\documentclass[12pt,a4paper]{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \begin{document} \section{splines caclulations} Splines data points are calculated at fixed energies. The energy points are uniformly distributed in logarithmic range. The number of points and logarithmic limits are defined in \textit{constants.h}. The number of points is \textit{max\_datapoints}, log limits are \textit{logEmin} and \textit{logEmax}. The energy points are stored in \textit{EnergyTable} class and precalculated values are stored in \textit{energy\_table} variable. the double array can be accessed as energy\_table.values. The integration is done using GSL numerical integration library. \subsection{range spline precision} The range spline precision is checked via calculating dE/dx from inverse derivative of range spline and compared to directly calculated dE/dx. \begin{figure}[h] \centering \includegraphics[width=6.5cm]{plots/dedx_difs_n500.png} \includegraphics[width=6.5cm]{plots/dedx_difs_n400.png} \includegraphics[width=6.5cm]{plots/dedx_difs_n300.png} \includegraphics[width=6.5cm]{plots/dedx_difs_n200.png} \caption{Relative difference of dE/dx calculated directly and from range spline, number of range spline datapoints = 500(top left), 400(top right), 300(bottom left), 200(bottom right)} \end{figure} \section{Benchmarks} \subsection{Thin Target Approximation} test: projectile: 238U@700MeV/u - 30GeV/u, material: C(1mg/cm2), 30000 calculation in loop. reults: with thin target pproximation: 2.4s, without: 2.4s \end{document}