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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.
+//
+// -----------------------------------------------------------------------------
+// File: uniform_int_distribution.h
+// -----------------------------------------------------------------------------
+//
+// This header defines a class for representing a uniform integer distribution
+// over the closed (inclusive) interval [a,b]. You use this distribution in
+// combination with an Abseil random bit generator to produce random values
+// according to the rules of the distribution.
+//
+// `absl::uniform_int_distribution` is a drop-in replacement for the C++11
+// `std::uniform_int_distribution` [rand.dist.uni.int] but is considerably
+// faster than the libstdc++ implementation.
+
+#ifndef ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_
+#define ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_
+
+#include <cassert>
+#include <istream>
+#include <limits>
+#include <type_traits>
+
+#include "absl/base/optimization.h"
+#include "absl/random/internal/distribution_impl.h"
+#include "absl/random/internal/fast_uniform_bits.h"
+#include "absl/random/internal/iostream_state_saver.h"
+#include "absl/random/internal/traits.h"
+
+namespace absl {
+
+// absl::uniform_int_distribution<T>
+//
+// This distribution produces random integer values uniformly distributed in the
+// closed (inclusive) interval [a, b].
+//
+// Example:
+//
+// absl::BitGen gen;
+//
+// // Use the distribution to produce a value between 1 and 6, inclusive.
+// int die_roll = absl::uniform_int_distribution<int>(1, 6)(gen);
+//
+template <typename IntType = int>
+class 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 = uniform_int_distribution;
+
+ explicit param_type(
+ result_type lo = 0,
+ result_type hi = (std::numeric_limits<result_type>::max)())
+ : lo_(lo),
+ range_(static_cast<unsigned_type>(hi) -
+ static_cast<unsigned_type>(lo)) {
+ // [rand.dist.uni.int] precondition 2
+ assert(lo <= hi);
+ }
+
+ result_type a() const { return lo_; }
+ result_type b() const {
+ return static_cast<result_type>(static_cast<unsigned_type>(lo_) + range_);
+ }
+
+ friend bool operator==(const param_type& a, const param_type& b) {
+ return a.lo_ == b.lo_ && a.range_ == b.range_;
+ }
+
+ friend bool operator!=(const param_type& a, const param_type& b) {
+ return !(a == b);
+ }
+
+ private:
+ friend class uniform_int_distribution;
+ unsigned_type range() const { return range_; }
+
+ result_type lo_;
+ unsigned_type range_;
+
+ static_assert(std::is_integral<result_type>::value,
+ "Class-template absl::uniform_int_distribution<> must be "
+ "parameterized using an integral type.");
+ }; // param_type
+
+ uniform_int_distribution() : uniform_int_distribution(0) {}
+
+ explicit uniform_int_distribution(
+ result_type lo,
+ result_type hi = (std::numeric_limits<result_type>::max)())
+ : param_(lo, hi) {}
+
+ explicit uniform_int_distribution(const param_type& param) : param_(param) {}
+
+ // uniform_int_distribution<T>::reset()
+ //
+ // Resets the uniform int distribution. Note that this function has no effect
+ // because the distribution already produces independent values.
+ void reset() {}
+
+ template <typename URBG>
+ result_type operator()(URBG& gen) { // NOLINT(runtime/references)
+ return (*this)(gen, param());
+ }
+
+ template <typename URBG>
+ result_type operator()(
+ URBG& gen, const param_type& param) { // NOLINT(runtime/references)
+ return param.a() + Generate(gen, param.range());
+ }
+
+ result_type a() const { return param_.a(); }
+ result_type b() const { return param_.b(); }
+
+ param_type param() const { return param_; }
+ void param(const param_type& params) { param_ = params; }
+
+ result_type(min)() const { return a(); }
+ result_type(max)() const { return b(); }
+
+ friend bool operator==(const uniform_int_distribution& a,
+ const uniform_int_distribution& b) {
+ return a.param_ == b.param_;
+ }
+ friend bool operator!=(const uniform_int_distribution& a,
+ const uniform_int_distribution& b) {
+ return !(a == b);
+ }
+
+ private:
+ // Generates a value in the *closed* interval [0, R]
+ template <typename URBG>
+ unsigned_type Generate(URBG& g, // NOLINT(runtime/references)
+ unsigned_type R);
+ param_type param_;
+};
+
+// -----------------------------------------------------------------------------
+// Implementation details follow
+// -----------------------------------------------------------------------------
+template <typename CharT, typename Traits, typename IntType>
+std::basic_ostream<CharT, Traits>& operator<<(
+ std::basic_ostream<CharT, Traits>& os,
+ const 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.a()) << os.fill()
+ << static_cast<stream_type>(x.b());
+ return os;
+}
+
+template <typename CharT, typename Traits, typename IntType>
+std::basic_istream<CharT, Traits>& operator>>(
+ std::basic_istream<CharT, Traits>& is,
+ uniform_int_distribution<IntType>& x) {
+ using param_type = typename uniform_int_distribution<IntType>::param_type;
+ using result_type = typename uniform_int_distribution<IntType>::result_type;
+ using stream_type =
+ typename random_internal::stream_format_type<IntType>::type;
+
+ stream_type a;
+ stream_type b;
+
+ auto saver = random_internal::make_istream_state_saver(is);
+ is >> a >> b;
+ if (!is.fail()) {
+ x.param(
+ param_type(static_cast<result_type>(a), static_cast<result_type>(b)));
+ }
+ return is;
+}
+
+template <typename IntType>
+template <typename URBG>
+typename random_internal::make_unsigned_bits<IntType>::type
+uniform_int_distribution<IntType>::Generate(
+ URBG& g, // NOLINT(runtime/references)
+ typename random_internal::make_unsigned_bits<IntType>::type R) {
+ random_internal::FastUniformBits<unsigned_type> fast_bits;
+ unsigned_type bits = fast_bits(g);
+ const unsigned_type Lim = R + 1;
+ if ((R & Lim) == 0) {
+ // If the interval's length is a power of two range, just take the low bits.
