<random>

Defines facilities for random number generation, allowing creation of uniformly distributed random numbers.

#include <random>

Summary

A random number generator is an object that produces a sequence of pseudo-random values. A generator that produces values that are uniformly distributed in a specified range is a Uniform Random Number Generator (URNG). A template class designed to function as a URNG is referred to as an engine if that class has certain common traits, which are discussed later in this article. A URNG can be—and usually is—combined with a distribution by passing the URNG as an argument to the distribution's operator() to produce values that are distributed in a manner that is defined by the distribution.

These links jump to the major sections of this article:

• Code Examples

• Categorized Listing

• Engines and Distributions

• Remarks

Quick Tips

Here are some tips to keep in mind when using <random>:

• For most purposes, URNGs produce raw bits that must be shaped by distributions. (A notable exception to this is std::shuffle() because it uses a URNG directly.)

• A single instantiation of a URNG or distribution cannot safely be called concurrently because running a URNG or distribution is a modifying operation. For more information, see Thread Safety in the C++ Standard Library.

• Predefined typedefs of several engines are provided; this is the preferred way to create a URNG if an engine is being used.

• The most useful pairing for most applications is the mt19937 engine with uniform_int_distribution, as shown in the code example later in this article.

There are many options to choose from in the <random> header, and any of them is preferable to the outdated C Runtime function rand(). For information about what's wrong with rand() and how <random> addresses these shortcomings, see this video.

Examples

The following code example shows how to generate some random numbers in this case five of them using a generator created with non-deterministic seed.

#include <random>
#include <iostream>

using namespace std;

int main()
{
    random_device rd;   // non-deterministic generator
    mt19937 gen(rd());  // to seed mersenne twister.
                        // replace the call to rd() with a
                        // constant value to get repeatable
                        // results.

    for (int i = 0; i < 5; ++i) {
        cout << gen() << " "; // print the raw output of the generator.
    }
    cout << endl;
}

Output:

2430338871 3531691818 2723770500 3252414483 3632920437

While these are high quality random numbers and different every time this program is run, they are not necessarily in a useful range. To control the range, use a uniform distribution as shown in the following code:

#include <random>
#include <iostream>

using namespace std;

int main()
{
    random_device rd;   // non-deterministic generator
    mt19937 gen(rd());  // to seed mersenne twister.
    uniform_int_distribution<> dist(1,6); // distribute results between 1 and 6 inclusive.

    for (int i = 0; i < 5; ++i) {
        cout << dist(gen) << " "; // pass the generator to the distribution.
    }
    cout << endl;
}

Output:

5 1 6 1 2

The next code example shows a more realistic set of use cases with uniformly distributed random number generators shuffling the contents of a vector and an array.

// cl.exe /EHsc /nologo /W4 /MTd
#include <algorithm>
#include <array>
#include <iostream>
#include <random>
#include <string>
#include <vector>
#include <functional> // ref()

using namespace std;

template <typename C> void print(const C& c) {
    for (const auto& e : c) {
        cout << e << " ";
    }

    cout << endl;
}

template <class URNG>
void test(URNG& urng) {

    // Uniform distribution used with a vector
    // Distribution is [-5, 5] inclusive
    uniform_int_distribution<int> dist(-5, 5);
    vector<int> v;

    for (int i = 0; i < 20; ++i) {
        v.push_back(dist(urng));
    }

    cout << "Randomized vector: ";
    print(v);

    // Shuffle an array 
    // (Notice that shuffle() takes a URNG, not a distribution)
    array<string, 26> arr = { { "H", "He", "Li", "Be", "B", "C", "N", "O", "F",
        "Ne", "Na", "Mg", "Al", "Si", "P", "S", "Cl", "Ar", "K", "Ca", "Sc",
        "Ti", "V", "Cr", "Mn", "Fe" } };

    shuffle(arr.begin(), arr.end(), urng);

    cout << "Randomized array: ";
    print(arr);
    cout << "--" << endl;
}

int main()
{
    // First run: non-seedable, non-deterministic URNG random_device
    // Slower but crypto-secure and non-repeatable.
    random_device rd;
    cout << "Using random_device URNG:" << endl;
    test(rd);

    // Second run: simple integer seed, repeatable results
    cout << "Using constant-seed mersenne twister URNG:" << endl;
    mt19937 engine1(12345);
    test(engine1);

    // Third run: random_device as a seed, different each run
    // (Desirable for most purposes)
    cout << "Using non-deterministic-seed mersenne twister URNG:" << endl;
    mt19937 engine2(rd());
    test(engine2);

    // Fourth run: "warm-up" sequence as a seed, different each run
    // (Advanced uses, allows more than 32 bits of randomness)
    cout << "Using non-deterministic-seed \"warm-up\" sequence mersenne twister URNG:" << endl;
    array<unsigned int, mt19937::state_size> seed_data;
    generate_n(seed_data.begin(), seed_data.size(), ref(rd));
    seed_seq seq(begin(seed_data), end(seed_data));
    mt19937 engine3(seq);
    test(engine3);
}

