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							- // 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/distribution_impl.h"
 
- #include "absl/random/internal/fast_uniform_bits.h"
 
- #include "absl/random/internal/fastmath.h"
 
- #include "absl/random/internal/iostream_state_saver.h"
 
- namespace absl {
 
- // 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::PositiveValueT;
 
-   using random_internal::RandU64ToDouble;
 
-   using random_internal::SignedValueT;
 
-   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 *= RandU64ToDouble<PositiveValueT, true>(fast_u64_(g));
 
-         ++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 =
 
-         RandU64ToDouble<PositiveValueT, false>(fast_u64_(g));  // (0, 1)
 
-     const double v =
 
-         RandU64ToDouble<SignedValueT, false>(fast_u64_(g));  // (-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;
 
- }
 
- }  // namespace absl
 
- #endif  // ABSL_RANDOM_POISSON_DISTRIBUTION_H_
 
 
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