flint_mpn_gcdext

Sets $(\mathit{gp}, \ell)$ to $g = \gcd(a, b)$, returning $\ell$, and $(\mathit{sp}, |{*\mathit{sn}}|)$ with the sign of $*\mathit{sn}$ to the cofactor $s$ of $a$ in $g = s a + t b$ that mpz_gcdext gives: normally $|s| < b/(2g)$, and the conventions for the exceptional cases determine $s$ uniquely. The other cofactor is $t = (g - s a)/b$. The operands must be nonzero with nonzero top limbs; they are not modified. gp needs room for $\min(\mathit{an}, \mathit{bn})$ limbs and sp for $\mathit{bn}$ limbs. The outputs must not overlap each other; each may be equal to ap or bp (if that has the room) but must not otherwise overlap them. When $\mathit{an} < \mathit{bn}$, $s$ is obtained from the cofactor of $b$ by a multiplication and an exact division.