# C++ Program to Implement the Schonhage-Strassen Algorithm for Multiplication of Two Numbers

Schonhage-Strassen Algorithm is used to multiply two numbers. The SchonhageStrassen algorithm is an asymptotically fast multiplication algorithm for large integers. In practice the Schonhage-Strassen algorithm starts to outperform older methods like karatsuba and Toom-CooK for numbers beyond 2215 to 2217 (10,000 to 40,000 decimal) digits.

## Algorithm

Begin
function noOfDigit( x)
Declare a variable n and assign n = 0;
while (x > 0)
x = x /10
Increment n
return n
End

Begin
Algorithm for schonhageStrassenMultiplication:
schonhageStrassenMultiplication(a, b, n, m)
define an array linearConvolution[n + m - 1]
for i = 0 to (n + m - 1)-1
linearConvolution[i] = 0;
long p = a
for i = 0 to m-1
a = p
for j = 0 to n-1
linearConvolution[i + j] += (b mod 10) * (a mod 10);
a /= 10
b /= 10
for i = (n + m - 2) to 0
Print linearConvolution[i]
long product = 0
nextCarry = 0, base = 1
for i = 0 to (n + m - 1)-1
linearConvolution[i] += nextCarry;
product = product + (base * (linearConvolution[i] % 10));
nextCarry = linearConvolution[i] / 10;
base *= 10;
Print the product of numbers.
End

## Example Code

#include <iostream>
using namespace std;
int noOfDigit(long x) {
int n = 0;
while (x > 0) {
x /= 10;
n++;
}
return n;
}
void schonhageStrassenMultiplication(long a, long b, int n, int m) {
int linearConvolution[n + m - 1];
for (int i = 0; i < (n + m - 1); i++)
linearConvolution[i] = 0;
long p = a;
for (int i = 0; i < m; i++) {
a = p;
for (int j = 0; j < n; j++) {
linearConvolution[i + j] += (b % 10) * (a % 10);
a /= 10;
}
b /= 10;
}
cout << "The Linear Convolution is: ( ";
for (int i = (n + m - 2); i >= 0; i--) {
cout << linearConvolution[i] << " ";
}
cout << ")";
long product = 0;
int nextCarry = 0, base = 1;
for (int i = 0; i < n + m - 1; i++) {
linearConvolution[i] += nextCarry;
product = product + (base * (linearConvolution[i] % 10));
nextCarry = linearConvolution[i] / 10;
base *= 10;
}
cout << "\nThe Product of the numbers is: " << product;
}
int main(int argc, char **argv) {
cout << "Enter the numbers:";
long a, b;
cin >> a >> b;
int n = noOfDigit(a);
int m = noOfDigit(b);
schonhageStrassenMultiplication(a, b, n, m);
}

## Output

Enter the numbers:1234 5679
The Linear Convolution is: ( 5 16 34 61 63 55 36 )
The Product of the numbers is: 7007886