Wasteful conversion to BigFloat?

[andreasKroepelin]

By profiling my code that uses logerf(a::Float64, b::Float64), I realised that most time is spent in performing conversion to BigFloat. The reason is that this line compares the input values to the irrational value invsqrt2. This comparison, in turn, is defined in terms of comparing BigFloats, and dwarfs the computation time of the rest of the function.

Actually, I wonder why the constant invsqrt2 is used at all. I think the compiler can very well compile inv(sqrt(oftype(a, 2)) into a single statically known number.

I can't judge the numerical situation, though. Is it necessary, for some reason, to have the higher precision in this comparison?

EDIT: A quick benchmark using BenchmarkTools shows a 7x speedup when switching to the "naive" computation of invsqrt2.

[stevengj]

Seems like this is a problem with IrrationalConstants.jl: JuliaMath/IrrationalConstants.jl#40

A simple workaround should be to replace abs(a) ≤ invsqrt2 with:

abs(a) ≤ oftype(float(a), invsqrt2)

and similarly for b.

[devmotion]

I opened JuliaMath/IrrationalConstants.jl#41 which seems to fix the underlying issue caused by the recent change in JuliaLang/julia#55886.

[stevengj]

Thanks! We can close this issue once JuliaRegistries/General#123932 is merged, it seems.