Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit de6a24e

Browse files
committed
Minor code style fixes for bitwise multiplication.
1 parent bc8943d commit de6a24e

File tree

5 files changed

+41
-17
lines changed

5 files changed

+41
-17
lines changed

‎src/algorithms/math/bits/README.md

Lines changed: 10 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -38,12 +38,14 @@ This method is a combination of "Clear Bit" and "Set Bit" methods.
3838
#### isEven
3939

4040
This method determines if the number provided is even.
41+
It is based on the fact that odd numbers have their last
42+
right bit to be set to 1.
4143

42-
```
43-
Number: 5
44+
```text
45+
Number: 5 = 0b0101
4446
isEven: false
4547
46-
Number: 4
48+
Number: 4 = 0b0100
4749
isEven: true
4850
```
4951

@@ -108,18 +110,19 @@ inverting all of the bits of the number and adding 1 to it.
108110
#### Multiply Two Signed Numbers
109111

110112
This method multiplies two signed integer numbers using bitwise operators.
111-
This method is based on the following :
113+
This method is based on the following facts:
112114

113115
```text
114-
a * b can be written in the below formats
116+
a * b can be written in the below formats:
115117
0 if a is zero or b is zero or both a and b are zeroes
116118
2a * (b/2) if b is even
117119
2a * (b - 1)/2 + a if b is odd and positive
118120
2a * (b + 1)/2 - a if b is odd and negative
119121
```
120122

121-
The advantage of this approach is that in each recursive step one of the operands reduces to half its original value.
122-
Hence, the run time complexity is O(log b) where b is the operand that reduces to half on each recursive step.
123+
The advantage of this approach is that in each recursive step one of the operands
124+
reduces to half its original value. Hence, the run time complexity is `O(log(b)` where `b` is
125+
the operand that reduces to half on each recursive step.
123126

124127
> See [multiply.js](multiply.js) for further details.
125128

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

Lines changed: 8 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -7,5 +7,13 @@ describe('isEven', () => {
77
expect(isEven(-2)).toBe(true);
88
expect(isEven(1)).toBe(false);
99
expect(isEven(-1)).toBe(false);
10+
expect(isEven(-3)).toBe(false);
11+
expect(isEven(3)).toBe(false);
12+
expect(isEven(8)).toBe(true);
13+
expect(isEven(9)).toBe(false);
14+
expect(isEven(121)).toBe(false);
15+
expect(isEven(122)).toBe(true);
16+
expect(isEven(1201)).toBe(false);
17+
expect(isEven(1202)).toBe(true);
1018
});
1119
});

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

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -12,5 +12,7 @@ describe('multiply', () => {
1212
expect(multiply(4, -2)).toBe(-8);
1313
expect(multiply(-4, -4)).toBe(16);
1414
expect(multiply(4, -5)).toBe(-20);
15+
expect(multiply(2, 121)).toBe(242);
16+
expect(multiply(121, 2)).toBe(242);
1517
});
1618
});

‎src/algorithms/math/bits/isEven.js

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,6 @@
11
/**
22
* @param {number} number
3-
* @return bool
3+
* @return {boolean}
44
*/
55
export default function isEven(number) {
66
return (number & 1) === 0;

‎src/algorithms/math/bits/multiply.js

Lines changed: 20 additions & 9 deletions
Original file line numberDiff line numberDiff line change
@@ -1,27 +1,38 @@
1+
import multiplyByTwo from './multiplyByTwo';
12
import divideByTwo from './divideByTwo';
23
import isEven from './isEven';
3-
import multiplyByTwo from './multiplyByTwo';
44

55
/**
6-
* FUNCTION DEFINITION
7-
* multiply(a, b) = 0 if a is zero or b is zero or if both a and b are zeros
8-
* multiply(a, b) = multiply(2a, b/2) if b is even
9-
* multiply(a, b) = multiply(2a, (b-1)/2) + a if b is odd and b is positive
10-
* multiply(a, b) = multiply(2a, (b+1)/2) - a if b is odd and b is negative
6+
* Multiply two signed numbers using bitwise operations.
7+
*
8+
* If a is zero or b is zero or if both a and b are zeros:
9+
* multiply(a, b) = 0
10+
*
11+
* If b is even:
12+
* multiply(a, b) = multiply(2a, b/2)
13+
*
14+
* If b is odd and b is positive:
15+
* multiply(a, b) = multiply(2a, (b-1)/2) + a
16+
*
17+
* If b is odd and b is negative:
18+
* multiply(a, b) = multiply(2a, (b+1)/2) - a
19+
*
20+
* Time complexity: O(log b)
1121
*
12-
* COMPLEXITY
13-
* O(log b)
1422
* @param {number} a
1523
* @param {number} b
16-
* @return {number} a * b
24+
* @return {number}
1725
*/
1826
export default function multiply(a, b) {
27+
// If a is zero or b is zero or if both a and b are zeros then the production is also zero.
1928
if (b === 0 || a === 0) {
2029
return 0;
2130
}
2231

32+
// Otherwise we will have four different cases that are described above.
2333
const multiplyByOddPositive = () => multiply(multiplyByTwo(a), divideByTwo(b - 1)) + a;
2434
const multiplyByOddNegative = () => multiply(multiplyByTwo(a), divideByTwo(b + 1)) - a;
35+
2536
const multiplyByEven = () => multiply(multiplyByTwo(a), divideByTwo(b));
2637
const multiplyByOdd = () => (b > 0 ? multiplyByOddPositive() : multiplyByOddNegative());
2738

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /