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]:

\(c_n=c_{n-1} + 1\)
\(\omega_n = f(c_n)\), 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 \(N = 10\)
Integer output: \(r_{4n + k} = \omega_n(k)\), where \(\omega_n(k)\) is the k-th 32-bit integer in quadruple \(\omega_n, k = 0, 1, 2, 3\)
Real output: \(u_n=(int)r_n / 2^{32} + 1/2\)

class philox4x32x10#

Syntax

namespace oneapi::math::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::math::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::math::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: Host Engines (Basic Random Number Generators)

philox4x32x10

Contents

philox4x32x10#

class philox4x32x10#