Exact and reproducible are very different things though., even if the former implies the latter. Also, when do you need 53 bits of precision for a standard deviation? At worst, simple scaling can keep things within the precision of a double precision floating point number.
"Exact and reproducible" are somewhat sad proxies for "accurate and precise." I once had a mathematician working for me who produced very precise standard deviations, the only problem was that the numbers were sometimes negative.