If there were arithmetic operators that were not overloaded, Perl would invoke numeric conversion before using the builtin arithmetic operations, but I expect Math::GMP to overload all of them, so int may be the only built-in that actually invokes the numeric conversion.

I expect (but am not certain) that the '0+' overload is also invoked if an XSUB attempts to convert an object to an IV or UV. This is probably (but I have not traced the code) also how builtin arithmetic operations (which are not used on Math::GMP objects) would end up invoking it.

I expect (but am not certain) that the '0+' overload is also invoked if an XSUB attempts to convert an object to an IV or UV

No, I'm quite certain that doesn't happen. (And if I'm wrong about that, then I'm also now quite certain that I'll be told about it ;-)
It's just that the '0+' overloading calls an XSUB that converts the value in the object to a signed/unsigned long and returns that signed/unsigned long as an IV/UV.
Of course, you can always call intify or uintify (though the Math::GMP docs recommend avoiding the latter) without invoking any overloading.

Still not sure if calling int($obj) is the only way to activate the overload '0+' sub, but it's the only way that I could find.
There's probably good lessons to be learned from working through this, but I think I'll give it a miss for now, mainly because I don't see much value in what this Math::GMP overloading of '0+' provides.

Interesting stuff, but.

UPDATE: I took a look at Math::BigInt, and found that the '0+' overloading allows stuff like:

C:\>perl -MMath::GMP -wle "@x = qw(a b c d e f g h i j k l m n); print
+ $x[Math::GMP->new(-2)];"
m
[download]

Can do the same with Math::GMPz ... not exactly sure how it works there (as there's no explicit '0+' overloading) :

C:\>perl -MMath::GMPz -wle "@x = ('a' .. 'n'); for(Math::GMPz->new(0) 
+.. Math::GMPz->new(@x - 1)) { print $x[$_] }"
a
b
c
d
e
f
g
h
i
j
k
l
m
n
[download]

UPDATE 2: This capability of '0+' overloading definitely provides a useful feature.
And then Haarg has also pointed out that it contributes to sprintf() and pack() functionality - which adds to its usefulness.

Cheers,
Rob

sprintf and pack can trigger the 0+ overload, even if all other ops are overloaded.

Is there a string conversion overload in Math::GMPz? Perl has quite a few ways to construct overloaded operators from other operators, and one possibility is to first convert the object to a string and then use the builtin string->number conversion.