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std::mersenne_twister_engine - cppreference.com

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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 [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. Xj stands for the j mod nth value (starting from 0) of X.

Given the following bitwise operation notations:

The transition algorithm of mersenne_twister_engine (TA(xi)) is defined as follows:

  1. Concatenate the upper w - r bits of Xi-n with the lower r bits of Xi+1-n to obtain an unsigned integer value Y.
  2. Let y be a·(Y bitand 1), and set Xi to Xi+m−n xor (Y rshift 1) xor y.

The generation algorithm of mersenne_twister_engine (GA(xi)) is defined as follows:

  1. Let z1 be Xi xor ((Xi rshift u) bitand d).
  2. Let z2 be Xi xor (((Xi lshift s) mod 2w
    ) bitand b)    .
  3. Let z3 be Xi xor (((Xi lshift t) mod 2w
    ) bitand c)    .
  4. Let z4 be z3 xor (z3 rshift l).
  5. Deliver z4 as the result (i.e. GA(xi)=z4).

Predefined specializations

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

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[edit]

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[edit]

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
constructs the engine
(public member function) [edit]
sets the current state of the engine
(public member function) [edit]
Generation
advances the engine's state and returns the generated value
(public member function) [edit]
advances the engine's state by a specified amount
(public member function) [edit]
Characteristics

[static]

 gets the smallest possible value in the output range
(public static member function) [edit]

[static]

 gets the largest possible value in the output range
(public static member function) [edit]

Non-member functions

Example