Asking for methods that exist on builtin float types but not numpy types gives:

>>> set(dir(float)) - set(dir(np.float32))
{'__getformat__',
 '__getnewargs__',
 '__setformat__',
 '__trunc__',
 'as_integer_ratio',
 'fromhex',
 'hex',
 'is_integer'}

Filtering these to the ones that are not CPython implementation details, we have:

• __trunc__(self) -> int, which will enable math.trunc(numpy_float)
• is_integer(self) -> bool (done in ENH: Add is_integer to np.floating & np.integer  #19803)
• as_integer_ratio(self) -> Tuple[int, int] (done in ENH: Implement np.floating.as_integer_ratio #10741)
• hex(self) -> str
• fromhex(cls: Type[FloatType], s: str) -> FloatType

For all of these, the best approach is probably to port the CPython implementations, taking care to handle the extended precision of long doubles.

Note that we get these methods for free on np.float64 due to inheriting from float