Notes for oneMKL Vector Statistics

Developer Reference

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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:
  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
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) 
  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. 

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.