fmpq_dedekind_sum, fmpq_dedekind_sum_naive

By the reciprocity law s(h,k) + s(k,h) = (h/k + k/h + 1/(hk))/12 - 1/4 for coprime h, k > 0, the sum telescopes along the Euclidean algorithm [Hickerson1977]. With the partial quotients a_1, \ldots, a_n of k/(h \bmod k), the convergent matrix \prod_i \left(\begin{smallmatrix} a_i & 1 \\ 1 & 0 \end{smallmatrix}\right) = \left(\begin{smallmatrix} m_{11} & m_{12} \\ m_{21} & m_{22} \end{smallmatrix}\right) and the alternating sum t = a_1 - a_2 + \cdots \pm a_n,

The function evaluates this in machine words when k fits in a slong and with the half-GCD continued fraction code otherwise. Writing s(h,k) = p/q in lowest terms, |s| < k/12 and q \mid 6k.