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 k0 and k1. 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 k00 = k0 and k10 = k1.

    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 u0, u1, ...

Integer Implementation

The output vector of 32-bit integers r0, r1, ...

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 k0 and k1 initialized in the following way:

  1. Assume k0 = seed.
  2. Assume the other values are equal to 0, that is k1 = 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 = k0 = k1 = 0.
  2. If n = 1, assume k = params[0], c = 0.
  3. If n = 2, assume k = params[0] + params[1]*232, c = 0.
  4. If n = 3, assume k = params[0] + params[1]*232, c = params[2].
  5. If n = 4, assume k = params[0] + params[1]*232, c = params[2] + params[3]*232.
  6. If n = 5, assume k = params[0] + params[1]*232, c = params[2] + params[3]*232+ params[4]*264.
  7. If n >= 6, assume k = params[0] + params[1]*232, c = params[2] + params[3]*232+ params[4]*264+ params[5]*296.

Subsequences Selection Methods

vslSkipAheadStream

supported

vslLeapfrogStream

not supported

vslSkipAheadStream

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)

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. 

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