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author | 2019-08-08 10:56:58 -0700 | |
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committer | 2019-08-08 14:19:45 -0400 | |
commit | aa844899c937bde5d2b24f276b59997e5b668bde (patch) | |
tree | cd18e64150abc74b85bbbf6abf990f66fa47cacd /absl/random/poisson_distribution.h | |
parent | fcb104594b0bb4b8ac306cb2f55ecdad40974683 (diff) |
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GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d
Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced
Diffstat (limited to 'absl/random/poisson_distribution.h')
-rw-r--r-- | absl/random/poisson_distribution.h | 256 |
1 files changed, 256 insertions, 0 deletions
diff --git a/absl/random/poisson_distribution.h b/absl/random/poisson_distribution.h new file mode 100644 index 00000000..66c75091 --- /dev/null +++ b/absl/random/poisson_distribution.h @@ -0,0 +1,256 @@ +// 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_ |