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272 lines
8.9 KiB
272 lines
8.9 KiB
// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
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#define ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
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#include <cassert>
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#include <cmath>
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#include <istream>
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#include <limits>
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#include <ostream>
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#include <type_traits>
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#include "absl/random/internal/iostream_state_saver.h"
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#include "absl/random/uniform_real_distribution.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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// absl::zipf_distribution produces random integer-values in the range [0, k],
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// distributed according to the discrete probability function:
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//
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// P(x) = (v + x) ^ -q
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//
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// The parameter `v` must be greater than 0 and the parameter `q` must be
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// greater than 1. If either of these parameters take invalid values then the
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// behavior is undefined.
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//
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// IntType is the result_type generated by the generator. It must be of integral
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// type; a static_assert ensures this is the case.
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//
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// The implementation is based on W.Hormann, G.Derflinger:
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//
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// "Rejection-Inversion to Generate Variates from Monotone Discrete
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// Distributions"
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//
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// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
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//
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template <typename IntType = int>
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class zipf_distribution {
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public:
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using result_type = IntType;
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class param_type {
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public:
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using distribution_type = zipf_distribution;
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// Preconditions: k > 0, v > 0, q > 1
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// The precondidtions are validated when NDEBUG is not defined via
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// a pair of assert() directives.
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// If NDEBUG is defined and either or both of these parameters take invalid
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// values, the behavior of the class is undefined.
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explicit param_type(result_type k = (std::numeric_limits<IntType>::max)(),
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double q = 2.0, double v = 1.0);
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result_type k() const { return k_; }
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double q() const { return q_; }
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double v() const { return v_; }
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friend bool operator==(const param_type& a, const param_type& b) {
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return a.k_ == b.k_ && a.q_ == b.q_ && a.v_ == b.v_;
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}
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friend bool operator!=(const param_type& a, const param_type& b) {
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return !(a == b);
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}
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private:
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friend class zipf_distribution;
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inline double h(double x) const;
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inline double hinv(double x) const;
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inline double compute_s() const;
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inline double pow_negative_q(double x) const;
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// Parameters here are exactly the same as the parameters of Algorithm ZRI
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// in the paper.
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IntType k_;
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double q_;
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double v_;
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double one_minus_q_; // 1-q
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double s_;
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double one_minus_q_inv_; // 1 / 1-q
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double hxm_; // h(k + 0.5)
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double hx0_minus_hxm_; // h(x0) - h(k + 0.5)
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static_assert(std::is_integral<IntType>::value,
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"Class-template absl::zipf_distribution<> must be "
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"parameterized using an integral type.");
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};
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zipf_distribution()
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: zipf_distribution((std::numeric_limits<IntType>::max)()) {}
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explicit zipf_distribution(result_type k, double q = 2.0, double v = 1.0)
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: param_(k, q, v) {}
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explicit zipf_distribution(const param_type& p) : param_(p) {}
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void reset() {}
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template <typename URBG>
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result_type operator()(URBG& g) { // NOLINT(runtime/references)
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return (*this)(g, param_);
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}
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template <typename URBG>
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result_type operator()(URBG& g, // NOLINT(runtime/references)
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const param_type& p);
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result_type k() const { return param_.k(); }
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double q() const { return param_.q(); }
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double v() const { return param_.v(); }
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param_type param() const { return param_; }
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void param(const param_type& p) { param_ = p; }
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result_type(min)() const { return 0; }
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result_type(max)() const { return k(); }
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friend bool operator==(const zipf_distribution& a,
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const zipf_distribution& b) {
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return a.param_ == b.param_;
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}
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friend bool operator!=(const zipf_distribution& a,
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const zipf_distribution& b) {
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return a.param_ != b.param_;
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}
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private:
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param_type param_;
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};
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// --------------------------------------------------------------------------
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// Implementation details follow
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// --------------------------------------------------------------------------
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template <typename IntType>
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zipf_distribution<IntType>::param_type::param_type(
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typename zipf_distribution<IntType>::result_type k, double q, double v)
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: k_(k), q_(q), v_(v), one_minus_q_(1 - q) {
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assert(q > 1);
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assert(v > 0);
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assert(k > 0);
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one_minus_q_inv_ = 1 / one_minus_q_;
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// Setup for the ZRI algorithm (pg 17 of the paper).
