MT19937

This is a Mersenne Twister pseudorandom number generator:

,

,

,                   

,                                     

,                

,

.

Matrix A (32x32) has the following format:

where the 32-bit vector a = a31 ... a0 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 219937-1 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 u0, u1, ...

Integer Implementation

The output vector of 32-bit integers y0, y1, ...

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 x0, ..., x623, 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:

  1. If n ≥ 1, perform initialization as described in [MT2002] using array params[]on input.

  2. If n = 0, assume params[0] = 1, n = 1 and perform initialization as described in the previous item.

Subsequences Selection Methods

vslSkipAheadStream

Supported

vslLeapfrogStream

Not supported

vslSkipAheadStream

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) 

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) 

Note

  1. 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].

  2. The stream tested is generated by calling the function vslNewStream with seed=7,777,777. 

For more complete information about compiler optimizations, see our Optimization Notice.
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