Program Listing for File rocrand_poisson.h
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// Copyright (c) 2017-2022 Advanced Micro Devices, Inc. All rights reserved.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
#ifndef ROCRAND_POISSON_H_
#define ROCRAND_POISSON_H_
#ifndef FQUALIFIERS
#define FQUALIFIERS __forceinline__ __device__
#endif // FQUALIFIERS
#include <math.h>
#include "rocrand/rocrand_lfsr113.h"
#include "rocrand/rocrand_mrg31k3p.h"
#include "rocrand/rocrand_mrg32k3a.h"
#include "rocrand/rocrand_mtgp32.h"
#include "rocrand/rocrand_philox4x32_10.h"
#include "rocrand/rocrand_scrambled_sobol32.h"
#include "rocrand/rocrand_scrambled_sobol64.h"
#include "rocrand/rocrand_sobol32.h"
#include "rocrand/rocrand_sobol64.h"
#include "rocrand/rocrand_threefry2x32_20.h"
#include "rocrand/rocrand_threefry2x64_20.h"
#include "rocrand/rocrand_threefry4x32_20.h"
#include "rocrand/rocrand_threefry4x64_20.h"
#include "rocrand/rocrand_xorwow.h"
#include "rocrand/rocrand_normal.h"
#include "rocrand/rocrand_uniform.h"
namespace rocrand_device {
namespace detail {
constexpr double lambda_threshold_small = 64.0;
constexpr double lambda_threshold_huge = 4000.0;
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution_small(State& state, double lambda)
{
// Knuth's method
const double limit = exp(-lambda);
Result_Type k = 0;
double product = 1.0;
do
{
k++;
product *= rocrand_uniform_double(state);
}
while (product > limit);
return k - 1;
}
FQUALIFIERS
double lgamma_approx(const double x)
{
// Lanczos approximation (g = 7, n = 9)
const double z = x - 1.0;
const int g = 7;
const int n = 9;
const double coefs[n] = {
0.99999999999980993227684700473478,
676.520368121885098567009190444019,
-1259.13921672240287047156078755283,
771.3234287776530788486528258894,
-176.61502916214059906584551354,
12.507343278686904814458936853,
-0.13857109526572011689554707,
9.984369578019570859563e-6,
1.50563273514931155834e-7
};
double sum = 0.0;
#pragma unroll
for (int i = n - 1; i > 0; i--)
{
sum += coefs[i] / (z + i);
}
sum += coefs[0];
const double log_sqrt_2_pi = 0.9189385332046727418;
const double e = 2.718281828459045090796;
return (log_sqrt_2_pi + log(sum) - g) + (z + 0.5) * log((z + g + 0.5) / e);
}
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution_large(State& state, double lambda)
{
// Rejection method PA, A. C. Atkinson
const double c = 0.767 - 3.36 / lambda;
const double beta = ROCRAND_PI_DOUBLE / sqrt(3.0 * lambda);
const double alpha = beta * lambda;
const double k = log(c) - lambda - log(beta);
const double log_lambda = log(lambda);
while (true)
{
const double u = rocrand_uniform_double(state);
const double x = (alpha - log((1.0 - u) / u)) / beta;
const double n = floor(x + 0.5);
if (n < 0)
{
continue;
}
const double v = rocrand_uniform_double(state);
const double y = alpha - beta * x;
const double t = 1.0 + exp(y);
const double lhs = y + log(v / (t * t));
const double rhs = k + n * log_lambda - lgamma_approx(n + 1.0);
if (lhs <= rhs)
{
return static_cast<Result_Type>(n);
}
}
}
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution_huge(State& state, double lambda)
{
// Approximate Poisson distribution with normal distribution
const double n = rocrand_normal_double(state);
return static_cast<Result_Type>(round(sqrt(lambda) * n + lambda));
}
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution(State& state, double lambda)
{
if (lambda < lambda_threshold_small)
{
return poisson_distribution_small<State, Result_Type>(state, lambda);
}
else if (lambda <= lambda_threshold_huge)
{
return poisson_distribution_large<State, Result_Type>(state, lambda);
}
else
{
return poisson_distribution_huge<State, Result_Type>(state, lambda);
}
}
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution_itr(State& state, double lambda)
{
// Algorithm ITR
// George S. Fishman
// Discrete-Event Simulation: Modeling, Programming, and Analysis
// p. 333
double L;
double x = 1.0;
double y = 1.0;
Result_Type k = 0;
int pow = 0;
// Algorithm ITR uses u from (0, 1) and uniform_double returns (0, 1]
// Change u to ensure that 1 is never generated,
// otherwise the inner loop never ends.
