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+// Copyright 2016 Ismael Jimenez Martinez. All rights reserved.
+//
+// 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
+//
+//     http://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.
+
+// Source project : https://github.com/ismaelJimenez/cpp.leastsq
+// Adapted to be used with google benchmark
+
+#include "benchmark/benchmark.h"
+
+#include <algorithm>
+#include <cmath>
+#include "check.h"
+#include "complexity.h"
+
+namespace benchmark {
+
+// Internal function to calculate the different scalability forms
+BigOFunc* FittingCurve(BigO complexity) {
+  static const double kLog2E = 1.44269504088896340736;
+  switch (complexity) {
+    case oN:
+      return [](IterationCount n) -> double { return static_cast<double>(n); };
+    case oNSquared:
+      return [](IterationCount n) -> double { return std::pow(n, 2); };
+    case oNCubed:
+      return [](IterationCount n) -> double { return std::pow(n, 3); };
+    case oLogN:
+      /* Note: can't use log2 because Android's GNU STL lacks it */
+      return
+          [](IterationCount n) { return kLog2E * log(static_cast<double>(n)); };
+    case oNLogN:
+      /* Note: can't use log2 because Android's GNU STL lacks it */
+      return [](IterationCount n) {
+        return kLog2E * n * log(static_cast<double>(n));
+      };
+    case o1:
+    default:
+      return [](IterationCount) { return 1.0; };
+  }
+}
+
+// Function to return an string for the calculated complexity
+std::string GetBigOString(BigO complexity) {
+  switch (complexity) {
+    case oN:
+      return "N";
+    case oNSquared:
+      return "N^2";
+    case oNCubed:
+      return "N^3";
+    case oLogN:
+      return "lgN";
+    case oNLogN:
+      return "NlgN";
+    case o1:
+      return "(1)";
+    default:
+      return "f(N)";
+  }
+}
+
+// Find the coefficient for the high-order term in the running time, by
+// minimizing the sum of squares of relative error, for the fitting curve
+// given by the lambda expression.
+//   - n             : Vector containing the size of the benchmark tests.
+//   - time          : Vector containing the times for the benchmark tests.
+//   - fitting_curve : lambda expression (e.g. [](int64_t n) {return n; };).
+
+// For a deeper explanation on the algorithm logic, please refer to
+// https://en.wikipedia.org/wiki/Least_squares#Least_squares,_regression_analysis_and_statistics
+
+LeastSq MinimalLeastSq(const std::vector<int64_t>& n,
+                       const std::vector<double>& time,
+                       BigOFunc* fitting_curve) {
+  double sigma_gn_squared = 0.0;
+  double sigma_time = 0.0;
+  double sigma_time_gn = 0.0;
+
+  // Calculate least square fitting parameter
+  for (size_t i = 0; i < n.size(); ++i) {
+    double gn_i = fitting_curve(n[i]);
+    sigma_gn_squared += gn_i * gn_i;
+    sigma_time += time[i];
+    sigma_time_gn += time[i] * gn_i;
+  }
+
+  LeastSq result;
+  result.complexity = oLambda;
+
+  // Calculate complexity.
+  result.coef = sigma_time_gn / sigma_gn_squared;
+
+  // Calculate RMS
+  double rms = 0.0;
+  for (size_t i = 0; i < n.size(); ++i) {
+    double fit = result.coef * fitting_curve(n[i]);
+    rms += pow((time[i] - fit), 2);
+  }
+
+  // Normalized RMS by the mean of the observed values
+  double mean = sigma_time / n.size();
+  result.rms = sqrt(rms / n.size()) / mean;
+
+  return result;
+}
+
+// Find the coefficient for the high-order term in the running time, by
+// minimizing the sum of squares of relative error.
+//   - n          : Vector containing the size of the benchmark tests.
+//   - time       : Vector containing the times for the benchmark tests.
+//   - complexity : If different than oAuto, the fitting curve will stick to
+//                  this one. If it is oAuto, it will be calculated the best
+//                  fitting curve.
