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Commit 2be0fdc

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lvltegithub-actionsraklaptudirm
authored
merge: Decimal Expansion (TheAlgorithms#787)
* Add Math function for representing the decimal expansion of a given fraction (decimal or any base from 2 to 10). * Auto-update DIRECTORY.md * DecimalExpansion Jest tests. * chore: trigger update * Auto-update DIRECTORY.md * Auto-update DIRECTORY.md * chore: trigger checks Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Rak Laptudirm <rak@laptudirm.com> Co-authored-by: Rak Laptudirm <raklaptudirm@gmail.com>
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‎DIRECTORY.md‎

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* [LFUCache](https://github.com/TheAlgorithms/Javascript/blob/master/Cache/LFUCache.js)
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* [LRUCache](https://github.com/TheAlgorithms/Javascript/blob/master/Cache/LRUCache.js)
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* [Memoize](https://github.com/TheAlgorithms/Javascript/blob/master/Cache/Memoize.js)
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* test
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* [cacheTest](https://github.com/TheAlgorithms/Javascript/blob/master/Cache/test/cacheTest.js)
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## Cellular-Automata
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* [ConwaysGameOfLife](https://github.com/TheAlgorithms/Javascript/blob/master/Cellular-Automata/ConwaysGameOfLife.js)
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* Graph
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* [Graph](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Graph/Graph.js)
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* [Graph2](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Graph/Graph2.js)
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* [Graph3](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Graph/Graph3.js)
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* Heap
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* [MaxHeap](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Heap/MaxHeap.js)
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* [MinHeap](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Heap/MinHeap.js)
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* [MinPriorityQueue](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Heap/MinPriorityQueue.js)
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* Linked-List
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* [AddTwoNumbers](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Linked-List/AddTwoNumbers.js)
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* [CycleDetection](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Linked-List/CycleDetection.js)
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* [DoublyLinkedList](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Linked-List/DoublyLinkedList.js)
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* [RotateListRight](https://github.com/TheAlgorithms/Javascript/blob/master/Data-Structures/Linked-List/RotateListRight.js)
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* [Abs](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Abs.js)
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* [AliquotSum](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/AliquotSum.js)
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* [Area](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Area.js)
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* [ArithmeticGeometricMean](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/ArithmeticGeometricMean.js)
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* [ArmstrongNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/ArmstrongNumber.js)
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* [AverageMean](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/AverageMean.js)
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* [AverageMedian](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/AverageMedian.js)
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* [CheckKishnamurthyNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CheckKishnamurthyNumber.js)
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* [Coordinate](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Coordinate.js)
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* [CoPrimeCheck](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CoPrimeCheck.js)
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* [DecimalExpansion](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/DecimalExpansion.js)
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* [DecimalIsolate](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/DecimalIsolate.js)
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* [DegreeToRadian](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/DegreeToRadian.js)
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* [EulerMethod](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/EulerMethod.js)
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* [FindHcf](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/FindHcf.js)
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* [FindLcm](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/FindLcm.js)
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* [FindMin](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/FindMin.js)
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* [FindMinIterator](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/FindMinIterator.js)
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* [GetEuclidGCD](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/GetEuclidGCD.js)
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* [GridGet](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/GridGet.js)
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* [IsDivisible](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/IsDivisible.js)
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* [AlternativeStringArrange](https://github.com/TheAlgorithms/Javascript/blob/master/String/AlternativeStringArrange.js)
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* [CheckAnagram](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckAnagram.js)
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* [CheckCamelCase](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckCamelCase.js)
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* [CheckExceeding](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckExceeding.js)
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* [CheckFlatCase](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckFlatCase.js)
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* [CheckKebabCase](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckKebabCase.js)
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* [CheckPalindrome](https://github.com/TheAlgorithms/Javascript/blob/master/String/CheckPalindrome.js)

