From dde42b7628265687db6bdeff7989eab33391a103 Mon Sep 17 00:00:00 2001
From: "g.mandl" <g.mandl@noreply.imsc.uni-graz.at>
Date: Wed, 22 Oct 2025 23:15:15 +0200
Subject: [PATCH] =?UTF-8?q?Dateien=20nach=20=E2=80=9EBSP=5F1=5FD=E2=80=9C?=
 =?UTF-8?q?=20hochladen?=
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---
 BSP_1_D/bsp_1_d.cbp | 40 ++++++++++++++++++++++++++++++++++++++++
 BSP_1_D/bsp_1_d.cpp | 34 ++++++++++++++++++++++++++++++++++
 BSP_1_D/bsp_1_d.h   | 25 +++++++++++++++++++++++++
 BSP_1_D/main.cpp    | 28 ++++++++++++++++++++++++++++
 4 files changed, 127 insertions(+)
 create mode 100644 BSP_1_D/bsp_1_d.cbp
 create mode 100644 BSP_1_D/bsp_1_d.cpp
 create mode 100644 BSP_1_D/bsp_1_d.h
 create mode 100644 BSP_1_D/main.cpp

diff --git a/BSP_1_D/bsp_1_d.cbp b/BSP_1_D/bsp_1_d.cbp
new file mode 100644
index 0000000..b750014
--- /dev/null
+++ b/BSP_1_D/bsp_1_d.cbp
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
+<CodeBlocks_project_file>
+	<FileVersion major="1" minor="6" />
+	<Project>
+		<Option title="bsp_1_d" />
+		<Option pch_mode="2" />
+		<Option compiler="gcc" />
+		<Build>
+			<Target title="Debug">
+				<Option output="bin/Debug/bsp_1_d" prefix_auto="1" extension_auto="1" />
+				<Option object_output="obj/Debug/" />
+				<Option type="1" />
+				<Option compiler="gcc" />
+				<Compiler>
+					<Add option="-g" />
+				</Compiler>
+			</Target>
+			<Target title="Release">
+				<Option output="bin/Release/bsp_1_d" prefix_auto="1" extension_auto="1" />
+				<Option object_output="obj/Release/" />
+				<Option type="1" />
+				<Option compiler="gcc" />
+				<Compiler>
+					<Add option="-O2" />
+				</Compiler>
+				<Linker>
+					<Add option="-s" />
+				</Linker>
+			</Target>
+		</Build>
+		<Compiler>
+			<Add option="-Wall" />
+			<Add option="-fexceptions" />
+		</Compiler>
+		<Unit filename="bsp_1_d.cpp" />
+		<Unit filename="bsp_1_d.h" />
+		<Unit filename="main.cpp" />
+		<Extensions />
+	</Project>
+</CodeBlocks_project_file>
diff --git a/BSP_1_D/bsp_1_d.cpp b/BSP_1_D/bsp_1_d.cpp
new file mode 100644
index 0000000..6125d10
--- /dev/null
+++ b/BSP_1_D/bsp_1_d.cpp
@@ -0,0 +1,34 @@
+#include "bsp_1_d.h"
+
+#include <cassert>       // assert()
+#include <cmath>
+
+using namespace std;
+
+double scalar(vector<double> const &x, vector<double> const &y)
+{
+    assert(x.size() == y.size()); // switch off via compile flag: -DNDEBUG
+    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)
+{
+    assert(x.size() == y.size()); // switch off via compile flag: -DNDEBUG
+    size_t const N = x.size();
+    double sum = 0.0;
+    double c = 0.0;
+    for (size_t i = 0; i < N; ++i)
+    {
+        double z = x[i]*y[i] - c;
+        double t = sum + z;
+        c = (t - sum) - z;
+        sum = t;
+    }
+    return sum;
+}
diff --git a/BSP_1_D/bsp_1_d.h b/BSP_1_D/bsp_1_d.h
new file mode 100644
index 0000000..097ba0c
--- /dev/null
+++ b/BSP_1_D/bsp_1_d.h
@@ -0,0 +1,25 @@
+#ifndef BSP_1_D_H_INCLUDED
+#define BSP_1_D_H_INCLUDED
+
+#include <vector>
+
+/** \brief  Berechnet das Skalarprodukt zweier Vektoren
+ *
+ * \param[in]   x   erster Vektor
+ * \param[in]   y   zweiter Vektor
+ * \return  Skalarprodukt von @x und @y
+ *
+ */
+double scalar(std::vector<double> const &x, std::vector<double> const &y);
+
+
+/** \brief  Berechnet das Skalarprodukt zweier Vektoren unter Anwendung der Kahan-Summation
+ *
+ * \param[in]   x   erster Vektor
+ * \param[in]   y   zweiter Vektor
+ * \return  Skalarprodukt von @x und @y
+ *
+ */
+double Kahan_skalar(std::vector<double> const &x, std::vector<double> const &y);
+
+#endif // BSP_1_D_H_INCLUDED
diff --git a/BSP_1_D/main.cpp b/BSP_1_D/main.cpp
new file mode 100644
index 0000000..d57d121
--- /dev/null
+++ b/BSP_1_D/main.cpp
@@ -0,0 +1,28 @@
+#include "bsp_1_d.h"
+#include <iostream>
+#include <math.h>
+// BSP 1_D
+using namespace std;
+
+int main()
+{
+    vector<int> nvec{100,500,1000,10000,100000,1000000,10000000,100000000}; // Vektor mit verschiedene n zum Testen
+    double exact = M_PI*M_PI/6;
+    for(size_t k = 0; k<nvec.size(); ++k)
+    {
+        vector<double> x;
+        for(int i = 0; i<nvec[k]; ++i)
+        {
+            x.push_back(1.0/(i+1));
+        }
+        double sum = scalar(x,x);
+        double sumkahan = Kahan_skalar(x,x);
+
+        cout << "n = " << nvec[k] << endl;
+        cout << "sum = " << sum << endl;
+        cout << "sumkahan = " << sumkahan << endl;
+        cout << "Differenz mit/ohne Kahan: " << abs(sum - sumkahan) << endl;
+        cout << "Differenz zu exakt fuer n to inf (mit/ohne Kahan): " << abs(exact - sum) << " / " << abs(exact - sumkahan) << endl << endl;
+    }
+    return 0;
+}