poisson_distribution.h (8902B)
1 // Copyright 2017 The Abseil Authors. 2 // 3 // Licensed under the Apache License, Version 2.0 (the "License"); 4 // you may not use this file except in compliance with the License. 5 // You may obtain a copy of the License at 6 // 7 // https://www.apache.org/licenses/LICENSE-2.0 8 // 9 // Unless required by applicable law or agreed to in writing, software 10 // distributed under the License is distributed on an "AS IS" BASIS, 11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 // See the License for the specific language governing permissions and 13 // limitations under the License. 14 15 #ifndef ABSL_RANDOM_POISSON_DISTRIBUTION_H_ 16 #define ABSL_RANDOM_POISSON_DISTRIBUTION_H_ 17 18 #include <cassert> 19 #include <cmath> 20 #include <cstdint> 21 #include <istream> 22 #include <limits> 23 #include <ostream> 24 25 #include "absl/base/config.h" 26 #include "absl/random/internal/fast_uniform_bits.h" 27 #include "absl/random/internal/fastmath.h" 28 #include "absl/random/internal/generate_real.h" 29 #include "absl/random/internal/iostream_state_saver.h" 30 #include "absl/random/internal/traits.h" 31 32 namespace absl { 33 ABSL_NAMESPACE_BEGIN 34 35 // absl::poisson_distribution: 36 // Generates discrete variates conforming to a Poisson distribution. 37 // p(n) = (mean^n / n!) exp(-mean) 38 // 39 // Depending on the parameter, the distribution selects one of the following 40 // algorithms: 41 // * The standard algorithm, attributed to Knuth, extended using a split method 42 // for larger values 43 // * The "Ratio of Uniforms as a convenient method for sampling from classical 44 // discrete distributions", Stadlober, 1989. 45 // http://www.sciencedirect.com/science/article/pii/0377042790903495 46 // 47 // NOTE: param_type.mean() is a double, which permits values larger than 48 // poisson_distribution<IntType>::max(), however this should be avoided and 49 // the distribution results are limited to the max() value. 50 // 51 // The goals of this implementation are to provide good performance while still 52 // being thread-safe: This limits the implementation to not using lgamma 53 // provided by <math.h>. 54 // 55 template <typename IntType = int> 56 class poisson_distribution { 57 public: 58 using result_type = IntType; 59 60 class param_type { 61 public: 62 using distribution_type = poisson_distribution; 63 explicit param_type(double mean = 1.0); 64 65 double mean() const { return mean_; } 66 67 friend bool operator==(const param_type& a, const param_type& b) { 68 return a.mean_ == b.mean_; 69 } 70 71 friend bool operator!=(const param_type& a, const param_type& b) { 72 return !(a == b); 73 } 74 75 private: 76 friend class poisson_distribution; 77 78 double mean_; 79 double emu_; // e ^ -mean_ 80 double lmu_; // ln(mean_) 81 double s_; 82 double log_k_; 83 int split_; 84 85 static_assert(random_internal::IsIntegral<IntType>::value, 86 "Class-template absl::poisson_distribution<> must be " 87 "parameterized using an integral type."); 88 }; 89 90 poisson_distribution() : poisson_distribution(1.0) {} 91 92 explicit poisson_distribution(double mean) : param_(mean) {} 93 94 explicit poisson_distribution(const param_type& p) : param_(p) {} 95 96 void reset() {} 97 98 // generating functions 99 template <typename URBG> 100 result_type operator()(URBG& g) { // NOLINT(runtime/references) 101 return (*this)(g, param_); 102 } 103 104 template <typename URBG> 105 result_type operator()(URBG& g, // NOLINT(runtime/references) 106 const param_type& p); 107 108 param_type param() const { return param_; } 109 void param(const param_type& p) { param_ = p; } 110 111 result_type(min)() const { return 0; } 112 result_type(max)() const { return (std::numeric_limits<result_type>::max)(); } 113 114 double mean() const { return param_.mean(); } 115 116 friend bool operator==(const poisson_distribution& a, 117 const poisson_distribution& b) { 118 return a.param_ == b.param_; 119 } 120 friend bool operator!=(const poisson_distribution& a, 121 const poisson_distribution& b) { 122 return a.param_ != b.param_; 123 } 124 125 private: 126 param_type param_; 127 random_internal::FastUniformBits<uint64_t> fast_u64_; 128 }; 129 130 // ----------------------------------------------------------------------------- 131 // Implementation details follow 132 // ----------------------------------------------------------------------------- 133 134 template <typename IntType> 135 poisson_distribution<IntType>::param_type::param_type(double mean) 136 : mean_(mean), split_(0) { 137 assert(mean >= 0); 138 assert(mean <= 139 static_cast<double>((std::numeric_limits<result_type>::max)())); 140 // As a defensive measure, avoid large values of the mean. The rejection 141 // algorithm used does not support very large values well. It my be worth 142 // changing algorithms to better deal with these cases. 