‎Maths/DecimalExpansion.js‎

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/**
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* @author Eric Lavault <https://github.com/lvlte>
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*
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* Represents the decimal (or binary, octal, any base from 2 to 10) expansion
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* of a/b using euclidean division.
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*
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* Because this function is recursive, it may throw an error when reaching the
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* maximum call stack size.
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*
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* Returns an array containing : [
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* 0: integer part of the division
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* 1: array of decimals (if any, or an empty array)
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* 2: indexOf 1st cycle digit in decimals array if a/b is periodic, or undef.
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* ]
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*
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* @see https://mathworld.wolfram.com/DecimalExpansion.html
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*
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* @param {number} a
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* @param {number} b
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* @param {number} [base=10]
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* @returns {array}
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*/
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export function decExp (a, b, base = 10, exp = [], d = {}, dlen = 0) {
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if (base < 2 || base > 10) {
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throw new RangeError('Unsupported base. Must be in range [2, 10]')
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}
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if (a === 0) {
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return [0, [], undefined]
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}
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if (a === b && dlen === 0) {
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return [1, [], undefined]
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}
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// d contains the dividends used so far and the corresponding index of its
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// euclidean division by b in the expansion array.
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d[a] = dlen++
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if (a < b) {
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exp.push(0)
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return decExp(a * base, b, base, exp, d, dlen)
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}
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// Euclid's division lemma : a = bq + r
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const r = a % b
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const q = (a - r) / b
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// Decimal expansion (1st element is the integer part)
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exp.push(+q.toString(base))
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if (r === 0) {
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// got a regular number (division terminates)
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return [exp[0], exp.slice(1), undefined]
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}
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// For the next iteration
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a = r * base
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// Check if `a` has already been used as a dividend, in which case it means
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// the expansion is periodic.
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if (a in d) {
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return [exp[0], exp.slice(1), d[a] - 1]
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}
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return decExp(a, b, base, exp, d, dlen)
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}

