# philox4x32x10#

The Philox4x32x10 counter-based pseudorandom number generator.

Description

The Philox4x32x10 engine is a keyed family of generator of counter-based BRNG. The state consists of 128-bit integer counter $$c$$ and two 32-bits keys $$k_0$$ and $$k_1$$.

Generation algorithm

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

1. $$c_n=c_{n-1} + 1$$

2. $$\omega_n = f(c_n)$$, where $$f$$ is a function that takes 128-bit argument and returns a 128-bit number. The returned number is obtained as follows:

2.1. The argument $$c$$ is interpreted as four 32-bit numbers $$c = \overline{L_1 R_1 L_0 R_0}$$, where $$\overline{A B C D} = A \cdot 2^{96} + B \cdot 2^{64} + C \cdot 2^{32} + D$$, put $$k_0^0 =k_0, k_1^0=k_1$$.

2.2. The following recurrence is calculated:

$$L_1^{i+1} =mullo(R_1^i, 0xD2511F53)$$

$$R_1^{i+1} =mulhi(R_0^i, 0xCD9E8D57) \oplus k_0^i \oplus L_0^i$$

$$L_0^{i+1} =mullo(R_0^i, 0xCD9E8D57)$$

$$R_0^{i+1} =mulhi(R_1^i, 0xD2511F53) \oplus k_1^i \oplus L_1^i$$

$$k_0^{i+1} =k_0^i + 0xBB67AE85$$

$$k_1^{i+1} =k_1^i + 0x9E3779B9$$, where $$mulhi(a, b)$$ and $$mullo(a, b)$$ are high and low parts of the $$a \cdot b$$ product respectively.

2.3. Put $$f(c) = \overline{L_1^N R_1^N L_0^N R_0^N}$$, where $$N = 10$$

3. Integer output: $$r_{4n + k} = \omega_n(k)$$, where $$\omega_n(k)$$ is the k-th 32-bit integer in quadruple $$\omega_n, k = 0, 1, 2, 3$$

4. Real output: $$u_n=(int)r_n / 2^{32} + 1/2$$

## class philox4x32x10#

Syntax

namespace oneapi::mkl::rng {
class philox4x32x10 {
public:
static constexpr std::uint64_t default_seed = 0;

philox4x32x10(sycl::queue queue, std::uint64_t seed = default_seed);

philox4x32x10(sycl::queue queue, std::initializer_list<std::uint64_t> seed);

philox4x32x10(const philox4x32x10& other);

philox4x32x10(philox4x32x10&& other);

philox4x32x10& operator=(const philox4x32x10& other);

philox4x32x10& operator=(philox4x32x10&& other);

~philox4x32x10();
};
}


Class Members

Routine

Description

philox4x32x10(sycl::queue queue, std::uint64_t seed = default_seed)

Constructor for common seed initialization of the engine

philox4x32x10(sycl::queue queue, std::initializer_list<std::uint64_t> seed)

Constructor for extended seed initialization of the engine

philox4x32x10(const philox4x32x10& other)

Copy constructor

philox4x32x10(philox4x32x10&& other)

Move constructor

philox4x32x10& operator=(const philox4x32x10& other)

Copy assignment operator

philox4x32x10& operator=(philox4x32x10&& other)

Move assignment operator

Constructors

philox4x32x10::philox4x32x10(sycl::queue queue, std::uint64_t seed = default_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 $$k = seed, c = 0$$, where $$k$$ is a 64-bit key, $$c$$ is a 128-bit counter.

philox4x32x10::philox4x32x10(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 $$n = 1: k = seed[0], c = 0$$

if $$n = 2: k = seed[0], c = seed[1]$$

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

for $$n > 3$$ following arguments are ignored

philox4x32x10::philox4x32x10(const philox4x32x10& other)


Input Parameters

other

Valid philox4x32x10 object. The queue and state of the other engine is copied and applied to the current engine.

philox4x32x10::philox4x32x10(philox4x32x10&& other)


Input Parameters

other

Valid philox4x32x10 r-value object. The queue and state of the other engine is moved to the current engine.

philox4x32x10::philox4x32x10& operator=(const philox4x32x10& other)


Input Parameters

other

Valid philox4x32x10 object. The queue and state of the other engine is copied and applied to the current engine.

philox4x32x10::philox4x32x10& operator=(philox4x32x10&& other)


Input Parameters

other

Valid philox4x32x10 r-value object. The queue and state of the other engine is moved to the current engine.

Parent topic: Engines (Basic Random Number Generators)