New developments in the ROOT function and fitting classes
Author: L. Moneta, A. Flandi
Several improvements have been introduced in the new version 6 of ROOT in the Math work package. We will report on the improvements in the ROOT function classes used for fitting data objects like histograms or trees. These include the usage of a new TFormula class, based on the capabilities Cling, which makes easier for the user to build complex expressions, which can be compiled on-the fly using the JIT provided by Cling. We will present also how the ROOT function classes have been now extended with the capabilities to auto-normalise,  making them usable as probability density functions in  fitting. We will show how the functions can be added together, to perform an extended likelihood fit of several normalised components, and also how is posse also to perform function convolution using the Fourier transforms, provided in ROOT by the FFTW package. Finally, we will present the changes in the function interfaces needed to speed-up the function evaluation in fitting, by using SIMD vectorisation.