XAD: Fast, easy automatic differentiation in C++

XAD is a high-performance C++ automatic differentiation library designed for large-scale, performance-critical systems.

It provides forward and adjoint (reverse) mode automatic differentiation via operator overloading, with a strong focus on:

• Low runtime overhead
• Minimal memory footprint
• Straightforward integration into existing C++ codebases

For Monte Carlo and other repetitive workloads, XAD also provides an abstract JIT backend interface, enabling record-once / replay-many execution for additional performance. A high-performance native code generation backend (xad-codegen) is available under a separate commercial license -- contact us for more information.

<a href="https://github.com/auto-differentiation/xad/releases/latest">
    <img src="https://img.shields.io/github/v/release/auto-differentiation/xad?label=Download&sort=semver" alt="Download" style="max-width: 100%;">
</a>
<a href="https://github.com/auto-differentiation/xad/blob/main/CONTRIBUTING.md">
    <img src="https://img.shields.io/badge/PRs%20-welcome-brightgreen.svg" alt="PRs Welcome" style="max-width: 100%;">
</a>
<a href="https://github.com/auto-differentiation/xad/actions/workflows/ci.yml">
    <img src="https://img.shields.io/github/actions/workflow/status/auto-differentiation/xad/ci.yml?label=Build&logo" alt="Build Status" style="max-width: 100%;">
</a>
<a href="https://coveralls.io/github/auto-differentiation/xad?branch=main">
    <img src="https://coveralls.io/repos/github/auto-differentiation/xad/badge.svg?branch=main" alt="Coverage" style="max-width: 100%;">
</a>
<a href="https://www.codacy.com/gh/auto-differentiation/xad/dashboard">
    <img src="https://img.shields.io/codacy/grade/1826d0a6c8ce4feb81ef3b482d65c7b4?logo=codacy&label=Quality%20%28Codacy%29" alt="Codacy Quality" style="max-width: 100%;">
</a>

Key Features

• Forward & Reverse (Adjoint) Mode: Supports any order using operator overloading.
• Vector mode: Compute multiple derivatives at once.
• Checkpointing Support: Efficient tape memory management for large-scale applications.
• External Function Interface: Seamlessly connect with external libraries.
• Eigen support: Works with the popular linear algebra library Eigen.
• JIT Backend Support (optional): Infrastructure for pluggable JIT backends, enabling record-once/replay-many workflows. See samples/jit_tutorial. A native code generation backend is available separately under commercial license.

Example

Calculate first-order derivatives of an arbitrary function with two inputs and one output using XAD in adjoint mode.

Adouble x0 = 1.3;              // initialise inputs
Adouble x1 = 5.2;
tape.registerInput(x0);        // register independent variables
tape.registerInput(x1);        // with the tape
tape.newRecording();           // start recording derivatives
Adouble y = func(x0, x1);      // run main function
tape.registerOutput(y);        // register the output variable
derivative(y) = 1.0;           // seed output adjoint to 1.0
tape.computeAdjoints();        // roll back adjoints to inputs
cout << "dy/dx0=" << derivative(x0) << "\n"
     << "dy/dx1=" << derivative(x1) << "\n";

Getting Started

Build XAD from source using CMake:

git clone https://github.com/auto-differentiation/xad.git
cd xad
mkdir build
cd build
cmake ..
make

For more detailed guides, refer to our Installation Guide and explore Tutorials.

Documentation

Full documentation, including API reference and usage examples, is available at: https://auto-differentiation.github.io/

Contributing

Contributions are welcome. Please see the Contributing Guide for details, and feel free to start a discussion in our GitHub Discussions.

Found a Bug?

Please report bugs and issues via the GitHub Issue Tracker.

Related Projects

• XAD-Py: XAD in Python.
• QuantLibAAD: AAD integration in QuantLib.
• xad-codegen: High-performance native code generation backend for XAD (commercial license -- contact us).