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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
// Copyright (C) 2018 Mehdi Goli <eigen@codeplay.com> Codeplay Software Ltd.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H
#define EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE uint64_t get_random_seed() {
#if defined(EIGEN_GPU_COMPILE_PHASE)
// We don't support 3d kernels since we currently only use 1 and
// 2d kernels.
gpu_assert(threadIdx.z == 0);
return blockIdx.x * blockDim.x + threadIdx.x + gridDim.x * blockDim.x * (blockIdx.y * blockDim.y + threadIdx.y);
#else
// Rely on Eigen's random implementation.
return random<uint64_t>();
#endif
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE unsigned PCG_XSH_RS_generator(uint64_t* state, uint64_t stream) {
// TODO: Unify with the implementation in the non blocking thread pool.
uint64_t current = *state;
// Update the internal state
*state = current * 6364136223846793005ULL + (stream << 1 | 1);
// Generate the random output (using the PCG-XSH-RS scheme)
return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE uint64_t PCG_XSH_RS_state(uint64_t seed) {
seed = seed ? seed : get_random_seed();
return seed * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T RandomToTypeUniform(uint64_t* state, uint64_t stream) {
unsigned rnd = PCG_XSH_RS_generator(state, stream);
return static_cast<T>(rnd);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half RandomToTypeUniform<Eigen::half>(uint64_t* state, uint64_t stream) {
// Generate 10 random bits for the mantissa, merge with exponent.
unsigned rnd = PCG_XSH_RS_generator(state, stream);
const uint16_t half_bits = static_cast<uint16_t>(rnd & 0x3ffu) | (static_cast<uint16_t>(15) << 10);
Eigen::half result = Eigen::numext::bit_cast<Eigen::half>(half_bits);
// Return the final result
return result - Eigen::half(1.0f);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::bfloat16 RandomToTypeUniform<Eigen::bfloat16>(uint64_t* state,
uint64_t stream) {
// Generate 7 random bits for the mantissa, merge with exponent.
unsigned rnd = PCG_XSH_RS_generator(state, stream);
const uint16_t half_bits = static_cast<uint16_t>(rnd & 0x7fu) | (static_cast<uint16_t>(127) << 7);
Eigen::bfloat16 result = Eigen::numext::bit_cast<Eigen::bfloat16>(half_bits);
// Return the final result
return result - Eigen::bfloat16(1.0f);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float RandomToTypeUniform<float>(uint64_t* state, uint64_t stream) {
typedef union {
uint32_t raw;
float fp;
} internal;
internal result;
// Generate 23 random bits for the mantissa mantissa
const unsigned rnd = PCG_XSH_RS_generator(state, stream);
result.raw = rnd & 0x7fffffu;
// Set the exponent
result.raw |= (static_cast<uint32_t>(127) << 23);
// Return the final result
return result.fp - 1.0f;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double RandomToTypeUniform<double>(uint64_t* state, uint64_t stream) {
typedef union {
uint64_t raw;
double dp;
} internal;
internal result;
result.raw = 0;
// Generate 52 random bits for the mantissa
// First generate the upper 20 bits
unsigned rnd1 = PCG_XSH_RS_generator(state, stream) & 0xfffffu;
// The generate the lower 32 bits
unsigned rnd2 = PCG_XSH_RS_generator(state, stream);
result.raw = (static_cast<uint64_t>(rnd1) << 32) | rnd2;
// Set the exponent
result.raw |= (static_cast<uint64_t>(1023) << 52);
// Return the final result
return result.dp - 1.0;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<float> RandomToTypeUniform<std::complex<float> >(uint64_t* state,
uint64_t stream) {
return std::complex<float>(RandomToTypeUniform<float>(state, stream), RandomToTypeUniform<float>(state, stream));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<double> RandomToTypeUniform<std::complex<double> >(uint64_t* state,
uint64_t stream) {
return std::complex<double>(RandomToTypeUniform<double>(state, stream), RandomToTypeUniform<double>(state, stream));
}
template <typename T>
class UniformRandomGenerator {
public:
static constexpr bool PacketAccess = true;
// Uses the given "seed" if non-zero, otherwise uses a random seed.
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(uint64_t seed = 0) {
m_state = PCG_XSH_RS_state(seed);
#ifdef EIGEN_USE_SYCL
// In SYCL it is not possible to build PCG_XSH_RS_state in one step.
// Therefore, we need two steps to initializate the m_state.
// IN SYCL, the constructor of the functor is s called on the CPU
// and we get the clock seed here from the CPU. However, This seed is
// the same for all the thread. As unlike CUDA, the thread.ID, BlockID, etc is not a global function.
// and only available on the Operator() function (which is called on the GPU).
// Thus for CUDA (((CLOCK + global_thread_id)* 6364136223846793005ULL) + 0xda3e39cb94b95bdbULL) is passed to each
// thread but for SYCL ((CLOCK * 6364136223846793005ULL) + 0xda3e39cb94b95bdbULL) is passed to each thread and each
// thread adds the (global_thread_id* 6364136223846793005ULL) for itself only once, in order to complete the
// construction similar to CUDA Therefore, the thread Id injection is not available at this stage.
