convert(Float64, ::BigInt) – rounding and corner cases

[StefanKarpinski]

See f04aa6f and https://gmplib.org/manual/Converting-Integers.html#Converting-Integers.

[JeffBezanson]

To expand on this a bit, the problem is that mpz_get_d always rounds towards zero, and it would be nice for the default conversion to use unbiased rounding instead (round to nearest, resolve ties to even).

[jiahao]

In principle @simonbyrne's recent work on incorporating RoundingModes into Float64 constructors offers a simple resolution: simply define only Float64(::BigInt, RoundToZero) to work.

However, this issue is somewhat mind-bending: the edge cases here are when a BigInt is converted to Float64 where the granularity of Float64 is > 1.0 (the magnitude of the number must be ~1e16 or greater). I'm not sure if all the usual notions of rounding modes apply. What does "resolve ties to even" mean when eps(x) = 16384.0 ?

[simonbyrne]

Ties to even is still well-defined: the even one is the number with the zero in last place of the significand (bits(x)[end]).

We could probably do this ourselves via an explicit branch if the returned absolute value is greater than maxintfloat?

[jiahao]

That makes sense. (I didn't know maxintfloat existed!)