Notes for Intel® oneAPI Math Kernel Library Vector Statistics

Developer Reference

Contents

UniformBits (VSL_RNG_METHOD_UNIFORMBITS_STD)

A random number generator of uniform distribution that produces an integer (non-normalized to the interval (0, 1)) sequence. You can identify the underlying BRNG by passing the random stream descriptor
stream
 as a parameter. Then
UniformBits
 function calls integer implementation of this basic generator.
Basic generators differ in bit capacity and structure of the integer output, therefore you should interpret the output integer array of the function
viRngUniformBits
 correctly. The following list provides rules for interpreting 32-bit integer output
r[i]
 for each VS BRNG.

MCG31m1

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

R250

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

MRG32k3a

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

MCG59

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

WH

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

MT19937

Integer Recurrence
,
,
,
,
where
,
with .
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

MT2203

Integer Recurrence
,
where
,
with , .
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

SFMT19937

Integer Recurrence
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits
r
[
i
] =
wi/4
(
i
 % 4)

SOBOL

Integer Recurrence
,
where
,
and
s
 is the dimension of quasi-random vector.
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

NIEDERR

Integer Recurrence
,
where
,
and
s
 is the dimension of quasi-random vector.
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits

PHILOX4X32X10

Integer Recurrence
c
n
 =
c
n-1
 + 1
w
n
 =
f(c
n
)
f(c)
 is computed as follows:
k
0
0
 =
k
0
k
1
0
 =
k
1
f(c)
= ,
N
= 10
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits
r
[
i
] =
w
i/4
(
i
 % 4)
w
i
(k)
 is the
k
-th 32-bit integer in quadruple
w
n
,
k
= 0, 1, 2, 3

ARS5

Integer Recurrence
c
n
 =
c
n-1
 + 1
w
n
 =
f(c
n
)
f(c)
 is computed as follows:
c
0
 =
c xor k
and
k
0
 =
k
c
i+1
=
SubBytes(
c
)
c
i+1
=
ShiftRows(
c
i+1
)
c
i+1
=
MixColumns(
c
i+1
)
, omitted if
i + 1 = N
c
i+1
=
AddRoundKey(
c
i+1
,
k
j
)
Lo(k
i+1
)
=
Lo(k
)
+ 0x9E3779B97F4A7C15
Hi(k
i+1
)
=
Hi(k
)
+ 0xBB67AE8584CAA73B
f(
c
) = c
N
,
N
= 5
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits
r
[
i
] =
w
i/4
(
i
 % 4)
w
i
(k)
 is the
k
-th 32-bit integer in quadruple
w
n
,
k
= 0, 1, 2, 3

NON-DETERMINISTIC

Integer Recurrence
Non-deterministic random generator [BMT] available in the latest Intel® CPUs [AVX].
Interpretation of 32-bit integer output array
r[i]
 after calling
viRngUniformBits
  1. Lo(x)
     means obtaining lower 32 bits of the 64-bit unsigned integer
    x
    , that is,
    Lo(x) = x
    mod2
    32
    .
  2. Hi(x)
     means obtaining upper 32 bits of the 64-bit unsigned integer
    x
    , that is,
    Hi(x) =
     ⌊
    x
    /2
    32
    ⌋.
  3. ABCD
     means a 128-bit number composed of four 32-bit numbers A, B, C and D, that is
So, when you generate an integer sequence of
n
 elements, the output array
r[i]
 of the function
viRngUniformBits
 comprises:
  1. n
     elements for the basic generators MCG31m1, R250, MRG32k3a, MT19937, MT2203, SOBOL, NIEDERR, Philox4x32-10 and ARS5.
  2. 2
    n
     elements for the basic generator MCG59.
  3. 4
    n
     elements for the basic generators WH and SFMT19937.
You may use the integer output, in particular, for fast generation of bit vectors. However, in this case some bits (or groups of them) might be non-random. For example, lower bits produced by linear congruential generators are less random than their higher bits. Note that quasi-random numbers are not random at all. Thoroughly check the integer output bits and bit groups for randomness before forming bit vectors from
r[i]
 array.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.