+ return bits & R;
+ }
+
+ // Generates a uniform variate on [0, Lim) using fixed-point multiplication.
+ // The above fast-path guarantees that Lim is representable in unsigned_type.
+ //
+ // Algorithm adapted from
+ // http://lemire.me/blog/2016/06/30/fast-random-shuffling/, with added
+ // explanation.
+ //
+ // The algorithm creates a uniform variate `bits` in the interval [0, 2^N),
+ // and treats it as the fractional part of a fixed-point real value in [0, 1),
+ // multiplied by 2^N. For example, 0.25 would be represented as 2^(N - 2),
+ // because 2^N * 0.25 == 2^(N - 2).
+ //
+ // Next, `bits` and `Lim` are multiplied with a wide-multiply to bring the
+ // value into the range [0, Lim). The integral part (the high word of the
+ // multiplication result) is then very nearly the desired result. However,
+ // this is not quite accurate; viewing the multiplication result as one
+ // double-width integer, the resulting values for the sample are mapped as
+ // follows:
+ //
+ // If the result lies in this interval: Return this value:
+ // [0, 2^N) 0
+ // [2^N, 2 * 2^N) 1
+ // ... ...
+ // [K * 2^N, (K + 1) * 2^N) K
+ // ... ...
+ // [(Lim - 1) * 2^N, Lim * 2^N) Lim - 1
+ //
+ // While all of these intervals have the same size, the result of `bits * Lim`
+ // must be a multiple of `Lim`, and not all of these intervals contain the
+ // same number of multiples of `Lim`. In particular, some contain
+ // `F = floor(2^N / Lim)` and some contain `F + 1 = ceil(2^N / Lim)`. This
+ // difference produces a small nonuniformity, which is corrected by applying
+ // rejection sampling to one of the values in the "larger intervals" (i.e.,
+ // the intervals containing `F + 1` multiples of `Lim`.
+ //
+ // An interval contains `F + 1` multiples of `Lim` if and only if its smallest
+ // value modulo 2^N is less than `2^N % Lim`. The unique value satisfying
+ // this property is used as the one for rejection. That is, a value of
+ // `bits * Lim` is rejected if `(bit * Lim) % 2^N < (2^N % Lim)`.
+
+ using helper = random_internal::wide_multiply<unsigned_type>;
+ auto product = helper::multiply(bits, Lim);
+
+ // Two optimizations here:
+ // * Rejection occurs with some probability less than 1/2, and for reasonable
+ // ranges considerably less (in particular, less than 1/(F+1)), so
+ // ABSL_PREDICT_FALSE is apt.
+ // * `Lim` is an overestimate of `threshold`, and doesn't require a divide.
+ if (ABSL_PREDICT_FALSE(helper::lo(product) < Lim)) {
+ // This quantity is exactly equal to `2^N % Lim`, but does not require high
+ // precision calculations: `2^N % Lim` is congruent to `(2^N - Lim) % Lim`.
+ // Ideally this could be expressed simply as `-X` rather than `2^N - X`, but
+ // for types smaller than int, this calculation is incorrect due to integer
+ // promotion rules.
+ const unsigned_type threshold =
+ ((std::numeric_limits<unsigned_type>::max)() - Lim + 1) % Lim;
+ while (helper::lo(product) < threshold) {
+ bits = fast_bits(g);
+ product = helper::multiply(bits, Lim);
+ }
+ }
+
+ return helper::hi(product);
+}
+
+} // namespace absl
+
+#endif // ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_