Skip to content
A dual number type for automatic differentiation.
Branch: master
Clone or download

Latest commit

Fetching latest commit…
Cannot retrieve the latest commit at this time.


Type Name Latest commit message Commit time
Failed to load latest commit information.


A dual number type for automatic differentiation.

Build StatusCoverage Status


Dual numbers are similar to complex numbers a pair of two numbers. A dual number is written as a + εb, where a is called the real part and b is called the dual part of the number. ε² is defined to be zero.

Given a function f(x) and a value f(a) which is the result of the function for x = a, then f(a + εb) is equal to f(a) + εb * f ' (a). This can be shown with a Taylor series.

In practice this means that we get the derivative of an arbitrary complicated function for free, if we calculate it with a dual number. All we have to do is to set the dual part of the variable, by which we want to differentiate, to one (all other dual parts should be zero). The result of the function will contain its derivative as the dual part.

For more information about theory see


The documentation can be found here. There are also some examples in the documentation.

Current Limitations

  • ^^ operator only works for integral exponents


Feel free to create issues or pull requests. A unittest is expected for every added function.


Distributed under the Boost Software Licence. See licence file for more information.

You can’t perform that action at this time.