  We explore the systematics of the density dependence of nuclear matter
symmetry energy in the ambit of microscopic calculations with various energy
density functionals, and find that the symmetry energy from subsaturation
density to supra-saturation density can be well determined by three
characteristic parameters of the symmetry energy at saturation density $\rho_0
$, i.e., the magnitude $E_{\text{sym}}({\rho_0 })$, the density slope $L$ and
the density curvature $K_{\text{sym}}$. This finding opens a new window to
constrain the supra-saturation density behavior of the symmetry energy from its
(sub-)saturation density behavior. In particular, we obtain $L=46.7 \pm 12.8$
MeV and $K_{\text{sym}}=-166.9 \pm 168.3$ MeV as well as $E_{\text{sym}}({2\rho
_{0}}) \approx 40.2 \pm 12.8$ MeV and $L({2\rho _{0}}) \approx 8.9 \pm 108.7$
MeV based on the present knowledge of $E_{\text{sym}}({\rho_{0}}) = 32.5 \pm
0.5$ MeV, $E_{\text{sym}}({\rho_c}) = 26.65 \pm 0.2$ MeV and $L({\rho_c}) =
46.0 \pm 4.5$ MeV at $\rho_{\rm{c}}= 0.11$ fm$^{-3}$ extracted from nuclear
mass and the neutron skin thickness of Sn isotopes. Our results indicate that
the symmetry energy cannot be stiffer than a linear density dependence.In
addition, we also discuss the quark matter symmetry energy since the deconfined
quarks could be the right degree of freedom in dense matter at high baryon
densities.
