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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) {
switch (complexity) {
case oN:
return [](int64_t n) -> double { return static_cast<double>(n); };
case oNSquared:
return [](int64_t n) -> double { return std::pow(n, 2); };
case oNCubed:
return [](int64_t n) -> double { return std::pow(n, 3); };
case oLogN:
return [](int64_t n) { return log2(n); };
case oNLogN:
return [](int64_t n) { return n * log2(n); };
case o1:
default:
return [](int64_t) { 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, look the README file at
// http://github.com/ismaelJimenez/Minimal-Cpp-Least-Squared-Fit
LeastSq MinimalLeastSq(const std::vector<int64_t>& n,
const std::vector<double>& time,
BigOFunc* fitting_curve) {
double sigma_gn = 0.0;
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 += gn_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);
}
std::string benchmark_name =
reports[0].benchmark_name.substr(0, reports[0].benchmark_name.find('/'));
// Get the data from the accumulator to BenchmarkReporter::Run's.
Run big_o;
big_o.benchmark_name = benchmark_name + "_BigO";
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;
big_o.report_label = reports[0].report_label;
rms.benchmark_name = benchmark_name + "_RMS";
rms.report_label = big_o.report_label;
rms.iterations = 0;
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
|