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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>
//
// 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
namespace Eigen {
namespace internal {
namespace {
EIGEN_DEVICE_FUNC uint64_t get_random_seed() {
#ifdef __CUDA_ARCH__
// We don't support 3d kernels since we currently only use 1 and
// 2d kernels.
assert(threadIdx.z == 0);
return clock64() +
blockIdx.x * blockDim.x + threadIdx.x +
gridDim.x * blockDim.x * (blockIdx.y * blockDim.y + threadIdx.y);
#elif defined _WIN32
// Use the current time as a baseline.
SYSTEMTIME st;
GetSystemTime(&st);
int time = st.wSecond + 1000 * st.wMilliseconds;
// Mix in a random number to make sure that we get different seeds if
// we try to generate seeds faster than the clock resolution.
// We need 2 random values since the generator only generate 16 bits at
// a time (https://msdn.microsoft.com/en-us/library/398ax69y.aspx)
int rnd1 = ::rand();
int rnd2 = ::rand();
uint64_t rnd = (rnd1 | rnd2 << 16) ^ time;
return rnd;
#elif defined __APPLE__
// Same approach as for win32, except that the random number generator
// is better (// https://developer.apple.com/legacy/library/documentation/Darwin/Reference/ManPages/man3/random.3.html#//apple_ref/doc/man/3/random).
uint64_t rnd = ::random() ^ mach_absolute_time();
return rnd;
#else
// Augment the current time with pseudo random number generation
// to ensure that we get different seeds if we try to generate seeds
// faster than the clock resolution.
timespec ts;
clock_gettime(CLOCK_REALTIME, &ts);
uint64_t rnd = ::random() ^ ts.tv_nsec;
return rnd;
#endif
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE unsigned PCG_XSH_RS_generator(uint64_t* state) {
// TODO: Unify with the implementation in the non blocking thread pool.
uint64_t current = *state;
// Update the internal state
*state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
// Generate the random output (using the PCG-XSH-RS scheme)
return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));
}
static 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;
}
} // namespace
template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
T RandomToTypeUniform(uint64_t* state) {
unsigned rnd = PCG_XSH_RS_generator(state);
return static_cast<T>(rnd);
}
template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Eigen::half RandomToTypeUniform<Eigen::half>(uint64_t* state) {
Eigen::half result;
// Generate 10 random bits for the mantissa
unsigned rnd = PCG_XSH_RS_generator(state);
result.x = static_cast<uint16_t>(rnd & 0x3ffu);
// Set the exponent
result.x |= (static_cast<uint16_t>(15) << 10);
// Return the final result
return result - Eigen::half(1.0f);
}
template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
float RandomToTypeUniform<float>(uint64_t* state) {
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);
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) {
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) & 0xfffffu;
// The generate the lower 32 bits
unsigned rnd2 = PCG_XSH_RS_generator(state);
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) {
return std::complex<float>(RandomToTypeUniform<float>(state),
RandomToTypeUniform<float>(state));
}
template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<double> RandomToTypeUniform<std::complex<double> >(uint64_t* state) {
return std::complex<double>(RandomToTypeUniform<double>(state),
RandomToTypeUniform<double>(state));
}
template <typename T> class UniformRandomGenerator {
public:
static const 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);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(
const UniformRandomGenerator& other) {
m_state = other.m_state;
}
template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
T operator()(Index i) const {
uint64_t local_state = m_state + i;
T result = RandomToTypeUniform<T>(&local_state);
m_state = local_state;
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];
uint64_t local_state = m_state + i;
for (int j = 0; j < packetSize; ++j) {
values[j] = RandomToTypeUniform<T>(&local_state);
}
m_state = local_state;
return internal::pload<Packet>(values);
}
private:
mutable uint64_t m_state;
};
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) {
// 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);
v = T(1.7156) * (RandomToTypeUniform<T>(state) - 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) {
return std::complex<float>(RandomToTypeNormal<float>(state),
RandomToTypeNormal<float>(state));
}
template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<double> RandomToTypeNormal<std::complex<double> >(uint64_t* state) {
return std::complex<double>(RandomToTypeNormal<double>(state),
RandomToTypeNormal<double>(state));
}
template <typename T> class NormalRandomGenerator {
public:
static const 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);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(
const NormalRandomGenerator& other) {
m_state = other.m_state;
}
template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
T operator()(Index i) const {
uint64_t local_state = m_state + i;
T result = RandomToTypeNormal<T>(&local_state);
m_state = local_state;
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];
uint64_t local_state = m_state + i;
for (int j = 0; j < packetSize; ++j) {
values[j] = RandomToTypeNormal<T>(&local_state);
}
m_state = local_state;
return internal::pload<Packet>(values);
}
private:
mutable uint64_t m_state;
};
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