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Lisa Pizzo 2025-10-29 18:19:05 +01:00
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mainEx4.cpp
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#include <iostream>
#include <cmath>
#include <cassert>
#include <vector>
#include <iomanip>
using namespace std;
double NormalSeries(size_t N)
{
double sum = 0.0;
for (size_t i = 1; i <= N; ++i)
{
sum += 1.0 / (double(i) * double(i));
}
return sum;
}
double KahanSeries(size_t N)
{
double sum = 0.0;
double c = 0.0;
for (size_t i = 1; i <= N; ++i) {
double term = 1.0 / (double(i) * double(i));
double y = term - c;
double t = sum + y;
c = (t - sum) - y;
sum = t;
}
return sum;
}
int main()
{
const double pi2_over_6 = (M_PI * M_PI) / 6.0;
// vector<size_t> ns = {10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000};
vector<size_t> ns = {1000000, 10000000, 100000000, 500000000, 1000000000};
for (size_t n : ns)
{
double s_norm = NormalSeries(n);
double s_kahan = KahanSeries(n);
double err_norm = fabs(s_norm - pi2_over_6);
double err_kahan = fabs(s_kahan - pi2_over_6);
cout.setf(ios::fixed);
cout.precision(10);
cout << "\n--- n = " << n << " ---" << endl;
cout << "Normal summation: " << s_norm << endl;
cout << "Normal error: " << err_norm << endl;
cout << "Kahan summation: " << s_kahan << endl;
cout << "Kahan error: " << err_kahan << endl;
}
return 0;
}