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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.
+
+#ifndef ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
+#define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
+
+// The chi-square statistic.
+//
+// Useful for evaluating if `D` independent random variables are behaving as
+// expected, or if two distributions are similar.  (`D` is the degrees of
+// freedom).
+//
+// Each bucket should have an expected count of 10 or more for the chi square to
+// be meaningful.
+
+#include <cassert>
+
+namespace absl {
+inline namespace lts_2019_08_08 {
+namespace random_internal {
+
+constexpr const char kChiSquared[] = "chi-squared";
+
+// Returns the measured chi square value, using a single expected value.  This
+// assumes that the values in [begin, end) are uniformly distributed.
+template <typename Iterator>
+double ChiSquareWithExpected(Iterator begin, Iterator end, double expected) {
+  // Compute the sum and the number of buckets.
+  assert(expected >= 10);  // require at least 10 samples per bucket.
+  double chi_square = 0;
+  for (auto it = begin; it != end; it++) {
+    double d = static_cast<double>(*it) - expected;
+    chi_square += d * d;
+  }
+  chi_square = chi_square / expected;
+  return chi_square;
+}
+
+// Returns the measured chi square value, taking the actual value of each bucket
+// from the first set of iterators, and the expected value of each bucket from
+// the second set of iterators.
+template <typename Iterator, typename Expected>
+double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend) {
+  double chi_square = 0;
+  for (; it != end && eit != eend; ++it, ++eit) {
+    if (*it > 0) {
+      assert(*eit > 0);
+    }
+    double e = static_cast<double>(*eit);
+    double d = static_cast<double>(*it - *eit);
+    if (d != 0) {
+      assert(e > 0);
+      chi_square += (d * d) / e;
+    }
+  }
+  assert(it == end && eit == eend);
+  return chi_square;
+}
+
+// ======================================================================
+// The following methods can be used for an arbitrary significance level.
+//
+
+// Calculates critical chi-square values to produce the given p-value using a
+// bisection search for a value within epsilon, relying on the monotonicity of
+// ChiSquarePValue().
+double ChiSquareValue(int dof, double p);
+
+// Calculates the p-value (probability) of a given chi-square value.
+double ChiSquarePValue(double chi_square, int dof);
+
+}  // namespace random_internal
+}  // inline namespace lts_2019_08_08
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_