+LeastSq MinimalLeastSq(const std::vector<int64_t>& n,
+                       const std::vector<double>& time, const BigO complexity) {
+  CHECK_EQ(n.size(), time.size());
+  CHECK_GE(n.size(), 2);  // Do not compute fitting curve is less than two
+                          // benchmark runs are given
+  CHECK_NE(complexity, oNone);
+
+  LeastSq best_fit;
+
+  if (complexity == oAuto) {
+    std::vector<BigO> fit_curves = {oLogN, oN, oNLogN, oNSquared, oNCubed};
+
+    // Take o1 as default best fitting curve
+    best_fit = MinimalLeastSq(n, time, FittingCurve(o1));
+    best_fit.complexity = o1;
+
+    // Compute all possible fitting curves and stick to the best one
+    for (const auto& fit : fit_curves) {
+      LeastSq current_fit = MinimalLeastSq(n, time, FittingCurve(fit));
+      if (current_fit.rms < best_fit.rms) {
+        best_fit = current_fit;
+        best_fit.complexity = fit;
+      }
+    }
+  } else {
+    best_fit = MinimalLeastSq(n, time, FittingCurve(complexity));
+    best_fit.complexity = complexity;
+  }
+
+  return best_fit;
+}
+
+std::vector<BenchmarkReporter::Run> ComputeBigO(
+    const std::vector<BenchmarkReporter::Run>& reports) {
+  typedef BenchmarkReporter::Run Run;
+  std::vector<Run> results;
+
+  if (reports.size() < 2) return results;
+
+  // Accumulators.
+  std::vector<int64_t> n;
+  std::vector<double> real_time;
+  std::vector<double> cpu_time;
+
+  // Populate the accumulators.
+  for (const Run& run : reports) {
+    CHECK_GT(run.complexity_n, 0) << "Did you forget to call SetComplexityN?";
+    n.push_back(run.complexity_n);
+    real_time.push_back(run.real_accumulated_time / run.iterations);
+    cpu_time.push_back(run.cpu_accumulated_time / run.iterations);
+  }
+
+  LeastSq result_cpu;
+  LeastSq result_real;
+
+  if (reports[0].complexity == oLambda) {
+    result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity_lambda);
+    result_real = MinimalLeastSq(n, real_time, reports[0].complexity_lambda);
+  } else {
+    result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity);
+    result_real = MinimalLeastSq(n, real_time, result_cpu.complexity);
+  }
+
+  // Drop the 'args' when reporting complexity.
+  auto run_name = reports[0].run_name;
+  run_name.args.clear();
+
+  // Get the data from the accumulator to BenchmarkReporter::Run's.
+  Run big_o;
+  big_o.run_name = run_name;
+  big_o.family_index = reports[0].family_index;
+  big_o.per_family_instance_index = reports[0].per_family_instance_index;
+  big_o.run_type = BenchmarkReporter::Run::RT_Aggregate;
+  big_o.repetitions = reports[0].repetitions;
+  big_o.repetition_index = Run::no_repetition_index;
+  big_o.threads = reports[0].threads;
+  big_o.aggregate_name = "BigO";
+  big_o.report_label = reports[0].report_label;
+  big_o.iterations = 0;
+  big_o.real_accumulated_time = result_real.coef;
+  big_o.cpu_accumulated_time = result_cpu.coef;
+  big_o.report_big_o = true;
+  big_o.complexity = result_cpu.complexity;
+
+  // All the time results are reported after being multiplied by the
+  // time unit multiplier. But since RMS is a relative quantity it
+  // should not be multiplied at all. So, here, we _divide_ it by the
+  // multiplier so that when it is multiplied later the result is the
+  // correct one.
+  double multiplier = GetTimeUnitMultiplier(reports[0].time_unit);
+
+  // Only add label to mean/stddev if it is same for all runs
+  Run rms;
+  rms.run_name = run_name;
+  rms.family_index = reports[0].family_index;
+  rms.per_family_instance_index = reports[0].per_family_instance_index;
+  rms.run_type = BenchmarkReporter::Run::RT_Aggregate;
+  rms.aggregate_name = "RMS";
+  rms.report_label = big_o.report_label;
+  rms.iterations = 0;
+  rms.repetition_index = Run::no_repetition_index;
+  rms.repetitions = reports[0].repetitions;
+  rms.threads = reports[0].threads;
+  rms.real_accumulated_time = result_real.rms / multiplier;
+  rms.cpu_accumulated_time = result_cpu.rms / multiplier;
+  rms.report_rms = true;
+  rms.complexity = result_cpu.complexity;
+  // don't forget to keep the time unit, or we won't be able to
+  // recover the correct value.
+  rms.time_unit = reports[0].time_unit;
+
+  results.push_back(big_o);
+  results.push_back(rms);
+  return results;
+}
+
+}  // end namespace benchmark