CoDiPack  1.9.3
A Code Differentiation Package
SciComp TU Kaiserslautern
CoDiPack: Fast gradient evaluation in C++ based on Expression Templates.

CoDiPack (Code Differentiation Package) is a tool for gradient evaluation in computer programs. It supports the features:

  • Forward mode of Algorithmic Differentiation(AD)
  • Reverse mode of Algorithmic Differentiation(AD)
  • Different tape implementations
  • An AdjointMPI interface
  • External functions
  • Higher order derivatives

The design principle for CoDiPack is that it is easy to use. However, it also gives experienced AD developers the full access to all the data structures.

The Scientific Computing Group at the TU Kaiserslautern develops CoDiPack and will enhance and extend CoDiPack in the future.


CoDiPack is a header only library. The only file the user needs to include is codi.hpp. The only other requirement is a c++11 compliant compiler where one usually needs to specify '–std=c++11' in compiler arguments. CoDiPack is tested with gcc and the intel compiler.

The file codi.hpp defines several datatypes. The most important ones are:

We recommend to use the codi::RealReverse type when AD is first introduced to an application. After that there should be no difficulties in replacing the codi::RealReverse type with other types.

For the handling of libraries and the memory optimization of the tape exist several helper structures. Most of them are introduced in the tutorial section:

The full type list of the file 'codi.hpp' is:

The reverse types support various use cases. The regular type codi::RealReverse is the most used type and provides the most common use case. This type can be used in c-like memory operations like memset and memcpy. The 'Index' variant of the reverse type uses an indexing scheme that reuses freed indices and therefore reduces the amount of memory that is needed. This type is no longer compatible with c-like memory operations. The 'Primal' variants implement a different strategy for storing the data. Instead of storing the partial derivatives for each statement, they store the primal values. This change reduces the required memory of the 'Primal' types. The 'Unchecked' variant is also an implementation of the reverse mode of AD but it should only be used by experienced users. This type performs no bounds checking for the memory access. For each type there is also a type with generalized calculation types e.g. codi::RealReverseGen. These types can be used to use arbitrary types for the primal compuation as well as the gradient computation. The 'Vec' variant implements the vector mode of the corresponding AD type. The dimension is fixed and can be defined via the template argument.

Hello World Example

A very small and simple example for the usage of the RealForward type is the code:

#include <codi.hpp>
#include <iostream>
int main(int nargs, char** args) {
codi::RealForward y = x * x;
std::cout << "f(4.0) = " << y << std::endl;
std::cout << "df/dx(4.0) = " << y.getGradient() << std::endl;
return 0;

It is compiled with

g++ -I<path to codi>/include -std=c++11 -g -o forward forward.cpp

for the gcc compiler or with

icpc -I<path to codi>/include -std=c++11 -g -o forward forward.cpp

for the intel compiler.

Please visit the tutorial page for further information.


If you use CoDiPack in one of your applications and write a paper it would be nice if you could cite the paper High-Performance Derivative Computations using CoDiPack (submitted to ACM TOMS).

title={{High-Performance Derivative Computations using CoDiPack}},
author={Sagebaum, Max and Albring, Tim and Gauger, Nicolas R.},
journal={arXiv preprint arXiv:1709.07229},