Calculating π for no good reason

So the other day I had some time to kill and was thinking that I might be fun to repeat some of the exercises I did when I was studying high performance computing in the data center of RWTH-Aachen University of Technology.

After all that years I actually had to lookup that formula for π that was used all the time to burn some cpu cycles. Still knowing some things about C++ and adding some C++11 functions, I could come up with this program.

#include <iostream>
#include <chrono>

int main() {

  auto before = std::chrono::system_clock::now();
  auto beforeMilliseconds = std::chrono::duration_cast<std::chrono::milliseconds>(before.time_since_epoch()).count();
  int nmax=1000000000;
  int i=3;
  double pi=4.0;
  bool sign=true;
  
  while (i<=nmax) {
    if (sign) {
      pi-=4.0/i;
    } else {
      pi+=4.0/i;
    }
    sign=!sign;
    i+=2.0;
  }

  std::cout << "PI=" << pi << std::endl;

  auto after = std::chrono::system_clock::now();
  auto afterMilliseconds = std::chrono::duration_cast<std::chrono::milliseconds>(after.time_since_epoch()).count();

  int nflops = nmax; // nmax/2 iterations with 2 flops per iteration 
  double seconds = (afterMilliseconds - beforeMilliseconds)/1000.0;
  int flops = nflops / seconds;
  std::cout << "MFLOPS=" << flops/1000000.0 << std::endl;
  return 0;
}

Of course, this code needs to be compiled. So I saw need for a Makefile:

DEBUG:=

OPT:=

CPPFLAGS:=$(DEBUG) $(OPT)

app.exe: app.cpp
	g++ $(CPPFLAGS) -o app.exe app.cpp

My program is having a look on the stopclock to see how long the main loop is running. Knowing that each loop iteration consists of two floating point operations, I can then calculate the number of floating point operations per second – an important metric when looking at high performance code. In my case I wanted to compare the performance of an un-optimized binary (app.exe) against that of an optimized binary (app-O3.exe) and it turned out that the optimized binary is with a factor of 2.3 more performanat than the un-optimized version. Nice!

matthias@localhost$ ./app.exe 
PI=3.14159
MFLOPS=411.353
matthias@localhost$ ./app-O3.exe 
PI=3.14159
MFLOPS=949.668