Source code
Revision control
Copy as Markdown
Other Tools
// 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
//
//
// 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/internal/traits.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 unnormalized 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"
//
//
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(random_internal::IsIntegral<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 > static_cast<double>(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_