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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_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 {
+inline namespace lts_2019_08_08 {
+
+// 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_type
+zipf_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;
+}
+
+}  // inline namespace lts_2019_08_08
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_ZIPF_DISTRIBUTION_H_