path: root/contrib/restricted/abseil-cpp/absl/random/poisson_distribution.h

// Copyright 2017 The Abseil Authors. 
// 
// Licensed under the Apache License, Version 2.0 (the "License"); 
// you may not use this file except in compliance with the License. 
// You may obtain a copy of the License at 
// 
//      https://www.apache.org/licenses/LICENSE-2.0 
// 
// Unless required by applicable law or agreed to in writing, software 
// distributed under the License is distributed on an "AS IS" BASIS, 
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 
// See the License for the specific language governing permissions and 
// limitations under the License. 
 
#ifndef ABSL_RANDOM_POISSON_DISTRIBUTION_H_ 
#define ABSL_RANDOM_POISSON_DISTRIBUTION_H_ 
 
#include <cassert> 
#include <cmath> 
#include <istream> 
#include <limits> 
#include <ostream> 
#include <type_traits> 
 
#include "absl/random/internal/fast_uniform_bits.h" 
#include "absl/random/internal/fastmath.h" 
#include "absl/random/internal/generate_real.h" 
#include "absl/random/internal/iostream_state_saver.h" 
 
namespace absl { 
ABSL_NAMESPACE_BEGIN
 
// absl::poisson_distribution: 
// Generates discrete variates conforming to a Poisson distribution. 
//   p(n) = (mean^n / n!) exp(-mean) 
// 
// Depending on the parameter, the distribution selects one of the following 
// algorithms: 
// * The standard algorithm, attributed to Knuth, extended using a split method 
// for larger values 
// * The "Ratio of Uniforms as a convenient method for sampling from classical 
// discrete distributions", Stadlober, 1989. 
// http://www.sciencedirect.com/science/article/pii/0377042790903495 
// 
// NOTE: param_type.mean() is a double, which permits values larger than 
// poisson_distribution<IntType>::max(), however this should be avoided and 
// the distribution results are limited to the max() value. 
// 
// The goals of this implementation are to provide good performance while still 
// beig thread-safe: This limits the implementation to not using lgamma provided 
// by <math.h>. 
// 
template <typename IntType = int> 
class poisson_distribution { 
 public: 
  using result_type = IntType; 
 
  class param_type { 
   public: 
    using distribution_type = poisson_distribution; 
    explicit param_type(double mean = 1.0); 
 
    double mean() const { return mean_; } 
 
    friend bool operator==(const param_type& a, const param_type& b) { 
      return a.mean_ == b.mean_; 
    } 
 
    friend bool operator!=(const param_type& a, const param_type& b) { 
      return !(a == b); 
    } 
 
   private: 
    friend class poisson_distribution; 
 
    double mean_; 
    double emu_;  // e ^ -mean_ 
    double lmu_;  // ln(mean_) 
    double s_; 
    double log_k_; 
    int split_; 
 
    static_assert(std::is_integral<IntType>::value, 
                  "Class-template absl::poisson_distribution<> must be " 
                  "parameterized using an integral type."); 
  }; 
 
  poisson_distribution() : poisson_distribution(1.0) {} 
 
  explicit poisson_distribution(double mean) : param_(mean) {} 
 
  explicit poisson_distribution(const param_type& p) : param_(p) {} 
 
  void reset() {} 
 
  // generating functions 
  template <typename URBG> 
  result_type operator()(URBG& g) {  // NOLINT(runtime/references) 
    return (*this)(g, param_); 
  } 
 
  template <typename URBG> 
  result_type operator()(URBG& g,  // NOLINT(runtime/references) 
                         const param_type& p); 
 
  param_type param() const { return param_; } 
  void param(const param_type& p) { param_ = p; } 
 
  result_type(min)() const { return 0; } 
  result_type(max)() const { return (std::numeric_limits<result_type>::max)(); } 
 
  double mean() const { return param_.mean(); } 
 
  friend bool operator==(const poisson_distribution& a, 
                         const poisson_distribution& b) { 
    return a.param_ == b.param_; 
  } 
  friend bool operator!=(const poisson_distribution& a, 
                         const poisson_distribution& b) { 
    return a.param_ != b.param_; 
  } 
 
 private: 
  param_type param_; 
  random_internal::FastUniformBits<uint64_t> fast_u64_; 
}; 
 
