  We present an algorithm that unconditionally computes a representation of the
unit group of a number field of discriminant $\Delta_K$, given a full-rank
subgroup as input, in asymptotically fewer bit operations than the baby-step
giant-step algorithm. If the input is assumed to represent the full unit group,
for example, under the assumption of the Generalized Riemann Hypothesis, then
our algorithm can unconditionally certify its correctness in expected time
$O(\Delta_K^{n/(4n + 2) + \epsilon}) = O(\Delta_K^{1/4 - 1/(8n+4) + \epsilon})$
where $n$ is the unit rank.
