rapsoulCecil rapsoulCecil - 2 months ago 19
C++ Question

Why I always get 2.8284 when estimating Pi using PRNGs?

I'm new to C++. I'm trying to statistically determine the value of Pi based on Ernesto Cesaro's Theorem using the computer system's random number generator. But what I have done now can input a seed number and generate 100 pseudo random numbers and then estimate the value of pi. The generator can generate different group of Pseudo random numbers. However the confusion is I always get the estimate of pi for 2.8284 with no change. Here is the code:

#include <iostream>
#include <math.h>
using namespace std;
int main()
{
int seed;
cout << "input a seed number: " << endl;
cin >> seed;
srand(seed);
int i, a[100];
for (i = 0; i < 100; i++)
a[i] = rand() % 100 + 1;
cout << "The generated random numbers are: " << endl;
for (i = 0; i < 100; i++)
cout << a[i] << "\t";
int m, n, j, r;
int sum = 0;
for (j = 0; j < 100; j++)
{
m = a[j];
n = a[j + 1];
j = j + 2;
do
{
r = m%n;
m = n;
n = r;
} while (r != 0);
if (n = 1)
sum = sum + 1;
}
double Pi, p;
p = 300 / sum;
Pi = sqrt(p);
cout << "The estimate value of Pi is: " << Pi << endl;
system("pause");
return 0;
}


Note that Cesaro's theorem states that given two random integers, x and y, the probability that gcd(x, y) = 1 is 6/(Pi^2). And PRNG used affects how close the resulting estimate is to Pi(3.1416).

Answer

There are several issues with your code.

Issue #1:

if (n = 1)

It should be if (n == 1) or else you are assigning 1 to n and always evaluating to true.

Issue #2:

      n = r;
  } while (r != 0);
  if (n == 1)

If you think about it, the loop will end only when r is 0, but then n will also be 0 because of the last line of the loop. So n will never be equal to 1. You probably want if (m == 1).

Issue #3:

for (j = 0; j < 100; j++)
{
    ...
    j = j + 2;

You are incrementing the j in the for line and in the loop body. You just need one.

for (j = 0; j < 100; j += 2)
{
    //no j increment

Issue #4:

p = 300 / sum;

That is an integer division, because both numbers are integers. You want foating point: p = 300.0 / sum;.

With those changes I'm getting about 3.16.