Exercise 4, Sheet 1

mainEx4.cpp

@@ -0,0 +1,57 @@
+#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;
+}