  We present and discuss a wide-range hydrogen equation of state model based on
a consistent set of ab initio simulations including quantum protons and
electrons. Both the process of constructing this model and its predictions are
discussed in detail. The cornerstones of this work are the specification of
simple physically motivated free energy models, a general
multiparameter/multiderivative fitting method, and the use of the most accurate
simulation methods to date. The resulting equation of state aims for a global
range of validity ($T = 1-10^9 K$ and $V_m = 10^{-9}-1 m^3/mol$), as the models
are specifically constructed to reproduce exact thermodynamic and mechanical
limits. Our model is for the most part analytic or semianalytic and is
thermodynamically consistent by construction; the problem of interpolating
between distinctly different models -often a cause for thermodynamic
inconsistencies and spurious discontinuities- is avoided entirely.
