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ex1D_kahan_summation/mylib.cpp

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+#include "mylib.h"
+#include <cassert>       // assert()
+#include <cmath>
+#include <vector>
+using namespace std;
+
+double scalar(vector<double> const &x, vector<double> const &y)
+{
+    assert(x.size() == y.size());
+    size_t const N = x.size();
+    double sum = 0.0;
+    for (size_t i = 0; i < N; ++i)
+    {
+        sum += x[i] * y[i];
+    }
+    return sum;
+}
+
+
+
+double Kahan_skalar(vector<double> const &x, vector<double> const &y)
+{
+    double sum = 0;
+    double c = 0;
+    size_t n = x.size();
+    for (size_t i = 0; i < n; ++i)
+    {
+        double z = x[i]*y[i] - c;    // c is the part that got lost in the last iteration
+        double t = sum + z;          // when adding sum + z, the lower digits are lost if sum is large
+        c = (t - sum) - z;           // now we recover the lower digits to add in the next iteration
+        sum = t;
+    }
+    return sum;
+}