Add 'third_party/abseil_cpp/' from commit '768eb2ca28'

git-subtree-dir: third_party/abseil_cpp
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third_party/abseil_cpp/absl/random/poisson_distribution.h

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+// 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"
+
+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(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::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 > (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_