Example Output and Code Remarks

Using random_device URNG:
Randomized vector: 5 -4 2 3 0 5 -2 0 4 2 -1 2 -4 -3 1 4 4 1 2 -2
Randomized array: O Li V K C Ti N Mg Ne Sc Cl B Cr Mn Ca Al F P Na Be Si Ar Fe S He H
--
Using constant-seed mersenne twister URNG:
Randomized vector: 3 -1 -5 0 0 5 3 -4 -3 -4 1 -3 0 -3 -2 -4 5 1 -1 -1
Randomized array: Al O Ne Si Na Be C N Cr Mn H V F Sc Mg Fe K Ca S Ti B P Ar Cl Li He
--
Using non-deterministic-seed mersenne twister URNG:
Randomized vector: 5 -4 0 2 1 -2 4 4 -4 0 0 4 -5 4 -5 -1 -3 0 0 3
Randomized array: Si Fe Al Ar Na P B Sc H F Mg Li C Ti He N Mn Be O Ca Cr V K Ne Cl S
--
Using non-deterministic-seed "warm-up" sequence mersenne twister URNG:
Randomized vector: -1 3 -2 4 1 3 0 -5 5 -5 0 0 5 0 -3 3 -4 2 5 0
Randomized array: Si C Sc H Na O S Cr K Li Al Ti Cl B Mn He Fe Ne Be Ar V P Ca N Mg F
--

This code demonstrates two different randomizations—randomize a vector of integers and shuffle an array of indexed data—with a test template function. The first call to the test function uses the crypto-secure, non-deterministic, not-seedable, non-repeatable URNG random_device. The second test run uses mersenne_twister_engine as URNG, with a deterministic 32-bit constant seed, which means the results are repeatable. The third test run seeds mersenne_twister_engine with a 32-bit non-deterministic result from random_device. The fourth test run expands on this by using a seed sequence filled with random_device results, which effectively gives more than 32-bit non-deterministic randomness (but still not crypto-secure). For more information, read on.

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Categorized Listing

Uniform Random Number Generators

URNGs are often described in terms of these properties:

1. Period length: How many iterations it takes to repeat the sequence of numbers generated. The longer the better.

2. Performance: How quickly numbers can be generated and how much memory it takes. The smaller the better.

3. Quality: How close to true random numbers the generated sequence is. This is often called "randomness".

The following sections list the uniform random number generators (URNGs) provided in the <random> header.

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Non-Deterministic Generator

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Engine Typedefs with Predefined Parameters

For instantiating engines and engine adaptors. For more information, see Engines and Distributions.

typedef mt19937 default_random_engine;

typedef shuffle_order_engine<minstd_rand0, 256> knuth_b;

typedef linear_congruential_engine<unsigned int, 16807, 0, 2147483647> minstd_rand0;

typedef linear_congruential_engine<unsigned int, 48271, 0, 2147483647> minstd_rand;

typedef mersenne_twister_engine<unsigned int, 32, 624, 397, 
    31, 0x9908b0df, 
    11, 0xffffffff, 
    7, 0x9d2c5680, 
    15, 0xefc60000, 
    18, 1812433253> mt19937;

typedef mersenne_twister_engine<unsigned long long, 64, 312, 156, 
    31, 0xb5026f5aa96619e9ULL, 
    29, 0x5555555555555555ULL, 
    17, 0x71d67fffeda60000ULL, 
    37, 0xfff7eee000000000ULL, 
    43, 6364136223846793005ULL> mt19937_64;

typedef discard_block_engine<ranlux24_base, 223, 23> ranlux24;

typedef subtract_with_carry_engine<unsigned int, 24, 10, 24> ranlux24_base;

typedef discard_block_engine<ranlux48_base, 389, 11> ranlux48;

typedef subtract_with_carry_engine<unsigned long long, 48, 5, 12> ranlux48_base;

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Engine Templates

Engine templates are used as standalone URNGs or as base engines passed to engine adaptors. Usually these are instantiated with a predefined engine typedef and passed to a distribution. For more information, see the Engines and Distributions section.

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Engine Adaptor Templates

Engine adaptors are templates that adapt other (base) engines. Usually these are instantiated with a predefined engine typedef and passed to a distribution. For more information, see the Engines and Distributions section.

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Random Number Distributions

The following sections list the distributions provided in the <random> header. Distributions are a post-processing mechanism, usually using URNG output as input and distributing the output by a defined statistical probability density function. For more information, see the Engines and Distributions section.

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Uniform Distributions

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Bernoulli Distributions

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Normal Distributions

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Poisson Distributions

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Sampling Distributions

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Utility Functions

This section lists the general utility functions provided in the <random> header.

Operators

This section lists the operators provided in the <random> header.

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Engines and Distributions

Refer to the following sections for information about each of these template class categories defined in <random>. Both of these template class categories take a type as an argument and use shared template parameter names to describe the properties of the type that are permitted as an actual argument type, as follows:

• IntType indicates a short, int, long, long long, unsigned short, unsigned int, unsigned long, or unsigned long long.

• UIntType indicates unsigned short, unsigned int, unsigned long, or unsigned long long.

• RealType indicates a float, double, or long double.

Engines

Engines and engine adaptors are templates whose parameters customize the generator created.

