Problems with big numbers

[cscherrer]

This package would seem to be a good fit for solving this Discourse question. It's easy to see that we should be able to represent 10^(10^100), since

julia> m = exp(ULogarithmic, floatmax(BigFloat))
exp(5.875653789111587590936911998878442589938516392745498308333779606469323584389875e+1388255822130839282)

julia> log10(log10(m))
1.388255822130839282406840509258088745814167339601572288185265795534139656091031e+18

But when I try, I get

julia> ten = ULogarithmic(big(10.0))
exp(2.302585092994045684017991454684364207601101488628772976033327900967572609677367)

julia> ten^(ten^100)
ERROR: StackOverflowError:
Stacktrace:
     [1] promote_type(#unused#::Type{BigFloat}, #unused#::Type{Logarithmic{BigFloat}})
       @ Base ./promotion.jl:298
     [2] promote_result(#unused#::Type, #unused#::Type, #unused#::Type{BigFloat}, #unused#::Type{Logarithmic{BigFloat}})
       @ Base ./promotion.jl:312
--- the last 2 lines are repeated 39990 more times ---
 [79983] promote_type(#unused#::Type{BigFloat}, #unused#::Type{Logarithmic{BigFloat}})
       @ Base ./promotion.jl:298

At this scale, log2 also has trouble:

julia> log(m)
5.875653789111587590936911998878442589938516392745498308333779606469323584389875e+1388255822130839282

julia> log10(m)
2.551764018185095407552308798312362545661809468659242820931240956675926749716967e+1388255822130839282

julia> log2(m)
Inf

[cjdoris]

Thanks, that first issue is because BigFloat and ULogarithmic disagree on how to promote. An extra method for promote_rule should fix it.

The second issue is simply because you're trying to compute a value larger than floatmax(BigFloat) so it's overflowing. This package doesn't promise to prevent overflow.

[cscherrer]

Ok, great. I'll add a note here in case the log2 issue isn't clear to others.

It's unusual to have a case where we can represent m, but log2(m) is too large. But I see that this is just because logs of this type are represented in the "parent" type, and log(2) < 1. If we anticipate this, we could just do

julia> ULogarithmic(log(m)) / log(2)
+exp(3.19657716130066391462052341495733198684227139220399038349420313355764454299943e+18)

But putting this into the log2 method itself is a bad idea, because that would kill type stability.

So I think this issue can be closed once the stack overflow issue is addressed. Thank you!

[cjdoris]

OK the issue with promotion with BigFloat has been fixed now. A new version (1.2.1) is being registered. Thanks for the report!