Russian Peasant (Multiply two numbers using bitwise operators)

Given two integers, write a function to multiply them without using multiplication operator.
There are many other ways to multiply two numbers (For example, see this). One interesting method is the Russian peasant algorithm. The idea is to double the first number and halve the second number repeatedly till the second number doesn’t become 1. In the process, whenever the second number become odd, we add the first number to result (result is initialized as 0) 
The following is simple algorithm. 

Let the two given numbers be 'a' and 'b'
1) Initialize result 'res' as 0.
2) Do following while 'b' is greater than 0
   a) If 'b' is odd, add 'a' to 'res'
   b) Double 'a' and halve 'b'
3) Return 'res'. 

C++

#include <iostream>
using namespace std;

// A method to multiply two numbers using Russian Peasant method
unsigned int russianPeasant(unsigned int a, unsigned int b)
{
    int res = 0; // initialize result

    // While second number doesn't become 1
    while (b > 0)
    {
        // If second number becomes odd, add the first number to result
        if (b & 1)
            res = res + a;

        // Double the first number and halve the second number
        a = a << 1;
        b = b >> 1;
    }
    return res;
}

// Driver program to test above function
int main()
{
    cout << russianPeasant(18, 1) << endl;
    cout << russianPeasant(20, 12) << endl;
    return 0;
}

Java

// Java program for Russian Peasant Multiplication
import java.io.*;

class GFG
{
    // Function to multiply two
    // numbers using Russian Peasant method
    static int russianPeasant(int a, int b)
    {
        // initialize result
        int res = 0;

        // While second number doesn't become 1
        while (b > 0)
        {
             // If second number becomes odd,
             // add the first number to result
             if ((b & 1) != 0)
                 res = res + a;

            // Double the first number
            // and halve the second number
            a = a << 1;
            b = b >> 1;
        }
        return res;
    }

    // driver program
    public static void main (String[] args)
    {
        System.out.println(russianPeasant(18, 1));
        System.out.println(russianPeasant(20, 12));
    }
}

// Contributed by Pramod Kumar

Python 3

# A method to multiply two numbers
# using Russian Peasant method

# Function to multiply two numbers
# using Russian Peasant method
def russianPeasant(a, b):

    res = 0 # initialize result

    # While second number doesn't
    # become 1
    while (b > 0):

        # If second number becomes
        # odd, add the first number
        # to result
        if (b & 1):
            res = res + a

        # Double the first number
        # and halve the second
        # number
        a = a << 1
        b = b >> 1

    return res

# Driver program to test
# above function
print(russianPeasant(18, 1))
print(russianPeasant(20, 12))
# This code is contributed by
# Smitha Dinesh Semwal

C#

// C# program for Russian Peasant Multiplication
using System;

class GFG {

    // Function to multiply two
    // numbers using Russian Peasant method
    static int russianPeasant(int a, int b)
    {
        // initialize result
        int res = 0;

        // While second number doesn't become 1
        while (b > 0) {

            // If second number becomes odd,
            // add the first number to result
            if ((b & 1) != 0)
                res = res + a;

            // Double the first number
            // and halve the second number
            a = a << 1;
            b = b >> 1;
        }
        return res;
    }

    // driver program
    public static void Main()
    {
        Console.WriteLine(russianPeasant(18, 1));
        Console.WriteLine(russianPeasant(20, 12));
    }
}

// This code is contributed by Sam007.

PHP

<?php
// PHP Code to multiply two numbers
// using Russian Peasant method

// function returns the result
function russianPeasant($a, $b)
{

    // initialize result
    $res = 0;

    // While second number
    // doesn't become 1
    while ($b > 0)
    {

        // If second number becomes odd,
        // add the first number to result
        if ($b & 1)
            $res = $res + $a;

        // Double the first number and
        // halve the second number
        $a = $a << 1;
        $b = $b >> 1;
    }
    return $res;
}

    // Driver Code
    echo russianPeasant(18, 1), "\n";
    echo russianPeasant(20, 12), "\n";

// This code is contributed by Ajit
?>

Javascript

<script>

// A method to multiply two numbers using Russian Peasant method
function russianPeasant(a, b)
{
    var res = 0; // initialize result

    // While second number doesn't become 1
    while (b > 0)
    {

        // If second number becomes odd, add the first number to result
        if (b & 1)
            res = res + a;

        // Double the first number and halve the second number
        a = a << 1;
        b = b >> 1;
    }
    return res;
}

// Driver program to test above function
document.write(russianPeasant(18, 1)+"<br>");
document.write(russianPeasant(20, 12));

    // This code is contributed by noob2000.
</script>

Output: 

18
240

Time Complexity: O(log₂b)

Auxiliary Space: O(1)

How does this work?
The value of a*b is same as (a*2)*(b/2) if b is even, otherwise the value is same as ((a*2)*(b/2) + a). In the while loop, we keep multiplying ‘a’ with 2 and keep dividing ‘b’ by 2. If ‘b’ becomes odd in loop, we add ‘a’ to ‘res’. When value of ‘b’ becomes 1, the value of ‘res’ + ‘a’, gives us the result. 
Note that when ‘b’ is a power of 2, the ‘res’ would remain 0 and ‘a’ would have the multiplication. See the reference for more information.
Reference:
http://mathforum.org/dr.math/faq/faq.peasant.html
This article is compiled by Shalki Agarwal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above