C++ Program to Generate Random Numbers Using Multiply with Carry Method

The multiply-with-carry method is a variant of the add-with-carry generator introduced by Marsaglia and Zaman (1991). The main advantages of this method are that it invokes simple computer integer arithmetic and leads to a very fast generation of sequences of random numbers with immense periods, ranging from around 260 to 22000000.

In this article, our task is to generate random numbers using the multiply-with-carry method. Here is the formula of multiply-with-carry method:

Multiply With Carry (MWC) Formula

The multiply-with-carry formula is as follows:

X<sub>n</sub> = (a * X<sub>n-1</sub> + C<sub>n-1</sub>) mod 2<sup>32</sup>
C<sub>n</sub> = (a * X<sub>n-1</sub> + C<sub>n-1</sub>) / 2<sup>32</sup>

Where, 
X<sub>n</sub> = Next random number
C<sub>n</sub> = Carry
a = Constant multiplier
X<sub>n-1</sub> = Previous random number
C<sub>n-1</sub> = Previous carry

Steps for Generate Random Numbers

The following steps implement the multiply-with-carry method to generate random numbers:

• We have used the uint32_t to declare 'x' and 'c'. The uint32_t defines a 32-bit unsigned integer.
• The MWCGenerator constructor sets the starting seed and creates an initial carry using the right shift operator.
• Then, we used the formula of the multiply-with-carry method and stored it in uint64_t t. After that, we have updated the value of the carry and the state.
• In the end, we returned the random number and printed the numbers using the for loop in the main() function.

C++ Program for Generate Random Numbers

Here is the C++ code implementation of the above steps to generate random numbers using the Multiply With Carry method.

#include <iostream>
#include <cstdint>
using namespace std;

class MWCGenerator {
private:
    uint32_t x;
    uint32_t c;  // carry
    static constexpr uint32_t a = 4294957665U;  // good multiplier

public:
    MWCGenerator(uint32_t seed = 12345) : x(seed), c(seed >> 1) {}

    uint32_t next() {
        uint64_t t = static_cast<uint64_t>(a) * x + c;
        c = t >> 32;           // upper 32 bits: new carry
        x = t & 0xFFFFFFFF;    // lower 32 bits: new state
        return x;
    }
};

int main() {
    MWCGenerator rng(123456789);  // initialize with a seed

    cout << "Multiply with Carry Random Numbers:\n";
    for (int i = 0; i < 5; ++i) {
        cout << rng.next() << "\n";
    }

    return 0;
}

The output of the above code is as follows:

Multiply with Carry Random Numbers:
755334527
1171226399
3552970656
515283068
1548961661