Add fibonacci Binet's formula.

Author: trekhleb

README.md

@@ -61,7 +61,7 @@ a set of rules that precisely define a sequence of operations.
 * **Math**
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
   * `B` [Factorial](src/algorithms/math/factorial) 
-  * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
+  * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions.
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
   * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM)

src/algorithms/math/fibonacci/README.md

@@ -17,4 +17,4 @@ The Fibonacci spiral: an approximation of the golden spiral created by drawing c
 
 ## References
 
-[Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)
+- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)

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

@@ -19,5 +19,7 @@ describe('fibonacciNth', () => {
     expect(fibonacciNth(73)).toBe(806515533049393);
     expect(fibonacciNth(74)).toBe(1304969544928657);
     expect(fibonacciNth(75)).toBe(2111485077978050);
+    expect(fibonacciNth(80)).toBe(23416728348467685);
+    expect(fibonacciNth(90)).toBe(2880067194370816120);
   });
 });

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

@@ -0,0 +1,31 @@
+import fibonacciNthClosedForm from '../fibonacciNthClosedForm';
+
+describe('fibonacciClosedForm', () => {
+  it('should throw an error when trying to calculate fibonacci for not allowed positions', () => {
+    const calculateFibonacciForNotAllowedPosition = () => {
+      fibonacciNthClosedForm(76);
+    };
+
+    expect(calculateFibonacciForNotAllowedPosition).toThrow();
+  });
+
+  it('should calculate fibonacci correctly', () => {
+    expect(fibonacciNthClosedForm(1)).toBe(1);
+    expect(fibonacciNthClosedForm(2)).toBe(1);
+    expect(fibonacciNthClosedForm(3)).toBe(2);
+    expect(fibonacciNthClosedForm(4)).toBe(3);
+    expect(fibonacciNthClosedForm(5)).toBe(5);
+    expect(fibonacciNthClosedForm(6)).toBe(8);
+    expect(fibonacciNthClosedForm(7)).toBe(13);
+    expect(fibonacciNthClosedForm(8)).toBe(21);
+    expect(fibonacciNthClosedForm(20)).toBe(6765);
+    expect(fibonacciNthClosedForm(30)).toBe(832040);
+    expect(fibonacciNthClosedForm(50)).toBe(12586269025);
+    expect(fibonacciNthClosedForm(70)).toBe(190392490709135);
+    expect(fibonacciNthClosedForm(71)).toBe(308061521170129);
+    expect(fibonacciNthClosedForm(72)).toBe(498454011879264);
+    expect(fibonacciNthClosedForm(73)).toBe(806515533049393);
+    expect(fibonacciNthClosedForm(74)).toBe(1304969544928657);
+    expect(fibonacciNthClosedForm(75)).toBe(2111485077978050);
+  });
+});

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

@@ -0,0 +1,23 @@
+/**
+ * Calculate fibonacci number at specific position using closed form function (Binet's formula).
+ * @see: https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression
+ *
+ * @param {number} position - Position number of fibonacci sequence (must be number from 1 to 75).
+ * @return {number}
+ */
+export default function fibonacciClosedForm(position) {
+  const topMaxValidPosition = 75;
+
+  // Check that position is valid.
+  if (position < 1 || position > topMaxValidPosition) {
+    throw new Error(`Can't handle position smaller than 1 or greater than ${topMaxValidPosition}`);
+  }
+
+  // Calculate √5 to re-use it in further formulas.
+  const sqrt5 = Math.sqrt(5);
+  // Calculate φ constant (≈ 1.61803).
+  const phi = (1 + sqrt5) / 2;
+
+  // Calculate fibonacci number using Binet's formula.
+  return Math.floor((phi ** position) / sqrt5 + 0.5);
+}