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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_