import { Digit, Digits, TrimZeros } from "../utils";
import { CompareDigits } from "../compare";
import { AddDigits } from "./addition";
import { SubDigits } from "./substraction";
export type Rest<T extends Digit[]> = T extends [
    Digit,
    ...infer R extends Digit[]
] ? R : never;
type TruncateWith<T extends Digit[], U extends Digit[], Acc extends Digit[] = []> = U extends [] ? [T, Acc] : T extends [infer D extends Digit, ...infer DR extends Digit[]] ? TruncateWith<DR, Rest<U>, [...Acc, D]> : [T, Acc];
type DivModByDigit<D extends Digit[], M extends Digit[], Mul extends Digit[] = [0], IterTable extends Digit[] = Digits, NextMul extends Digit[] = AddDigits<M, Mul>, Comp = CompareDigits<D, NextMul>> = IterTable extends [
    infer Iteration extends Digit,
    ...infer Next extends Digit[]
] ? Comp extends 0 ? {
    Quotient: Next[0];
    Remainder: [0];
} : Comp extends 1 ? DivModByDigit<D, M, NextMul, Next> : {
    Quotient: Iteration;
    Remainder: SubDigits<D, Mul>;
} : never;
/**
 * compute the long division of a number by a divisor
 * @param A the Numerator Cut after M digits
 * @param D the Numerator Cut with M first digits
 * @param M the Divisor
 * @param Q the Quotient
 * @see https://en.wikipedia.org/wiki/Long_division#Algorithm_for_arbitrary_base
 */
export type _DivModDigits<A extends Digit[], D extends Digit[], M extends Digit[], Q extends Digit[] = []> = DivModByDigit<D, M> extends {
    Quotient: infer B extends Digit;
    Remainder: infer R extends Digit[];
} ? A extends [infer A1 extends Digit, ...infer AR extends Digit[]] ? _DivModDigits<AR, TrimZeros<[...R, A1]>, M, [...Q, B]> : {
    Quotient: [...Q, B];
    Remainder: R;
} : never;
export type DivDigits<N extends Digit[], M extends Digit[]> = TruncateWith<N, M> extends [infer A extends Digit[], infer D extends Digit[]] ? _DivModDigits<A, D, M>["Quotient"] : never;
export type ModDigits<N extends Digit[], M extends Digit[]> = TruncateWith<N, M> extends [infer A extends Digit[], infer D extends Digit[]] ? _DivModDigits<A, D, M>["Remainder"] : never;
export type DivModDigits<N extends Digit[], M extends Digit[]> = TruncateWith<N, M> extends [infer A extends Digit[], infer D extends Digit[]] ? _DivModDigits<A, D, M> : never;
export {};