absl/random/poisson_distribution.h - third_party/abseil-cpp - Git at Google

 // 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"
 #include "absl/random/internal/traits.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(random_internal::IsIntegral<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 <=
          static_cast<double>((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 > static_cast<double>((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_
	// 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"
	#include "absl/random/internal/traits.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(random_internal::IsIntegral<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 <=
	static_cast<double>((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 > static_cast<double>((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_