feat: add prime sieve and generator

Author: khreenberg

Maths/Prime.ts

@@ -0,0 +1,57 @@
+const assert = (condition: boolean, message: string) => {
+  if (!condition) throw Error(message);
+};
+
+/**
+ * https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+ * @param limit An integer _n_ > 1
+ * @returns All prime numbers from 2 through {@linkcode limit}
+ */
+export function sieveOfEratosthenes(limit: number): number[] {
+  assert(limit > 1, "limit should be an integer greater than 1");
+  assert(Number.isInteger(limit), "limit should be an integer greater than 1");
+
+  const maybePrime: boolean[] = new Array(limit + 1).fill(true);
+  for (let i = 2; i * i <= limit; i++) {
+    if (!maybePrime[i]) continue;
+    for (let j = i * i; j <= limit; j += i) {
+      maybePrime[j] = false;
+    }
+  }
+
+  return maybePrime
+    .reduce(
+      (primes, isPrime, number) => (isPrime ? [...primes, number] : primes),
+      [] as number[]
+    )
+    .slice(2);
+}
+
+/**
+ * Generator that yields primes.
+ *
+ * Inspired by https://gist.github.com/e-nikolov/cd94db0de2a6b70da144124ae93a6458
+ */
+export function* primeGenerator() {
+  type NumberGen = Generator<number, void, any>;
+
+  function* filter(input: NumberGen, prime: number): NumberGen {
+    while (true) {
+      const { done, value } = input.next();
+      if (done) break;
+      if (value % prime !== 0) yield value;
+    }
+  }
+
+  let chain: NumberGen = (function* () {
+    let i = 2;
+    while (true) yield i++;
+  })();
+
+  while (true) {
+    const { done, value } = chain.next();
+    if (done) break;
+    yield value;
+    chain = filter(chain, value);
+  }
+}

Maths/test/Prime.test.ts

@@ -0,0 +1,35 @@
+import { primeGenerator, sieveOfEratosthenes } from "../Prime";
+
+describe(sieveOfEratosthenes, () => {
+  test.each([-1, 0, 1, 2.123, 1337.80085])(
+    "should throw an error when given an invalid limit=%d",
+    (invalidLimit) => {
+      expect(() => sieveOfEratosthenes(invalidLimit)).toThrow();
+    }
+  );
+  test.each([
+    [2, [2]],
+    [3, [2, 3]],
+    [4, [2, 3]],
+    [5, [2, 3, 5]],
+    [6, [2, 3, 5]],
+    [7, [2, 3, 5, 7]],
+    [8, [2, 3, 5, 7]],
+    [9, [2, 3, 5, 7]],
+  ])(
+    "should return the expected list of primes for limit=%i",
+    (limit, expected) => {
+      expect(sieveOfEratosthenes(limit)).toEqual(expected);
+    }
+  );
+});
+
+describe(primeGenerator, () => {
+  it("should generate prime numbers", () => {
+    const expectedPrimes = sieveOfEratosthenes(123);
+    const primeGen = primeGenerator();
+    for (const prime of expectedPrimes) {
+      expect(primeGen.next().value).toBe(prime);
+    }
+  });
+});