llvm/utils/benchmark/src/complexity.cc

   1 // Copyright 2016 Ismael Jimenez Martinez. All rights reserved.
   2 //
   3 // Licensed under the Apache License, Version 2.0 (the "License");
   4 // you may not use this file except in compliance with the License.
   5 // You may obtain a copy of the License at
   6 //
   7 //     http://www.apache.org/licenses/LICENSE-2.0
   8 //
   9 // Unless required by applicable law or agreed to in writing, software
  10 // distributed under the License is distributed on an "AS IS" BASIS,
  11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  12 // See the License for the specific language governing permissions and
  13 // limitations under the License.
  14
  15 // Source project : https://github.com/ismaelJimenez/cpp.leastsq
  16 // Adapted to be used with google benchmark
  17
  18 #include "benchmark/benchmark.h"
  19
  20 #include <algorithm>
  21 #include <cmath>
  22 #include "check.h"
  23 #include "complexity.h"
  24
  25 namespace benchmark {
  26
  27 // Internal function to calculate the different scalability forms
  28 BigOFunc* FittingCurve(BigO complexity) {
  29   switch (complexity) {
  30     case oN:
  31       return [](int64_t n) -> double { return static_cast<double>(n); };
  32     case oNSquared:
  33       return [](int64_t n) -> double { return std::pow(n, 2); };
  34     case oNCubed:
  35       return [](int64_t n) -> double { return std::pow(n, 3); };
  36     case oLogN:
  37       return [](int64_t n) { return log2(n); };
  38     case oNLogN:
  39       return [](int64_t n) { return n * log2(n); };
  40     case o1:
  41     default:
  42       return [](int64_t) { return 1.0; };
  43   }
  44 }
  45
  46 // Function to return an string for the calculated complexity
  47 std::string GetBigOString(BigO complexity) {
  48   switch (complexity) {
  49     case oN:
  50       return "N";
  51     case oNSquared:
  52       return "N^2";
  53     case oNCubed:
  54       return "N^3";
  55     case oLogN:
  56       return "lgN";
  57     case oNLogN:
  58       return "NlgN";
  59     case o1:
  60       return "(1)";
  61     default:
  62       return "f(N)";
  63   }
  64 }
  65
  66 // Find the coefficient for the high-order term in the running time, by
  67 // minimizing the sum of squares of relative error, for the fitting curve
  68 // given by the lambda expression.
  69 //   - n             : Vector containing the size of the benchmark tests.
  70 //   - time          : Vector containing the times for the benchmark tests.
  71 //   - fitting_curve : lambda expression (e.g. [](int64_t n) {return n; };).
  72
  73 // For a deeper explanation on the algorithm logic, look the README file at
  74 // http://github.com/ismaelJimenez/Minimal-Cpp-Least-Squared-Fit
  75
  76 LeastSq MinimalLeastSq(const std::vector<int64_t>& n,
  77                        const std::vector<double>& time,
  78                        BigOFunc* fitting_curve) {
  79   double sigma_gn_squared = 0.0;
  80   double sigma_time = 0.0;
  81   double sigma_time_gn = 0.0;
  82
  83   // Calculate least square fitting parameter
  84   for (size_t i = 0; i < n.size(); ++i) {
  85     double gn_i = fitting_curve(n[i]);
  86     sigma_gn_squared += gn_i * gn_i;
  87     sigma_time += time[i];
  88     sigma_time_gn += time[i] * gn_i;
  89   }
  90
  91   LeastSq result;
  92   result.complexity = oLambda;
  93
  94   // Calculate complexity.
  95   result.coef = sigma_time_gn / sigma_gn_squared;
  96
  97   // Calculate RMS
  98   double rms = 0.0;
  99   for (size_t i = 0; i < n.size(); ++i) {
 100     double fit = result.coef * fitting_curve(n[i]);
 101     rms += pow((time[i] - fit), 2);
 102   }
 103
 104   // Normalized RMS by the mean of the observed values
 105   double mean = sigma_time / n.size();
 106   result.rms = sqrt(rms / n.size()) / mean;
 107
 108   return result;
 109 }
 110
 111 // Find the coefficient for the high-order term in the running time, by
 112 // minimizing the sum of squares of relative error.
 113 //   - n          : Vector containing the size of the benchmark tests.
 114 //   - time       : Vector containing the times for the benchmark tests.
 115 //   - complexity : If different than oAuto, the fitting curve will stick to
 116 //                  this one. If it is oAuto, it will be calculated the best
 117 //                  fitting curve.
