MT19937
This is a Mersenne Twister pseudorandom number generator:







Matrix A (32x32) has the following format:

where the 32-bit vector
a = a
31
... a
0
has the value a
= 0x9908B0DF.Mersenne Twister pseudorandom number generator MT19937 is a modification of twisted generalized feedback shift register generator [Matsum92], [Matsum94]. MT19937 has the period length of 2
19937
-1 and is 623-dimensionally equidistributed with up to 32-bit accuracy. These properties make the generator applicable for simulations in various fields of science and engineering. The initialization procedure is essentially the same as described in [MT2002]. The state of the generator is represented by 624 32-bit unsigned integer numbers.Real Implementation (Single and Double Precision)
The output vector is the sequence of the floating-point values
u
0
, u
1
, ...Integer Implementation
The output vector of 32-bit integers
y
0
, y
1
, ...Stream Initialization by Function
vslNewStream
MT19937 generates the stream and initializes it specifying the input 32-bit unsigned integer parameter seed. The stream state, that is, the array of 624 32-bit integers
x
0
, ..., x
623
, is initialized by the procedure described in [MT2002] and based on the seed value.Stream Initialization of Function
vslNewStreamEx
MT19937 generates the stream and initializes it specifying the array the array
params[]
of n
32-bit integers:- Ifn= 0, assume params[0] = 1,n= 1 and perform initialization as described in the previous item.
Subsequences Selection Methods
vslSkipAheadStream |
Supported
|
vslSkipAheadStreamEx |
Not supported
|
vslLeapfrogStream |
Not supported
|
Skip-ahead method supported by MT19937 is based on algorithms described in [Haram08].
Generator Period

Empirical Testing Results Summary
Test Name
| vsRngUniform | vdRngUniform | viRngUniform | viRngUniformBits |
---|---|---|---|---|
3D Spheres Test
|
OK (0% errors)
|
OK (0% errors)
|
Not applicable
|
OK (0% errors)
|
Birthday Spacing Test
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (10% errors)
|
Bitstream Test
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (10% errors)
|
Rank of 31x31 Binary Matrices Test
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (10% errors)
|
Rank of 32x32 Binary Matrices Test
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (0% errors)
|
Rank of 6x8 Binary Matrices Test
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (0% errors)
|
Counts-the-1’s Test (stream of bits)
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (20% errors)
|
Counts-the-1’s Test (stream of specific bytes)
|
Not applicable
|
Not applicable
|
Not applicable
|
OK (0% errors)
|
Craps Test
|
OK (30% errors)
|
OK (30% errors)
|
OK (30% errors)
|
OK (30% errors)
|
Parking Lot Test
|
OK (0% errors)
|
OK (0% errors)
|
Not applicable
|
OK (0% errors)
|
2D Self-Avoiding Random Walk Test
|
OK (0% errors)
|
OK (10% errors)
|
Not applicable
|
OK (10% errors)
|
- The tabulated data is obtained using the one-level (threshold) testing technique. The OK result indicates FAIL < 50%. The run fails when p-value falls outside the interval [0.05, 0.95].
- The stream tested is generated by calling the functionvslNewStreamwith seed=7,777,777.