  Hydrogen at extreme temperatures and pressures is ubiquitous throughout our
universe and naturally occurs in a variety of astrophysical objects. In
addition, it is of key relevance for cutting-edge technological applications,
with inertial confinement fusion research being a prime example. In the present
work, we present exact \emph{ab initio} path integral Monte Carlo (PIMC)
results for the electronic density of warm dense hydrogen along a line of
constant degeneracy across a broad range of densities. Using the well-known
concept of reduced density gradients, we develop a new framework to identify
the breaking of bound states due to pressure ionization in bulk hydrogen.
Moreover, we use our PIMC results as a reference to rigorously assess the
accuracy of a variety of exchange--correlation (XC) functionals in density
functional theory calculations for different density regions. Here a key
finding is the importance of thermal XC effects for the accurate description of
density gradients in high-energy density systems. Our exact PIMC test set is
freely available online and can be used to guide the development of new
methodologies for the simulation of warm dense matter and beyond.
