DomainError in bigint_pow

[xyproto]

big(3)^big(9)^big(9)^big(9)

gives

ERROR: DomainError in bigint_pow at gmp.jl:352 in ^ at gmp.jl:356

This is for Julia 0.3.4 on 64-bit Arch Linux.

[aviks]

Not sure if this is a bug.

From the source of biginit_pow it looks like the exponent has to be less than the largest unsigned integer (which is 18446744073709551615 on 64 bits).

^ is parsed as right associative, which means that the exponent in your expression above becomes larger that that value.

julia> Base.Meta.show_sexpr( :( big(3)^big(9)^big(9)^big(9)))
(:call, :^, (:call, :big, 3), (:call, :^, (:call, :big, 9), (:call, :^, (:call, :big, 9), (:call, :big, 9))))

If you really wanted right associative exponentiation, then I don't know if there is a way. GMP's exponentiation function is limited to an uint exponent: https://gmplib.org/manual/Integer-Exponentiation.html#Integer-Exponentiation

However, if you force the expression to be left associative, then you could do:

julia> ((big(3)^9)^9)^9
662818605424187176105172864214479748588986673875686419462793267420461248113287928124072014075084032555900857691049061274135779819474602180821485109388447092848836753879024702508785576075431392037236950553064188689954912598712398079759040464474717726449363185622056684690721420542800623411346656785162817900551337542270334990205437212700131838846883

[xyproto]

Thank you for the great reply. I'm not sure if this is a bug either. If this is not a bug, I think this issue should be considered a feature request for a slightly more informative error message.

[jiahao]

The answer to this computation has ~10^(3e8) digits...

[JeffBezanson]

Yes, this is hitting a hard limit in GMP and, really, in the size of the universe.

[jiahao]

Technically speaking the current DomainError is correct for the reasons above. However, an OverflowError may be more in line with what users expect since the result would certainly overflow for |x|>1 anyway.

[aviks]

I'm uncertain if an OverflowError is any better than a DomainError without any more context.

We cant catch exceptions by type, so this is really a message to the user. You are therefore assigning a lot of meaning to the words "DomainError" vs "OverflowError" . Which may be true in some domains (sic) but I'm not sure is universally understood. At least at first glance, I'll personally find these hard to disambiguate these from each other, or from "ArgumentError".

In my mind, the goal is, when the user gets this error, does he understand what is wrong without reading library code?

[jiahao]

To me DomainError indicates a problem with the domain, i.e. the function is not defined for its inputs, whereas OverflowError indicates a problem with the range, specifically that the output is too large to be represented. I think the distinction is quite clear, although this case happens to trigger both.

However, the OverflowError seems more appropriate to me when just looking at the operation x^y purely as the mathematical exponentiation operation. The DomainError makes sense only if I know something about the implementation of x^y as you have explained above.

See also #8286, where doing very large arithmetic in GMP leads to nasty SIGABRTs when it overflows.