[BUG/pandas-compat]: Handling of type promotion and division/mod by zero for boolean columns

[wence-]

After #12074, most type promotions between columns of mixed types (and non-mixed types) match pandas. The exception is columns with boolean dtypes.

Pandas have taken the decision to disallow division and exponentiation on boolean types when both operands are booleans (https://github.com/pandas-dev/pandas/blob/d13c9e034ce8a1d738766c4b1cec80c76f5523be/pandas/core/ops/array_ops.py#L503).

Aside: I kind of disagree with this since this is all perfectly well defined (excepting the usual caveat of division by zero).

When only one of the operands is bool, the status quo depends on the dtype of the other operand:

Pandas behaviour:

For a % b, with a == 1, b == 0 for various dtypes

dtype-a \ dtype-b	bool	int	float
bool	int8(0) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)
int	int64(0) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)
float	float64(NaN) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)

For a / b (or a // b) with a == 1, b = 0

dtype-a \ dtype-b	bool	int	float
bool	NotImplemented (or ZeroDivisionError1)	float64(inf)	float64(inf)
int	float64(inf)(or ZeroDivisionError1)	float64(inf)	float64(inf)
float	float64(inf) (or ZeroDivisionError1)	float64(inf)	float64(inf)

For a % b, with a == 0, b == 0 for various dtypes

dtype-a \ dtype-b	bool	int	float
bool	int8(0)(or ZeroDivisionError1)	float64(NaN)	float64(NaN)
int	int64(0) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)
float	float64(NaN) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)

For a / b (or a // b) with a == 0, b = 0

dtype-a \ dtype-b	bool	int	float
bool	NotImplemented (or ZeroDivisionError1)	float64(NaN)	float64(NaN)
int	float64(NaN) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)
float	float64(NaN) (or ZeroDivisionError1)	float64(NaN)	float64(NaN)

cuDF behaviour:

For a % b, with a == 1, b == 0 for various dtypes

dtype-a \ dtype-b	bool	int	float
bool	bool(0)	float64(NaN)	float64(NaN)
int	int64(2**32 - 1)	float64(NaN)	float64(NaN)
float	float64(NaN)	float64(NaN)	float64(NaN)

For a // b with a == 1, b = 0

dtype-a \ dtype-b	bool	int	float
bool	bool(1)	float64(inf)	float64(inf)
int	int64(2**32 - 1)	float64(inf)	float64(inf)
float	float64(inf)	float64(inf)	float64(inf)

For a / b with a == 1, b = 0

dtype-a \ dtype-b	bool	int	float
bool	float32(inf)	float64(inf)	float64(inf)
int	float64(inf)	float64(inf)	float64(inf)
float	float64(inf)	float64(inf)	float64(inf)

For a % b, with a == 0, b == 0 for various dtypes

dtype-a \ dtype-b	bool	int	float
bool	bool(0)	float64(NaN)	float64(NaN)
int	int64(2**32 - 1)	float64(NaN)	float64(NaN)
float	float64(NaN)	float64(NaN)	float64(NaN)

For a // b with a == 0, b = 0

dtype-a \ dtype-b	bool	int	float
bool	bool(False)	float64(NaN)	float64(NaN)
int	int64(2**32 - 1)	float64(NaN)	float64(NaN)
float	float64(NaN)	float64(NaN)	float64(NaN)

For a / b with a == 0, b = 0

dtype-a \ dtype-b	bool	int	float
bool	float32(NaN)	float64(NaN)	float64(NaN)
int	float64(NaN)	float64(NaN)	float64(NaN)
float	float64(NaN)	float64(NaN)	float64(NaN)

Footnotes

1. If the operands are different lengths, we get a ZeroDivisionError (see https://github.com/pandas-dev/pandas/issues/49699) ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷ ↩⁸ ↩⁹ ↩¹⁰ ↩¹¹ ↩¹²