/**

* @author Eric Lavault <https://github.com/lvlte>

*

* Represents the decimal (or binary, octal, any base from 2 to 10) expansion

* of a/b using euclidean division.

*

* Because this function is recursive, it may throw an error when reaching the

* maximum call stack size.

*

* Returns an array containing : [

* 0: integer part of the division

* 1: array of decimals (if any, or an empty array)

* 2: indexOf 1st cycle digit in decimals array if a/b is periodic, or undef.

* ]

*

* @see https://mathworld.wolfram.com/DecimalExpansion.html

*

* @param {number} a

* @param {number} b

* @param {number} [base=10]

* @returns {array}

*/

export function decExp (a, b, base = 10, exp = [], d = {}, dlen = 0) {

if (base < 2 || base > 10) {

throw new RangeError('Unsupported base. Must be in range [2, 10]')

}

if (a === 0) {

return [0, [], undefined]

}

if (a === b && dlen === 0) {

return [1, [], undefined]

}

// d contains the dividends used so far and the corresponding index of its

// euclidean division by b in the expansion array.

d[a] = dlen++

if (a < b) {

exp.push(0)

return decExp(a * base, b, base, exp, d, dlen)

}

// Euclid's division lemma : a = bq + r

const r = a % b

const q = (a - r) / b

// Decimal expansion (1st element is the integer part)

exp.push(+q.toString(base))

if (r === 0) {

// got a regular number (division terminates)

return [exp[0], exp.slice(1), undefined]

}

// For the next iteration

a = r * base

// Check if `a` has already been used as a dividend, in which case it means

// the expansion is periodic.

if (a in d) {

return [exp[0], exp.slice(1), d[a] - 1]

}

return decExp(a, b, base, exp, d, dlen)

}