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Generating integers in a range
Generating integers with different probabilities
Generating a random password
Generating quasi-random line-sphere intersections

For the source of this example see die.cpp. First we include the headers we need for mt19937 and uniform_int_distribution.

#include <boost/random/mersenne_twister.hpp>
#include <boost/random/uniform_int_distribution.hpp>

We use mt19937 with the default seed as a source of randomness. The numbers produced will be the same every time the program is run. One common method to change this is to seed with the current time (std::time(0) defined in ctime).

boost::random::mt19937 gen;

[Note] Note

We are using a global generator object here. This is important because we don't want to create a new pseudo-random number generator at every call

Now we can define a function that simulates an ordinary six-sided die.

int roll_die() {
    1boost::random::uniform_int_distribution<> dist(1, 6);
    2return dist(gen);


mt19937 produces integers in the range [0, 232-1]. However, we want numbers in the range [1, 6]. The distribution uniform_int_distribution performs this transformation.

[Warning] Warning

Contrary to common C++ usage uniform_int_distribution does not take a half-open range. Instead it takes a closed range. Given the parameters 1 and 6, uniform_int_distribution can produce any of the values 1, 2, 3, 4, 5, or 6.


A distribution is a function object. We generate a random number by calling dist with the generator.

For the source of this example see weighted_die.cpp.

#include <boost/random/mersenne_twister.hpp>
#include <boost/random/discrete_distribution.hpp>

boost::mt19937 gen;

This time, instead of a fair die, the probability of rolling a 1 is 50% (!). The other five faces are all equally likely.

discrete_distribution works nicely here by allowing us to assign weights to each of the possible outcomes.

[Tip] Tip

If your compiler supports std::initializer_list, you can initialize discrete_distribution directly with the weights.

double probabilities[] = {
    0.5, 0.1, 0.1, 0.1, 0.1, 0.1
boost::random::discrete_distribution<> dist(probabilities);

Now define a function that simulates rolling this die.

int roll_weighted_die() {
    1return dist(gen) + 1;


Add 1 to make sure that the result is in the range [1,6] instead of [0,5].

For the source of this example see password.cpp.

This example demonstrates generating a random 8 character password.

#include <boost/random/random_device.hpp>
#include <boost/random/uniform_int_distribution.hpp>
#include <iostream>

int main() {
    1std::string chars(
        "`~-_=+[{]}\\|;:'\",<.>/? ");
    2boost::random::random_device rng;
    3boost::random::uniform_int_distribution<> index_dist(0, chars.size() - 1);
    for(int i = 0; i < 8; ++i) {
        std::cout << chars[index_dist(rng)];
    std::cout << std::endl;


We first define the characters that we're going to allow. This is pretty much just the characters on a standard keyboard.


We use random_device as a source of entropy, since we want passwords that are not predictable.


Finally we select 8 random characters from the string and print them to cout.

For the source of this example see intersections.cpp.

This example demonstrates generating quasi-randomly distributed chord entry and exit points on an S2 sphere.

First we include the headers we need for niederreiter_base2 and uniform_01 distribution.

#include <boost/random/niederreiter_base2.hpp>
#include <boost/random/uniform_01.hpp>

#include <boost/math/constants/constants.hpp>

#include <boost/tuple/tuple.hpp>

We use 4-dimensional niederreiter_base2 as a source of randomness.

boost::random::niederreiter_base2 gen(4);

int main()
  typedef boost::tuple<double, double, double> point_t;

  const std::size_t n_points = 100; // we will generate 100 points

  std::vector<point_t> points;

  1boost::random::uniform_01<double> dist;

  for (std::size_t i = 0; i != n_points; ++i)

Using formula from J. Rovira et al., "Point sampling with uniformly distributed lines", 2005 to compute uniformly distributed chord entry and exit points on the surface of a sphere.

double cos_theta = 1 - 2 * dist(gen);
double sin_theta = std::sqrt(1 - cos_theta * cos_theta);
double phi = boost::math::constants::two_pi<double>() * dist(gen);
double sin_phi = std::sin(phi), cos_phi = std::cos(phi);

point_t point_on_sphere(sin_theta*sin_phi, cos_theta, sin_theta*cos_phi);

Here we assume that our sphere is a unit sphere at origin. If your sphere was different then now would be the time to scale and translate the point_on_sphere.


Vector points now holds generated 3D points on a sphere.

  return 0;


niederreiter_base2 produces integers in the range [0, 264-1]. However, we want numbers in the range [0, 1). The distribution uniform_01 performs this transformation.