First commit

CMakeLists.txt

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+cmake_minimum_required(VERSION 2.6)
+project(quaternion)
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++17")
+
+find_package(Boost COMPONENTS unit_test_framework system REQUIRED)
+include_directories (${Boost_INCLUDE_DIRS})
+
+add_executable(quaternion_example example.cpp Quaternion.h)
+
+add_executable(quaternion_test test.cpp Quaternion.h)
+
+target_link_libraries(quaternion_test ${Boost_LIBRARIES})
+
+add_test(NAME quaternion_test WORKING_DIRECTORY ${PROJECT_BINARY_DIR} COMMAND ${PROJECT_BINARY_DIR}/quaternion_test)
+
+enable_testing()

Quaternion.h

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+/*
+ * Copyright © 2019 Andrea Bontempi All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ * 
+ * - Redistributions of source code must retain the above copyright notice, this
+ *   list of conditions and the following disclaimer.
+ * 
+ * - Redistributions in binary form must reproduce the above copyright notice, this
+ *   list of conditions and the following disclaimer in the documentation and/or
+ *   other materials provided with the distribution.
+ * 
+ * - Neither the name of Andrea Bontempi nor the names of its contributors may be used to
+ *   endorse or promote products derived from this software without specific prior
+ *   written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ * 
+ */
+
+#ifndef QUATER_H
+#define QUATER_H
+
+#include <cmath>
+#include <type_traits>
+#include <complex>
+
+template<typename T = double>
+class Quaternion {
+    
+private:
+    
+    T n, ni, nj, nk;
+    
+public:
+    
+    using value_type = T; ///< value_type trait for STL compatibility
+    
+    /**
+     * Default constuctor
+     */
+    Quaternion(const T& n = static_cast<T>(0), const T& ni = static_cast<T>(0), const T& nj = static_cast<T>(0), const T& nk = static_cast<T>(0))
+        : n(n), ni(ni), nj(nj), nk(nk) {}
+
+    /**
+     * Specialized constructor for std::complex
+     */
+    Quaternion(const std::complex<T>& complex_a, const std::complex<T>& complex_b = std::complex<T>(static_cast<T>(0), static_cast<T>(0)))
+        : n(complex_a.real()), ni(complex_a.imag()), nj(complex_b.real()), nk(complex_b.imag()) {}
+    
+    /**
+     * Copy constructor 
+     */
+    template<typename U>
+    Quaternion(const Quaternion<U>& rhs)
+        : n(rhs.a()), ni(rhs.b()), nj(rhs.c()), nk(rhs.d()) {}
+    
+    /**
+     * Default copy assignment operator
+     */
+    template<typename U>
+    Quaternion<T>& operator=(const Quaternion<U>& rhs) {
+        this->n = rhs.a();
+        this->ni = rhs.b();
+        this->nj = rhs.c();
+        this->nk = rhs.d();
+    }
+    
+    /**
+     * Specialized copy assignment operator for std::complex
+     */
+    template<typename U>
+    Quaternion<T>& operator=(const std::complex<U> rhs) {
+        this->n = rhs.real();
+        this->ni = rhs.imag();
+        this->nj = static_cast<T>(0);
+        this->nk = static_cast<T>(0);
+    }
+    
+    T a() const {
+        return this->n;
+    }
+    
+    T b() const {
+        return this->ni;
+    }
+    
+    T c() const {
+        return this->nj;
+    }
+    
+    T d() const {
+        return this->nk;
+    }
+    
+    std::complex<T> complex_a() const {
+        return {this->n, this->ni};
+    }
+    
+    std::complex<T> complex_b() const {
+        return {this->nj, this->nk};
+    }
+    
+    T real() const {
+        return this->n;
+    }
+    
+    Quaternion<T> unreal() const {
+        return {static_cast<T>(0), this->ni, this->nj, this->nk};
+    }
+       
+};
+
+namespace std {
+    
+    /**
+     * Norm of quaternion
+     */
+    template<typename T>
+    T norm(const Quaternion<T>& quat) {
+        return (quat.a() * quat.a()) + (quat.b() * quat.b()) + (quat.c() * quat.c()) + (quat.d() * quat.d());
+    }
+    
+    /**
+    * Implementation of abs with float sqrt 
+    */
+    float abs(const Quaternion<float>& quat) {
+        return std::sqrt(std::norm(quat));
+    }
+
+    /**
+    * Implementation of abs with double sqrt 
+    */
+    double abs(const Quaternion<double>& quat) {
+        return std::sqrt(std::norm(quat));
+    }
+
+    /**
+    * Implementation of abs with long double sqrt 
+    */
+    long double abs(const Quaternion<long double>& quat) {
+        return std::sqrt(std::norm(quat));
+    }
+    
+    /**
+    * The conjugate of quaternion
+    */
+    template<typename T>
+    Quaternion<T> conj(const Quaternion<T>& quat) {
+        return {quat.a(), quat.b() * -1, quat.c() * -1, quat.d() * -1};
+    }
+    
+    /**
+     * Is not a number?
