acb_theta_agm_mul_tight

The function computes m and \varepsilon such that |a_k| \le m e^{-d_k} and \operatorname{rad}(a_k) \le \varepsilon e^{-d_k} for all k, and m_0, \varepsilon_0 for a0 similarly, calls acb_theta_agm_mul on the midpoints at a higher precision, and adds 2^g e^{-d_k} (m_0 \varepsilon + m \varepsilon_0 + \varepsilon\varepsilon_0) to the radius of entry k. This is valid because for v = -Y^{-1} y,

if x \in \mathbb{Z}^g + \frac b2 and w \in v + \mathbb{Z}^g + \frac{b+k}{2} realise the two distances, then so does -x, and choosing the sign with \langle x, w \rangle_\tau \le 0 gives \lVert x + w \rVert_\tau^2 \le \lVert x \rVert_\tau^2 + \lVert w \rVert_\tau^2 with x + w \in v + \mathbb{Z}^g + \frac k2.