  We show how to generalize Gama and Nguyen's slide reduction algorithm [STOC
'08] for solving the approximate Shortest Vector Problem over lattices (SVP).
As a result, we show the fastest provably correct algorithm for
$\delta$-approximate SVP for all approximation factors $n^{1/2+\varepsilon}
\leq \delta \leq n^{O(1)}$. This is the range of approximation factors most
relevant for cryptography.
