Notes for oneMKL Vector Statistics

Developer Reference

Contents

R250

This is a generalized feedback shift register generator:
Feedback shift register generators possess ample theoretical foundation and were initially intended for cryptographic and communication applications. Physicists widely use R250 generator, as it is simple and fast in implementation. However, this generator fails in some types of tests, one of which is the 2D Self-Avoiding Random Walk Test.
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
x
0
,
x
1
, ...
Stream Initialization by Function
vslNewStream
R250 generates the stream and initializes it specifying the input 32-bit integer parameter seed. The stream state is the array of 250 32-bit integers
x
-250
,
x
-249
,
x
-1
, initialized in the following way:
  1. If seed = 0, assume seed = 1. Assume
    x
    -250
     = seed.
  2. Initialize
    x
    -249
    , ...,
    x
    0
     according to recurrent correlation
    x
    n+1
     = 69069
    x
    n
    (mod2
    32
    ).
  3. Interpret the values
    x
    7
    k
    -247
    ,
    k
     = 0, 1, ..., 31 as a binary matrix of size 32x32 and perform the following: set the diagonal bits to 1, and the under-diagonal bits to 0.
Stream Initialization by Function
vslNewStreamEx
R250 generates a stream and initializes it specifying the array
n
 of 32-bit integer
params[]
 :
  1. If
    n
     ≥ 0, assume x
    k-250
     = params[k] ,
    k
    =0,1,...,249.
If
n
 = 0, assume seed = 1, and perform the initialization as described in the above section on stream initialization by the function
vslNewStream
 .
Subsequences Selection Methods
vslSkipAheadStream
Not supported
vslSkipAheadStreamEx
Not supported
vslLeapfrogStream
Not supported
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 (0% errors) 
Bitstream Test
Not applicable
Not applicable
Not applicable
OK (25% 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 (30% errors) 
Counts-the-1’s Test (stream of specific bytes)
Not applicable
Not applicable
Not applicable
OK (0% errors) 
Craps Test
OK (20% errors) 
OK (20% errors) 
OK (20% errors) 
OK (20% errors) 
Parking Lot Test
OK (0% errors) 
OK (0% errors) 
Not applicable
OK (0% errors) 
2D Self-Avoiding Random Walk Test
FAIL (70% errors) 
FAIL (80% errors) 
Not applicable
FAIL (80% 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.