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. cn
    =
    cn-1
    + 1
  2. wn
    =
    f(cn)
    , 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:
    r4n+k
     =
    wn(k)
    , where
    wn(k)
    is the
    k
    -th 32-bit integer in quadruple
    wn
    ,
    k
     = 0, 1, 2, 3
  4. Real output:
    un = (int)rn/232 + 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)
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. 

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804