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