  Molecular clouds, which harbor the birthplaces of stars, form out of the
atomic phase of the interstellar medium (ISM). We aim to characterize the
atomic and molecular phases of the ISM and set their physical properties into
the context of cloud formation processes. We studied the cold neutral medium
(CNM) by means of $\rm HI$ self-absorption (HISA) toward the giant molecular
filament GMF20.0-17.9 and compared our results with molecular gas traced by
$^{13}\rm CO$ emission. We fitted baselines of HISA features to $\rm HI$
emission spectra using first and second order polynomial functions. The CNM
identified by this method spatially correlates with the morphology of the
molecular gas toward the western region. However, no spatial correlation
between HISA and $^{13}\rm CO$ is evident toward the eastern part of the
filament. The distribution of HISA peak velocities and line widths agrees well
with $^{13}\rm CO$ within the whole filament. The column density probability
density functions (N-PDFs) of HISA (CNM) and $\rm HI$ emission (tracing both
the CNM and the warm neutral medium, WNM) have a log-normal shape for all parts
of the filament, indicative of turbulent motions as the main driver for these
structures. The $\rm H_2$ N-PDFs show a broad log-normal distribution with a
power-law tail suggesting the onset of gravitational contraction. The
saturation of $\rm HI$ column density is observed at
$\sim$25$\rm\,M_{\odot}\,pc^{-2}$. We conjecture that different evolutionary
stages are evident within the filament. In the eastern region, we witness the
onset of molecular cloud formation out of the atomic gas reservoir while the
western part is more evolved, as it reveals pronounced $\rm H_2$ column density
peaks and signs of active star formation.