143 assert(mean <= 1e10); 144 if (mean_ < 10) { 145 // For small lambda, use the knuth method. 146 split_ = 1; 147 emu_ = std::exp(-mean_); 148 } else if (mean_ <= 50) { 149 // Use split-knuth method. 150 split_ = 1 + static_cast<int>(mean_ / 10.0); 151 emu_ = std::exp(-mean_ / static_cast<double>(split_)); 152 } else { 153 // Use ratio of uniforms method. 154 constexpr double k2E = 0.7357588823428846; 155 constexpr double kSA = 0.4494580810294493; 156 157 lmu_ = std::log(mean_); 158 double a = mean_ + 0.5; 159 s_ = kSA + std::sqrt(k2E * a); 160 const double mode = std::ceil(mean_) - 1; 161 log_k_ = lmu_ * mode - absl::random_internal::StirlingLogFactorial(mode); 162 } 163 } 164 165 template <typename IntType> 166 template <typename URBG> 167 typename poisson_distribution<IntType>::result_type 168 poisson_distribution<IntType>::operator()( 169 URBG& g, // NOLINT(runtime/references) 170 const param_type& p) { 171 using random_internal::GeneratePositiveTag; 172 using random_internal::GenerateRealFromBits; 173 using random_internal::GenerateSignedTag; 174 175 if (p.split_ != 0) { 176 // Use Knuth's algorithm with range splitting to avoid floating-point 177 // errors. Knuth's algorithm is: Ui is a sequence of uniform variates on 178 // (0,1); return the number of variates required for product(Ui) < 179 // exp(-lambda). 180 // 181 // The expected number of variates required for Knuth's method can be 182 // computed as follows: 183 // The expected value of U is 0.5, so solving for 0.5^n < exp(-lambda) gives 184 // the expected number of uniform variates 185 // required for a given lambda, which is: 186 // lambda = [2, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17] 187 // n = [3, 8, 13, 15, 16, 18, 19, 21, 22, 24, 25] 188 // 189 result_type n = 0; 190 for (int split = p.split_; split > 0; --split) { 191 double r = 1.0; 192 do { 193 r *= GenerateRealFromBits<double, GeneratePositiveTag, true>( 194 fast_u64_(g)); // U(-1, 0) 195 ++n; 196 } while (r > p.emu_); 197 --n; 198 } 199 return n; 200 } 201 202 // Use ratio of uniforms method. 203 // 204 // Let u ~ Uniform(0, 1), v ~ Uniform(-1, 1), 205 // a = lambda + 1/2, 206 // s = 1.5 - sqrt(3/e) + sqrt(2(lambda + 1/2)/e), 207 // x = s * v/u + a. 208 // P(floor(x) = k | u^2 < f(floor(x))/k), where 209 // f(m) = lambda^m exp(-lambda)/ m!, for 0 <= m, and f(m) = 0 otherwise, 210 // and k = max(f). 211 const double a = p.mean_ + 0.5; 212 for (;;) { 213 const double u = GenerateRealFromBits<double, GeneratePositiveTag, false>( 214 fast_u64_(g)); // U(0, 1) 215 const double v = GenerateRealFromBits<double, GenerateSignedTag, false>( 216 fast_u64_(g)); // U(-1, 1) 217 218 const double x = std::floor(p.s_ * v / u + a); 219 if (x < 0) continue; // f(negative) = 0 220 const double rhs = x * p.lmu_; 221 // clang-format off 222 double s = (x <= 1.0) ? 0.0 223 : (x == 2.0) ? 0.693147180559945 224 : absl::random_internal::StirlingLogFactorial(x); 225 // clang-format on 226 const double lhs = 2.0 * std::log(u) + p.log_k_ + s; 227 if (lhs < rhs) { 228 return x > static_cast<double>((max)()) 229 ? (max)() 230 : static_cast<result_type>(x); // f(x)/k >= u^2 231 } 232 } 233 } 234 235 template <typename CharT, typename Traits, typename IntType> 236 std::basic_ostream<CharT, Traits>& operator<<( 237 std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references) 238 const poisson_distribution<IntType>& x) { 239 auto saver = random_internal::make_ostream_state_saver(os); 240 os.precision(random_internal::stream_precision_helper<double>::kPrecision); 241 os << x.mean(); 242 return os; 243 } 244 245 template <typename CharT, typename Traits, typename IntType> 246 std::basic_istream<CharT, Traits>& operator>>( 247 std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references) 248 poisson_distribution<IntType>& x) { // NOLINT(runtime/references) 249 using param_type = typename poisson_distribution<IntType>::param_type; 250 251 auto saver = random_internal::make_istream_state_saver(is); 252 double mean = random_internal::read_floating_point<double>(is); 253 if (!is.fail()) { 254 x.param(param_type(mean)); 255 } 256 return is; 257 } 258 259 ABSL_NAMESPACE_END 260 } // namespace absl 261 262 #endif // ABSL_RANDOM_POISSON_DISTRIBUTION_H_