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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2018 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: wjr@google.com (William Rucklidge)
+
+#ifndef CERES_INTERNAL_PARALLEL_UTILS_H_
+#define CERES_INTERNAL_PARALLEL_UTILS_H_
+
+namespace ceres {
+namespace internal {
+
+// Converts a linear iteration order into a triangular iteration order.
+// Suppose you have nested loops that look like
+// for (int i = 0; i < n; i++) {
+//   for (int j = i; j < n; j++) {
+//     ... use i and j
+//   }
+// }
+// Naively using ParallelFor to parallelise those loops might look like
+// ParallelFor(..., 0, n * n, num_threads,
+//   [](int thread_id, int k) {
+//     int i = k / n, j = k % n;
+//     if (j < i) return;
+//     ...
+//    });
+// but these empty work items can lead to very unbalanced threading. Instead,
+// do this:
+// int actual_work_items = (n * (n + 1)) / 2;
+// ParallelFor(..., 0, actual_work_items, num_threads,
+//   [](int thread_id, int k) {
+//     int i, j;
+//     UnfoldIteration(k, n, &i, &j);
+//     ...
+//    });
+// which in each iteration will produce i and j satisfying
+// 0 <= i <= j < n
+void LinearIndexToUpperTriangularIndex(int k, int n, int* i, int* j);
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_INTERNAL_PARALLEL_UTILS_H_