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
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,
c
= 0.
3. If
n
= 2, assume
k
= params + params*2
32
,
c
= 0.
4. If
n
= 3, assume
k
= params + params*2
32
,
c
= params.
5. If
n
= 4, assume
k
= params + params*2
32
,
c
= params + params*2
32
.
6. If
n
= 5, assume
k
= params + params*2
32
,
c
= params + params*2
32
+ params*2
64
.
7. If
n
>= 6, assume
k
= params + params*2
32
,
c
= params + params*2
32
+ params*2
64
+ params*2
96
.
Subsequences Selection Methods
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

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Notice revision #20110804