 118 LeastSq MinimalLeastSq(const std::vector<int64_t>& n,
 119                        const std::vector<double>& time, const BigO complexity) {
 120   CHECK_EQ(n.size(), time.size());
 121   CHECK_GE(n.size(), 2);  // Do not compute fitting curve is less than two
 122                           // benchmark runs are given
 123   CHECK_NE(complexity, oNone);
 124
 125   LeastSq best_fit;
 126
 127   if (complexity == oAuto) {
 128     std::vector<BigO> fit_curves = {oLogN, oN, oNLogN, oNSquared, oNCubed};
 129
 130     // Take o1 as default best fitting curve
 131     best_fit = MinimalLeastSq(n, time, FittingCurve(o1));
 132     best_fit.complexity = o1;
 133
 134     // Compute all possible fitting curves and stick to the best one
 135     for (const auto& fit : fit_curves) {
 136       LeastSq current_fit = MinimalLeastSq(n, time, FittingCurve(fit));
 137       if (current_fit.rms < best_fit.rms) {
 138         best_fit = current_fit;
 139         best_fit.complexity = fit;
 140       }
 141     }
 142   } else {
 143     best_fit = MinimalLeastSq(n, time, FittingCurve(complexity));
 144     best_fit.complexity = complexity;
 145   }
 146
 147   return best_fit;
 148 }
 149
 150 std::vector<BenchmarkReporter::Run> ComputeBigO(
 151     const std::vector<BenchmarkReporter::Run>& reports) {
 152   typedef BenchmarkReporter::Run Run;
 153   std::vector<Run> results;
 154
 155   if (reports.size() < 2) return results;
 156
 157   // Accumulators.
 158   std::vector<int64_t> n;
 159   std::vector<double> real_time;
 160   std::vector<double> cpu_time;
 161
 162   // Populate the accumulators.
 163   for (const Run& run : reports) {
 164     CHECK_GT(run.complexity_n, 0) << "Did you forget to call SetComplexityN?";
 165     n.push_back(run.complexity_n);
 166     real_time.push_back(run.real_accumulated_time / run.iterations);
 167     cpu_time.push_back(run.cpu_accumulated_time / run.iterations);
 168   }
 169
 170   LeastSq result_cpu;
 171   LeastSq result_real;
 172
 173   if (reports[0].complexity == oLambda) {
 174     result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity_lambda);
 175     result_real = MinimalLeastSq(n, real_time, reports[0].complexity_lambda);
 176   } else {
 177     result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity);
 178     result_real = MinimalLeastSq(n, real_time, result_cpu.complexity);
 179   }
 180   std::string benchmark_name =
 181       reports[0].benchmark_name.substr(0, reports[0].benchmark_name.find('/'));
 182
 183   // Get the data from the accumulator to BenchmarkReporter::Run's.
 184   Run big_o;
 185   big_o.benchmark_name = benchmark_name + "_BigO";
 186   big_o.iterations = 0;
 187   big_o.real_accumulated_time = result_real.coef;
 188   big_o.cpu_accumulated_time = result_cpu.coef;
 189   big_o.report_big_o = true;
 190   big_o.complexity = result_cpu.complexity;
 191
 192   // All the time results are reported after being multiplied by the
 193   // time unit multiplier. But since RMS is a relative quantity it
 194   // should not be multiplied at all. So, here, we _divide_ it by the
 195   // multiplier so that when it is multiplied later the result is the
 196   // correct one.
 197   double multiplier = GetTimeUnitMultiplier(reports[0].time_unit);
 198
 199   // Only add label to mean/stddev if it is same for all runs
 200   Run rms;
 201   big_o.report_label = reports[0].report_label;
 202   rms.benchmark_name = benchmark_name + "_RMS";
 203   rms.report_label = big_o.report_label;
 204   rms.iterations = 0;
 205   rms.real_accumulated_time = result_real.rms / multiplier;
 206   rms.cpu_accumulated_time = result_cpu.rms / multiplier;
 207   rms.report_rms = true;
 208   rms.complexity = result_cpu.complexity;
 209   // don't forget to keep the time unit, or we won't be able to
 210   // recover the correct value.
 211   rms.time_unit = reports[0].time_unit;
 212
 213   results.push_back(big_o);
 214   results.push_back(rms);
 215   return results;
 216 }
 217
 218 }  // end namespace benchmark