Rotation number of 2-interval piecewise affine maps

We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\text{p}}$ are parametrized by a quintuple $\text{p}$ of real numbers satisfying inequations. Viewing $f_{\text{p}}$ as a circle map, we show that it has a rotation number $\rho (f_{\text{p}})$ and we compute $\rho (f_{\text{p}})$ as a function of $\text{p}$ in terms of Hecke-Mahler series. As a corollary, we prove that $\rho (f_{\text{p}})$ is a rational number when the components of $\text{p}$ are algebraic numbers.