// ----------------------------------------------------------------------------- 
// Implementation details follow 
// ----------------------------------------------------------------------------- 
 
template <typename IntType> 
poisson_distribution<IntType>::param_type::param_type(double mean) 
    : mean_(mean), split_(0) { 
  assert(mean >= 0); 
  assert(mean <= (std::numeric_limits<result_type>::max)()); 
  // As a defensive measure, avoid large values of the mean.  The rejection 
  // algorithm used does not support very large values well.  It my be worth 
  // changing algorithms to better deal with these cases. 
  assert(mean <= 1e10); 
  if (mean_ < 10) { 
    // For small lambda, use the knuth method. 
    split_ = 1; 
    emu_ = std::exp(-mean_); 
  } else if (mean_ <= 50) { 
    // Use split-knuth method. 
    split_ = 1 + static_cast<int>(mean_ / 10.0); 
    emu_ = std::exp(-mean_ / static_cast<double>(split_)); 
  } else { 
    // Use ratio of uniforms method. 
    constexpr double k2E = 0.7357588823428846; 
    constexpr double kSA = 0.4494580810294493; 
 
    lmu_ = std::log(mean_); 
    double a = mean_ + 0.5; 
    s_ = kSA + std::sqrt(k2E * a); 
    const double mode = std::ceil(mean_) - 1; 
    log_k_ = lmu_ * mode - absl::random_internal::StirlingLogFactorial(mode); 
  } 
} 
 
template <typename IntType> 
template <typename URBG> 
typename poisson_distribution<IntType>::result_type 
poisson_distribution<IntType>::operator()( 
    URBG& g,  // NOLINT(runtime/references) 
    const param_type& p) { 
  using random_internal::GeneratePositiveTag; 
  using random_internal::GenerateRealFromBits; 
  using random_internal::GenerateSignedTag; 
 
  if (p.split_ != 0) { 
    // Use Knuth's algorithm with range splitting to avoid floating-point 
    // errors. Knuth's algorithm is: Ui is a sequence of uniform variates on 
    // (0,1); return the number of variates required for product(Ui) < 
    // exp(-lambda). 
    // 
    // The expected number of variates required for Knuth's method can be 
    // computed as follows: 
    // The expected value of U is 0.5, so solving for 0.5^n < exp(-lambda) gives 
    // the expected number of uniform variates 
    // required for a given lambda, which is: 
    //  lambda = [2, 5,  9, 10, 11, 12, 13, 14, 15, 16, 17] 
    //  n      = [3, 8, 13, 15, 16, 18, 19, 21, 22, 24, 25] 
    // 
    result_type n = 0; 
    for (int split = p.split_; split > 0; --split) { 
      double r = 1.0; 
      do { 
        r *= GenerateRealFromBits<double, GeneratePositiveTag, true>( 
            fast_u64_(g));  // U(-1, 0) 
        ++n; 
      } while (r > p.emu_); 
      --n; 
    } 
    return n; 
  } 
 
  // Use ratio of uniforms method. 
  // 
  // Let u ~ Uniform(0, 1), v ~ Uniform(-1, 1), 
  //     a = lambda + 1/2, 
  //     s = 1.5 - sqrt(3/e) + sqrt(2(lambda + 1/2)/e), 
  //     x = s * v/u + a. 
  // P(floor(x) = k | u^2 < f(floor(x))/k), where 
  // f(m) = lambda^m exp(-lambda)/ m!, for 0 <= m, and f(m) = 0 otherwise, 
  // and k = max(f). 
  const double a = p.mean_ + 0.5; 
  for (;;) { 
    const double u = GenerateRealFromBits<double, GeneratePositiveTag, false>( 
        fast_u64_(g));  // U(0, 1) 
    const double v = GenerateRealFromBits<double, GenerateSignedTag, false>( 
        fast_u64_(g));  // U(-1, 1) 
 
    const double x = std::floor(p.s_ * v / u + a); 
    if (x < 0) continue;  // f(negative) = 0 
    const double rhs = x * p.lmu_; 
    // clang-format off 
    double s = (x <= 1.0) ? 0.0 
             : (x == 2.0) ? 0.693147180559945 
             : absl::random_internal::StirlingLogFactorial(x); 
    // clang-format on 
    const double lhs = 2.0 * std::log(u) + p.log_k_ + s; 
    if (lhs < rhs) { 
      return x > (max)() ? (max)() 
                         : static_cast<result_type>(x);  // f(x)/k >= u^2 
    } 
  } 
} 
 
template <typename CharT, typename Traits, typename IntType> 
std::basic_ostream<CharT, Traits>& operator<<( 
    std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references) 
    const poisson_distribution<IntType>& x) { 
  auto saver = random_internal::make_ostream_state_saver(os); 
  os.precision(random_internal::stream_precision_helper<double>::kPrecision); 
  os << x.mean(); 
  return os; 
} 
 
template <typename CharT, typename Traits, typename IntType> 
std::basic_istream<CharT, Traits>& operator>>( 
    std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references) 
    poisson_distribution<IntType>& x) {     // NOLINT(runtime/references) 
  using param_type = typename poisson_distribution<IntType>::param_type; 
 
  auto saver = random_internal::make_istream_state_saver(is); 
  double mean = random_internal::read_floating_point<double>(is); 
  if (!is.fail()) { 
    x.param(param_type(mean)); 
  } 
  return is; 
} 
 
ABSL_NAMESPACE_END
}  // namespace absl 
 
#endif  // ABSL_RANDOM_POISSON_DISTRIBUTION_H_