summaryrefslogtreecommitdiff
path: root/absl/random/poisson_distribution.h
blob: cb5f5d5d0ff71ee5bd65333bcfce0f5fc87a8e8f (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
// 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_