An engine is a class or template class whose instances (generators) act as a source of random numbers uniformly distributed between a minimum and maximum value. An engine adaptor delivers a sequence of values that have different randomness properties by taking values produced by some other random number engine and applying an algorithm of some kind to those values.

Every engine and engine adaptor has the following members:

• typedef numeric-type result_type is the type that is returned by the generator's operator(). The numeric-type is passed as a template parameter on instantiation.

• result_type operator() returns values that are uniformly distributed between min() and max().

• result_type min() returns the minimum value that is returned by the generator's operator(). Engine adaptors use the base engine's min() result.

• result_type max() returns the maximum value that is returned by the generator's operator(). When result_type is an integral (integer-valued) type, max() is the maximum value that can actually be returned (inclusive); when result_type is a floating-point (real-valued) type, max() is the smallest value greater than all values that can be returned (non-inclusive). Engine adaptors use the base engine's max() result.

• void seed(result_type s) seeds the generator with seed value s. For engines, the signature is void seed(result_type s = default_seed) for default parameter support (engine adaptors define a separate void seed(), see next subsection).

• template <class Seq> void seed(Seq& q) seeds the generator by using a seed_seqSeq.

• An explicit constructor with argument result_type x that creates a generator seeded as if by calling seed(x).

• An explicit constructor with argument seed_seq& seq that creates a generator seeded as if by calling seed(seq).

• void discard(unsigned long long count) effectively calls operator()count times and discards each value.

Engine adaptors additionally support these members (Engine is the first template parameter of an engine adaptor, designating the base engine's type):

• A default constructor to initialize the generator as if from the base engine's default constructor.

• An explicit constructor with argument const Engine& eng. This is to support copy construction using the base engine.

• An explicit constructor with argument Engine&& eng. This is to support move construction using the base engine.

• void seed() that initializes the generator with the base engine's default seed value.

• const Engine& base() property function that returns the base engine that was used to construct the generator.

Every engine maintains a state that determines the sequence of values that will be generated by subsequent calls to operator(). The states of two generators instantiated from engines of the same type can be compared by using operator== and operator!=. If the two states compare as equal, they will generate the same sequence of values. The state of an object can be saved to a stream as a sequence of 32-bit unsigned values by using the operator<< of the generator. The state is not changed by saving it. A saved state can be read into generator instantiated from an engine of the same type by using operator>>.

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Distributions

A distribution is a class or template class whose instances transform a stream of uniformly distributed random numbers obtained from an engine into a stream of random numbers that have a particular distribution. Every distribution has the following members:

• typedef numeric-type result_type is the type that is returned by the distribution's operator(). The numeric-type is passed as a template parameter on instantiation.

• template <class URNG> result_type operator()(URNG& gen) returns values that are distributed according to the distribution's definition, by using gen as a source of uniformly distributed random values and the stored parameters of the distribution.

• template <class URNG> result_type operator()(URNG& gen, param_type p) returns values distributed in accordance with the distribution's definition, using gen as a source of uniformly distributed random values and the parameters structure p.

• typedef unspecified-type param_type is the package of parameters optionally passed to operator() and is used in place of the stored parameters to generate its return value.

• A const param& constructor initializes the stored parameters from its argument.

• param_type param() const gets the stored parameters.

• void param(const param_type&) sets the stored parameters from its argument.

• result_type min() returns the minimum value that is returned by the distribution's operator().

• result_type max() returns the maximum value that is returned by the distribution's operator(). When result_type is an integral (integer-valued) type, max() is the maximum value that can actually be returned (inclusive); when result_type is a floating-point (real-valued) type, max() is the smallest value greater than all values that can be returned (non-inclusive).

• void reset() discards any cached values, so that the result of the next call to operator() does not depend on any values obtained from the engine before the call.

A parameter structure is an object that stores all of the parameters needed for a distribution. It contains:

• typedef distribution-type distribution_type, which is the type of its distribution.

• One or more constructors that take the same parameter lists as the distribution constructors take.

• The same parameter-access functions as the distribution.

• Equality and inequality comparison operators.

For more information, see the reference subtopics below this one, linked previously in this article.

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Remarks

There are two highly useful URNGs in Visual Studio—mt19937 and random_device—as shown in this comparison table:

* When provided with a known seed.

Although the ISO C++ Standard does not require random_device to be cryptographically secure, in Visual Studio it is implemented to be cryptographically secure. (The term "cryptographically secure" does not imply guarantees, but refers to a minimum level of entropy—and therefore, the level of predictability—a given randomization algorithm provides. For more information, see the Wikipedia article Cryptographically secure pseudorandom number generator.) Because the ISO C++ Standard does not require this, other platforms may implement random_device as a simple pseudo-random number generator (not cryptographically secure) and may only be suitable as a seed source for another generator. Check the documentation for those platforms when using random_device in cross-platform code.

By definition, random_device results are not reproducible, and a side-effect is that it may run significantly slower than other URNGs. Most applications that are not required to be cryptographically secure use mt19937 or a similar engine, although you may want to seed it with a call to random_device, as shown in the code example.

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See Also

Other Resources

C++ Standard Library Header Files