Added Sieve of Eratosthenes

Algorithms.ts

@@ -65,6 +65,73 @@ export function sqrtBig(value: bigint): bigint{
 	return x;
 }
 
+//Generate an infinite sequence of prime numbers using the Sieve of Eratosthenes
+export function* sieveOfEratosthenes(){
+	//Return 2 the first time, this lets us skip all even numbers later
+	yield 2;
+
+	//Dictionary to hold the primes we have already found
+	let dict = new Map<number, number[]>();
+
+	//Start checking for primes with the number 3 and skip all even numbers
+	for(let possiblePrime = 3;true;possiblePrime += 2){
+		//If possiblePrime is not in the dictionary it is a new prime number
+		//Return it and mark its next multiple
+		if(!dict.has(possiblePrime)){
+			yield possiblePrime;
+			dict.set(possiblePrime * possiblePrime, [possiblePrime]);
+		}
+		//If possiblePrime is in the dictionary it is a composite number
+		else{
+			//Move each witness to its next multiple
+			for(let num of dict.get(possiblePrime)){
+				let loc: number = possiblePrime + num + num;
+				if(dict.has(loc)){
+					dict.get(loc).push(num);
+				}
+				else{
+					dict.set(loc, [num]);
+				}
+				//We no longer need this, free the memory
+				dict.delete(possiblePrime);
+			}
+		}
+	}
+}
+
+export function* sieveOfEratosthenesBig(){
+	//Return 2 the first time, this lets us skip all even numbers later
+	yield 2n;
+
+	//Dictionary to hold the priems we have already found
+	let dict = new Map<bigint, bigint[]>();
+
+	//Start checking for primes with the number 3 and skip all even numbers
+	for(let possiblePrime = 3n;true;possiblePrime += 2n){
+		//If possiblePrime is not in the dictionary it is a new prime number
+		//Return it and mark its next multiple
+		if(!dict.has(possiblePrime)){
+			yield possiblePrime;
+			dict.set(possiblePrime * possiblePrime, [possiblePrime]);
+		}
+		//If possiblePrime is in the dictionary it is a composite number
+		else{
+			//Move each witness to its next multiple
+			for(let num of dict.get(possiblePrime)){
+				let loc: bigint = possiblePrime + num + num;
+				if(dict.has(loc)){
+					dict.get(loc).push(num);
+				}
+				else{
+					dict.set(loc, [num]);
+				}
+				//We no longer need this, free the memory
+				dict.delete(possiblePrime);
+			}
+		}
+	}
+}
+
 export function getAllFib(goalNumber: number): number[]{
 	//Setup the variables
 	let fibNums: number[] = [];

TestAlgorithms.ts

@@ -22,8 +22,9 @@ Copyright (C) 2021  Matthew Ellison
 
 
 import assert = require("assert");
+import { nextTick } from "process";
 import { arrayEquals, getAllFib, getAllFibBig, getFactors, getFactorsBig, getPrimes, getPrimesBig, getNumPrimes, getNumPrimesBig,
-		sqrtBig, getSum, getSumBig, getProd, getProdBig, getDivisors, getDivisorsBig, factorial, factorialBig, isPalindrome, toBin, toBinBig, isPrime, isPrimeBig } from "./Algorithms";
+		sqrtBig, getSum, getSumBig, getProd, getProdBig, getDivisors, getDivisorsBig, factorial, factorialBig, isPalindrome, toBin, toBinBig, isPrime, isPrimeBig, sieveOfEratosthenes, sieveOfEratosthenesBig } from "./Algorithms";
 
 
 function testArrayEquals(){
@@ -95,6 +96,34 @@ function testSqrtBig(){
 	console.log("testSqrtBig passed");
 }
 
+function testSieveOfEratosthenes(){
+	//Test 1
+	let sieve = sieveOfEratosthenes();
+	let correctAnswer: number[] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];
+	let answer: number[] = [];
+	for(let cnt = 0;cnt < 25;++cnt){
+		let prime = sieve.next().value;
+		if(typeof prime == "number"){
+			answer.push(prime);
+		}
+	}
+	assert.ok(arrayEquals(answer, correctAnswer), "sieveOfEratosthenes failed");
+
+	//Test 2
+	let bigSieve = sieveOfEratosthenesBig();
+	let bigCorrectAnswer: bigint[] = [2n, 3n, 5n, 7n, 11n, 13n, 17n, 19n, 23n, 29n, 31n, 37n, 41n, 43n, 47n, 53n, 59n, 61n, 67n, 71n, 73n, 79n, 83n, 89n, 97n];
+	let bigAnswer: bigint[] = [];
+	for(let cnt = 0;cnt < 25;++cnt){
+		let prime = bigSieve.next().value;
+		if(typeof prime == "bigint"){
+			bigAnswer.push(prime);
+		}
+	}
+	assert.ok(arrayEquals(bigAnswer, bigCorrectAnswer), "sieveOfEratosthenes big failed");
+
+	console.log("sieveOfEratosthenes passed");
+}
+
 function testGetAllFib(){
 	//Test 1
 	let correctAnswer = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89];
@@ -359,6 +388,7 @@ function testToBin(){
 //Run all of the tests
 testArrayEquals();
 testSqrtBig();
+testSieveOfEratosthenes();
 testGetAllFib();
 testGetPrimes();
 testGetNumPrimes();