import { Type, Kind, Digit, DigitList } from '..';
type _$divideBySubtraction2<
/**
 * A represents the digit list to be divided, i.e., the dividend.
 */
A extends DigitList.DigitList, 
/**
 * B represents the digit list by which A is to be divided, i.e., the
 * divisor.
 */
B extends DigitList.DigitList, 
/**
 * OPERATION specifies the operation to perform (either "DIVIDE" or "MODULO").
 *
 * Default is "DIVIDE". The reason that we 'combine' the divide and modulo
 * operations into one implementation is that they're very similar in nature,
 * and the only difference is the final result.
 */
OPERATION extends 'DIVIDE' | 'MODULO' = 'DIVIDE', 
/**
 * QUOTIENT is our current guess and accumulator of the result of division.
 * Initially, it is assigned '0' - so that we can increment it as we subtract
 * from the remainder.
 */
QUOTIENT extends DigitList.DigitList = [Digit.Zero], 
/**
 * REMAINDER or the rest of the numbers that were not yet covered by the
 * multiples of B, starts as the original input number A.
 *
 * As we iterate, we reduce this variable by subtracting B from it. Once
 * REMAINDER is less than B, we know that we've covered all the multiples of B
 * in A, and that the remainder is the result of the modulo operation.
 */
REMAINDER extends DigitList.DigitList = A, 
/**
 * NEXT_QUOTIENT prepares our next version of the quotient by incrementing
 * the current one, to be carried over to the next operation.
 */
NEXT_QUOTIENT extends DigitList.DigitList = DigitList._$increment<QUOTIENT>, 
/**
 * NEXT_REMAINDER is the result of subtracting the divisor B from the current
 * remainder, which will be carried into the next round of operation.
 */
NEXT_REMAINDER extends DigitList.DigitList = DigitList._$subtract<REMAINDER, B>, 
/**
 * PERFECTLY_DIVISIBLE indicates if the remainder is perfectly divisible by B.
 */
PERFECTLY_DIVISIBLE extends boolean = REMAINDER extends B ? true : false, 
/**
 * DONE is a type predicate that helps us establish if we've successfully
 * completed the division operation - when the remainder equals 0 or when the
 * number is perfectly divisible by the divisor.
 */
DONE extends boolean = NEXT_REMAINDER extends [Digit.Zero] ? true : PERFECTLY_DIVISIBLE, 
/**
 * DIV_RESULT holds the final result of division if A was perfectly divisible
 * by B.
 */
DIV_RESULT extends DigitList.DigitList = PERFECTLY_DIVISIBLE extends true ? NEXT_QUOTIENT : QUOTIENT, 
/**
 * MOD_RESULT holds the final result of modulo operation if A was perfectly
 * divisible by B.
 */
MOD_RESULT extends DigitList.DigitList = PERFECTLY_DIVISIBLE extends true ? [Digit.Zero] : REMAINDER, 
/**
 * RESULT holds the final result of the operation.
 */
RESULT extends DigitList.DigitList = OPERATION extends 'DIVIDE' ? DIV_RESULT : MOD_RESULT> = DONE extends true ? RESULT : _$divideBySubtraction2<A, B, OPERATION, NEXT_QUOTIENT, NEXT_REMAINDER>;
/**
 * `_$divideBySubtraction` is a type-level function that performs the division or modulo operation by subtraction.
 * It takes in two digit lists `A` and `B` representing the dividend and divisor respectively, and an operation type
 * which can be either "DIVIDE" or "MODULO". It returns the result of the operation (division or substraction).
 *
 * @template A - A digit list representing a number to divide.
 * @template B - A digit list representing a number to divide by.
 * @template OPERATION - A string type representing the operation to be performed. Can be either "DIVIDE" or "MODULO".
 *
 * @example
 * For example, we can use `_$divideBySubtraction` to divide a digit list representing the number 10 by 2:
 *
 * ```ts
 * import { DigitList } from "hkt-toolbelt";
 *
 * type Result = DigitList._$divideBySubtraction<["1", "0"], ["2"]>; // ["5"]
 * ```
 *
 * @example
 * We can also use `_$divideBySubtraction` to find the remainder when a digit list representing the number 123 is divided by 17:
 *
 * ```ts
 * import { DigitList } from "hkt-toolbelt";
 *
 * type Result = DigitList._$divideBySubtraction<["1", "2", "3"], ["1", "7"], "MODULO">; // ["4"]
 * ```
 */
export type _$divideBySubtraction<A extends DigitList.DigitList, B extends DigitList.DigitList, OPERATION extends 'DIVIDE' | 'MODULO' = 'DIVIDE'> = B extends [Digit.Zero] ? [Digit.Zero] : B extends ['1'] ? OPERATION extends 'DIVIDE' ? A : [Digit.Zero] : _$divideBySubtraction2<A, B, OPERATION>;
interface DivideBySubtraction_T<A extends DigitList.DigitList> extends Kind.Kind {
    f(x: Type._$cast<this[Kind._], DigitList.DigitList>): _$divideBySubtraction<A, typeof x>;
}
/**
 * `DivideBySubtraction` is a type-level function that performs a division by subtraction.
 * It returns the result of the division.
 *
 * @template A - A digit list representing a number to divide.
 * @template B - A digit list representing a number to divide by.
 *
 * @example
 * For example, we can use `DivideBySubtraction` to divide a digit list representing the number 10 by 2:
 *
 * ```ts
 * import { $, DigitList } from "hkt-toolbelt";
 *
 * type Result = $<$<DigitList.DivideBySubtraction, ["1", "0"]>, ["2"]>; // ["5"] quotient is 5, and the remainder is 0.
 * ```
 */
export interface DivideBySubtraction extends Kind.Kind {
    f(x: Type._$cast<this[Kind._], DigitList.DigitList>): DivideBySubtraction_T<typeof x>;
}
export {};