absl/random/zipf_distribution.h

0001 // Copyright 2017 The Abseil Authors.
0002 //
0003 // Licensed under the Apache License, Version 2.0 (the "License");
0004 // you may not use this file except in compliance with the License.
0005 // You may obtain a copy of the License at
0006 //
0007 //      https://www.apache.org/licenses/LICENSE-2.0
0008 //
0009 // Unless required by applicable law or agreed to in writing, software
0010 // distributed under the License is distributed on an "AS IS" BASIS,
0011 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
0012 // See the License for the specific language governing permissions and
0013 // limitations under the License.
0014
0015 #ifndef ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
0016 #define ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
0017
0018 #include <cassert>
0019 #include <cmath>
0020 #include <istream>
0021 #include <limits>
0022 #include <ostream>
0023 #include <type_traits>
0024
0025 #include "absl/random/internal/iostream_state_saver.h"
0026 #include "absl/random/internal/traits.h"
0027 #include "absl/random/uniform_real_distribution.h"
0028
0029 namespace absl {
0030 ABSL_NAMESPACE_BEGIN
0031
0032 // absl::zipf_distribution produces random integer-values in the range [0, k],
0033 // distributed according to the unnormalized discrete probability function:
0034 //
0035 //  P(x) = (v + x) ^ -q
0036 //
0037 // The parameter `v` must be greater than 0 and the parameter `q` must be
0038 // greater than 1. If either of these parameters take invalid values then the
0039 // behavior is undefined.
0040 //
0041 // IntType is the result_type generated by the generator. It must be of integral
0042 // type; a static_assert ensures this is the case.
0043 //
0044 // The implementation is based on W.Hormann, G.Derflinger:
0045 //
0046 // "Rejection-Inversion to Generate Variates from Monotone Discrete
0047 // Distributions"
0048 //
0049 // http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
0050 //
0051 template <typename IntType = int>
0052 class zipf_distribution {
0053  public:
0054   using result_type = IntType;
0055
0056   class param_type {
0057    public:
0058     using distribution_type = zipf_distribution;
0059
0060     // Preconditions: k > 0, v > 0, q > 1
0061     // The precondidtions are validated when NDEBUG is not defined via
0062     // a pair of assert() directives.
0063     // If NDEBUG is defined and either or both of these parameters take invalid
0064     // values, the behavior of the class is undefined.
0065     explicit param_type(result_type k = (std::numeric_limits<IntType>::max)(),
0066                         double q = 2.0, double v = 1.0);
0067
0068     result_type k() const { return k_; }
0069     double q() const { return q_; }
0070     double v() const { return v_; }
0071
0072     friend bool operator==(const param_type& a, const param_type& b) {
0073       return a.k_ == b.k_ && a.q_ == b.q_ && a.v_ == b.v_;
0074     }
0075     friend bool operator!=(const param_type& a, const param_type& b) {
0076       return !(a == b);
0077     }
0078
0079    private:
0080     friend class zipf_distribution;
0081     inline double h(double x) const;
0082     inline double hinv(double x) const;
0083     inline double compute_s() const;
0084     inline double pow_negative_q(double x) const;
0085
0086     // Parameters here are exactly the same as the parameters of Algorithm ZRI
0087     // in the paper.
0088     IntType k_;
0089     double q_;
0090     double v_;
0091
0092     double one_minus_q_;  // 1-q
0093     double s_;
0094     double one_minus_q_inv_;  // 1 / 1-q
0095     double hxm_;              // h(k + 0.5)
0096     double hx0_minus_hxm_;    // h(x0) - h(k + 0.5)
0097
0098     static_assert(random_internal::IsIntegral<IntType>::value,
0099                   "Class-template absl::zipf_distribution<> must be "
0100                   "parameterized using an integral type.");
0101   };
0102
0103   zipf_distribution()
0104       : zipf_distribution((std::numeric_limits<IntType>::max)()) {}
0105
0106   explicit zipf_distribution(result_type k, double q = 2.0, double v = 1.0)
0107       : param_(k, q, v) {}
0108
0109   explicit zipf_distribution(const param_type& p) : param_(p) {}
0110
0111   void reset() {}
0112
0113   template <typename URBG>
0114   result_type operator()(URBG& g) {  // NOLINT(runtime/references)
0115     return (*this)(g, param_);
0116   }
0117
0118   template <typename URBG>
0119   result_type operator()(URBG& g,  // NOLINT(runtime/references)
0120                          const param_type& p);
0121
0122   result_type k() const { return param_.k(); }
0123   double q() const { return param_.q(); }
0124   double v() const { return param_.v(); }
0125
0126   param_type param() const { return param_; }
0127   void param(const param_type& p) { param_ = p; }
0128
0129   result_type(min)() const { return 0; }
0130   result_type(max)() const { return k(); }
0131
0132   friend bool operator==(const zipf_distribution& a,
0133                          const zipf_distribution& b) {
0134     return a.param_ == b.param_;
0135   }
0136   friend bool operator!=(const zipf_distribution& a,
0137                          const zipf_distribution& b) {
0138     return a.param_ != b.param_;
0139   }
0140
0141  private:
0142   param_type param_;
0143 };
0144
0145 // --------------------------------------------------------------------------
0146 // Implementation details follow
0147 // --------------------------------------------------------------------------
0148
0149 template <typename IntType>
0150 zipf_distribution<IntType>::param_type::param_type(
0151     typename zipf_distribution<IntType>::result_type k, double q, double v)
0152     : k_(k), q_(q), v_(v), one_minus_q_(1 - q) {
0153   assert(q > 1);
0154   assert(v > 0);
0155   assert(k > 0);
0156   one_minus_q_inv_ = 1 / one_minus_q_;
0157
0158   // Setup for the ZRI algorithm (pg 17 of the paper).
