Use rem2pi and rem with BigFloats in _quadrant

[lbenet]

This PR proposes to use rem2pi and rem with BigFloats, instead of the same methods for the specific AbsrtracFloats. The reason is that, in order to guarantee the precision one needs more "guard digits" than the actual precision; see J-M Muller, "Elementary Functions: Algorithms and implementations", Birkhäuser, 3rd ed (2005), chap. 11. While the solution to use BigFloats should have a performance impact, it seems to be at least safe, without implementing more elaborate range reduction methods.

The following illustrates such a case:

julia> x = 6381956970095103 * 2.0^797 # worst case for C = pi/2 for Float64
5.319372648326541e255

julia> xb = big(x) 5.319372648326541416707296656673541083813475031793921822105998164685326343987747e+255

julia> rem2pi(x, RoundNearest)
1.5707963267948966

julia> rem2pi(xb, RoundNearest)
-2.545982325227109106133284489709240971297101919468998568916440481134254101023789

As far as I have checked, or the tests show, there haven't been any issues with this change.

This approach could be adapted for the mod (or should it be rem?) function; cf #129, #145 and #178).

[codecov-commenter]

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[OlivierHnt]

Thx for looking into this! I will need to have a close look at the reference you provided as I know nothing about this topic.

Nota bene: at first glance Section 11.3.2 seems to give us a way to estimate the required number of guard digits, denoted by $-\log_\beta(\epsilon)$ in the text. Then we can infer the necessary precision needed for safely performing rem2pi, so that we can construct bx = BigFloat(x; precision = precision(x) + N).

[lbenet]

Nota bene: at first glance Section 11.3.2 seems to give us a way to estimate the required number of guard digits, denoted by −logβ⁡(ϵ) in the text. Then we can infer the necessary precision needed for safely performing rem2pi, so that we can construct bx = BigFloat(x; precision = precision(x) + N).

I fully agree; it is much smaller the actual guard bits needed. Yet, I thought it was a bit more messy to get the minimum precision, compute whatever for that precision, and go back, than simply check that the BigFloat precision is large enough.