double u = rocrand_uniform_double(state) - ROCRAND_2POW32_INV_DOUBLE / 2.0;
double upow = pow + 500.0;
double ex = exp(-500.0);
do{
if (lambda > upow)
L = ex;
else
L = exp((double)(pow - lambda));
x *= L;
y *= L;
pow += 500;
while (u > y)
{
k++;
x *= ((double)lambda / (double) k);
y += x;
}
} while((double)pow < lambda);
return k;
}
template<class State, typename Result_Type = unsigned int>
FQUALIFIERS Result_Type poisson_distribution_inv(State& state, double lambda)
{
if (lambda < 1000.0)
{
return poisson_distribution_itr<State, Result_Type>(state, lambda);
}
else
{
return poisson_distribution_huge<State, Result_Type>(state, lambda);
}
}
} // end namespace detail
} // end namespace rocrand_device
#ifndef ROCRAND_DETAIL_PHILOX_BM_NOT_IN_STATE
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_philox4x32_10 * state, double lambda)
{
return rocrand_device::detail::poisson_distribution<rocrand_state_philox4x32_10*, unsigned int>(
state,
lambda);
}
FQUALIFIERS
uint4 rocrand_poisson4(rocrand_state_philox4x32_10 * state, double lambda)
{
return uint4{
rocrand_device::detail::poisson_distribution<rocrand_state_philox4x32_10*, unsigned int>(
state,
lambda),
rocrand_device::detail::poisson_distribution<rocrand_state_philox4x32_10*, unsigned int>(
state,
lambda),
rocrand_device::detail::poisson_distribution<rocrand_state_philox4x32_10*, unsigned int>(
state,
lambda),
rocrand_device::detail::poisson_distribution<rocrand_state_philox4x32_10*, unsigned int>(
state,
lambda)};
}
#endif // ROCRAND_DETAIL_PHILOX_BM_NOT_IN_STATE
#ifndef ROCRAND_DETAIL_MRG31K3P_BM_NOT_IN_STATE
FQUALIFIERS unsigned int rocrand_poisson(rocrand_state_mrg31k3p* state, double lambda)
{
return rocrand_device::detail::poisson_distribution<rocrand_state_mrg31k3p*, unsigned int>(
state,
lambda);
}
#endif // ROCRAND_DETAIL_MRG31K3P_BM_NOT_IN_STATE
#ifndef ROCRAND_DETAIL_MRG32K3A_BM_NOT_IN_STATE
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_mrg32k3a * state, double lambda)
{
return rocrand_device::detail::poisson_distribution<rocrand_state_mrg32k3a*, unsigned int>(
state,
lambda);
}
#endif // ROCRAND_DETAIL_MRG32K3A_BM_NOT_IN_STATE
#ifndef ROCRAND_DETAIL_XORWOW_BM_NOT_IN_STATE
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_xorwow * state, double lambda)
{
return rocrand_device::detail::poisson_distribution<rocrand_state_xorwow*, unsigned int>(
state,
lambda);
}
#endif // ROCRAND_DETAIL_XORWOW_BM_NOT_IN_STATE
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_mtgp32 * state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_mtgp32*, unsigned int>(
state,
lambda);
}
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_sobol32 * state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_sobol32*, unsigned int>(
state,
lambda);
}
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_scrambled_sobol32* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_scrambled_sobol32*,
unsigned int>(state, lambda);
}
FQUALIFIERS
unsigned long long int rocrand_poisson(rocrand_state_sobol64* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_sobol64*,
unsigned long long int>(state, lambda);
}
FQUALIFIERS
unsigned long long int rocrand_poisson(rocrand_state_scrambled_sobol64* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_scrambled_sobol64*,
unsigned long long int>(state, lambda);
}
FQUALIFIERS
unsigned int rocrand_poisson(rocrand_state_lfsr113* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv<rocrand_state_lfsr113*, unsigned int>(
state,
lambda);
}
FQUALIFIERS unsigned int rocrand_poisson(rocrand_state_threefry2x32_20* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv(state, lambda);
}
FQUALIFIERS unsigned int rocrand_poisson(rocrand_state_threefry2x64_20* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv(state, lambda);
}
FQUALIFIERS unsigned int rocrand_poisson(rocrand_state_threefry4x32_20* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv(state, lambda);
}
FQUALIFIERS unsigned int rocrand_poisson(rocrand_state_threefry4x64_20* state, double lambda)
{
return rocrand_device::detail::poisson_distribution_inv(state, lambda);
}
// end of group rocranddevice
#endif // ROCRAND_POISSON_H_