import { DigitsToNumber, SplitDigits, Digit, TupleForDigit } from ".";


export type Add<A extends number, B extends number> = DigitsToNumber<AddDigitArrays<SplitDigits<A>, SplitDigits<B>>> & number

type AddDigitArrays<A extends Digit[], B extends Digit[], Carry extends boolean = false> = 
    [A, B] extends [[...infer HeadA extends Digit[], infer TailA extends Digit], [...infer HeadB extends Digit[], infer TailB extends Digit]] 
        ? AddTails<HeadA, TailA, HeadB, TailB, Carry> 
        : [A, B] extends [[...infer HeadA extends Digit[], infer TailA extends Digit], []] 
            ? AddTails<HeadA, TailA, [], 0, Carry> 
            : [A, B] extends [[], [...infer HeadB extends Digit[], infer TailB extends Digit]] 
                ? AddTails<[], 0, HeadB, TailB, Carry> 
                : [A, B] extends [[], []] 
                    ? Carry extends true 
                        ? [1] 
                        : [] 
                    : []

type AddTails<HeadA extends Digit[], TailA extends Digit, HeadB extends Digit[], TailB extends Digit, Carry extends boolean> = 
    SplitDigits<AddDigits<TailA, TailB, Carry>> extends [1, infer Result extends Digit] 
        ? [...AddDigitArrays<HeadA, HeadB, true>, Result] 
        : [...AddDigitArrays<HeadA, HeadB>, SplitDigits<AddDigits<TailA, TailB, Carry>>[0]]

type AddDigits<A extends Digit, B extends Digit, Carry extends boolean = false> =
    [...TupleForDigit<A>, ...TupleForDigit<B>, ...(Carry extends false ? [] : [0])]['length'] & number

export function add<A extends number, B extends number>(a: A, b: B) {
    return a + b as Add<A, B>
}