  In this paper we construct a generating function quadratic at infinity for
any exact Lagrangian in $\mathbb R^{2n}$ equal to $\mathbb R^n$ outside a
compact set. This type of Lagrangian is equivalent to a Lagrangian filling in
$D^{2n}$ of the standard Legendrian unknot $S^{n-1}$. Generating functions of
the type we construct are related to the space $\mathcal M_\infty$ considered
by Eliashberg and Gromov. We also show that $\mathcal M_\infty$ is the homotopy
fiber of the so-called Hatcher-Waldhausen map. This further relates the
understanding of exact Lagrangians (and Legendrians) to algebraic K-theory of
spaces. As a result of this and the result by B\"okstedt that the
Hatcher-Waldhausen map is a rational homotopy equivalence we prove that the
stable Lagrangian Gauss map (relative boundary) of the Lagrangian is homotopy
trivial.
