Comparison operators with AbstractIrrational are GPU incompatible

[Red-Portal]

Hi,

Currently, the comparison operators defined for AbstractIrrational v.s. AbstractFloat is causing problems for GPUs:
The precision of AbstractIrrational is currently matched by invoking Float(x, RoundUp/Down) by default:

julia/base/irrationals.jl

Lines 93 to 104 in 6e2e6d0

	<(x::AbstractIrrational, y::Float64) = Float64(x,RoundUp) <= y
	<(x::Float64, y::AbstractIrrational) = x <= Float64(y,RoundDown)
	<(x::AbstractIrrational, y::Float32) = Float32(x,RoundUp) <= y
	<(x::Float32, y::AbstractIrrational) = x <= Float32(y,RoundDown)
	<(x::AbstractIrrational, y::Float16) = Float32(x,RoundUp) <= y
	<(x::Float16, y::AbstractIrrational) = x <= Float32(y,RoundDown)
	<(x::AbstractIrrational, y::BigFloat) = setprecision(precision(y)+32) do
	big(x) < y
	end
	<(x::BigFloat, y::AbstractIrrational) = setprecision(precision(x)+32) do
	x < big(y)
	end

This internally calls setprecision(BigFloat, p):

julia/base/irrationals.jl

Lines 68 to 72 in 6e2e6d0

	@assume_effects :total function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
	setprecision(BigFloat, 256) do
	T(BigFloat(x)::BigFloat, r)
	end
	end

And this depends on libmpfr, which is not supported on the GPU.
This implementation has been causing problems downstream

• LogExpFunctions
• GPUCompiler

These issues shouldn't happen when a certain AbstractIrrational's conversion is defined statically by specializing Float(BigFloat).
To fix this, we need to change the behavior of the comparison operators to check whether a specialization Float(BigFloat) exist, and then try to do dynamic precision adjustment.

[simonbyrne]

I would have thought that @assume_effects :total would allow it to evaluate the result at compile time?

[vchuravy]

The problem may be that it is calling something in an overlayed method table and this gets tainted.

[oscardssmith]

see #51080