The differential cross-sections are integrated and sampled using the CERNLIB package DIVON4 [13]. The package consists of a collection of routines to aid in the numerical integration of functions of several variables and to sample points in a multi-dimensional coordinate space from a specified probability density function. The algorithm adaptively partitions a multi-dimensional coordinate space into a set of axis oriented hyper-rectangular regions, based on a user provided function. These regions are then used for a stratified sampling estimate of the integral of the function, or to sample random vectors from the coordinate space with probability density that of the function.
The variables x and y are chosen for the integration of the cross-section. To improve the calculation, coordinate transformations are applied to x and y to smooth the differential cross-section before integration. These transformations are perform in the DIVON4 interface function DFUN and depend on the type of cross-section being integrated or importance sampled. For the DIS cross-section we use
If only the Born cross-section is being calculated a simple call to LQXSEC is made. If radiative corrections are included a transformation to the hadronic variables is made and the convolution of the Born term and hard bremsstruhlung function is calculated. A constant part for the soft photon contribution is also included to handle the singularity.
To smooth the breamstruhlung spectrum we make the following change of variable
where 
is the soft photon cut-off value mentioned
previously.