ruff/crates/red_knot_python_semantic/resources/mdtest/binary/integers.md

Binary operations on integers

Basic Arithmetic

reveal_type(2 + 1)  # revealed: Literal[3]
reveal_type(3 - 4)  # revealed: Literal[-1]
reveal_type(3 * -1)  # revealed: Literal[-3]
reveal_type(-3 // 3)  # revealed: Literal[-1]
reveal_type(-3 / 3)  # revealed: float
reveal_type(5 % 3)  # revealed: Literal[2]

Power

For power if the result fits in the int literal type it will be a Literal type. Otherwise the outcome is int.

largest_u32 = 4_294_967_295
reveal_type(2**2)  # revealed: Literal[4]
reveal_type(1 ** (largest_u32 + 1))  # revealed: int
reveal_type(2**largest_u32)  # revealed: int

Division by Zero

This error is really outside the current Python type system, because e.g. int.__truediv__ and friends are not annotated to indicate that it's an error, and we don't even have a facility to permit such an annotation. So arguably divide-by-zero should be a lint error rather than a type checker error. But we choose to go ahead and error in the cases that are very likely to be an error: dividing something typed as int or float by something known to be Literal[0].

This isn't definitely an error, because the object typed as int or float could be an instance of a custom subclass which overrides division behavior to handle zero without error. But if this unusual case occurs, the error can be avoided by explicitly typing the dividend as that safe custom subclass; we only emit the error if the LHS type is exactly int or float, not if its a subclass.

a = 1 / 0  # error: "Cannot divide object of type `Literal[1]` by zero"
reveal_type(a)  # revealed: float

b = 2 // 0  # error: "Cannot floor divide object of type `Literal[2]` by zero"
reveal_type(b)  # revealed: int

c = 3 % 0  # error: "Cannot reduce object of type `Literal[3]` modulo zero"
reveal_type(c)  # revealed: int

# error: "Cannot divide object of type `int` by zero"
# revealed: float
reveal_type(int() / 0)

# error: "Cannot divide object of type `Literal[1]` by zero"
# revealed: float
reveal_type(1 / False)
# error: [division-by-zero] "Cannot divide object of type `Literal[True]` by zero"
True / False
# error: [division-by-zero] "Cannot divide object of type `Literal[True]` by zero"
bool(1) / False

# error: "Cannot divide object of type `float` by zero"
# revealed: float
reveal_type(1.0 / 0)

class MyInt(int): ...

# No error for a subclass of int
# revealed: float
reveal_type(MyInt(3) / 0)