Abseil Common Libraries (C++) (grcp 依赖)
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254 lines
8.4 KiB
254 lines
8.4 KiB
// 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/distribution_impl.h" |
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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/iostream_state_saver.h" |
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namespace absl { |
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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::PositiveValueT; |
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using random_internal::RandU64ToDouble; |
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using random_internal::SignedValueT; |
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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 *= RandU64ToDouble<PositiveValueT, true>(fast_u64_(g)); |
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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 = |
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RandU64ToDouble<PositiveValueT, false>(fast_u64_(g)); // (0, 1) |
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const double v = |
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RandU64ToDouble<SignedValueT, false>(fast_u64_(g)); // (-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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} // namespace absl |
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#endif // ABSL_RANDOM_POISSON_DISTRIBUTION_H_
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