std::mersenne_twister_engine

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Execution support library (C++26)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

Pseudo-random number generation

Uniform random bit generators   uniform_random_bit_generator (C++20) Random number engines linear_congruential_engine (C++11) mersenne_twister_engine (C++11) subtract_with_carry_engine (C++11) philox_engine (C++26) Random number engine adaptors discard_block_engine (C++11) independent_bits_engine (C++11) shuffle_order_engine (C++11) Predefined random number generators Non-deterministic random numbers random_device (C++11) Utilities generate_canonical (C++11) seed_seq (C++11) Random number algorithms ranges::generate_random (C++26) C random library rand    srand    RAND_MAX

Random number distributions Uniform distributions uniform_int_distribution (C++11) uniform_real_distribution (C++11) generate_canonical (C++11) Bernoulli distributions bernoulli_distribution (C++11) binomial_distribution (C++11) negative_binomial_distribution (C++11) geometric_distribution (C++11) Poisson distributions poisson_distribution (C++11) exponential_distribution (C++11) gamma_distribution (C++11) weibull_distribution (C++11) extreme_value_distribution (C++11) Normal distributions normal_distribution (C++11) lognormal_distribution (C++11) chi_squared_distribution (C++11) cauchy_distribution (C++11) fisher_f_distribution (C++11) student_t_distribution (C++11) Sampling distributions discrete_distribution (C++11) piecewise_constant_distribution (C++11) piecewise_linear_distribution (C++11)

 

std::mersenne_twister_engine

Member functions

mersenne_twister_engine::mersenne_twister_engine

mersenne_twister_engine::seed

Generation

mersenne_twister_engine::operator()

mersenne_twister_engine::discard

Characteristics

mersenne_twister_engine::min

mersenne_twister_engine::max

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, but not cryptographically secure, unsigned integer random numbers of type UIntType on the interval \(\scriptsize {[0,2^w)}\)[0, 2w
).

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 state
r	-	the number of bits of the lower bit-mask, also known as the twist value
a	-	the conditional xor-mask, i.e. the coefficients of the rational normal form twist matrix
u, d, s, b, t, c, l	-	the 1st to 7th components of the bit-scrambling (tempering) matrix
f	-	the initialization multiplier

If any of the following restrictions is violated, the program is ill-formed:

• m is in [1, n].
• The following expressions are all true:

• w >= 3
• w >= r
• w >= u
• w >= s
• w >= t
• w >= l
• w <= std::numeric_limits<UIntType>::digits

• Given (1u << w) - 1u as w1, the following expressions are all true:

• a <= w1
• b <= w1
• c <= w1
• d <= w1
• f <= w1

Generator properties

The size of the states of mersenne_twister_engine is n, each of them consists of a sequence X of n values of type result_type. \(\scriptsize X_j\)X
j stands for the \(\scriptsize j\mod n\)j mod nth value (starting from 0) of X.

Given the following bitwise operation notations:

• \(\scriptsize \mathsf{bitand}\)bitand, built-in bitwise AND.
• \(\scriptsize \mathsf{xor}\)xor, built-in bitwise XOR.
• \(\scriptsize \mathsf{lshift}\)lshift, built-in bitwise left-shift.
• \(\scriptsize \mathsf{rshift}\)rshift, built-in bitwise right-shift.

The transition algorithm of mersenne_twister_engine (\(\scriptsize TA(x_i)\)TA(x
i)) is defined as follows:

1. Concatenate the upper w - r bits of \(\scriptsize X_{i-n}\)X
   i-n with the lower r bits of \(\scriptsize X_{i+1-n}\)X
   i+1-n to obtain an unsigned integer value Y.
2. Let y be \(\scriptsize a \cdot (Y\ \mathsf{bitand}\ 1)\)a·(Y bitand 1), and set \(\scriptsize X_i\)X
   i to \(\scriptsize X_{i+m−n}\ \mathsf{xor}\ (Y\ \mathsf{rshift}\ 1)\ \mathsf{xor}\ y\)X
   i+m−n xor (Y rshift 1) xor y.

The generation algorithm of mersenne_twister_engine (\(\scriptsize GA(x_i)\)GA(x
i)) is defined as follows:

1. Let \(\scriptsize z_1\)z
   1 be \(\scriptsize X_i\ \mathsf{xor}\ ((X_i\ \mathsf{rshift}\ u)\ \mathsf{bitand}\ d)\)X
   i xor ((X
   i rshift u) bitand d).
2. Let \(\scriptsize z_2\)z
   2 be \(\scriptsize z_1\ \mathsf{xor}\ (((z_1\ \mathsf{lshift}\ s)\mod 2^w)\ \mathsf{bitand}\ b)\)X
   i xor (((X
   i lshift s) mod 2w
   ) bitand b).
3. Let \(\scriptsize z_3\)z
   3 be \(\scriptsize z_2\ \mathsf{xor}\ (((z_2\ \mathsf{lshift}\ t)\mod 2^w)\ \mathsf{bitand}\ c)\)X
   i xor (((X
   i lshift t) mod 2w
   ) bitand c).
4. Let \(\scriptsize z_4\)z
   4 be \(\scriptsize z_3\ \mathsf{xor}\ (z_3\ \mathsf{rshift}\ l)\)z
   3 xor (z
   3 rshift l).
5. Deliver \(\scriptsize z_4\)z
   4 as the result (i.e. \(\scriptsize GA(x_i)=z_4\)GA(x
   i)=z
   4).

Predefined specializations

The following specializations 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

Nested types

Type	Definition
result_type	UIntType

Data members

constexpr size_t word_size [static]	w (public static member constant)
constexpr size_t state_size [static]	n (public static member constant)
constexpr size_t shift_size [static]	m (public static member constant)
constexpr size_t mask_bits [static]	r (public static member constant)
constexpr UIntType xor_mask [static]	a (public static member constant)
constexpr size_t tempering_u [static]	u (public static member constant)
constexpr UIntType tempering_d [static]	d (public static member constant)
constexpr size_t tempering_s [static]	s (public static member constant)
constexpr UIntType tempering_b [static]	b (public static member constant)
constexpr size_t tempering_t [static]	t (public static member constant)
constexpr UIntType tempering_c [static]	c (public static member constant)
constexpr size_t tempering_l [static]	l (public static member constant)
constexpr UIntType initialization_multiplier [static]	f (public static member constant)
constexpr UIntType default_seed [static]	5489u (public static member constant)

Member functions

Construction and Seeding
(constructor)	constructs the engine (public member function)
seed	sets the current state of the engine (public member function)
Generation
operator()	advances the engine's state and returns the generated value (public member function)
discard	advances the engine's state by a specified amount (public member function)
Characteristics
min [static]	gets the smallest possible value in the output range (public static member function)
max [static]	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)