std::mersenne_twister_engine

 

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linear_congruential_engine (C++11)

mersenne_twister_engine (C++11)

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normal_distribution (C++11)

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C library

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RAND_MAX

 

std::mersenne_twister_engine

Member functions

mersenne_twister_engine::mersenne_twister_engine (C++11)

mersenne_twister_engine::seed (C++11)

Generation

mersenne_twister_engine::operator() (C++11)

mersenne_twister_engine::discard (C++11)

Characteristics

mersenne_twister_engine::min (C++11)

mersenne_twister_engine::max (C++11)

Non-member functions

operator==operator!= (C++11)(C++11)(until C++20)

operator<<operator>> (C++11)(C++11)

 

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 \(\scriptsize {[0,2^w)}\)[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
(constructor) (C++11)	constructs the engine (public member function)
seed (C++11)	sets the current state of the engine (public member function)
Generation
operator() (C++11)	advances the engine's state and returns the generated value (public member function)
discard (C++11)	advances the engine's state by a specified amount (public member function)
Characteristics
min [static] (C++11)	gets the smallest possible value in the output range (public static member function)
max [static] (C++11)	gets the largest possible value in the output range (public static member function)

Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20)	compares the internal states of two pseudo-random number engines (function)
operator<<operator>> (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

Run this code

#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);
}