+     */
+    template<typename T>
+    bool isnan(Quaternion<T> quat) {
+        return std::isnan(quat.a()) || std::isnan(quat.b()) || std::isnan(quat.c()) || std::isnan(quat.d());
+    }
+    
+    /**
+     * Is infinite?
+     */
+    template<typename T>
+    bool isinf(Quaternion<T> quat) {
+        return std::isinf(quat.a()) || std::isinf(quat.b()) || std::isinf(quat.c()) || std::isinf(quat.d());
+    }
+    
+    /**
+     * Is finite?
+     */
+    template<typename T>
+    bool isfinite(Quaternion<T> quat) {
+        return std::isfinite(quat.a()) && std::isfinite(quat.b()) && std::isfinite(quat.c()) && std::isfinite(quat.d());
+    }
+    
+}
+
+/**
+ * Add operator between two quaternios.
+ */
+template<typename _tA, typename _tB>
+auto operator+(const Quaternion<_tA>& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs.a() + rhs.a())> {
+    return {lhs.a() + rhs.a(), lhs.b() + rhs.b(), lhs.c() + rhs.c(), lhs.d() + rhs.d()};
+}
+
+/**
+ * Add operator between quaternion and std::complex.
+ */
+template<typename _tA, typename _tB>
+auto operator+(const Quaternion<_tA>& lhs, const std::complex<_tB>& rhs) -> Quaternion<decltype(lhs.a() + rhs.real())> {
+    return {lhs.a() + rhs.real(), lhs.b() + rhs.imag(), lhs.c(), lhs.d()};
+}
+
+/**
+ * Add operator between std::complex and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator+(const std::complex<_tB>& lhs, const Quaternion<_tA>& rhs) -> Quaternion<decltype(lhs.real() + rhs.a())> {
+    return operator+(rhs, lhs);
+}
+
+/**
+ * Add operator between quaternion and scalar.
+ */
+template<typename _tA, typename _tB>
+auto operator+(const Quaternion<_tA>& lhs, const _tB& rhs) -> Quaternion<decltype(lhs.a() + rhs)> {
+    return {lhs.a() + rhs, lhs.b(), lhs.c(), lhs.d()};
+}
+
+/**
+ * Add operator between scalar and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator+(const _tA& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs + rhs.a())> {
+    return operator+(rhs, lhs);
+}
+
+/**
+ * Sub operator between two quaternions.
+ */
+template<typename _tA, typename _tB>
+auto operator-(const Quaternion<_tA>& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs.a() - rhs.a())> {
+    return {lhs.a() - rhs.a(), lhs.b() - rhs.b(), lhs.c() - rhs.c(), lhs.d() - rhs.d()};
+}
+
+/**
+ * Sub operator between quaternion and std:complex.
+ */
+template<typename _tA, typename _tB>
+auto operator-(const Quaternion<_tA>& lhs, const std::complex<_tB>& rhs) -> Quaternion<decltype(lhs.a() - rhs.real())> {
+    return {lhs.a() - rhs.real(), lhs.b() - rhs.imag(), lhs.c(), lhs.d()};
+}
+
+/**
+ * Sub operator between std:complex and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator-(const std::complex<_tB>& lhs, const Quaternion<_tA>& rhs) -> Quaternion<decltype(lhs.real() - rhs.a())> {
+    return {lhs.real() - rhs.a(), lhs.imag() - rhs.b(), -rhs.c(), -rhs.d()};
+}
+
+/**
+ * Sub operator between quaternion and scalar.
