mersenne_twister_engine is a random number engine based onMersenne Twister algorithm. It produces high quality, but not cryptographically secure, unsigned integer random numbers of typeUIntType 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 alltrue:

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

• Given(1u<< w)- 1u asw1, the following expressions are alltrue:

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

[edit]Generator properties

Thesize of the states ofmersenne_twister_engine isn, each of them consists of a sequenceX ofn values of typeresult_type.\(\scriptsize X_j\)Xj stands for the\(\scriptsize j\mod n\)j mod nth value (starting from 0) ofX.

Given the following bitwise operation notations:

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

Thetransition algorithm ofmersenne_twister_engine (\(\scriptsize TA(x_i)\)TA(xi)) is defined as follows:

1. Concatenate the upperw- r bits of\(\scriptsize X_{i-n}\)Xi-n with the lowerr bits of\(\scriptsize X_{i+1-n}\)Xi+1-n to obtain an unsigned integer valueY.
2. Lety 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.

Thegeneration algorithm ofmersenne_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

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