I think this looks good.

Perhaps it could be for a separate PR but it looks like these methods could be simplified more along the lines of the _mpc methods:

Probably the _mpf methods should delegate the complex case to _mpc rather than having inline logic to handle it. Then you could have something like:

# class _mpf
def __eq__(self, other):
    # handle the common case up front
    if isinstance(other, _mpf):
        return mpf_eq(self._mpf_, other._mpf_)
    self_new, other_new = ctx.convert_pair(self, other)
    if self_new is NotImplemented:
        return NotImplemented
    # might both be _mpc so we call __eq__ rather than mpf_eq
    return self_new.__eq__(other_new)

Probably the _mpf methods should delegate the complex case to _mpc

I think it's a good idea, but I doubt it should be implemented there.

We also could, for example, just return NotImplemented for anything except mpf/int/floats in mpf methods. Such changes, however, must be carefully benchmarked.