+ */
+template<typename _tA, typename _tB>
+auto operator-(const Quaternion<_tA>& lhs, const _tB& rhs) -> Quaternion<decltype(lhs.a() - rhs)> {
+    return {lhs.a() - rhs, lhs.b(), lhs.c(), lhs.d()};
+}
+
+/**
+ * Sub operator between scalar and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator-(const _tA& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs - rhs.a())> {
+    return {lhs - rhs.a(), -rhs.b(), -rhs.c(), -rhs.d()};
+}
+
+/**
+ * Mul operator between two quaternions.
+ */
+template<typename _tA, typename _tB>
+auto operator*(const Quaternion<_tA>& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs.a() * rhs.a())> {
+    decltype(lhs.a() * rhs.a()) tn = (lhs.a() * rhs.a()) - (lhs.b() * rhs.b()) - (lhs.c() * rhs.c()) - (lhs.d() * rhs.d());
+    decltype(lhs.a() * rhs.a()) tni = (lhs.a() * rhs.b()) + (lhs.b() * rhs.a()) + (lhs.c() * rhs.d()) - (lhs.d() * rhs.c());
+    decltype(lhs.a() * rhs.a()) tnj = (lhs.a() * rhs.c()) + (lhs.c() * rhs.a()) + (lhs.d() * rhs.b()) - (lhs.b() * rhs.d());
+    decltype(lhs.a() * rhs.a()) tnk = (lhs.a() * rhs.d()) + (lhs.d() * rhs.a()) + (lhs.b() * rhs.c()) - (lhs.c() * rhs.b());
+    return {tn, tni, tnj, tnk};
+}
+
+/**
+ * Mul operator between quaternion and std:complex.
+ */
+template<typename _tA, typename _tB>
+auto operator*(const Quaternion<_tA>& lhs, const std::complex<_tB>& rhs) -> Quaternion<decltype(lhs.a() * rhs.real())> {
+    decltype(lhs.a() * rhs.real()) tn = (lhs.a() * rhs.real()) - (lhs.b() * rhs.imag());
+    decltype(lhs.a() * rhs.real()) tni = (lhs.a() * rhs.imag()) + (lhs.b() * rhs.real());
+    decltype(lhs.a() * rhs.real()) tnj = (lhs.c() * rhs.real()) + (lhs.d() * rhs.imag());
+    decltype(lhs.a() * rhs.real()) tnk = (lhs.d() * rhs.real()) - (lhs.c() * rhs.imag());
+    return {tn, tni, tnj, tnk};
+}
+
+/**
+ * Mul operator between std:complex and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator*(const std::complex<_tB>& lhs, const Quaternion<_tA>& rhs) -> Quaternion<decltype(lhs.real() * rhs.a())> {
+    decltype(lhs.real() * rhs.a()) tn = (lhs.real() * rhs.a()) - (lhs.imag() * rhs.b());
+    decltype(lhs.real() * rhs.a()) tni = (lhs.real() * rhs.b()) + (lhs.imag() * rhs.a());
+    decltype(lhs.real() * rhs.a()) tnj = (lhs.real() * rhs.c()) - (lhs.imag() * rhs.d());
+    decltype(lhs.real() * rhs.a()) tnk = (lhs.real() * rhs.d()) + (lhs.imag() * rhs.c());
+    return {tn, tni, tnj, tnk};
+}
+
+/**
+ * Mul operator between quaternion and scalar.
+ */
+template<typename _tA, typename _tB>
+auto operator*(const Quaternion<_tA>& lhs, const _tB& rhs) -> Quaternion<decltype(lhs.a() * rhs)> {
+    return {lhs.a() * rhs, lhs.b() * rhs, lhs.c() * rhs, lhs.d() * rhs};
+}
+
+/**
+ * Mul operator between scalar and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator*(const _tA& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype(lhs * rhs.a())> {
+    return operator*(rhs, lhs);
+}
+
+/**
+ * Div operator between two quaternions.
