Add bit manipulation section.

Author: trekhleb

README.md

@@ -49,6 +49,7 @@ a set of rules that precisely define a sequence of operations.
 ### Algorithms by Topic
 
 * **Math**
+  * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits
   * `B` [Factorial](src/algorithms/math/factorial) 
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)

src/algorithms/math/bits/README.md

@@ -0,0 +1,37 @@
+# Bit Manipulation
+
+#### Get Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a 
+value that looks like `00100`. Then we perform `AND` operation
+that clears all bits from the original number except the
+`bitPosition` one. Then we compare the result with zero. If 
+result is zero that would mean that original number has `0` at
+position `bitPosition`.
+
+> See `getBit` function for further details.
+
+#### Set Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a
+value that looks like `00100`. Then we perform `OR` operation
+that sets specific bit into `1` but it does not affect on
+other bits of the number.
+
+> See `setBit` function for further details.
+
+#### Clear Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a
+value that looks like `00100`. Than it inverts this mask to get
+the number that looks like `11011`. Then `AND` operation is
+being applied to both the number and the mask. That operation 
+unsets the bit.
+
+> See `clearBit` function for further details.
+
+#### Update Bit
+
+This method is a combination of "Clear Bit" and "Set Bit" methods.
+
+> See `updateBit` function for further details.

src/algorithms/math/bits/__test__/clearBit.test.js

@@ -0,0 +1,15 @@
+import clearBit from '../clearBit';
+
+describe('clearBit', () => {
+  it('should clear bit at specific position', () => {
+    // 1 = 0b0001
+    expect(clearBit(1, 0)).toBe(0);
+    expect(clearBit(1, 1)).toBe(1);
+    expect(clearBit(1, 2)).toBe(1);
+
+    // 10 = 0b1010
+    expect(clearBit(10, 0)).toBe(10);
+    expect(clearBit(10, 1)).toBe(8);
+    expect(clearBit(10, 3)).toBe(2);
+  });
+});

src/algorithms/math/bits/__test__/getBit.test.js

@@ -0,0 +1,23 @@
+import getBit from '../getBit';
+
+describe('getBit', () => {
+  it('should get bit at specific position', () => {
+    // 1 = 0b0001
+    expect(getBit(1, 0)).toBe(1);
+    expect(getBit(1, 1)).toBe(0);
+
+    // 2 = 0b0010
+    expect(getBit(2, 0)).toBe(0);
+    expect(getBit(2, 1)).toBe(1);
+
+    // 3 = 0b0011
+    expect(getBit(3, 0)).toBe(1);
+    expect(getBit(3, 1)).toBe(1);
+
+    // 10 = 0b1010
+    expect(getBit(10, 0)).toBe(0);
+    expect(getBit(10, 1)).toBe(1);
+    expect(getBit(10, 2)).toBe(0);
+    expect(getBit(10, 3)).toBe(1);
+  });
+});

src/algorithms/math/bits/__test__/setBit.test.js

@@ -0,0 +1,15 @@
+import setBit from '../setBit';
+
+describe('setBit', () => {
+  it('should set bit at specific position', () => {
+    // 1 = 0b0001
+    expect(setBit(1, 0)).toBe(1);
+    expect(setBit(1, 1)).toBe(3);
+    expect(setBit(1, 2)).toBe(5);
+
+    // 10 = 0b1010
+    expect(setBit(10, 0)).toBe(11);
+    expect(setBit(10, 1)).toBe(10);
+    expect(setBit(10, 2)).toBe(14);
+  });
+});

src/algorithms/math/bits/__test__/updateBit.test.js

@@ -0,0 +1,19 @@
+import updateBit from '../updateBit';
+
+describe('updateBit', () => {
+  it('should update bit at specific position', () => {
+    // 1 = 0b0001
+    expect(updateBit(1, 0, 1)).toBe(1);
+    expect(updateBit(1, 0, 0)).toBe(0);
+    expect(updateBit(1, 1, 1)).toBe(3);
+    expect(updateBit(1, 2, 1)).toBe(5);
+
+    // 10 = 0b1010
+    expect(updateBit(10, 0, 1)).toBe(11);
+    expect(updateBit(10, 0, 0)).toBe(10);
+    expect(updateBit(10, 1, 1)).toBe(10);
+    expect(updateBit(10, 1, 0)).toBe(8);
+    expect(updateBit(10, 2, 1)).toBe(14);
+    expect(updateBit(10, 2, 0)).toBe(10);
+  });
+});

src/algorithms/math/bits/clearBit.js

@@ -0,0 +1,10 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function clearBit(number, bitPosition) {
+  const mask = ~(1 << bitPosition);
+
+  return number & mask;
+}

src/algorithms/math/bits/getBit.js

@@ -0,0 +1,8 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function getBit(number, bitPosition) {
+  return (number & (1 << bitPosition)) === 0 ? 0 : 1;
+}

src/algorithms/math/bits/setBit.js

@@ -0,0 +1,8 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function setBit(number, bitPosition) {
+  return number | (1 << bitPosition);
+}

src/algorithms/math/bits/updateBit.js

@@ -0,0 +1,16 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @param {number} bitValue - 0 or 1.
+ * @return {number}
+ */
+export default function updateBit(number, bitPosition, bitValue) {
+  // Normalized bit value.
+  const bitValueNormalized = bitValue ? 1 : 0;
+
+  // Init clear mask.
+  const clearMask = ~(1 << bitPosition);
+
+  // Cleat bit value and then set it up to required value.
+  return (number & clearMask) | (bitValueNormalized << bitPosition);
+}