The completed class of GPS covers all bent functions

The so called "generalized partial spread" (GPS) class unifies almost all the known classes of binary bent functions. A function of GPS and its dual take the same value at the zero vector. This necessary condition is in fact sufficient. This proves that the completed class under composition with translations covers all bent functions. Moreover, the elements of GPS are characterized in terms of solutions of a quadratic Diophantine equation that may lead to count all bent functions.