ars5¶

The ars5 counter-based pseudorandom number generator.

Description

The ars5 engine is a keyed family of counter-based BRNG. The state consists of a 128-bit integer counter $c$ and a 128-bit key $k$ . The BRNG is based on the AES encryption algorithm [FIPS-197].

Generation algorithm

The generator has a 32-bit integer output obtained in the following way [Salmon11]:

The i-th number is defined by the following formula $r_{i} = (f (i / 4) >> ((i m o d 4) * 32)) m o d 2^{32}$
Function $f (c)$ takes a 128-bit argument and returns a 128-bit number. The returned number is obtained as follows:
2.1. $c_{0} = c \oplus k$ and $k_{0} = k$ .

2.2. The following recurrence is calculated N = 5 times:

$c_{i + 1} = S u b B y t e s (c)$

$c_{i + 1} = S h i f t R o w s (c_{i + 1})$

$c_{i + 1} = M i x C o l u m n s (c_{i + 1})$ , this step is omitted if $i + 1 = N$

$c_{i + 1} = A d d R o u n d K e y (c_{i + 1}, k_{j})$

$L o (k_{i + 1}) = L o (k) + 0 x 9 E 3779 B 97 F 4 A 7 C 15$

$H i (k_{i + 1}) = H i (k) + 0 x B B 67 A E 8584 C A A 73 B$

Specification for $S u b B y t e s, S h i f t R o w s, M i x C o l u m n s, A d d R o u n d K e y$ functions can be found in [FIPS-197].

2.3. Put $f (c) = c_{N}$ , where $N = 10$
Real output: $u_{n} = (i n t) r_{n} / 2^{32} + 1 / 2$

class ars5¶

Syntax

namespace oneapi::mkl::rng {
class ars5 {
public:
        static constexpr std::uint64_t default_seed = 0;

        ars5(sycl::queue queue, std::uint64_t seed = default_seed);

        ars5(sycl::queue queue, std::initializer_list<std::uint64_t> seed);

        ars5(const ars5& other);

        ars5(ars5&& other);

        ars5& operator=(const ars5& other);

        ars5& operator=(ars5&& other);

        ~ars5();
};
}

Class Members

Routine	Description
ars5(sycl::queue queue, std::uint64_t seed)	Constructor for common seed initialization of the engine
ars5(sycl::queue queue, std::initializer_list<std::uint64_t> seed)	Constructor for extended seed initialization of the engine
ars5(const ars5& other)	Copy constructor
ars5(ars5&& other)	Move constructor
ars5& operator=(const ars5& other)	Copy assignment operator
ars5& operator=(ars5&& other)	Move assignment operator

Constructors

ars5::ars5(sycl::queue queue, std::uint64_t seed)

Input Parameters

queue: Valid sycl::queue object, calls of the oneapi::mkl::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.
seed: The initial conditions of the generator state, assume $k = s e e d, c = 0$ , where $k$ is 128-bit key, $c$ is 128-bit counter.

ars5::ars5(sycl::queue queue, std::initializer_list<std::uint64_t> seed)

Input Parameters

queue

Valid sycl::queue object, calls of the oneapi::mkl::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.

seed

The initial conditions of the generator state, assume if $n = 0 : k = 0, c = 0$

if $n = 1 : k = s e e d [0], c = 0$

if $n = 2 : k = s e e d [0] + s e e d [1] \cdot 2^{64}, c = 0$

if $n = 3 : k = s e e d [0] + s e e d [1] \cdot 2^{64}, c = s e e d [2]$

if $n = 4 : k = s e e d [0] + s e e d [1] \cdot 2^{64}, c = s e e d [2] + s e e d [3] \cdot 2^{64}$

for $n > 4$ following arguments are ignored

ars5::ars5(const ars5& other)

Input Parameters

other: Valid ars5 object. The queue and state of the other engine is copied and applied to the current engine.

ars5::ars5(ars5&& other)

Input Parameters

other: Valid ars5 r-value object. The queue and state of the other engine is moved to the current engine.

ars5::ars5& operator=(const ars5& other)

Input Parameters

other: Valid ars5 object. The queue and state of the other engine is copied and applied to the current engine.

ars5::ars5& operator=(ars5&& other)

Input Parameters

other: Valid ars5 r-value object. The queue and state of the other engine is moved to the current engine.

Parent topic: Engines (Basic Random Number Generators)

oneAPI Specification 1.1-rev-1 documentation

ars5¶

class ars5¶