‎Maths/test/DecimalExpansion.test.js‎

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import { decExp } from '../DecimalExpansion'
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/**
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* Decimal
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*/
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describe('Finite Decimal Expansion', () => {
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it('1/2 = 0.5', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 2)
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expect(integer).toBe(0)
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expect(decimals).toEqual([5])
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expect(cycleIndex).toBeUndefined()
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})
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it('1/5 = 0.2', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 5)
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expect(integer).toBe(0)
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expect(decimals).toEqual([2])
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expect(cycleIndex).toBeUndefined()
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})
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it('1/8 = 0.125', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 8)
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expect(integer).toBe(0)
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expect(decimals).toEqual([1, 2, 5])
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expect(cycleIndex).toBeUndefined()
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})
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it('255/40 = 6.375', () => {
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const [integer, decimals, cycleIndex] = decExp(255, 40)
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expect(integer).toBe(6)
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expect(decimals).toEqual([3, 7, 5])
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expect(cycleIndex).toBeUndefined()
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})
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})
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describe('Repeating Decimal Expansion', () => {
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it('1/3 = 0.(3)', () => {
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expect(decExp(1, 3)).toStrictEqual([0, [3], 0])
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})
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it('1/6 = 0.1(6)', () => {
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expect(decExp(1, 6)).toStrictEqual([0, [1, 6], 1])
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})
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it('1/7 = 0.(142857)', () => {
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expect(decExp(1, 7)).toStrictEqual([0, [1, 4, 2, 8, 5, 7], 0])
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})
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})
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/**
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* Binary
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*/
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describe('Finite Binary Expansion', () => {
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it('1/2 = 0.12', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 2, 2)
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expect(integer).toBe(0)
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expect(decimals).toEqual([1])
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expect(cycleIndex).toBeUndefined()
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})
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it('1/8 = 0.0012', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 8, 2)
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expect(integer).toBe(0)
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expect(decimals).toEqual([0, 0, 1])
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expect(cycleIndex).toBeUndefined()
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})
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it('255/40 = 110.0112', () => {
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const [integer, decimals, cycleIndex] = decExp(255, 40, 2)
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expect(integer).toBe(110)
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expect(decimals).toEqual([0, 1, 1])
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expect(cycleIndex).toBeUndefined()
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})
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})
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describe('Repeating Binary Expansion', () => {
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it('1/3 = 0.(01)2', () => {
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expect(decExp(1, 3, 2)).toStrictEqual([0, [0, 1], 0])
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})
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it('1/5 = 0.(0011)2', () => {
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expect(decExp(1, 5, 2)).toStrictEqual([0, [0, 0, 1, 1], 0])
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})
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it('1/6 = 0.0(01)2', () => {
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expect(decExp(1, 6, 2)).toStrictEqual([0, [0, 0, 1], 1])
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})
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it('1/7 = 0.(001)2', () => {
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expect(decExp(1, 7, 2)).toStrictEqual([0, [0, 0, 1], 0])
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})
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})
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/**
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* Octal
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*/
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describe('Finite Octal Expansion', () => {
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it('1/2 = 0.48', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 2, 8)
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expect(integer).toBe(0)
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expect(decimals).toEqual([4])
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expect(cycleIndex).toBeUndefined()
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})
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it('1/8 = 0.18', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 8, 8)
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expect(integer).toBe(0)
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expect(decimals).toEqual([1])
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expect(cycleIndex).toBeUndefined()
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})
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it('255/40 = 6.38', () => {
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const [integer, decimals, cycleIndex] = decExp(255, 40, 8)
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expect(integer).toBe(6)
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expect(decimals).toEqual([3])
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expect(cycleIndex).toBeUndefined()
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})
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})
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describe('Repeating Octal Expansion', () => {
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it('1/3 = 0.(25)8', () => {
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expect(decExp(1, 3, 8)).toStrictEqual([0, [2, 5], 0])
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})
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it('1/5 = 0.(1463)8', () => {
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expect(decExp(1, 5, 8)).toStrictEqual([0, [1, 4, 6, 3], 0])
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})
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it('1/6 = 0.1(25)8', () => {
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expect(decExp(1, 6, 8)).toStrictEqual([0, [1, 2, 5], 1])
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})
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it('1/7 = 0.(1)8', () => {
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expect(decExp(1, 7, 8)).toStrictEqual([0, [1], 0])
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})
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})
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/**
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* Integers
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*/
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describe('Integers', () => {
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it('1/1 = 1', () => {
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const [integer, decimals, cycleIndex] = decExp(1, 1)
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expect(integer).toBe(1)
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expect(decimals).toStrictEqual([])
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expect(cycleIndex).toBeUndefined()
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})
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it('5/5 = 1', () => {
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const [integer, decimals, cycleIndex] = decExp(5, 5)
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expect(integer).toBe(1)
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expect(decimals).toStrictEqual([])
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expect(cycleIndex).toBeUndefined()
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})
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it('2/1 = 2', () => {
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const [integer, decimals, cycleIndex] = decExp(2, 1)
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expect(integer).toBe(2)
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expect(decimals).toStrictEqual([])
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expect(cycleIndex).toBeUndefined()
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})
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it('9/3 = 3', () => {
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const [integer, decimals, cycleIndex] = decExp(9, 3)
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expect(integer).toBe(3)
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expect(decimals).toStrictEqual([])
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expect(cycleIndex).toBeUndefined()
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})
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})
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/**
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* Unsupported base
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*/
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describe('Throws on unsupported base', () => {
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it('negative base', () => {
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expect(() => decExp(1, 1, -2)).toThrow(RangeError)
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})
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it('base 0', () => {
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expect(() => decExp(1, 1, 0)).toThrow(RangeError)
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})
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it('base 1', () => {
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expect(() => decExp(1, 1, 1)).toThrow(RangeError)
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})
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it('base 11', () => {
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expect(() => decExp(1, 1, 11)).toThrow(RangeError)
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})
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})

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