#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+=value;
  }
  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);
}
 
double getPercentageAlt2(int val, int mean, int stddev)
{
    return getPercentageNormalDistribution( ((double) val) + 0.5, mean, stddev ) - 
    getPercentageNormalDistribution( ((double) val) - 0.5, 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( ((double) val) + 0.5, mean, stddev ) - phi( ((double) 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 << getPercentageAlt2(i,mean,stddev) << '\n';                // tition
    }
 
    cout.flush();
}
 

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