### Benchmarking

#### Description

Benchmarking is a process of measuring the performance of any algorithm. In this article, we will see how to benchmark the performance of any algorithm. The basic idea behind this is to start a timer when the algorithm starts executing and stop the timer when the algorithm ends. We should repeat this many times and take the average. The more we repeat, the more accurate will be the time measured.
##### Basic Algorithm :

Repeat n time
{
Note the start time  Si

Run the Algorithm whose performance is to be measured.

Note the finish time   Fi

Time taken Ti = Fi - Si
}
Tavg  = ( T1 + T2 + T3 + T4 ... Tn ) / n
Output the average time Tavg

In C++, Chrono library is used to deal with dates and times.

###### Clock :
A clock consists of a starting point also called epoch and a tick rate. There are 3 types of clock in C++ :
1. system_clock-It is the current time according to the system. Syntax-std::chrono::system_clock
2. steady_clock-It is a monotonic clock that will never be adjusted. It goes at a uniform rate. Syntax- std::chrono::steady_clock
3. high_resolution_clock - It gives the smallest possible tick period. Syntax-std::chrono::high_resolution_clock
Timepoint :
A time_point object expresses a point in time relative to a clock's epoch.
Syntax -  std::chrono::time_point<std::chrono::clock type> s ;
Here clock type can be system_clock, steady_clock and high_resolution_clock.
now() function is used to get the current time relative to cloak epoch .
Syntax - std::chrono::clock type::now();

##### A simple program to measure the time of execution of a simple function
```#include<iostream>
#include<chrono>
using namespace std;

void function(int n) //function whose execution time is to be measured
{
long long sum=0;
for(int i=1;i<=n;i++)
sum+=i;
cout<<sum<<endl;
}
int main(void)
{
using namespace std::chrono;

time_point<high_resolution_clock> start_point, end_point; // creating time points

start_point = high_resolution_clock::now(); // storing the starting time point in start

function(100000); // function whose performance is to me measured.

end_point = high_resolution_clock::now(); //storing the ending time in end

auto start = time_point_cast<microseconds>(start_point).time_since_epoch().count();
// casting the time point to microseconds and measuring the time since time epoch

auto end = time_point_cast<microseconds>(end_point).time_since_epoch().count();

cout<<"Time taken = "<<(end-start)<<" microseconds"<<endl;

return 0;
}```

Output :
5000050000
Time taken = 1962 microseconds

NOTE: The output is machine-dependent.

So, by the above idea, we can measure the performance of various sorting algorithms. For example, lets measure the performance of std::sort over 1000000 random integers.

#### Benchmarking Code

```#include <iostream>
#include <sstream>
#include <chrono>
#include <numeric>
#include <array>
#include <algorithm>
#include <ctime>
#include <cstdlib>
namespace cpp_secrets{
///Runnable: A class which has a valid and public default ctor and a "run()" function.
///BenchmarkingTimer tests the "run()" function of Runnable
///num_run_cycles: It is the number of times run() needs to be run for a single test.
///One Runnable object is used for a single test.
///Note: if the run() function is statefull then it can only be run once for an object in order
///to get meaningful results.
///num_tests: It is the number of tests that need to be run.
template <typename Runnable, int num_run_cycles = 1000000, int num_tests = 10>
struct BenchmarkingTimer{
/// runs the run() function of the Runnable object and captures timestamps around each test
void run(){
for(int i = 0; i < num_tests; i++){
Runnable runnable_object_{};
Timer t{intervals_[i].first, intervals_[i].second};
for(int i = 0; i < num_run_cycles; i++){
runnable_object_.run();
}
}
}

///utility function to print durations of all tests
std::string durations() const{
std::stringstream ss;
int i{1};
for(const auto& interval: intervals_){
ss << "Test-" << i++  << " duration = " << (interval.second - interval.first) * 0.001 << " ms" << std::endl;
}
return ss.str();
}

///utility function to print average duration of all tests
double average_duration(){
auto duration_sum{0.0};
for(const auto& interval: intervals_){
duration_sum += (interval.second - interval.first) * 0.001;
}
if (num_tests) return (duration_sum/num_tests);
return 0;
}

private:
std::array<std::pair<double, double>, num_tests> intervals_{};

struct Timer{
Timer(double& start, double& finish):finish_(finish) { start = now(); }
~Timer() { finish_ = now(); }

private:
double& finish_;
double now(){
///utility function to return current time in microseconds since epoch
return std::chrono::time_point_cast<std::chrono::microseconds>(std::chrono::high_resolution_clock::now()).time_since_epoch().count();
}
};

};
}

///sample class which has a statefull run().
//run() function is stateful because it is not meaningful to sort a sorted array.
//that's why num_run_cycles = 1 in this case.
struct randomly_sorted{
randomly_sorted(){
srand(time(0));
for(int i=0;i<1000000;i++){
arr_.emplace_back(rand());
// making a vector filled with random elements
}
}

void run(){
sort(arr_.begin(), arr_.end(), std::less<int>());
}
private:
std::vector<int>arr_;
};
int main(){
cpp_secrets::BenchmarkingTimer<randomly_sorted, 1, 10> test; // randomly_sorted structure run function is run 10 time and average output is given.
test.run();
std::cout << test.durations() << std::endl; // outputs the duration of every test.
std::cout << "average duration = " << test.average_duration() << " ms" << std::endl;
return 0;
}

/*
Quick Explanation :
In the above code the code block coloured in red denotes the algorithm whose performance is to be
measured.The run() funtion in the structure randomly sorted is run 10 time and the average time is taken.
So, this code gives the average time required to measure the time taken to sort random integers
by the std::sort.
NOTE : The constructor of the the structure randomly_sorted is used to create a vector
filled with integers which is to be sorted by sort() in the run() function.
*/

Output :
Test-1 duration = 698.709 ms
Test-2 duration = 699.72 ms
Test-3 duration = 718.309 ms
Test-4 duration = 878.291 ms
Test-5 duration = 875.379 ms
Test-6 duration = 808.616 ms
Test-7 duration = 838.029 ms
Test-8 duration = 844.929 ms
Test-9 duration = 796.873 ms
Test-10 duration = 783.102 ms

average duration = 794.196 ms
NOTE: The output is machine-dependent.```

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