Abdulrahman7ossam Abdulrahman7ossam - 6 months ago 7
Python Question

Why is python 3 much faster than C++ when using the Monte Carlo Simulation to estimate PI?

I know that C++ should be much faster than python 3 because it is a compiled language as opposed to an interpreted language. I wrote two program that uses the Monte Carlo Simulation to calculate Pi, one in python 3 and the other in C++. Python turned out to be approximately 16x faster than C++. As seen in the photos bellow, with a repetition value of (10,000,000) python takes 8.5 seconds whilst C++ takes 137.4 seconds.

I'm new to C++ but I can't find posts online that explains this behavior.

According to this post (http://stackoverflow.com/a/801671/3883263) C++ in general should be 10x - 100x faster than python, which is clearly not the case with me. Please help me understand why python is significantly faster than C++ in my case.

My results:

Monte Carlo Simulation (Estimation of Pi) in C++
Monte Carlo Simulation (Estimation of Pi) using C++

Monte Carlo Simulation (Estimation of Pi) in Python 3
Monte Carlo Simulation (Estimation of Pi) using python 3

Python Source Code:

from random import random
import time
import sys

class MonteCarloSimulator(object):

def __init__(self, value):
self.value = value

if sys.platform == "win32":
self.G = ''
self.R = ''
self.END = ''
else:
self.G = '\033[92m'
self.R = '\033[1;31m'
self.END = '\033[0m'

def unit_circle(self, x, y):
if (x ** 2 + y ** 2) <= 1:
return True
else:
return False

def simulate(self):
print("\nProcessing calculations with a repetition value of " + self.R +
str(self.value) + self.END + " times.")

area_of_circle = 0
area_of_square = 0

start = time.clock()

for i in range(1, self.value):
x = random()
y = random()

if self.unit_circle(x, y):
area_of_circle += 1
area_of_square += 1

pi = (area_of_circle * 4) / area_of_square

runtime = time.clock() - start

print("\tCalculated Pi = " + self.G + str(pi) + self.END +
" ({0} seconds, {1} minutes)".format(round(runtime, 10),
round(runtime / 60, 10)))

print("Estimated Num of Pi is off by", abs(pi - 3.14159265359))

def main():
values = [1000, 10000, 100000, 1000000, 10000000, 100000000,1000000000, 10000000000]
for value in values: MonteCarloSimulator(value).simulate()
if __name__ == "__main__":
try:
main()
except KeyboardInterrupt:
print("\nQuitting...")
sys.exit(1)


C++ Source Code:

#include <iostream> // std library
#include <random> // random number generator
#include <ctime> // calculating runtime
#include <cmath> // absolute value function
#include "MonteCarloSimmulation.hpp" // function prototypes

using namespace std;

const double g_PI {3.141592653589793238463};

int main()
{
// repitition values
long values[5] = {1000, 10000, 100000, 1000000, 10000000};//, 100000000, 1000000000, 10000000000};

// runs the simulation with the different repetition values
for (auto value : values)
simulate(value);

cout << "\nPress return to exit";
cin.get();

return 0;
}

/**
* The actual simulation
*/
void simulate(unsigned long value)
{
// start time for calculating runtime
const clock_t startTime = clock();

// area's variables
unsigned long area_of_circle = 0;
unsigned long area_of_square = 0;

// print the repitiion value
cout << "\nProcessing calculations with a repetition value of " << value <<
" times." << endl;

for (unsigned long i = 0; i != value; i++)
{
// gets random values from 0 to 1 for (x) and (y)
float x = randomFloat();
float y = randomFloat();

// checks if (x, y) are in a unit circle, if so increment circle area
if (unit_circle(x, y))
area_of_circle++;
area_of_square++;
}

// pi = area of circle * 4 / area of square
double calculatedPi = static_cast<double>(area_of_circle * 4) / area_of_square;

float endTime = static_cast<float>(clock() - startTime) / CLOCKS_PER_SEC;

// prints the value of calculated pi
cout << "\tCalculated Value of Pi: " << calculatedPi <<
" (" << endTime << " seconds, " << endTime/60 << " minutes)" << endl;

// difference between the calc value and pi
cout << "Estimated Num of Pi is off by " << abs(calculatedPi - g_PI) << '\n';
}

/**
* returns a random number from 0 to 1
*/
float randomFloat()
{
random_device rd;
default_random_engine generator(rd()); // rd() provides a random seed
uniform_real_distribution<float> distribution(0,1);

float x = distribution(generator);

return x;
}

/**
* checks if the two input parameters are inside a unit circle
*/
bool unit_circle(float x, float y)
{
if ((x*x + y*y) <= 1)
return true;
else
return false;
}

Answer

The main problem is that you're reseeding a random number generator for each random number in your C++ code. Additionally you're not compiling with optimizations enabled (-O3).

I moved the initialization of the random number generator outside the randomFloat function (equally, you could use static variables inside the function):

random_device rd;
default_random_engine generator(rd()); // rd() provides a random seed
uniform_real_distribution<float> distribution(0,1);

float randomFloat() {
    float x = distribution(generator);
    return x;
}

and compiled with -O3 and now C++ is considerably faster than Python


Another possibility could be that python and C++ code use a different random number generator. Python random module (C code here) uses a MT19937 Mersenne Twister random number generator that is a fast PRNG optimized specifically for numerical problems such as Monte Carlo; the algorithm of default_random_engine in C++ is implementation-defined. As pointed out by Melak47, you can force the use of MT19937 PRNG in C++ with:

mt19937 generator(rd());

or

mt19937_64 generator(rd());

P.S., Python outperforming C++ is not unheard of; the C++ algorithms value genericity whereas the Python algorithms are often quite optimized for some use cases. See for example this question on substring matching.

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