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// Compute: h(i max) => h(k + 0.5)
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constexpr double kMax = 18446744073709549568.0;
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double kd = static_cast<double>(k);
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// TODO(absl-team): Determine if this check is needed, and if so, add a test
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// that fails for k > kMax
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if (kd > kMax) {
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// Ensure that our maximum value is capped to a value which will
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// round-trip back through double.
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kd = kMax;
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}
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hxm_ = h(kd + 0.5);
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// Compute: h(0)
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const bool use_precomputed = (v == 1.0 && q == 2.0);
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const double h0x5 = use_precomputed ? (-1.0 / 1.5) // exp(-log(1.5))
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: h(0.5);
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const double elogv_q = (v_ == 1.0) ? 1 : pow_negative_q(v_);
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// h(0) = h(0.5) - exp(log(v) * -q)
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hx0_minus_hxm_ = (h0x5 - elogv_q) - hxm_;
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// And s
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s_ = use_precomputed ? 0.46153846153846123 : compute_s();
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}
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template <typename IntType>
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double zipf_distribution<IntType>::param_type::h(double x) const {
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// std::exp(one_minus_q_ * std::log(v_ + x)) * one_minus_q_inv_;
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x += v_;
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return (one_minus_q_ == -1.0)
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? (-1.0 / x) // -exp(-log(x))
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: (std::exp(std::log(x) * one_minus_q_) * one_minus_q_inv_);
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}
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template <typename IntType>
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double zipf_distribution<IntType>::param_type::hinv(double x) const {
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// std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)) - v_;
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return -v_ + ((one_minus_q_ == -1.0)
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? (-1.0 / x) // exp(-log(-x))
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: std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)));
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}
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template <typename IntType>
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double zipf_distribution<IntType>::param_type::compute_s() const {
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// 1 - hinv(h(1.5) - std::exp(std::log(v_ + 1) * -q_));
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return 1.0 - hinv(h(1.5) - pow_negative_q(v_ + 1.0));
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}
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template <typename IntType>
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double zipf_distribution<IntType>::param_type::pow_negative_q(double x) const {
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// std::exp(std::log(x) * -q_);
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return q_ == 2.0 ? (1.0 / (x * x)) : std::exp(std::log(x) * -q_);
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}
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template <typename IntType>
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template <typename URBG>
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typename zipf_distribution<IntType>::result_type
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zipf_distribution<IntType>::operator()(
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URBG& g, const param_type& p) { // NOLINT(runtime/references)
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absl::uniform_real_distribution<double> uniform_double;
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double k;
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for (;;) {
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const double v = uniform_double(g);
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const double u = p.hxm_ + v * p.hx0_minus_hxm_;
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const double x = p.hinv(u);
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k = rint(x); // std::floor(x + 0.5);
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if (k > p.k()) continue; // reject k > max_k
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if (k - x <= p.s_) break;
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const double h = p.h(k + 0.5);
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const double r = p.pow_negative_q(p.v_ + k);
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if (u >= h - r) break;
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}
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IntType ki = static_cast<IntType>(k);
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assert(ki <= p.k_);
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return ki;
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}
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template <typename CharT, typename Traits, typename IntType>
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std::basic_ostream<CharT, Traits>& operator<<(
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std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references)
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const zipf_distribution<IntType>& x) {
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using stream_type =
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typename random_internal::stream_format_type<IntType>::type;
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auto saver = random_internal::make_ostream_state_saver(os);
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os.precision(random_internal::stream_precision_helper<double>::kPrecision);
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os << static_cast<stream_type>(x.k()) << os.fill() << x.q() << os.fill()
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<< x.v();
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return os;
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}
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template <typename CharT, typename Traits, typename IntType>
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std::basic_istream<CharT, Traits>& operator>>(
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std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references)
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zipf_distribution<IntType>& x) { // NOLINT(runtime/references)
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using result_type = typename zipf_distribution<IntType>::result_type;
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using param_type = typename zipf_distribution<IntType>::param_type;
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using stream_type =
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typename random_internal::stream_format_type<IntType>::type;
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stream_type k;
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double q;
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double v;
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auto saver = random_internal::make_istream_state_saver(is);
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is >> k >> q >> v;
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if (!is.fail()) {
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x.param(param_type(static_cast<result_type>(k), q, v));
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}
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return is;
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}
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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_RANDOM_ZIPF_DISTRIBUTION_H_
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