update MPFR to 4.2.0

[simonbyrne]

Updates MPFR library, and makes use of new trig functions

[giordano]

Should add tests for the new methods?

[simonbyrne]

I think it should be covered by tests in test/math.jl, but will check

[simonbyrne]

Hmm, looks like not. I'll update them

[PallHaraldsson]

Possibly you want to define e.g. tanpi since it's already implemented there: "mpfr_tanpi, mpfr_acospi, mpfr_asinpi, mpfr_atanpi and mpfr_atan2pi"? It seems trivial to add, for MPFR (though not for Float64).

It's not yet in Base for floats, but [a]tabpi is in C2x standard (and IEEE 754:2019 and C#/dotnet seems to implemente it, issue 20137 there):
https://en.cppreference.com/w/c/experimental/fpext4

https://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/tanpi.txt

754 and tanPi - exceptionally interesting

754-2008 defined sin, cos, tan, asin, acos, atan, and
atan2, but only sinPi, cosPi, atanPi, and atan2Pi. What
happened to tanPi, asinPi, acosPi? [..]

I see that you want to bring MPFR support in line with Base (floats), to be fully generic, so it's less than ideal to only have some functions for big/MPFR, not regular floats... the opposite problem, but we want to implement those at least eventually. We could actually do it by calling MPFR and then truncate to e.g. Float64? So not fast but could be improved later...

[simonbyrne]

I'm just adding methods to functions which are already are defined in Base, and which have corresponding functions that were added to MPFR in this release.

I think adding the additional functions to Base is a good idea, but should be a separate PR

[simonbyrne]

Not sure if we want to backport or not?

[oscardssmith]

why would we backport? This looks to me a lot like a new feature.

[StefanKarpinski]

Updating the library could be backported but adding methods should not.

[simonbyrne]

It doesn't look like there are any important bug fixes: https://www.mpfr.org/mpfr-4.2.0/#changes (their printing fix actually broke our printing, hence the change in this PR)

[StefanKarpinski]

Wow, all green CI! Haven't seen that recently.