I can see non-constant conversion times, especially with floats. Floats have lots of weird edge cases involved in them, especially when you get to the very big and the very small scales. If your number's too big, you have to see if you need to just throw back infinity and/or negative infinity. If your number's too small, positive and negative zero. Finally, if you're hanging out with tiny numbers near zero, a good floating point library will start to have to worry about denormal numbers, where you will start padding with zeroes, sacrificing precision to denote that the number isn't quite zero. So yeah, it would be N in respect to the size.

A conversion from string to int is O(n) in the length of the string (O(lg n) in the "size" of the number). Such a "cast" would be syntactically indistinguishable from builtin casts eg. in C++ which allows user-defined conversions.