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Lib/numbers.py

Source:

cpython 3.14 @ ab2d84fe1023/Lib/numbers.py

numbers defines the PEP 3141 numeric tower as a hierarchy of ABCs: Number > Complex > Real > Rational > Integral. Concrete types (int, float, complex, fractions.Fraction, decimal.Decimal) are registered with these ABCs, enabling isinstance checks against the abstract tower. The module has no runtime arithmetic logic.

Map​

LinesSymbolRole
1-30NumberRoot ABC; no abstract methods
31-180Complexreal, imag, __abs__, conjugate, __complex__, arithmetic ops
181-280RealAdds __float__, __floor__, __ceil__, __round__, __trunc__, comparison ops
281-340RationalAdds numerator, denominator; inherits Real
341-404IntegralAdds bitwise ops, __int__, __index__, __pow__

Reading​

Abstract method declarations​

The ABCs declare abstract methods that subclasses must implement. For example, Complex requires __complex__, real, imag, and conjugate:

# CPython: Lib/numbers.py:68 Complex
class Complex(Number):
    @abstractmethod
    def __complex__(self):
        """Return a builtin complex instance."""

    @abstractmethod
    def real(self):
        """Retrieve the real component of this number."""

    @abstractmethod
    def imag(self):
        """Retrieve the imaginary component of this number."""

Default implementations​

Many operator methods have default implementations in terms of the abstract ones. For example, Complex.__pos__ returns +self via complex(self), and Complex.__abs__ uses sqrt(self.real**2 + self.imag**2) as a default if not overridden.

# CPython: Lib/numbers.py:122 Complex.__abs__
def __abs__(self):
    return _math.hypot(self.real, self.imag)

Registration​

int is registered as Integral, float as Real, complex as Complex. fractions.Fraction registers itself as Rational. decimal.Decimal registers as Number only (it is not Real because it cannot be losslessly converted to float).

# CPython: Lib/numbers.py:400 bottom of file
Integral.register(int)
Real.register(float)
Complex.register(complex)

gopy notes​

Status: not yet ported. numbers has no runtime logic; it is purely ABC registration. The gopy port needs module/numbers/ to expose the five ABCs and to call register() on int, float, and complex at module init time. fractions.Fraction will register itself when module/fractions/ is ported.