| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271 | // 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_ZIPF_DISTRIBUTION_H_#define ABSL_RANDOM_ZIPF_DISTRIBUTION_H_#include <cassert>#include <cmath>#include <istream>#include <limits>#include <ostream>#include <type_traits>#include "absl/random/internal/iostream_state_saver.h"#include "absl/random/uniform_real_distribution.h"namespace absl {ABSL_NAMESPACE_BEGIN// absl::zipf_distribution produces random integer-values in the range [0, k],// distributed according to the discrete probability function:////  P(x) = (v + x) ^ -q//// The parameter `v` must be greater than 0 and the parameter `q` must be// greater than 1. If either of these parameters take invalid values then the// behavior is undefined.//// IntType is the result_type generated by the generator. It must be of integral// type; a static_assert ensures this is the case.//// The implementation is based on W.Hormann, G.Derflinger://// "Rejection-Inversion to Generate Variates from Monotone Discrete// Distributions"//// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz//template <typename IntType = int>class zipf_distribution { public:  using result_type = IntType;  class param_type {   public:    using distribution_type = zipf_distribution;    // Preconditions: k > 0, v > 0, q > 1    // The precondidtions are validated when NDEBUG is not defined via    // a pair of assert() directives.    // If NDEBUG is defined and either or both of these parameters take invalid    // values, the behavior of the class is undefined.    explicit param_type(result_type k = (std::numeric_limits<IntType>::max)(),                        double q = 2.0, double v = 1.0);    result_type k() const { return k_; }    double q() const { return q_; }    double v() const { return v_; }    friend bool operator==(const param_type& a, const param_type& b) {      return a.k_ == b.k_ && a.q_ == b.q_ && a.v_ == b.v_;    }    friend bool operator!=(const param_type& a, const param_type& b) {      return !(a == b);    }   private:    friend class zipf_distribution;    inline double h(double x) const;    inline double hinv(double x) const;    inline double compute_s() const;    inline double pow_negative_q(double x) const;    // Parameters here are exactly the same as the parameters of Algorithm ZRI    // in the paper.    IntType k_;    double q_;    double v_;    double one_minus_q_;  // 1-q    double s_;    double one_minus_q_inv_;  // 1 / 1-q    double hxm_;              // h(k + 0.5)    double hx0_minus_hxm_;    // h(x0) - h(k + 0.5)    static_assert(std::is_integral<IntType>::value,                  "Class-template absl::zipf_distribution<> must be "                  "parameterized using an integral type.");  };  zipf_distribution()      : zipf_distribution((std::numeric_limits<IntType>::max)()) {}  explicit zipf_distribution(result_type k, double q = 2.0, double v = 1.0)      : param_(k, q, v) {}  explicit zipf_distribution(const param_type& p) : param_(p) {}  void reset() {}  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);  result_type k() const { return param_.k(); }  double q() const { return param_.q(); }  double v() const { return param_.v(); }  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 k(); }  friend bool operator==(const zipf_distribution& a,                         const zipf_distribution& b) {    return a.param_ == b.param_;  }  friend bool operator!=(const zipf_distribution& a,                         const zipf_distribution& b) {    return a.param_ != b.param_;  } private:  param_type param_;};// --------------------------------------------------------------------------// Implementation details follow// --------------------------------------------------------------------------template <typename IntType>zipf_distribution<IntType>::param_type::param_type(    typename zipf_distribution<IntType>::result_type k, double q, double v)    : k_(k), q_(q), v_(v), one_minus_q_(1 - q) {  assert(q > 1);  assert(v > 0);  assert(k > 0);  one_minus_q_inv_ = 1 / one_minus_q_;  // Setup for the ZRI algorithm (pg 17 of the paper).  // Compute: h(i max) => h(k + 0.5)  constexpr double kMax = 18446744073709549568.0;  double kd = static_cast<double>(k);  // TODO(absl-team): Determine if this check is needed, and if so, add a test  // that fails for k > kMax  if (kd > kMax) {    // Ensure that our maximum value is capped to a value which will    // round-trip back through double.    kd = kMax;  }  hxm_ = h(kd + 0.5);  // Compute: h(0)  const bool use_precomputed = (v == 1.0 && q == 2.0);  const double h0x5 = use_precomputed ? (-1.0 / 1.5)  // exp(-log(1.5))                                      : h(0.5);  const double elogv_q = (v_ == 1.0) ? 1 : pow_negative_q(v_);  // h(0) = h(0.5) - exp(log(v) * -q)  hx0_minus_hxm_ = (h0x5 - elogv_q) - hxm_;  // And s  s_ = use_precomputed ? 0.46153846153846123 : compute_s();}template <typename IntType>double zipf_distribution<IntType>::param_type::h(double x) const {  // std::exp(one_minus_q_ * std::log(v_ + x)) * one_minus_q_inv_;  x += v_;  return (one_minus_q_ == -1.0)             ? (-1.0 / x)  // -exp(-log(x))             : (std::exp(std::log(x) * one_minus_q_) * one_minus_q_inv_);}template <typename IntType>double zipf_distribution<IntType>::param_type::hinv(double x) const {  // std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)) - v_;  return -v_ + ((one_minus_q_ == -1.0)                    ? (-1.0 / x)  // exp(-log(-x))                    : std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)));}template <typename IntType>double zipf_distribution<IntType>::param_type::compute_s() const {  // 1 - hinv(h(1.5) - std::exp(std::log(v_ + 1) * -q_));  return 1.0 - hinv(h(1.5) - pow_negative_q(v_ + 1.0));}template <typename IntType>double zipf_distribution<IntType>::param_type::pow_negative_q(double x) const {  // std::exp(std::log(x) * -q_);  return q_ == 2.0 ? (1.0 / (x * x)) : std::exp(std::log(x) * -q_);}template <typename IntType>template <typename URBG>typename zipf_distribution<IntType>::result_typezipf_distribution<IntType>::operator()(    URBG& g, const param_type& p) {  // NOLINT(runtime/references)  absl::uniform_real_distribution<double> uniform_double;  double k;  for (;;) {    const double v = uniform_double(g);    const double u = p.hxm_ + v * p.hx0_minus_hxm_;    const double x = p.hinv(u);    k = rint(x);              // std::floor(x + 0.5);    if (k > p.k()) continue;  // reject k > max_k    if (k - x <= p.s_) break;    const double h = p.h(k + 0.5);    const double r = p.pow_negative_q(p.v_ + k);    if (u >= h - r) break;  }  IntType ki = static_cast<IntType>(k);  assert(ki <= p.k_);  return ki;}template <typename CharT, typename Traits, typename IntType>std::basic_ostream<CharT, Traits>& operator<<(    std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references)    const zipf_distribution<IntType>& x) {  using stream_type =      typename random_internal::stream_format_type<IntType>::type;  auto saver = random_internal::make_ostream_state_saver(os);  os.precision(random_internal::stream_precision_helper<double>::kPrecision);  os << static_cast<stream_type>(x.k()) << os.fill() << x.q() << os.fill()     << x.v();  return os;}template <typename CharT, typename Traits, typename IntType>std::basic_istream<CharT, Traits>& operator>>(    std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references)    zipf_distribution<IntType>& x) {        // NOLINT(runtime/references)  using result_type = typename zipf_distribution<IntType>::result_type;  using param_type = typename zipf_distribution<IntType>::param_type;  using stream_type =      typename random_internal::stream_format_type<IntType>::type;  stream_type k;  double q;  double v;  auto saver = random_internal::make_istream_state_saver(is);  is >> k >> q >> v;  if (!is.fail()) {    x.param(param_type(static_cast<result_type>(k), q, v));  }  return is;}ABSL_NAMESPACE_END}  // namespace absl#endif  // ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
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