Definitely int for signed numbers. But I would call it "int64".
Clarity means saying what you mean. The typename int64 could not be clearer that you are getting 64 bits.
This is consistent with your (num32 -->) "int32".
And it would remain consistent if you later add smaller or larger integers.
This also fits your philosophy of letting the developer decide and getting out of their way. I.e. don't use naming to somehow shoehorn in the "standard" int size. Even if you would often be right. Make/let the developer make a conscious decision.
Later, "int" could be a big integer, with no bit limit. Or the name will be available for someone else to create that.
I do like your approach.
(For unsigned, I would call them "nat32", "nat64", if you ever go there. I.e. unsigned int is actually an oxymoron. A sign is what defines an integer. Natural numbers are the unsigned ones. This would be a case of using the standard math term for its standard meaning, instead of the odd historical accident found in C. Math is more universal, has more lasting and careful terminology - befitting universal clarity. I am not a fan of new names for things for specialized contexts. It just adds confusion or distance between branches of knowledge for no reason. Just a thought.)
Clarity means saying what you mean. The typename int64 could not be clearer that you are getting 64 bits.
This is consistent with your (num32 -->) "int32".
And it would remain consistent if you later add smaller or larger integers.
This also fits your philosophy of letting the developer decide and getting out of their way. I.e. don't use naming to somehow shoehorn in the "standard" int size. Even if you would often be right. Make/let the developer make a conscious decision.
Later, "int" could be a big integer, with no bit limit. Or the name will be available for someone else to create that.
I do like your approach.
(For unsigned, I would call them "nat32", "nat64", if you ever go there. I.e. unsigned int is actually an oxymoron. A sign is what defines an integer. Natural numbers are the unsigned ones. This would be a case of using the standard math term for its standard meaning, instead of the odd historical accident found in C. Math is more universal, has more lasting and careful terminology - befitting universal clarity. I am not a fan of new names for things for specialized contexts. It just adds confusion or distance between branches of knowledge for no reason. Just a thought.)