RX-wiki

Absolute ratio

Defined as the quotient between the maximum and minimum absolute-values of both input arguments.

Applications

It can be used to guarantee that integer division is always greater than 0, which “preserves” the information of the operands.

Implementation

PFP-style code in both Python and TypeScript, respectively:

from typing import Final, Callable
# there's `TypeVar` but `//` forces us to `def` 2 APIs

fabs_ratio: Final[Callable[[float, float], float]] = lambda x, y, /: (
	lambda x, y: max(x, y) / min(x, y)
)(abs(x), abs(y))

iabs_ratio: Final[Callable[[int, int], int]] = lambda x, y, /: (
	lambda x, y: max(x, y) // min(x, y)
)(abs(x), abs(y))

type numeric = number | bigint

const
	max = <T extends numeric,>(x: T, y: T) =>
		x < y ? y : x,
	min = <T extends numeric,>(x: T, y: T) =>
		x > y ? y : x,
	abs = <T extends numeric,>(x: T) =>
		x < 0 ? -x as T : x

const abs_ratio = <T extends numeric,>(x: T, y: T) =>
	(max(abs(x), abs(y)) / min(abs(x), abs(y))) as T

// as of TS v5, those type-asserts are necessary:
// https://github.com/microsoft/TypeScript/issues/49558#issuecomment-2177373544

See also

Rust lib