+ */
+template<typename _tA, typename _tB>
+auto operator/(const Quaternion<_tA>& lhs, const Quaternion<_tB>& rhs) -> Quaternion<decltype((lhs.a() * rhs.a()) / rhs.a())> {
+    decltype(lhs.a() * rhs.a()) tn  = (lhs.a() * rhs.a()) + (lhs.b() * rhs.b()) + (lhs.c() * rhs.c()) + (lhs.d() * rhs.d());
+    decltype(lhs.a() * rhs.a()) tni = - (lhs.a() * rhs.b()) + (lhs.b() * rhs.a()) - (lhs.c() * rhs.d()) + (lhs.d() * rhs.c());
+    decltype(lhs.a() * rhs.a()) tnj = - (lhs.a() * rhs.c()) + (lhs.c() * rhs.a()) - (lhs.d() * rhs.b()) + (lhs.b() * rhs.d());
+    decltype(lhs.a() * rhs.a()) tnk = - (lhs.a() * rhs.d()) + (lhs.d() * rhs.a()) - (lhs.b() * rhs.c()) + (lhs.c() * rhs.b());
+    decltype(rhs.a()) norm = std::norm(rhs);
+    return {tn / norm, tni / norm, tnj / norm, tnk / norm};
+}
+
+/**
+ * Div operator between quaternion and scalar.
+ */
+template<typename _tA, typename _tB>
+auto operator/(const Quaternion<_tA>& lhs, const _tB& rhs) -> Quaternion<decltype(lhs.a() / rhs)> {
+    return {lhs.a() / rhs, lhs.b() / rhs, lhs.c() / rhs, lhs.d() / rhs};
+}
+
+/**
+ * Div operator between scalar and quaternion.
+ */
+template<typename _tA, typename _tB>
+auto operator/(const _tB& lhs, const Quaternion<_tA>& rhs) -> Quaternion<decltype((rhs.a() * lhs) / rhs.a())> {
+    decltype(rhs.a()) norm = std::norm(rhs);
+    return {(rhs.a() * lhs) / norm, -(rhs.b() * lhs) / norm, -(rhs.c() * lhs) / norm, -(rhs.d() * lhs) / norm};
+}
+
+/**
+ * Trivial comparison operator between quaternions.
+ */
+template<typename _tA, typename _tB>
+bool operator==(const _tA& lhs, const _tB& rhs) {
+    return lhs.a() == rhs.a() && lhs.b() == rhs.b() && lhs.c() == rhs.c() && lhs.d() == rhs.d();
+}
+
+/**
+ * Stream operator for quaternion.
+ */
+template<typename T>
+std::ostream& operator<< (std::ostream& os, const Quaternion<T>& obj) {
+    os << "(" << obj.a() << "," << obj.b() << "," << obj.c() << "," << obj.d() << ")"; 
+    return os;
+}
+
+/**
+ * Normalization function
+ */
+template<typename T>
+auto normalized(const Quaternion<T>& quat) -> Quaternion<decltype(quat.a() / std::abs(quat))> {
+    return quat / std::abs(quat);
+}
+
+/**
+ * Inverse function
+ */
+template<typename T>
+auto inverse(const Quaternion<T>& quat) {
+    return std::conj(quat) / std::norm(quat);
+}
+
+#endif // QUATER_H

README.md

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+A simple header-only generic C++ quaternion class. 
+==========================================
+
+* Header-only.
+* No dynamic memory allocation.
+* Supports operations on mixed types.
+* Modern C++.
+* Compatible with Standard Template Library.
+
+### Run test suite
+```
+mkdir build
+cd build
+cmake ..
+make
+make test
+
+```

example.cpp

@@ -0,0 +1,91 @@
+/*
+ * Copyright © 2019 Andrea Bontempi All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ * 
+ * - Redistributions of source code must retain the above copyright notice, this
+ *   list of conditions and the following disclaimer.
+ * 
+ * - Redistributions in binary form must reproduce the above copyright notice, this
+ *   list of conditions and the following disclaimer in the documentation and/or
+ *   other materials provided with the distribution.
