  For any fixed globally F-regular projective variety X over an algebraically
closed field of positive characteristic, we study the F-signature of section
rings of X with respect to the ample Cartier divisors on X. In particular, we
define an F-signature function on the ample cone of X and show that it is
locally Lipschitz continuous. We further prove that the F-signature function
extends to the boundary of the ample cone. We also establish an effective
comparison between the F-signature function and the volume function on the
ample cone. As a consequence, we show that for divisors that are nef but not
big, the extension of the F-signature is zero.
