#include <iostream>
#include <cmath>
#include <iomanip>
 
using namespace std;
 
namespace c
{
    const double pi = 3.14159265358979323846;
    const double rad2pi = std::sqrt(2*pi);
    const int numIterations =100;
}
 
double getPercentage(int val, int mean, int stddev)
{
    double dif = (val - mean) / (double)(stddev);
    return std::exp(-0.5*dif*dif) / (c::rad2pi * stddev);
}
 
// tition
double getNormalDistributionPhi(double x)
{ //reference: http://e...content-available-to-author-only...a.org/wiki/Normal_distribution#Cumulative_distribution_function
  //code copied from pascal from Wikipedia and translated to c++. I have not made any checks for errors.   
  //Please give the code a second look. 
  //Original pascal code from wikipedia:
  //begin
  //  sum:=x;
  //  value:=x;
  //  for i:=1 to 100 do
  //    begin
  //      value:=(value*x*x/(2*i+1));
  //      sum:=sum+value;
  //    end;
  //  result:=0.5+(sum/sqrt(2*pi))*exp(-(x*x)/2);
  //end; 
  double value=x;
  double sum=x;
  for (int i=1; i<c::numIterations; i++)
  { value*=x*x/(2*i+1);
    sum+=sum;
  }
  return 0.5+(sum/std::sqrt(2*c::pi))*std::exp(-(x*x)/2);
}
 
double getPercentageNormalDistribution(double val, double mean, double stddev) //all arguments should be floating point, int is no good!
{ return getNormalDistributionPhi((val-mean)/stddev);
}
 
// JL Borges
double phi( double x, double mu, double sigma )
{ return 0.5 +  0.5 * (  std::erf( (x-mu) / ( std::sqrt(2.0) * sigma ) ) ) ; }
 
 
double getPercentageAlt(int val, int mean, int stddev)
{
    return phi( val + 0.5, mean, stddev ) - phi( val - 0.5, mean, stddev );
}
 
 
int main()
{
    int mean = 20;
    int stddev = 2;
    int drawcount = 40;
 
    cout << "mean    : " << mean << "\n";
    cout << "stddev  : " << stddev << "\n\n";
 
    for(int i = 0; i < drawcount; ++i)
    {
        cout << setw(2) << i << " -> " << fixed << getPercentage(i,mean,stddev) << '\t'         // ne555
             << fixed << getPercentageAlt(i,mean,stddev) << '\t'                                // JLBorges
             << fixed << getPercentageNormalDistribution(i,mean,stddev) << '\n';                // tition
    }
 
    cout.flush();
}
 

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