+ * 
+ * - Neither the name of Andrea Bontempi nor the names of its contributors may be used to
+ *   endorse or promote products derived from this software without specific prior
+ *   written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ * 
+ */
+
+#include <iostream>
+#include "Quaternion.h"
+
+int main(int argc, char **argv) {    
+
+    Quaternion<int> a(1,0,1,0);
+    Quaternion<double> b(1,0.5,0.5,0.75);
+    Quaternion<float> c(3,0.5,1.5,0.75);
+        
+    std::complex<double> ca(1,2);
+    std::complex<double> cb(3,4);
+        
+    std::cout << "Real part of " << a << " is " << a.real() << std::endl;
+    
+    std::cout << "Unreal part of " << b << " is " << b.unreal() << std::endl;
+    
+    std::cout << "Component of " << a << " is " << a.a() << ", " << a.b() << ", " << a.c() << ", " << a.d() << std::endl;
+    
+    std::cout << "Norm of " << a << " is " << std::norm(a) << std::endl;
+        
+    std::cout << "Modulus of " << c << " is " << std::abs(c) << std::endl;
+
+    std::cout << "Conjugate of " << b << " is " << std::conj(b) << std::endl;
+    
+    std::cout << "Normalization of " << b << " is " << normalized(b) << std::endl;
+        
+    std::cout << "Inverse of " << b << " is " << inverse(b) <<  std::endl;
+    
+    std::cout << a << " + " << b << " = " << a + b << std::endl;
+        
+    std::cout << a << " + " << 3 << " = " << a + 3 << std::endl;
+        
+    std::cout << b << " + complex " << ca << " = " << b + ca << std::endl;
+    
+    std::cout << a << " - " << b << " = " << a - b << std::endl;
+    
+    std::cout << a << " * " << b << " = " << a * b << std::endl;
+
+    std::cout << a << " * " << 2.2 << " = " << a * 2.2 << std::endl;
+    
+    std::cout << a << " / " << b << " = " << a / b << std::endl;
+
+    std::cout << a << " / " << 2.2 << " = " << a / 2.2 << std::endl;
+        
+    std::cout << 2.2 << " / " << b << " = " << 2.2 / b << std::endl;
+    
+    Quaternion<double> component (ca,cb);
+    
+    std::cout << "Construct quaternion from complex " << ca << " and " << cb << " = " << component <<  std::endl;
+    
+    std::cout << "Quaternion " << component << " has complex component " << component.complex_a() << " and " << component.complex_b() <<  std::endl;
+    
+    std::cout << a << " is NaN? " << std::boolalpha << std::isnan(a) << std::endl;
+    
+    std::cout << a << " is infinite? " << std::boolalpha << std::isinf(a) << std::endl;
+
+    std::cout << a << " is finite? " << std::boolalpha << std::isfinite(a) << std::endl;
+
+    return 0;
+    
+}

test.cpp

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+/*
+ * Copyright © 2019 Andrea Bontempi All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ * 
+ * - Redistributions of source code must retain the above copyright notice, this
+ *   list of conditions and the following disclaimer.
+ * 
+ * - Redistributions in binary form must reproduce the above copyright notice, this
+ *   list of conditions and the following disclaimer in the documentation and/or
+ *   other materials provided with the distribution.
