comparisons require `BigFloat`

[stevengj]

Comparisons seem to involve BigFloat conversions, which makes them way slower than Base.Irrational

julia> @btime 3.0 ≤ pi
  1.287 ns (0 allocations: 0 bytes)
true

julia> @btime 3.0 ≤ invsqrt2
  471.291 ns (8 allocations: 352 bytes)
false

This seems to be causing JuliaMath/SpecialFunctions.jl#484

In contrast, it's way faster to compare after conversion of the irrational value to floating point:

julia> @btime 3.0 ≤ oftype(3.0, invsqrt2)
  1.287 ns (0 allocations: 0 bytes)
false

I'm guessing this is some type of pedantry where you want to check that the exact rational floating-point value is ≤ the exact irrational value? Even so, can't you just compare to the RoundDown conversion?

(Why didn't you just use Base.Irrational, anyway?)

[devmotion]

(Why didn't you just use Base.Irrational, anyway?)

Base.Irrational is internal, by design definitions of new irrationals of type Base.Irrational (with or without the @irrational macro) are type piracy. The Julia documentation even warns against it.

[devmotion]

Note that it wouldn't have helped anyway since JuliaLang/julia#55886 moved the effect annotations only to the known Irrational subtypes in base, so also other Irrationals would miss those. I had suggested at some point to add these definitions automatically in the Base @irrational macro, so you would also get them for new Irrationals defined with the macro: JuliaLang/julia#55886 (comment) But there didn't seem any interest in such a change.

[devmotion]

#41 fixes this issue (and #37 which seem to be the same). However, probably #36 has to be approved and merged first.