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diff --git a/absl/random/discrete_distribution.cc b/absl/random/discrete_distribution.cc
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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.
+
+#include "absl/random/discrete_distribution.h"
+
+namespace absl {
+namespace random_internal {
+
+// Initializes the distribution table for Walker's Aliasing algorithm, described
+// in Knuth, Vol 2. as well as in https://en.wikipedia.org/wiki/Alias_method
+std::vector<std::pair<double, size_t>> InitDiscreteDistribution(
+    std::vector<double>* probabilities) {
+  // The empty-case should already be handled by the constructor.
+  assert(probabilities);
+  assert(!probabilities->empty());
+
+  // Step 1. Normalize the input probabilities to 1.0.
+  double sum = std::accumulate(std::begin(*probabilities),
+                               std::end(*probabilities), 0.0);
+  if (std::fabs(sum - 1.0) > 1e-6) {
+    // Scale `probabilities` only when the sum is too far from 1.0.  Scaling
+    // unconditionally will alter the probabilities slightly.
+    for (double& item : *probabilities) {
+      item = item / sum;
+    }
+  }
+
+  // Step 2. At this point `probabilities` is set to the conditional
+  // probabilities of each element which sum to 1.0, to within reasonable error.
+  // These values are used to construct the proportional probability tables for
+  // the selection phases of Walker's Aliasing algorithm.
+  //
+  // To construct the table, pick an element which is under-full (i.e., an
+  // element for which `(*probabilities)[i] < 1.0/n`), and pair it with an
+  // element which is over-full (i.e., an element for which
+  // `(*probabilities)[i] > 1.0/n`). The smaller value can always be retired.
+  // The larger may still be greater than 1.0/n, or may now be less than 1.0/n,
+  // and put back onto the appropriate collection.
+  const size_t n = probabilities->size();
+  std::vector<std::pair<double, size_t>> q;
+  q.reserve(n);
+
+  std::vector<size_t> over;
+  std::vector<size_t> under;
+  size_t idx = 0;
+  for (const double item : *probabilities) {
+    assert(item >= 0);
+    const double v = item * n;
+    q.emplace_back(v, 0);
+    if (v < 1.0) {
+      under.push_back(idx++);
+    } else {
+      over.push_back(idx++);
+    }
+  }
+  while (!over.empty() && !under.empty()) {
+    auto lo = under.back();
+    under.pop_back();
+    auto hi = over.back();
+    over.pop_back();
+
+    q[lo].second = hi;
+    const double r = q[hi].first - (1.0 - q[lo].first);
+    q[hi].first = r;
+    if (r < 1.0) {
+      under.push_back(hi);
+    } else {
+      over.push_back(hi);
+    }
+  }
+
+  // Due to rounding errors, there may be un-paired elements in either
+  // collection; these should all be values near 1.0.  For these values, set `q`
+  // to 1.0 and set the alternate to the identity.
+  for (auto i : over) {
+    q[i] = {1.0, i};
+  }
+  for (auto i : under) {
+    q[i] = {1.0, i};
+  }
+  return q;
+}
+
+}  // namespace random_internal
+}  // namespace absl