// 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_DISCRETE_DISTRIBUTION_H_
#define ABSL_RANDOM_DISCRETE_DISTRIBUTION_H_
#include <cassert>
#include <cmath>
#include <istream>
#include <limits>
#include <numeric>
#include <type_traits>
#include <utility>
#include <vector>
#include "absl/random/bernoulli_distribution.h"
#include "absl/random/internal/iostream_state_saver.h"
#include "absl/random/uniform_int_distribution.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
// absl::discrete_distribution
//
// A discrete distribution produces random integers i, where 0 <= i < n
// distributed according to the discrete probability function:
//
// P(i|p0,...,pn−1)=pi
//
// This class is an implementation of discrete_distribution (see
// [rand.dist.samp.discrete]).
//
// The algorithm used is Walker's Aliasing algorithm, described in Knuth, Vol 2.
// absl::discrete_distribution takes O(N) time to precompute the probabilities
// (where N is the number of possible outcomes in the distribution) at
// construction, and then takes O(1) time for each variate generation. Many
// other implementations also take O(N) time to construct an ordered sequence of
// partial sums, plus O(log N) time per variate to binary search.
//
template <typename IntType = int>
class discrete_distribution {
public:
using result_type = IntType;
class param_type {
public:
using distribution_type = discrete_distribution;
param_type() { init(); }
template <typename InputIterator>
explicit param_type(InputIterator begin, InputIterator end)
: p_(begin, end) {
init();
}
explicit param_type(std::initializer_list<double> weights) : p_(weights) {
init();
}
template <class UnaryOperation>
explicit param_type(size_t nw, double xmin, double xmax,
UnaryOperation fw) {
if (nw > 0) {
p_.reserve(nw);
double delta = (xmax - xmin) / static_cast<double>(nw);
assert(delta > 0);
double t = delta * 0.5;
for (size_t i = 0; i < nw; ++i) {
p_.push_back(fw(xmin + i * delta + t));
}
}
init();
}
const std::vector<double>& probabilities() const { return p_; }
size_t n() const { return p_.size() - 1; }
friend bool operator==(const param_type& a, const param_type& b) {
return a.probabilities() == b.probabilities();
}
friend bool operator!=(const param_type& a, const param_type& b) {
return !(a == b);
}
private:
friend class discrete_distribution;
void init();
std::vector<double> p_; // normalized probabilities
std::vector<std::pair<double, size_t>> q_; // (acceptance, alternate) pairs
static_assert(std::is_integral<result_type>::value,
"Class-template absl::discrete_distribution<> must be "
"parameterized using an integral type.");
};
discrete_distribution() : param_() {}
explicit discrete_distribution(const param_type& p) : param_(p) {}
template <typename InputIterator>
explicit discrete_distribution(InputIterator begin, InputIterator end)
: param_(begin, end) {}
explicit discrete_distribution(std::initializer_list<double> weights)
: param_(weights) {}
template <class UnaryOperation>
explicit discrete_distribution(size_t nw, double xmin, double xmax,
UnaryOperation fw)
: param_(nw, xmin, xmax, std::move(fw)) {}
void reset() {}
// generating functions
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);
const 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 static_cast<result_type>(param_.n());
} // inclusive
// NOTE [rand.dist.sample.discrete] returns a std::vector<double> not a
// const std::vector<double>&.
const std::vector<double>& probabilities() const {
return param_.probabilities();
}
friend bool operator==(const discrete_distribution& a,
const discrete_distribution& b) {
return a.param_ == b.param_;
}
friend bool operator!=(const discrete_distribution& a,
const discrete_distribution& b) {
return a.param_ != b.param_;
}
private:
param_type param_;
};
// --------------------------------------------------------------------------
// Implementation details only below
// --------------------------------------------------------------------------
namespace random_internal {
// Using the vector `*probabilities`, whose values are the weights or
// probabilities of an element being selected, constructs the proportional
// probabilities used by the discrete distribution. `*probabilities` will be
// scaled, if necessary, so that its entries sum to a value sufficiently close
// to 1.0.
std::vector<std::pair<double, size_t>> InitDiscreteDistribution(
std::vector<double>* probabilities);
} // namespace random_internal
template <typename IntType>
void discrete_distribution<IntType>::param_type::init() {
if (p_.empty()) {
p_.push_back(1.0);
q_.emplace_back(1.0, 0);
} else {
assert(n() <= (std::numeric_limits<IntType>::max)());
q_ = random_internal::InitDiscreteDistribution(&p_);
}
}
template <typename IntType>
template <typename URBG>
typename discrete_distribution<IntType>::result_type
discrete_distribution<IntType>::operator()(
URBG& g, // NOLINT(runtime/references)
const param_type& p) {
const auto idx = absl::uniform_int_distribution<result_type>(0, p.n())(g);
const auto& q = p.q_[idx];
const bool selected = absl::bernoulli_distribution(q.first)(g);
return selected ? idx : static_cast<result_type>(q.second);
}
template <typename CharT, typename Traits, typename IntType>
std::basic_ostream<CharT, Traits>& operator<<(
std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references)
const discrete_distribution<IntType>& x) {
auto saver = random_internal::make_ostream_state_saver(os);
const auto& probabilities = x.param().probabilities();
os << probabilities.size();
os.precision(random_internal::stream_precision_helper<double>::kPrecision);
for (const auto& p : probabilities) {
os << os.fill() << p;
}
return os;
}
template <typename CharT, typename Traits, typename IntType>
std::basic_istream<CharT, Traits>& operator>>(
std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references)
discrete_distribution<IntType>& x) { // NOLINT(runtime/references)
using param_type = typename discrete_distribution<IntType>::param_type;
auto saver = random_internal::make_istream_state_saver(is);
size_t n;
std::vector<double> p;
is >> n;
if (is.fail()) return is;
if (n > 0) {
p.reserve(n);
for (IntType i = 0; i < n && !is.fail(); ++i) {
auto tmp = random_internal::read_floating_point<double>(is);
if (is.fail()) return is;
p.push_back(tmp);
}
}
x.param(param_type(p.begin(), p.end()));
return is;
}
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_RANDOM_DISCRETE_DISTRIBUTION_H_
