XAD: The fastest automatic differentiation library for C++

Exact derivatives of your existing C++ code, in forward, adjoint and higher-order mode, with low runtime overhead and a small memory footprint. Python bindings: pip install xad.

For Monte Carlo and other repetitive workloads, XAD also provides a JIT backend interface for record-once / replay-many execution.

Documentation · Install · Samples · Benchmarks · Python · Discussions

Example

Every derivative of a function in one adjoint sweep:

#include <XAD/XAD.hpp>
#include <iostream>

using mode = xad::adj<double>;   // adjoint (reverse) mode
using AD = mode::active_type;

template <class T>
T f(T x, T y) { return x * sin(y) + exp(x * y); }   // your code, unchanged

int main() {
    mode::tape_type tape;
    AD x = 1.3, y = 5.2;
    tape.registerInput(x);
    tape.registerInput(y);
    tape.newRecording();
    AD z = f(x, y);
    tape.registerOutput(z);
    derivative(z) = 1.0;
    tape.computeAdjoints();       // every input derivative in one sweep
    std::cout << "dz/dx = " << derivative(x) << ", dz/dy = " << derivative(y) << "\n";
}

Install

With vcpkg:

vcpkg install xad

find_package(XAD CONFIG REQUIRED)
target_link_libraries(my_app PRIVATE XAD::xad)

With CMake, straight from GitHub:

include(FetchContent)
FetchContent_Declare(XAD GIT_REPOSITORY https://github.com/auto-differentiation/xad.git GIT_TAG v2.1.0)
FetchContent_MakeAvailable(XAD)
target_link_libraries(my_app PRIVATE XAD::xad)

Or build from source:

git clone https://github.com/auto-differentiation/xad.git
cmake -S xad -B xad/build
cmake --build xad/build

Python: pip install xad. More in the Installation Guide and the Tutorials.

Benchmarks

Compared against CppAD, Adept 2, autodiff, and finite differences on quant-finance workloads. We are rebuilding the suite with new workloads, pinned library versions and gradient checks, run on GitHub CI; new results in November 2026.

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.

Ecosystem

Repository	Description
xad-py	Python bindings for XAD
QuantLibAAD	Full QuantLib integration — compute all Greeks at once, up to 3 orders of magnitude faster than bump-and-reval
QuantLib-Risks-Py	QuantLib risks from Python
xad-codegen	Native code generation backend — maximum throughput (commercial)
AAD Training	Hands-on AAD training for quants and quant developers - delivered to dozens of tier 1 banks and financial services firms

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.

New here? Pick a good first issue. Each one is small, self-contained and comes with a clear task.

Thanks to everyone who has contributed:

Found a Bug?

Please report bugs and issues via the GitHub Issue Tracker.

License

XAD is free under the AGPL-3.0 (version 3 only) for evaluation, research and open-source use. For production use without AGPL obligations, a commercial subscription is available.