std::mersenne_twister_engine

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
).

[edit] Template parameters

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

[edit] 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. $\scriptsize X_j$Xj 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(xi)) is defined as follows:

1. Concatenate the upper w - r bits of $\scriptsize X_{i-n}$Xi-n with the lower r bits of $\scriptsize X_{i+1-n}$Xi+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 $\scriptsize X_i$Xi to $\scriptsize X_{i+m−n}\ \mathsf{xor}\ (Y\ \mathsf{rshift}\ 1)\ \mathsf{xor}\ y$Xi+m−n xor (Y rshift 1) xor y.

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

1. Let $\scriptsize z_1$z1 be $\scriptsize X_i\ \mathsf{xor}\ ((X_i\ \mathsf{rshift}\ u)\ \mathsf{bitand}\ d)$Xi xor ((Xi rshift u) bitand d).
2. Let $\scriptsize z_2$z2 be $\scriptsize z_1\ \mathsf{xor}\ (((z_1\ \mathsf{lshift}\ s)\mod 2^w)\ \mathsf{bitand}\ b)$Xi xor (((Xi lshift s) mod 2w
   ) bitand b).
3. Let $\scriptsize z_3$z3 be $\scriptsize z_2\ \mathsf{xor}\ (((z_2\ \mathsf{lshift}\ t)\mod 2^w)\ \mathsf{bitand}\ c)$Xi xor (((Xi lshift t) mod 2w
   ) bitand c).
4. Let $\scriptsize z_4$z4 be $\scriptsize z_3\ \mathsf{xor}\ (z_3\ \mathsf{rshift}\ l)$z3 xor (z3 rshift l).
5. Deliver $\scriptsize z_4$z4 as the result (i.e. $\scriptsize GA(x_i)=z_4$GA(xi)=z4).

[edit] Predefined specializations

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

[edit] Nested types

[edit] Data members

[edit] Member functions

[edit] Non-member functions

[edit] Example