0159   // Compute: h(i max) => h(k + 0.5)
0160   constexpr double kMax = 18446744073709549568.0;
0161   double kd = static_cast<double>(k);
0162   // TODO(absl-team): Determine if this check is needed, and if so, add a test
0163   // that fails for k > kMax
0164   if (kd > kMax) {
0165     // Ensure that our maximum value is capped to a value which will
0166     // round-trip back through double.
0167     kd = kMax;
0168   }
0169   hxm_ = h(kd + 0.5);
0170
0171   // Compute: h(0)
0172   const bool use_precomputed = (v == 1.0 && q == 2.0);
0173   const double h0x5 = use_precomputed ? (-1.0 / 1.5)  // exp(-log(1.5))
0174                                       : h(0.5);
0175   const double elogv_q = (v_ == 1.0) ? 1 : pow_negative_q(v_);
0176
0177   // h(0) = h(0.5) - exp(log(v) * -q)
0178   hx0_minus_hxm_ = (h0x5 - elogv_q) - hxm_;
0179
0180   // And s
0181   s_ = use_precomputed ? 0.46153846153846123 : compute_s();
0182 }
0183
0184 template <typename IntType>
0185 double zipf_distribution<IntType>::param_type::h(double x) const {
0186   // std::exp(one_minus_q_ * std::log(v_ + x)) * one_minus_q_inv_;
0187   x += v_;
0188   return (one_minus_q_ == -1.0)
0189              ? (-1.0 / x)  // -exp(-log(x))
0190              : (std::exp(std::log(x) * one_minus_q_) * one_minus_q_inv_);
0191 }
0192
0193 template <typename IntType>
0194 double zipf_distribution<IntType>::param_type::hinv(double x) const {
0195   // std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)) - v_;
0196   return -v_ + ((one_minus_q_ == -1.0)
0197                     ? (-1.0 / x)  // exp(-log(-x))
0198                     : std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)));
0199 }
0200
0201 template <typename IntType>
0202 double zipf_distribution<IntType>::param_type::compute_s() const {
0203   // 1 - hinv(h(1.5) - std::exp(std::log(v_ + 1) * -q_));
0204   return 1.0 - hinv(h(1.5) - pow_negative_q(v_ + 1.0));
0205 }
0206
0207 template <typename IntType>
0208 double zipf_distribution<IntType>::param_type::pow_negative_q(double x) const {
0209   // std::exp(std::log(x) * -q_);
0210   return q_ == 2.0 ? (1.0 / (x * x)) : std::exp(std::log(x) * -q_);
0211 }
0212
0213 template <typename IntType>
0214 template <typename URBG>
0215 typename zipf_distribution<IntType>::result_type
0216 zipf_distribution<IntType>::operator()(
0217     URBG& g, const param_type& p) {  // NOLINT(runtime/references)
0218   absl::uniform_real_distribution<double> uniform_double;
0219   double k;
0220   for (;;) {
0221     const double v = uniform_double(g);
0222     const double u = p.hxm_ + v * p.hx0_minus_hxm_;
0223     const double x = p.hinv(u);
0224     k = rint(x);              // std::floor(x + 0.5);
0225     if (k > static_cast<double>(p.k())) continue;  // reject k > max_k
0226     if (k - x <= p.s_) break;
0227     const double h = p.h(k + 0.5);
0228     const double r = p.pow_negative_q(p.v_ + k);
0229     if (u >= h - r) break;
0230   }
0231   IntType ki = static_cast<IntType>(k);
0232   assert(ki <= p.k_);
0233   return ki;
0234 }
0235
0236 template <typename CharT, typename Traits, typename IntType>
0237 std::basic_ostream<CharT, Traits>& operator<<(
0238     std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references)
0239     const zipf_distribution<IntType>& x) {
0240   using stream_type =
0241       typename random_internal::stream_format_type<IntType>::type;
0242   auto saver = random_internal::make_ostream_state_saver(os);
0243   os.precision(random_internal::stream_precision_helper<double>::kPrecision);
0244   os << static_cast<stream_type>(x.k()) << os.fill() << x.q() << os.fill()
0245      << x.v();
0246   return os;
0247 }
0248
0249 template <typename CharT, typename Traits, typename IntType>
0250 std::basic_istream<CharT, Traits>& operator>>(
0251     std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references)
0252     zipf_distribution<IntType>& x) {        // NOLINT(runtime/references)
0253   using result_type = typename zipf_distribution<IntType>::result_type;
0254   using param_type = typename zipf_distribution<IntType>::param_type;
0255   using stream_type =
0256       typename random_internal::stream_format_type<IntType>::type;
0257   stream_type k;
0258   double q;
0259   double v;
0260
0261   auto saver = random_internal::make_istream_state_saver(is);
0262   is >> k >> q >> v;
0263   if (!is.fail()) {
0264     x.param(param_type(static_cast<result_type>(k), q, v));
0265   }
0266   return is;
0267 }
0268
0269 ABSL_NAMESPACE_END
0270 }  // namespace absl
0271
0272 #endif  // ABSL_RANDOM_ZIPF_DISTRIBUTION_H_