Added Sieve of Atkin algorithm and tests. Updated README.md(s).

Author: sumtype

README.md

@@ -40,6 +40,7 @@ Common algorithms implemented in JavaScript with [Mocha](https://mochajs.org/)/[
 * [Is Prime](https://github.com/sumtype/common-algorithms-js/blob/master/algorithms/es/isPrime.js)
 * [Power Set](https://github.com/sumtype/common-algorithms-js/blob/master/algorithms/es/powerSet.js)
 * [Prime Factors](https://github.com/sumtype/common-algorithms-js/blob/master/algorithms/es/primeFactors.js)
+* [Sieve of Atkin](https://github.com/sumtype/common-algorithms-js/blob/master/algorithms/es/sieveOfAtkin.js)
 * [Sieve of Eratosthenes](https://github.com/sumtype/common-algorithms-js/blob/master/algorithms/es/sieveOfEratosthenes.js)
 
 ### String

algorithms/es/sieveOfAtkin.js

@@ -0,0 +1,31 @@
+/*
+  A JavaScript module to perform the Sieve of Atkin algorithm, which determines prime numbers up to the input integer.
+*/
+
+'use strict'
+
+const sieveOfAtkin = (limit = 0) => {
+  let primes = [2, 3]
+  let sieve = new Array(limit)
+  for (let x = 1, xSquared = x * x; xSquared < limit; x++) {
+    xSquared = x * x
+    for (let y = 1, ySquared = y * y; ySquared < limit; y++) {
+      ySquared = y * y
+      let n = (4 * xSquared) + ySquared
+      if (n <= limit) {
+        let mod12Check = n % 12
+        if (mod12Check === 1 || mod12Check === 5) sieve[n] = !sieve[n]
+      }
+      let threeXSquared = (3 * xSquared)
+      n = threeXSquared + ySquared
+      if (n <= limit && n % 12 === 7) sieve[n] = !sieve[n]
+      n = threeXSquared - ySquared
+      if (x > y && n <= limit && n % 12 === 11) sieve[n] = !sieve[n]
+    }
+  }
+  for (let r = 5; r * r < limit; r++) if (sieve[r]) for (let i = r * r; i < limit; i += r * r) sieve[i] = false
+  for (let a = 5; a < limit; a++) if (sieve[a]) primes.push(a)
+  return limit < 2 ? [] : limit === 2 ? [2] : limit === 3 ? [2, 3] : primes
+}
+
+export default sieveOfAtkin

algorithms/es5/sieveOfAtkin.js

@@ -0,0 +1,52 @@
+(function (global, factory) {
+  if (typeof define === 'function' && define.amd) {
+    define(['exports'], factory)
+  } else if (typeof exports !== 'undefined') {
+    factory(exports)
+  } else {
+    var mod = {
+      exports: {}
+    }
+    factory(mod.exports)
+    global.sieveOfAtkin = mod.exports
+  }
+})(this, function (exports) {
+  'use strict'
+
+  Object.defineProperty(exports, '__esModule', {
+    value: true
+  })
+  var sieveOfAtkin = function sieveOfAtkin () {
+    var limit = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0
+
+    var primes = [2, 3]
+    var sieve = new Array(limit)
+    for (var x = 1, xSquared = x * x; xSquared < limit; x++) {
+      xSquared = x * x
+      for (var y = 1, ySquared = y * y; ySquared < limit; y++) {
+        ySquared = y * y
+        var n = 4 * xSquared + ySquared
+        if (n <= limit) {
+          var mod12Check = n % 12
+          if (mod12Check === 1 || mod12Check === 5) sieve[n] = !sieve[n]
+        }
+        var threeXSquared = 3 * xSquared
+        n = threeXSquared + ySquared
+        if (n <= limit && n % 12 === 7) sieve[n] = !sieve[n]
+        n = threeXSquared - ySquared
+        if (x > y && n <= limit && n % 12 === 11) sieve[n] = !sieve[n]
+      }
+    }
+    for (var r = 5; r * r < limit; r++) {
+      if (sieve[r]) {
+        for (var i = r * r; i < limit; i += r * r) {
+          sieve[i] = false
+        }
+      }
+    } for (var a = 5; a < limit; a++) {
+      if (sieve[a]) primes.push(a)
+    } return limit < 2 ? [] : limit === 2 ? [2] : limit === 3 ? [2, 3] : primes
+  }
+
+  exports.default = sieveOfAtkin
+})

es.js

@@ -36,6 +36,7 @@ import fibonacciNumber from './algorithms/es/fibonacciNumber'
 import isPrime from './algorithms/es/isPrime'
 import powerSet from './algorithms/es/powerSet'
 import primeFactors from './algorithms/es/primeFactors'
+import sieveOfAtkin from './algorithms/es/sieveOfAtkin'
 import sieveOfEratosthenes from './algorithms/es/sieveOfEratosthenes'
 
 // String Algorithms
@@ -59,7 +60,7 @@ import sorensenDiceCoefficient from './algorithms/es/sorensenDiceCoefficient'
 const array = { binarySearch, bubbleSort, bucketSort, cocktailSort, countingSort, durstenfeldShuffle, gnomeSort, insertionSort, linearSearch, mergeSort, quickSort, radixSort, reservoirSampling, sattoloCycle, selectionSort, shellSort, sleepSort }
 const geometry = { bezierCurve, rayCasting }
 const graph = { breadthFirstSearch, depthFirstSearch }
-const math = { fibonacciNumber, isPrime, powerSet, primeFactors, sieveOfEratosthenes }
+const math = { fibonacciNumber, isPrime, powerSet, primeFactors, sieveOfAtkin, sieveOfEratosthenes }
 const string = { areAnagrams, arePalindromes, boyerMooreStringMatch, boyerMooreHorspoolStringMatch, bruteForceStringMatch, damerauLevenshteinDistance, hammingDistance, hasDuplicateCharacters, knuthMorrisPrattStringMatch, levenshteinDistance, longestCommonSubsequence, longestCommonSubstring, matchingDelimiters, rabinKarpStringMatch, sorensenDiceCoefficient }
 
 // Algorithm Exports
@@ -68,6 +69,6 @@ export {
   array, binarySearch, bubbleSort, bucketSort, cocktailSort, countingSort, durstenfeldShuffle, gnomeSort, insertionSort, linearSearch, mergeSort, quickSort, radixSort, reservoirSampling, sattoloCycle, selectionSort, shellSort, sleepSort,
   geometry, bezierCurve, rayCasting,
   graph, breadthFirstSearch, depthFirstSearch,
-  math, fibonacciNumber, isPrime, powerSet, primeFactors, sieveOfEratosthenes,
+  math, fibonacciNumber, isPrime, powerSet, primeFactors, sieveOfAtkin, sieveOfEratosthenes,
   string, areAnagrams, arePalindromes, boyerMooreStringMatch, boyerMooreHorspoolStringMatch, bruteForceStringMatch, damerauLevenshteinDistance, hammingDistance, hasDuplicateCharacters, knuthMorrisPrattStringMatch, levenshteinDistance, longestCommonSubsequence, longestCommonSubstring, matchingDelimiters, rabinKarpStringMatch, sorensenDiceCoefficient
 }