Notes for oneMKL Vector Statistics

Developer Reference

Contents

Philox4x32-10

This is a keyed family of counter-based BRNGs. The state consists of 128-bit integer counter
c
 and two 32-bit keys
k
0
 and
k
1
. The generator has 32-bit integer output obtained in the following way [Salmon2011]:
  1. c
    n
     =
    c
    n-1
     + 1
  2. w
    n
     =
    f(c
    n
    )
    , where
    f
     is a function that takes a 128-bit argument and returns a 128-bit number. The returned number is obtained as follows:
    1. The argument
      c
       is interpreted as four 32-bit numbers , where , put
      k
      0
      0
       =
      k
      0
       and
      k
      1
      0
       =
      k
      1
      .
    2. The following recurrence is calculated:
      Where
      mulhi(a,b)
       and
      mullo(a,b)
       are high and low 32-bit parts of the a*b product, respectively.
    3. Put
      f(c) =
       , where
      N
       = 10
  3. Integer output:
    r
    4n+k
     =
    w
    n
    (k)
    , where
    w
    n
    (k)
     is the
    k
    -th 32-bit integer in quadruple
    w
    n
    ,
    k
     = 0, 1, 2, 3
  4. Real output:
    u
    n
     =
    (int)r
    n
    /2
    32
     +
    ½
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
r
0
,
r
1
, ...
Stream Initialization by Function
vslNewStream
Philox4x32-10 generates the stream and initializes it specifying the 32-bit input integer parameter seed. The stream state is a 128-bit number
c
 and a pair of 32-bit integers
k
0
 and
k
1
 initialized in the following way:
  1. Assume
    k
    0
     = seed.
  2. Assume the other values are equal to 0, that is
    k
    1
     = 0 and
    c
     = 0.
Stream Initialization by Function
vslNewStreamEx
Philox4x32-10 generates the stream and initializes it specifying the array
params[]
 of
n
 32-bit integers:
  1. If
    n
     = 0, assume
    c
     =
    k
    0
     =
    k
    1
     = 0.
  2. If
    n
     = 1, assume
    k
     = params[0],
    c
     = 0.
  3. If
    n
     = 2, assume
    k
     = params[0] + params[1]*2
    32
    ,
    c
     = 0.
  4. If
    n
     = 3, assume
    k
     = params[0] + params[1]*2
    32
    ,
    c
     = params[2].
  5. If
    n
     = 4, assume
    k
     = params[0] + params[1]*2
    32
    ,
    c
     = params[2] + params[3]*2
    32
    .
  6. If
    n
     = 5, assume
    k
     = params[0] + params[1]*2
    32
    ,
    c
     = params[2] + params[3]*2
    32
    + params[4]*2
    64
    .
  7. If
    n
     >= 6, assume
    k
     = params[0] + params[1]*2
    32
    ,
    c
     = params[2] + params[3]*2
    32
    + params[4]*2
    64
    + params[5]*2
    96
    .
Subsequences Selection Methods
vslSkipAheadStream
Supported
vslSkipAheadStreamEx
Supported
vslLeapfrogStream
Not supported
Generator Period
Empirical Testing Results Summary
Test Name
vsRngUniform
vdRngUniform
viRngUniform
viRngUniformBits
3D Spheres Test
OK (20% errors)
OK (20% errors)
Not applicable
OK (20% errors)
Birthday Spacing Test
Not applicable
Not applicable
Not applicable
OK (0% errors)
Bitstream Test
Not applicable
Not applicable
Not applicable
OK (15% 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 (0% 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
OK (10% errors)
OK (0% errors)
Not applicable
OK (0% 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.