import { AddExponents } from "./generated/addition";
import { DivideExponents } from "./generated/division";
import { Exponent, MinExponent } from "./generated/exponent";
import { MultiplyExponents } from "./generated/multiplication";

export type PositiveExponent = Exclude<NonNegativeExponent, "0">;
type NonNegativeExponent = SubtractExponents<Exponent, MinExponent>;

export type SubtractExponents<
  L extends Exponent,
  R extends Exponent,
> = AddExponents<L, Negative<R>>;

/** Exponents that can be added to N without producing an error. */
export type AddendOf<N extends Exponent> = SubtractExponents<
  AddExponents<Exponent, N>,
  N
>;

/** Exponents that can be subtracted from N without producing an error. */
export type SubtrahendOf<N extends Exponent> = AddendOf<Negative<N>>;

/** Exponents that can be multiplied with N without producing an error. */
export type MultiplicandOf<N extends Exponent> = "0" extends N
  ? Exponent
  : DivideExponents<Exponent, ProductOf<N>>;

/** Exponents that are non-error multiples of N. */
export type ProductOf<N extends Exponent> = MultiplyExponents<Exponent, N>;

type Negative<N extends Exponent> = MultiplyExponents<N, "-1">;