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API library: /home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-rocrand/checkouts/latest/library/include/rocrand/rocrand_poisson.h Source File
API library
 // Copyright (c) 2017-2024 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
 // in the Software without restriction, including without limitation the rights
 // 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_
  
 #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>
 __forceinline__ __device__ __host__ 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;
 }
  
 __forceinline__ __device__ __host__ 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>
 __forceinline__ __device__ __host__ 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>
 __forceinline__ __device__ __host__ 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>
 __forceinline__ __device__ __host__ 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>
 __forceinline__ __device__ __host__ 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>
 __forceinline__ __device__ __host__ 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_BM_NOT_IN_STATE
 __forceinline__ __device__ __host__ 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);
 }
  
 __forceinline__ __device__ __host__ 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_BM_NOT_IN_STATE
  
 #ifndef ROCRAND_DETAIL_BM_NOT_IN_STATE
 __forceinline__ __device__ __host__ 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_BM_NOT_IN_STATE
  
 #ifndef ROCRAND_DETAIL_BM_NOT_IN_STATE
 __forceinline__ __device__ __host__ 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_BM_NOT_IN_STATE
  
 #ifndef ROCRAND_DETAIL_BM_NOT_IN_STATE
 __forceinline__ __device__ __host__ 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_BM_NOT_IN_STATE
  
 __forceinline__ __device__ __host__ unsigned int rocrand_poisson(rocrand_state_mtgp32* state,
                                                                  double                lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv<rocrand_state_mtgp32*, unsigned int>(
         state,
         lambda);
 }
  
 __forceinline__ __device__ __host__ unsigned int rocrand_poisson(rocrand_state_sobol32* state,
                                                                  double                 lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv<rocrand_state_sobol32*, unsigned int>(
         state,
         lambda);
 }
  
 __forceinline__ __device__ __host__ 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);
 }
  
 __forceinline__ __device__ __host__ 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);
 }
  
 __forceinline__ __device__ __host__ 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);
 }
  
 __forceinline__ __device__ __host__ unsigned int rocrand_poisson(rocrand_state_lfsr113* state,
                                                                  double                 lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv<rocrand_state_lfsr113*, unsigned int>(
         state,
         lambda);
 }
  
 __forceinline__ __device__ __host__ unsigned int
     rocrand_poisson(rocrand_state_threefry2x32_20* state, double lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv(state, lambda);
 }
  
 __forceinline__ __device__ __host__ unsigned int
     rocrand_poisson(rocrand_state_threefry2x64_20* state, double lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv(state, lambda);
 }
  
 __forceinline__ __device__ __host__ unsigned int
     rocrand_poisson(rocrand_state_threefry4x32_20* state, double lambda)
 {
     return rocrand_device::detail::poisson_distribution_inv(state, lambda);
 }
  
 __forceinline__ __device__ __host__ 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_