+ * 
+ * - Neither the name of Andrea Bontempi nor the names of its contributors may be used to
+ *   endorse or promote products derived from this software without specific prior
+ *   written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ * 
+ */
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "Quaternion tests"
+
+#include <complex>
+#include "Quaternion.h"
+#include <boost/test/unit_test.hpp> //VERY IMPORTANT - include this last
+
+
+/**
+ * Comparison operator for test
+ */
+
+const double epsilon = 1e-05;
+
+bool operator==(const Quaternion<double>& lhs, const Quaternion<double>& rhs) {
+    bool check_a = std::abs(lhs.a() - rhs.a()) <= ((std::abs(lhs.a()) < std::abs(rhs.a()) ? std::abs(rhs.a()) : std::abs(lhs.a())) * epsilon);
+    bool check_b = std::abs(lhs.b() - rhs.b()) <= ((std::abs(lhs.b()) < std::abs(rhs.b()) ? std::abs(rhs.b()) : std::abs(lhs.b())) * epsilon);
+    bool check_c = std::abs(lhs.c() - rhs.c()) <= ((std::abs(lhs.c()) < std::abs(rhs.c()) ? std::abs(rhs.c()) : std::abs(lhs.c())) * epsilon);
+    bool check_d = std::abs(lhs.d() - rhs.d()) <= ((std::abs(lhs.d()) < std::abs(rhs.d()) ? std::abs(rhs.d()) : std::abs(lhs.d())) * epsilon);
+    return check_a && check_b && check_c && check_d;
+}
+
+bool compare_double(const double& a, const double& b) {
+    return std::abs(a - b) <= ((std::abs(a) < std::abs(b) ? std::abs(b) : std::abs(a)) * epsilon);
+
+}
+
+/** CONSTRUCTION OF A QUATERNION **/
+
+BOOST_AUTO_TEST_CASE(quaternion_costruction_from_components) {
+    Quaternion<double> test(0.1,0.5,0.9,1);
+    BOOST_CHECK_EQUAL(test.a(), 0.1);
+    BOOST_CHECK_EQUAL(test.b(), 0.5);
+    BOOST_CHECK_EQUAL(test.c(), 0.9);
+    BOOST_CHECK_EQUAL(test.d(), 1);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_costruction_from_complex) {
+    std::complex<double> a(0.1,0.5);
+    std::complex<double> b(0.9,1);
+    Quaternion<double> test(a,b);
+    BOOST_CHECK_EQUAL(test.complex_a(), a);
+    BOOST_CHECK_EQUAL(test.complex_b(), b);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_costruction_from_copy) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    Quaternion<double> b(a);
+    BOOST_CHECK_EQUAL(a, b);
+}
+
+/** UNARY OPERATORS **/
+
+BOOST_AUTO_TEST_CASE(quaternion_conjugation) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    Quaternion<double> b(0.1,-0.5,-0.9,-1);
+    BOOST_CHECK_EQUAL(std::conj(a), b);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_norm) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    double b = 2.07000;
+    BOOST_CHECK_EQUAL(compare_double(std::norm(a), b), true);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_abs) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    double b = 1.43875;
+    BOOST_CHECK_EQUAL(compare_double(std::abs(a), b), true);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_normalization) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    Quaternion<double> b(0.0695048,0.347524,0.625543,0.695048);
+    BOOST_CHECK_EQUAL(normalized(a), b);
+}
+
+BOOST_AUTO_TEST_CASE(quaternion_inversion) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    Quaternion<double> b(0.0483092,-0.241546,-0.434783,-0.483092);
+    BOOST_CHECK_EQUAL(inverse(a), b);
+}
+
+/** BINARY OPERATOR: SUM **/
+
+BOOST_AUTO_TEST_CASE(sum_between_quaternions) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    Quaternion<double> b(0.9,0.5,0.1,0);
+    Quaternion<double> c(1,1,1,1);
+    BOOST_CHECK_EQUAL(a + b, c);
+}
+
+BOOST_AUTO_TEST_CASE(sum_between_scalar_and_quaternion) {
+    double a = 1;
+    Quaternion<double> b(0.9,0.5,0.1,0);
+    Quaternion<double> c(1.9,0.5,0.1,0);
