What Is The mt19937 Random Generator In Modern C++?
Random numbers are one of the most important parts of today’s modern programming technologies. They are used in mathematics, physics, in many engineering fields, and in programming such as generating random data for testing, random maps in levels, random trees on a planet – the list is endless. Since C++11, mt19937 (std::mt19937
) is implemented as a random number generator. In this post, we explain what mt19937 is and how we can use it.
What is a random number and a random number generator in C++?
A random number is a number that is randomly chosen in a given range. It is impossible to predict future values based on past or present values and they are uniformly distributed over a defined interval or set.
Mersenne prime is a prime number used in mathematics that is a number of the form Mn = 2n − 1 where the n is an integer. The Mersenne Twister is a pseudorandom number generator where the period length is chosen to be a Mersenne Prime. It was developed by Makoto Matsumoto in 1997.
Since C++11, the Mersenne Twister mathematical number generator is implemented as a random generator number, it is defined in the
header as a std::mersenne_twister_engine
that is a random number engine based on Mersenne Twister algorithm.
What is the std::mt19937 random number generator in modern C++?
In C we use rand()
, srand()
and in C++ we use std::rand()
, std::srand()
. While they are added to
to make modern C++ compatible, there are more useful and modern random number generators. These are std::mt19937
and std::mt19937_64
. The std::mt1993
is a 32bit Mersenne Twister by Matsumoto and Nishimura in 1998, and std::mt19937_64
is a 64bit Mersenne Twister by Matsumoto and Nishimura in 2000.
The std::mt19937
is a random number generator defined in the
header in C++17 standard and beyond, producing 32bit pseudorandom numbers by using the Mersenne Twister algorithm with a state size of 19937 bits. This is why it is called mt19937 and there is a 64bit version called mt19937_64. Both are defined as an instantiation of the mersenne_twister_engine. Now let’s see their definitions.
Since C++11, mt19937 is defined as below,
typedef mersenne_twister_engine<unsigned int, 32, 624, 397, 31, 0x9908b0df, 11, 0xffffffff, 7, 0x9d2c5680, 15, 0xefc60000, 18, 1812433253> mt19937;

Since C++11, mt19937_64 is defined as below,
typedef mersenne_twister_engine<_ULonglong, 64, 312, 156, 31, 0xb5026f5aa96619e9ULL, 29, 0x5555555555555555ULL, 17, 0x71d67fffeda60000ULL, 37, 0xfff7eee000000000ULL, 43, 6364136223846793005ULL> mt19937_64;

How can we use the random number generator std::mt19937 in modern C++?
Simply we can generate modern random number as shown below.
std::mt19937 rnd( std::time(nullptr) );

we can use it like so:
unsigned int r = rnd();

if you want to generate a number in a range you can use modulus operator %.
This is how can we generate random number between zero to n, i.e. 0 to 100.
unsigned int r = rnd()%100;

This is how can we generate random number between two numbers, i.e. 50 to 150,
unsigned int r = 50 + rnd()%100;

Is there a simple example to use std::mt19937 in modern C++?
Here is a simple example to use std::mt19937
.
#include #include #include
int main() { std::mt19937 rnd( std::time(nullptr) );
std::cout << “32bit Random MT Number:” << rnd() << std::endl;
system(“pause”); return 0; }

Is there a full example of how to use the std::mt19937 in modern C++?
The std::mt19937
and std::mt19937_64
can be initialized with a new seed values (as same as using std::srand()
) with the seed()
method. Thus, we can generate same random number in same processes. This is useful to generate same randomly generated numbers for the same processes, such as it can be used to generate maps for each level of a game. We can also check min()
and max()
values of this generator.
Here is a full example including all these above.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 
#include #include #include #include
int main() { std::srand(std::time(nullptr)); auto r = std::rand(); std::cout << “C Style Random Number:” << r << std::endl; std::cout << std::endl;
std::mt19937 rnd( std::time(nullptr) );
std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << “Random MT Number (0100):” << rnd()%100 << std::endl; std::cout << “Random MT Number (50150):” << 50+rnd()%100 << std::endl; std::cout << std::endl;
std::cout << “32bit Min MT Number:” << rnd.min() << std::endl; std::cout << “32bit Max MT Number:” << rnd.max() << std::endl; std::cout << std::endl;
// Initializing a new random sequence with a seed value rnd.seed(4194967295);
std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << std::endl;
// Initializing same random sequence with a seed value rnd.seed(4194967295);
std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << “32bit Random MT Number:” << rnd() << std::endl; std::cout << std::endl;
system(“pause”); return 0; }

The output will be as below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 
C Style Random Number:16170
32bit Random MT Number:3102484612 32bit Random MT Number:2117116903 Random MT Number (0–100):28 Random MT Number (50–150):93
32bit Min MT Number:0 32bit Max MT Number:4294967295
32bit Random MT Number:88738114 32bit Random MT Number:32125358
32bit Random MT Number:88738114 32bit Random MT Number:32125358
Press any key to continue . . .

As you see, we can use seed to generate same random number sequences as in the last 4 lines of the output above.
Here are more examples to generate random numbers in modern C++,
I should note that, personally, I found mt19937
name for this class is hard to remember, I would prefer rand32()
, rand64()
names for them.
For more details about this feature in C++11 standard, please see these papers; p0205r1
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