// 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_LOG_UNIFORM_INT_DISTRIBUTION_H_
#define ABSL_RANDOM_LOG_UNIFORM_INT_DISTRIBUTION_H_
#include <algorithm>
#include <cassert>
#include <cmath>
#include <istream>
#include <limits>
#include <ostream>
#include <type_traits>
#include "absl/random/internal/fastmath.h"
#include "absl/random/internal/generate_real.h"
#include "absl/random/internal/iostream_state_saver.h"
#include "absl/random/internal/traits.h"
#include "absl/random/uniform_int_distribution.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
// log_uniform_int_distribution:
//
// Returns a random variate R in range [min, max] such that
// floor(log(R-min, base)) is uniformly distributed.
// We ensure uniformity by discretization using the
// boundary sets [0, 1, base, base * base, ... min(base*n, max)]
//
template <typename IntType = int>
class log_uniform_int_distribution {
private:
using unsigned_type =
typename random_internal::make_unsigned_bits<IntType>::type;
public:
using result_type = IntType;
class param_type {
public:
using distribution_type = log_uniform_int_distribution;
explicit param_type(
result_type min = 0,
result_type max = (std::numeric_limits<result_type>::max)(),
result_type base = 2)
: min_(min),
max_(max),
base_(base),
range_(static_cast<unsigned_type>(max_) -
static_cast<unsigned_type>(min_)),
log_range_(0) {
assert(max_ >= min_);
assert(base_ > 1);
if (base_ == 2) {
// Determine where the first set bit is on range(), giving a log2(range)
// value which can be used to construct bounds.
log_range_ = (std::min)(random_internal::LeadingSetBit(range()),
std::numeric_limits<unsigned_type>::digits);
} else {
// NOTE: Computing the logN(x) introduces error from 2 sources:
// 1. Conversion of int to double loses precision for values >=
// 2^53, which may cause some log() computations to operate on
// different values.
// 2. The error introduced by the division will cause the result
// to differ from the expected value.
//
// Thus a result which should equal K may equal K +/- epsilon,
// which can eliminate some values depending on where the bounds fall.
const double inv_log_base = 1.0 / std::log(base_);
const double log_range = std::log(static_cast<double>(range()) + 0.5);
log_range_ = static_cast<int>(std::ceil(inv_log_base * log_range));
}
}
result_type(min)() const { return min_; }
result_type(max)() const { return max_; }
result_type base() const { return base_; }
friend bool operator==(const param_type& a, const param_type& b) {
return a.min_ == b.min_ && a.max_ == b.max_ && a.base_ == b.base_;
}
friend bool operator!=(const param_type& a, const param_type& b) {
return !(a == b);
}
private:
friend class log_uniform_int_distribution;
int log_range() const { return log_range_; }
unsigned_type range() const { return range_; }
result_type min_;
result_type max_;
result_type base_;
unsigned_type range_; // max - min
int log_range_; // ceil(logN(range_))
static_assert(std::is_integral<IntType>::value,
"Class-template absl::log_uniform_int_distribution<> must be "
"parameterized using an integral type.");
};
log_uniform_int_distribution() : log_uniform_int_distribution(0) {}
explicit log_uniform_int_distribution(
result_type min,
result_type max = (std::numeric_limits<result_type>::max)(),
result_type base = 2)
: param_(min, max, base) {}
explicit log_uniform_int_distribution(const param_type& p) : param_(p) {}
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) {
return (p.min)() + Generate(g, p);
}
result_type(min)() const { return (param_.min)(); }
result_type(max)() const { return (param_.max)(); }
result_type base() const { return param_.base(); }
param_type param() const { return param_; }
void param(const param_type& p) { param_ = p; }
friend bool operator==(const log_uniform_int_distribution& a,
const log_uniform_int_distribution& b) {
return a.param_ == b.param_;
}
friend bool operator!=(const log_uniform_int_distribution& a,
const log_uniform_int_distribution& b) {
return a.param_ != b.param_;
}
private:
// Returns a log-uniform variate in the range [0, p.range()]. The caller
// should add min() to shift the result to the correct range.
template <typename URNG>
unsigned_type Generate(URNG& g, // NOLINT(runtime/references)
const param_type& p);
param_type param_;
};
template <typename IntType>
template <typename URBG>
typename log_uniform_int_distribution<IntType>::unsigned_type
log_uniform_int_distribution<IntType>::Generate(
URBG& g, // NOLINT(runtime/references)
const param_type& p) {
// sample e over [0, log_range]. Map the results of e to this:
// 0 => 0
// 1 => [1, b-1]
// 2 => [b, (b^2)-1]
// n => [b^(n-1)..(b^n)-1]
const int e = absl::uniform_int_distribution<int>(0, p.log_range())(g);
if (e == 0) {
return 0;
}
const int d = e - 1;
unsigned_type base_e, top_e;
if (p.base() == 2) {
base_e = static_cast<unsigned_type>(1) << d;
top_e = (e >= std::numeric_limits<unsigned_type>::digits)
? (std::numeric_limits<unsigned_type>::max)()
: (static_cast<unsigned_type>(1) << e) - 1;
} else {
const double r = std::pow(p.base(), d);
const double s = (r * p.base()) - 1.0;
base_e =
(r > static_cast<double>((std::numeric_limits<unsigned_type>::max)()))
? (std::numeric_limits<unsigned_type>::max)()
: static_cast<unsigned_type>(r);
top_e =
(s > static_cast<double>((std::numeric_limits<unsigned_type>::max)()))
? (std::numeric_limits<unsigned_type>::max)()
: static_cast<unsigned_type>(s);
}
const unsigned_type lo = (base_e >= p.range()) ? p.range() : base_e;
const unsigned_type hi = (top_e >= p.range()) ? p.range() : top_e;
// choose uniformly over [lo, hi]
return absl::uniform_int_distribution<result_type>(lo, hi)(g);
}
template <typename CharT, typename Traits, typename IntType>
std::basic_ostream<CharT, Traits>& operator<<(
std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references)
const log_uniform_int_distribution<IntType>& x) {
using stream_type =
typename random_internal::stream_format_type<IntType>::type;
auto saver = random_internal::make_ostream_state_saver(os);
os << static_cast<stream_type>((x.min)()) << os.fill()
<< static_cast<stream_type>((x.max)()) << os.fill()
<< static_cast<stream_type>(x.base());
return os;
}
template <typename CharT, typename Traits, typename IntType>
std::basic_istream<CharT, Traits>& operator>>(
std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references)
log_uniform_int_distribution<IntType>& x) { // NOLINT(runtime/references)
using param_type = typename log_uniform_int_distribution<IntType>::param_type;
using result_type =
typename log_uniform_int_distribution<IntType>::result_type;
using stream_type =
typename random_internal::stream_format_type<IntType>::type;
stream_type min;
stream_type max;
stream_type base;
auto saver = random_internal::make_istream_state_saver(is);
is >> min >> max >> base;
if (!is.fail()) {
x.param(param_type(static_cast<result_type>(min),
static_cast<result_type>(max),
static_cast<result_type>(base)));
}
return is;
}
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_RANDOM_LOG_UNIFORM_INT_DISTRIBUTION_H_
