatives of ordinary MoonBit programs by forward-mode automatic differentiation. A program written against the Luna Flow traits is run on dual numbers $a + b\varepsilon$ with $\varepsilon^2 = 0$ , and the derivative appears in the $\varepsilon$ component. The repository provides the dual-number type, scalar drivers, checked domains for division and square roots, gradients and Jacobians over linear-algebra vectors, and derivatives of luna-poly polynomials.

This manual documents version 0.2.0 on MoonBit 0.10.

Packages

Package	Import path	Role	Pages
`autodiff`	`Luna-Flow/autodiff`	one-stop facade: `Dual`, `diff`, `value_and_diff`, re-exported traits	API · tutorial · design
`dual`	`Luna-Flow/autodiff/dual`	the `Dual[T]` type, its arithmetic, rules and instances	API · tutorial · design
`forward`	`Luna-Flow/autodiff/forward`	scalar drivers `diff` and `value_and_diff`	API · tutorial · design
`core`	`Luna-Flow/autodiff/core`	algebraic facade: `Dual` and the `luna-generic` structure traits	API · tutorial · design
`elementary`	`Luna-Flow/autodiff/elementary`	analytic facade: `Dual` and the `arithmetic` function traits	API · tutorial · design
`checked`	`Luna-Flow/autodiff/checked`	checked facade: `DivChecked`, `SqrtChecked`, context and errors	API · tutorial · design
`linalg`	`Luna-Flow/autodiff/linalg`	gradients and Jacobians over `linear-algebra/immut`	API · tutorial · design
`poly`	`Luna-Flow/autodiff/poly`	derivatives of dense and univariate sparse `luna-poly` polynomials	API · tutorial · design

Two more packages have no manual pages. examples holds five small functions (basic_diff_example, square_diff_example, gradient_example, jacobian_example, polynomial_derivative_example) that show each layer in a few lines; read src/examples/examples.mbt. tests is the black-box test suite of all packages, including the linear-algebra and luna-poly integration tests. The architecture guide shows how the packages depend on each other, and the repository conventions record the naming rules of this manual.

Reading paths

New to automatic differentiation. Start with the autodiff tutorial, then the dual tutorial, which compares dual numbers with finite differences.

Using the library. Import Luna-Flow/autodiff and keep the autodiff API and dual API at hand; add the linalg tutorial or the poly tutorial for vectors and polynomials, and the checked tutorial when failures must be values.

Contributing. Read the dual design for the algebra, the derivative rules and the error bounds that every new operation must respect, then the architecture guide and the design page of the package you change.

Installation

moon add Luna-Flow/autodiff@0.2.0

The bridges need their libraries too: moon add Luna-Flow/linear-algebra for linalg and moon add Luna-Flow/luna-poly for poly.

Toolchain

The code and the examples in this manual require MoonBit moonc 0.10 or newer and the moon.mod / moon.pkg manifest format. The test suite runs on the wasm-gc, wasm, js and native targets.

Validation

moon check --target all
./run_test.sh
moon info