Add fibonnaci sequence closed form function (trekhleb#130)

* Add fibonnaci sequence closed form function

* Revert package-lock.json

Author: TheKarlo95

src/algorithms/math/fibonacci/__test__/fibonacciClosedForm.test.js

@@ -0,0 +1,23 @@
+import fibonacciClosedForm from '../fibonacciClosedForm';
+
+describe('fibonacciClosedForm', () => {
+  it('should calculate fibonacci correctly', () => {
+    expect(fibonacciClosedForm(1)).toBe(1);
+    expect(fibonacciClosedForm(2)).toBe(1);
+    expect(fibonacciClosedForm(3)).toBe(2);
+    expect(fibonacciClosedForm(4)).toBe(3);
+    expect(fibonacciClosedForm(5)).toBe(5);
+    expect(fibonacciClosedForm(6)).toBe(8);
+    expect(fibonacciClosedForm(7)).toBe(13);
+    expect(fibonacciClosedForm(8)).toBe(21);
+    expect(fibonacciClosedForm(20)).toBe(6765);
+    expect(fibonacciClosedForm(30)).toBe(832040);
+    expect(fibonacciClosedForm(50)).toBe(12586269025);
+    expect(fibonacciClosedForm(70)).toBe(190392490709135);
+    expect(fibonacciClosedForm(71)).toBe(308061521170129);
+    expect(fibonacciClosedForm(72)).toBe(498454011879264);
+    expect(fibonacciClosedForm(73)).toBe(806515533049393);
+    expect(fibonacciClosedForm(74)).toBe(1304969544928657);
+    expect(fibonacciClosedForm(75)).toBe(2111485077978050);
+  });
+});

src/algorithms/math/fibonacci/fibonacciClosedForm.js

@@ -0,0 +1,11 @@
+/**
+ * Calculate fibonacci number at specific position using closed form function.
+ *
+ * @param n n-th number of fibonacci sequence (must be number from 1(inclusive) to 75(inclusive))
+ * @return {number}
+ */
+export default function fibonacciClosedForm(n) {
+  const sqrt5 = Math.sqrt(5);
+  const phi = (1 + sqrt5) / 2;
+  return Math.floor((phi ** n) / sqrt5 + 0.5);
+}