nfloat_hypot

With $|x| \ge |y|$ and $d$ the difference of the exponents, the result is $|x|(1 + \delta)$ with $0 < \delta < 2^{-p-3}$ ($p$ the precision) when $d$ exceeds about half the precision. Otherwise $x^2 + y^2 = S \cdot 2^{2e}$ for an integer $S$ of at most $3n + 2$ words (the squares of the mantissas, aligned exactly), whose truncated square root with an inexactness flag gives the result. At one word on 64-bit machines, $S$ is formed in registers and the truncated root is computed from the integer square root of its top two words, since the discarded low bits of $S$ do not change the floor of the square root. At two words, $S$ is formed in registers (the smaller square truncated to the four words of the larger) and its root is approximated with a guard word, which certifies the truncation in all but rare cases. From 12 words (or from 5 words when the exponents differ by at least $3/8$ of the precision), the exact squares are replaced by high squarings (flint_mpn_sqrhigh), whose sum is a lower bound within about $4n$ units of its last word, and the square root with a guard word certifies the truncation likewise, with the exact computation as the fallback.