I have an open bug report https://svn.boost.org/trac/boost/ticket/10082 that requests that conversions from floating point to rational multiprecision-types be made implicit (currently they're explicit).
But the doc says they are implicit.
Point taken.
2) Floating point values can result in arbitrarily large integer parts to the rational, effectively running the machine out of memory. Arguably the converting constructor should guard against that, though frankly exactly how is less clear :-(
Er, that might be true if you include mpfr numbers in "floating point", but if you only consider double, the maximum size of the numerator is extremely limited. Even for a binary128 it can't be very big (about 2ko).
Ah, my bad, I was thinking the exponent would make the number a lot larger than it actually is. Thanks, John.