add base keyword to precision/setprecision

[stevengj]

This is just a convenience feature, but I got tired of telling students things like "let's do setprecision(333), which corresponds to about 100 decimal digits". It's a lot easier to just do:

setprecision(100, base=10)

and let Julia multiply by log2(10) for you.

Given this, one also needs the corresponding base argument to precision, so that you can do e.g.

precision(Float64, base=10)

and it will return 15 (the maximum number of decimal digits represented exactly by a 53-bit significand).

[stevengj]

(This will also allow us to give a useful definition of precision for DecFP.jl — we can give the exact precision if base==10, and divide by log10(base) in other bases. cc @jmkuhn)

[stevengj]

(Since we can't dispatch on the presence/absence of keyword arguments, this means that if external packages like Arblib or DoubleFloats or MultiFloats that want to support the new base keyword will want to overload Base._precision instead of Base.precision.)

[stevengj]

Unrelated CI error on freebsd64:

Error in testset LinearAlgebra/matmul:
Error During Test at none:1
  Got exception outside of a @test
  ProcessExitedException(5)

[simeonschaub]

Could you add a test case for setprecision with a different base as well? Otherwise LGTM.

[stevengj]

Could you add a test case for setprecision with a different base as well?

There's already a test: test/mpfr.jl has a test setprecision(100, base=10) do ... end (which calls setprecision(BigFloat, 100, base=100))

Or do you mean you want a test for another base besides base=10? Okay, I added a test with setprecision(50, base=100).