+    BOOST_CHECK_EQUAL(a + b, c);
+}
+
+BOOST_AUTO_TEST_CASE(sum_between_quaternion_and_scalar) {
+    Quaternion<double> a(0.9,0.5,0.1,0);
+    double b = 1;
+    Quaternion<double> c(1.9,0.5,0.1,0);
+    BOOST_CHECK_EQUAL(a + b, c);
+}
+
+BOOST_AUTO_TEST_CASE(sum_between_complex_and_quaternion) {
+    std::complex<double> a (1,1);
+    Quaternion<double> b(0.9,0.5,0.1,0);
+    Quaternion<double> c(1.9,1.5,0.1,0);
+    BOOST_CHECK_EQUAL(a + b, c);
+}
+
+BOOST_AUTO_TEST_CASE(sum_between_quaternion_and_complex) {
+    Quaternion<double> a(0.9,0.5,0.1,0);
+    std::complex<double> b (1,1);
+    Quaternion<double> c(1.9,1.5,0.1,0);
+    BOOST_CHECK_EQUAL(a + b, c);
+}
+
+/** BINARY OPERATOR: DIFFERENCE **/
+
+BOOST_AUTO_TEST_CASE(difference_between_quaternions) {
+    Quaternion<double> a(1,1,1,1);
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(0.9,0.5,0.1,0);
+    BOOST_CHECK_EQUAL(a - b, c);
+}
+
+BOOST_AUTO_TEST_CASE(difference_between_scalar_and_quaternion) {
+    double a = 1;
+    Quaternion<double> b(0.9,0.5,0.1,0);
+    Quaternion<double> c(0.1,-0.5,-0.1,0);
+    BOOST_CHECK_EQUAL(a - b, c);
+}
+
+BOOST_AUTO_TEST_CASE(difference_between_quaternion_and_scalar) {
+    Quaternion<double> a(0.9,0.5,0.1,0);
+    double b = 1;
+    Quaternion<double> c(-0.1,0.5,0.1,0);
+    BOOST_CHECK_EQUAL(a - b, c);
+}
+
+BOOST_AUTO_TEST_CASE(difference_between_complex_and_quaternion) {
+    std::complex<double> a (1,1);
+    Quaternion<double> b(0.9,0.5,0.1,0);
+    Quaternion<double> c(0.1,0.5,-0.1,0);
+    BOOST_CHECK_EQUAL(a - b, c);
+}
+
+BOOST_AUTO_TEST_CASE(difference_between_quaternion_and_complex) {
+    Quaternion<double> a(0.9,0.5,0.1,0);
+    std::complex<double> b (1,1);
+    Quaternion<double> c(-0.1,-0.5,0.1,0);
+    BOOST_CHECK_EQUAL(a - b, c);
+}
+
+/** BINARY OPERATOR: MULTIPLICATION **/
+
+BOOST_AUTO_TEST_CASE(multiplication_between_quaternions) {
+    Quaternion<double> a(-1,1,-1,1);
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(-0.7,-2.3,-1.5,0.5);
+    BOOST_CHECK_EQUAL(a * b, c);
+}
+
+BOOST_AUTO_TEST_CASE(multiplication_between_scalar_and_quaternion) {
+    double a = 2;
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(0.2,1,1.8,2);
+    BOOST_CHECK_EQUAL(a * b, c);
+}
+
+BOOST_AUTO_TEST_CASE(multiplication_between_quaternion_and_scalar) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    double b = 2;
+    Quaternion<double> c(0.2,1,1.8,2);
+    BOOST_CHECK_EQUAL(a * b, c);
+}
+
+BOOST_AUTO_TEST_CASE(multiplication_between_complex_and_quaternion) {
+    std::complex<double> a (1,1);
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(-0.4,0.6,-0.1,1.9);
+    BOOST_CHECK_EQUAL(a * b, c);
+}
+
+BOOST_AUTO_TEST_CASE(multiplication_between_quaternion_and_complex) {
+    Quaternion<double> a(0.1,0.5,0.9,1);
+    std::complex<double> b (1,1);
+    Quaternion<double> c(-0.4,0.6,1.9,0.1);
+    BOOST_CHECK_EQUAL(a * b, c);
+}
+
+/** BINARY OPERATOR: DIVISION **/
+
+BOOST_AUTO_TEST_CASE(division_between_quaternions) {
+    Quaternion<double> a(-1,1,-1,1);
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(0.241546,1.207729,0.628019,-0.144928);
+    BOOST_CHECK_EQUAL(a / b, c);
+}
+
+BOOST_AUTO_TEST_CASE(division_between_scalar_and_quaternion) {
+    double a = 2;
+    Quaternion<double> b(0.1,0.5,0.9,1);
+    Quaternion<double> c(0.0966184,-0.483092,-0.869565,-0.966184);
+    BOOST_CHECK_EQUAL(a / b, c);
+}
+
+BOOST_AUTO_TEST_CASE(division_between_quaternion_and_scalar) {
+    Quaternion<double> a(-1,1,-1,1);
+    double b = 2;
+    Quaternion<double> c(-0.5,0.5,-0.5,0.5);
+    BOOST_CHECK_EQUAL(a / b, c);
+}