.. SPDX-FileCopyrightText: 2023 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_device_rng_philox4x32x10: philox4x32x10 ============= A Philox4x32-10 counter-based pseudorandom number generator [:ref:`Salmon11`]. .. rubric:: Description The Philox4x32x10 engine is a keyed family of generator of counter-based BRNG. The state consists of 128-bit integer counter :math:`c` and two 32-bits keys :math:`k_0` and :math:`k_1`. .. container:: section .. rubric:: Generation algorithm The generator has 32-bit integer output obtained in the following way [:ref:`Salmon11 `]: 1. :math:`c_n=c_{n-1} + 1` 2. :math:`\omega_n = f(c_n)`, where :math:`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 :math:`c` is interpreted as four 32-bit numbers :math:`c = \overline{L_1 R_1 L_0 R_0}`, where :math:`\overline{A B C D} = A \cdot 2^{96} + B \cdot 2^{64} + C \cdot 2^{32} + D`, put :math:`k_0^0 =k_0, k_1^0=k_1`. 2.2. The following recurrence is calculated: :math:`L_1^{i+1} =mullo(R_1^i, 0xD2511F53)` :math:`R_1^{i+1} =mulhi(R_0^i, 0xCD9E8D57) \oplus k_0^i \oplus L_0^i` :math:`L_0^{i+1} =mullo(R_0^i, 0xCD9E8D57)` :math:`R_0^{i+1} =mulhi(R_1^i, 0xD2511F53) \oplus k_1^i \oplus L_1^i` :math:`k_0^{i+1} =k_0^i + 0xBB67AE85` :math:`k_1^{i+1} =k_1^i + 0x9E3779B9`, where :math:`mulhi(a, b)` and :math:`mullo(a, b)` are high and low parts of the :math:`a \cdot b` product respectively. 2.3. Put :math:`f(c) = \overline{L_1^N R_1^N L_0^N R_0^N}`, where :math:`N = 10` 3. Integer output: :math:`r_{4n + k} = \omega_n(k)`, where :math:`\omega_n(k)` is the k-th 32-bit integer in quadruple :math:`\omega_n, k = 0, 1, 2, 3` 4. Real output: :math:`u_n=(int)r_n / 2^{32} + 1/2` class philox4x32x10 ------------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::rng::device { template class philox4x32x10 { public: static constexpr std::uint64_t default_seed = 1; static constexpr std::int32_t vec_size = VecSize; philox4x32x10(); philox4x32x10(std::uint64_t seed, std::uint64_t offset = 0); philox4x32x10(std::initializer_list seed, std::uint64_t offset = 0); philox4x32x10(std::uint64_t seed, std::initializer_list offset); philox4x32x10(std::initializer_list seed, std::initializer_list offset); }; } .. container:: section .. rubric:: Class Template Parameters VecSize Describes the size of vector which will be produced by generate function by this engine. VecSize values may be 1, 2, 3, 4, 8, 16 as ``sycl::vec`` class size. By default VecSize = 1, for this case, a single random number is returned by the ``generate`` function. .. container:: section .. rubric:: Class Members .. list-table:: :header-rows: 1 * - Routine - Description * - `philox4x32x10()`_ - Default constructor * - `philox4x32x10(std::uint32_t seed, std::uint64_t offset = 0)`_ - Constructor for common seed initialization of the engine and common number of skipped elements * - `philox4x32x10(std::initializer_list seed, std::uint64_t offset = 0)`_ - Constructor for extended seed initialization of the engine and common number of skipped elements * - `philox4x32x10(std::uint32_t seed, std::initializer_list offset)`_ - Constructor for common seed initialization of the engine and extended number of skipped elements * - `philox4x32x10(std::initializer_list seed, std::initializer_list offset)`_ - Constructor for extended seed initialization of the engine and extended number of skipped elements .. container:: section .. rubric:: Constructors .. _`philox4x32x10()`: .. code-block:: cpp philox4x32x10::philox4x32x10() .. _`philox4x32x10(std::uint32_t seed, std::uint64_t offset = 0)`: .. code-block:: cpp philox4x32x10::philox4x32x10(std::uint32_t seed, std::uint64_t offset = 0) .. container:: section .. rubric:: Input Parameters seed The initial conditions of the generator state, assume :math:`k = seed, c = 0`, where :math:`k` is a 64-bit key, :math:`c` is a 128-bit counter. offset Number of skipped elements. .. _`philox4x32x10(std::initializer_list seed, std::uint64_t offset = 0)`: .. code-block:: cpp philox4x32x10::philox4x32x10(std::initializer_list seed, std::uint64_t offset = 0) .. container:: section .. rubric:: Input Parameters seed The initial conditions of the generator state, assume if :math:`n = 0: k = 0, c = 0` if :math:`n = 1: k = seed[0], c = 0` if :math:`n = 2: k = seed[0], c = seed[1]` if :math:`n = 3: k = seed[0], c = seed[1] + seed[2] \cdot 2^{64}` for :math:`n > 3` following arguments are ignored. offset Number of skipped elements. .. _`philox4x32x10(std::uint32_t seed, std::initializer_list offset)`: .. code-block:: cpp philox4x32x10::philox4x32x10(std::uint32_t seed, std::initializer_list offset) .. container:: section .. rubric:: Input Parameters seed The initial conditions of the generator state, assume :math:`k = seed, c = 0`, where :math:`k` is a 64-bit key, :math:`c` is a 128-bit counter. offset Number of skipped elements. Offset is calculated as: ``num_to_skip`` [0]+ ``num_to_skip`` [1]*2\ :sup:`64` + ``num_to_skip`` [2]\* 2\ :sup:`128` + … + ``num_to_skip`` [``n``-1]\*2\ :sup:`64` \*(``n``-1). .. _`philox4x32x10(std::initializer_list seed, std::initializer_list offset)`: .. code-block:: cpp philox4x32x10::philox4x32x10(std::initializer_list seed, std::initializer_list offset) .. container:: section .. rubric:: Input Parameters seed The initial conditions of the generator state, assume if :math:`n = 0: k = 0, c = 0` if :math:`n = 1: k = seed[0], c = 0` if :math:`n = 2: k = seed[0], c = seed[1]` if :math:`n = 3: k = seed[0], c = seed[1] + seed[2] \cdot 2^{64}` for :math:`n > 3` following arguments are ignored. offset Number of skipped elements. Offset is calculated as: ``num_to_skip`` [0]+ ``num_to_skip`` [1]*2\ :sup:`64` + ``num_to_skip`` [2]\* 2\ :sup:`128` + … + ``num_to_skip`` [``n``-1]\*2\ :sup:`64` \*(``n``-1). **Parent topic:** :ref:`onemath_device_rng_engines`