// However when the operator() is called the thread ID will be available. So inside the opeator,
// we add the thrreadID, BlockId,... (which is equivalent of i)
// to the seed and construct the unique m_state per thead similar to cuda.
m_exec_once = false;
#endif
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(const UniformRandomGenerator& other) {
m_state = other.m_state;
#ifdef EIGEN_USE_SYCL
m_exec_once = other.m_exec_once;
#endif
}
template <typename Index>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(Index i) const {
#ifdef EIGEN_USE_SYCL
if (!m_exec_once) {
// This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
// The (i * 6364136223846793005ULL) is the remaining part of the PCG_XSH_RS_state on the GPU side
m_state += (i * 6364136223846793005ULL);
m_exec_once = true;
}
#endif
T result = RandomToTypeUniform<T>(&m_state, i);
return result;
}
template <typename Packet, typename Index>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(Index i) const {
const int packetSize = internal::unpacket_traits<Packet>::size;
EIGEN_ALIGN_MAX T values[packetSize];
#ifdef EIGEN_USE_SYCL
if (!m_exec_once) {
// This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
m_state += (i * 6364136223846793005ULL);
m_exec_once = true;
}
#endif
EIGEN_UNROLL_LOOP
for (int j = 0; j < packetSize; ++j) {
values[j] = RandomToTypeUniform<T>(&m_state, i);
}
return internal::pload<Packet>(values);
}
private:
mutable uint64_t m_state;
#ifdef EIGEN_USE_SYCL
mutable bool m_exec_once;
#endif
};
template <typename Scalar>
struct functor_traits<UniformRandomGenerator<Scalar> > {
enum {
// Rough estimate for floating point, multiplied by ceil(sizeof(T) / sizeof(float)).
Cost = 12 * NumTraits<Scalar>::AddCost * ((sizeof(Scalar) + sizeof(float) - 1) / sizeof(float)),
PacketAccess = UniformRandomGenerator<Scalar>::PacketAccess
};
};
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T RandomToTypeNormal(uint64_t* state, uint64_t stream) {
// Use the ratio of uniform method to generate numbers following a normal
// distribution. See for example Numerical Recipes chapter 7.3.9 for the
// details.
T u, v, q;
do {
u = RandomToTypeUniform<T>(state, stream);
v = T(1.7156) * (RandomToTypeUniform<T>(state, stream) - T(0.5));
const T x = u - T(0.449871);
const T y = numext::abs(v) + T(0.386595);
q = x * x + y * (T(0.196) * y - T(0.25472) * x);
} while (q > T(0.27597) && (q > T(0.27846) || v * v > T(-4) * numext::log(u) * u * u));
return v / u;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<float> RandomToTypeNormal<std::complex<float> >(uint64_t* state,
uint64_t stream) {
return std::complex<float>(RandomToTypeNormal<float>(state, stream), RandomToTypeNormal<float>(state, stream));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<double> RandomToTypeNormal<std::complex<double> >(uint64_t* state,
uint64_t stream) {
return std::complex<double>(RandomToTypeNormal<double>(state, stream), RandomToTypeNormal<double>(state, stream));
}
template <typename T>
class NormalRandomGenerator {
public:
static constexpr bool PacketAccess = true;
// Uses the given "seed" if non-zero, otherwise uses a random seed.
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(uint64_t seed = 0) {
m_state = PCG_XSH_RS_state(seed);
#ifdef EIGEN_USE_SYCL
// In SYCL it is not possible to build PCG_XSH_RS_state in one step.
// Therefore, we need two steps to initializate the m_state.
// IN SYCL, the constructor of the functor is s called on the CPU
// and we get the clock seed here from the CPU. However, This seed is
// the same for all the thread. As unlike CUDA, the thread.ID, BlockID, etc is not a global function.
// and only available on the Operator() function (which is called on the GPU).
// Therefore, the thread Id injection is not available at this stage. However when the operator()
// is called the thread ID will be available. So inside the operator,
// we add the thrreadID, BlockId,... (which is equivalent of i)
// to the seed and construct the unique m_state per thead similar to cuda.
m_exec_once = false;
#endif
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(const NormalRandomGenerator& other) {
m_state = other.m_state;
#ifdef EIGEN_USE_SYCL
m_exec_once = other.m_exec_once;
#endif
}
template <typename Index>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(Index i) const {
#ifdef EIGEN_USE_SYCL
if (!m_exec_once) {
// This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
m_state += (i * 6364136223846793005ULL);
m_exec_once = true;
}
#endif
T result = RandomToTypeNormal<T>(&m_state, i);
return result;
}
template <typename Packet, typename Index>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(Index i) const {
const int packetSize = internal::unpacket_traits<Packet>::size;
EIGEN_ALIGN_MAX T values[packetSize];
#ifdef EIGEN_USE_SYCL
if (!m_exec_once) {
// This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
m_state += (i * 6364136223846793005ULL);
m_exec_once = true;
}
#endif
EIGEN_UNROLL_LOOP
for (int j = 0; j < packetSize; ++j) {
values[j] = RandomToTypeNormal<T>(&m_state, i);
}
return internal::pload<Packet>(values);
}
private:
mutable uint64_t m_state;
#ifdef EIGEN_USE_SYCL
mutable bool m_exec_once;
#endif
};
template <typename Scalar>
struct functor_traits<NormalRandomGenerator<Scalar> > {
enum {
// On average, we need to generate about 3 random numbers
// 15 mul, 8 add, 1.5 logs
Cost = 3 * functor_traits<UniformRandomGenerator<Scalar> >::Cost + 15 * NumTraits<Scalar>::AddCost +
8 * NumTraits<Scalar>::AddCost + 3 * functor_traits<scalar_log_op<Scalar> >::Cost / 2,
PacketAccess = NormalRandomGenerator<Scalar>::PacketAccess
};
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H