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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 {
+inline namespace lts_2019_08_08 {
+
+// 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;
+}
+
+} // inline namespace lts_2019_08_08
+} // namespace absl
+
+#endif // ABSL_RANDOM_POISSON_DISTRIBUTION_H_
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