std::mersenne_twister_engine

< cpp‎ | numeric‎ | random
Defined in header <random>
template<

    class UIntType,
    std::size_t w, std::size_t n, std::size_t m, std::size_t r,
    UIntType a, std::size_t u, UIntType d, std::size_t s,
    UIntType b, std::size_t t,
    UIntType c, std::size_t l, UIntType f

> class mersenne_twister_engine;
 (since C++11)

mersenne_twister_engine is a random number engine based on Mersenne Twister algorithm. It produces high quality unsigned integer random numbers of type UIntType on the interval [0, 2w
).

The following type aliases define the random number engine with two commonly used parameter sets:

Defined in header <random>
Type Definition
mt19937(C++11)

std::mersenne_twister_engine<std::uint_fast32_t, 32, 624, 397, 31,
                             0x9908b0df, 11,
                             0xffffffff, 7,
                             0x9d2c5680, 15,
                             0xefc60000, 18, 1812433253>
32-bit Mersenne Twister by Matsumoto and Nishimura, 1998
mt19937_64(C++11)

std::mersenne_twister_engine<std::uint_fast64_t, 64, 312, 156, 31,
                             0xb5026f5aa96619e9, 29,
                             0x5555555555555555, 17,
                             0x71d67fffeda60000, 37,
                             0xfff7eee000000000, 43, 6364136223846793005>
64-bit Mersenne Twister by Matsumoto and Nishimura, 2000

Template parameters

UIntType - The result type generated by the generator. The effect is undefined if this is not one of unsigned short, unsigned int, unsigned long, or unsigned long long.
w - the power of two that determines the range of values generated by the engine
n - the degree of recurrence
m - the middle word, an offset used in the recurrence relation defining the series x, 1 ≤ m < n
r - the number of bits of the lower bit-mask, 0 ≤ r ≤ w - 1, also known as the twist value
a - the conditional xor-mask, i.e. the coefficients of the rational normal form twist matrix
u - 1st component of the bit-scrambling (tempering) matrix
d - 2nd component of the bit-scrambling (tempering) matrix
s - 3rd component of the bit-scrambling (tempering) matrix
b - 4th component of the bit-scrambling (tempering) matrix
t - 5th component of the bit-scrambling (tempering) matrix
c - 6th component of the bit-scrambling (tempering) matrix
l - 7th component of the bit-scrambling (tempering) matrix
f - the initialization multiplier


The following relations shall hold:

0 < m <= n,

2 < w,
r <= w,
u <= w,
s <= w,
t <= w,
l <= w,
w <= std::numeric_limits<UIntType>::digits,
a <= 2^w-1,
b <= 2^w-1,
c <= 2^w-1,
d <= 2^w-1, and

f <= 2^w-1 (a^b denotes a to the power of b)

Member types

Member type Definition
result_type(C++11) The integral type, UIntType, generated by the engine. Results are undefined if this is not an unsigned integral type.

Member functions

Construction and Seeding
(C++11)
 constructs the engine
(public member function)
(C++11)
 sets the current state of the engine
(public member function)
Generation
(C++11)
 advances the engine's state and returns the generated value
(public member function)
(C++11)
 advances the engine's state by a specified amount
(public member function)
Characteristics
[static] (C++11)
 gets the smallest possible value in the output range
(public static member function)
[static] (C++11)
 gets the largest possible value in the output range
(public static member function)

Non-member functions

(C++11)(C++11)(removed in C++20)
 compares the internal states of two pseudo-random number engines
(function)
(C++11)
 performs stream input and output on pseudo-random number engine
(function template)

Member constants

constexpr size_t word_size
[static] (C++11)
 the template parameter w, determines the range of values generated by the engine.
(public static member constant)
constexpr size_t state_size
[static] (C++11)
 the template parameter n. The engine state is n values of UIntType
(public static member constant)
constexpr size_t shift_size
[static] (C++11)
 the template parameter m
(public static member constant)
constexpr size_t mask_bits
[static] (C++11)
 the template parameter r, also known as the twist value.
(public static member constant)
constexpr UIntType xor_mask
[static] (C++11)
 the template parameter a, the conditional xor-mask.
(public static member constant)
constexpr size_t tempering_u
[static] (C++11)
 the template parameter u, first component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr UIntType tempering_d
[static] (C++11)
 the template parameter d, second component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr size_t tempering_s
[static] (C++11)
 the template parameter s, third component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr UIntType tempering_b
[static] (C++11)
 the template parameter b, fourth component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr size_t tempering_t
[static] (C++11)
 the template parameter t, fifth component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr UIntType tempering_c
[static] (C++11)
 the template parameter c, sixth component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr size_t tempering_l
[static] (C++11)
 the template parameter l, seventh component of the bit-scrambling (tempering) matrix
(public static member constant)
constexpr UIntType initialization_multiplier
[static] (C++11)
 the template parameter f
(public static member constant)
constexpr UIntType default_seed
[static] (C++11)
 the constant value 5489u
(public static member constant)

Notes

The Nth consecutive invocation of a default-constructed engine is required to produce the following value:

N The rangom engine type The value to produce
10000 std::mt19937 4123659995
10000 std::mt19937_64 9981545732273789042 
#include <random>
#include <cassert>
int main()
{
    std::mt19937 gen32;
    std::mt19937_64 gen64;
 
    for (auto n{1}; n != 10'000; gen32(), gen64(), ++n);
 
    assert(gen32() == 4'123'659'995 and
           gen64() == 9'981'545'732'273'789'042ULL);
}