magnum/src/Magnum/Math/Test/DualComplexTest.cpp

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019
              Vladimír Vondruš <mosra@centrum.cz>

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    Software is furnished to do so, subject to the following conditions:

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    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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*/

#include <sstream>
#include <Corrade/TestSuite/Tester.h>
#include <Corrade/Utility/DebugStl.h>

#include "Magnum/Math/DualComplex.h"
#include "Magnum/Math/DualQuaternion.h"
#include "Magnum/Math/StrictWeakOrdering.h"

struct DualCmpl {
    float re, im, x, y;
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct DualComplexConverter<Float, DualCmpl> {
    constexpr static DualComplex<Float> from(const DualCmpl& other) {
        return {{other.re, other.im}, {other.x, other.y}};
    }

    constexpr static DualCmpl to(const DualComplex<Float>& other) {
        return {other.real().real(), other.real().imaginary(), other.dual().real(), other.dual().imaginary() };
    }
};

}

namespace Test { namespace {

struct DualComplexTest: Corrade::TestSuite::Tester {
    explicit DualComplexTest();

    void construct();
    void constructIdentity();
    void constructZero();
    void constructNoInit();
    void constructFromVector();
    void constructConversion();
    void constructCopy();
    void convert();

    void data();

    void isNormalized();
    template<class T> void isNormalizedEpsilonRotation();
    template<class T> void isNormalizedEpsilonTranslation();

    void multiply();

    void lengthSquared();
    void length();
    void normalized();
    template<class T> void normalizedIterative();

    void complexConjugated();
    void dualConjugated();
    void conjugated();
    void inverted();
    void invertedNormalized();
    void invertedNormalizedNotNormalized();

    void rotation();
    void translation();
    void combinedTransformParts();
    void matrix();
    void matrixNotOrthogonal();
    void transformPoint();

    void strictWeakOrdering();

    void debug();
};

using namespace Math::Literals;

typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Complex<Float> Complex;
typedef Math::Dual<Float> Dual;
typedef Math::DualComplex<Float> DualComplex;
typedef Math::Matrix3<Float> Matrix3;
typedef Math::Vector2<Float> Vector2;

DualComplexTest::DualComplexTest() {
    addTests({&DualComplexTest::construct,
              &DualComplexTest::constructIdentity,
              &DualComplexTest::constructZero,
              &DualComplexTest::constructNoInit,
              &DualComplexTest::constructFromVector,
              &DualComplexTest::constructConversion,
              &DualComplexTest::constructCopy,
              &DualComplexTest::convert,

              &DualComplexTest::data,

              &DualComplexTest::isNormalized,
              &DualComplexTest::isNormalizedEpsilonRotation<Float>,
              &DualComplexTest::isNormalizedEpsilonRotation<Double>,
              &DualComplexTest::isNormalizedEpsilonTranslation<Float>,
              &DualComplexTest::isNormalizedEpsilonTranslation<Double>,

              &DualComplexTest::multiply,

              &DualComplexTest::lengthSquared,
              &DualComplexTest::length,
              &DualComplexTest::normalized});

    addRepeatedTests<DualComplexTest>({
        &DualComplexTest::normalizedIterative<Float>,
        &DualComplexTest::normalizedIterative<Double>}, 1000);

    addTests({&DualComplexTest::complexConjugated,
              &DualComplexTest::dualConjugated,
              &DualComplexTest::conjugated,
              &DualComplexTest::inverted,
              &DualComplexTest::invertedNormalized,
              &DualComplexTest::invertedNormalizedNotNormalized,

              &DualComplexTest::rotation,
              &DualComplexTest::translation,
              &DualComplexTest::combinedTransformParts,
              &DualComplexTest::matrix,
              &DualComplexTest::matrixNotOrthogonal,
              &DualComplexTest::transformPoint,

              &DualComplexTest::strictWeakOrdering,

              &DualComplexTest::debug});
}

void DualComplexTest::construct() {
    constexpr DualComplex a = {{-1.0f, 2.5f}, {3.0f, -7.5f}};
    CORRADE_COMPARE(a, DualComplex({-1.0f, 2.5f}, {3.0f, -7.5f}));
    CORRADE_COMPARE(a.real(), Complex(-1.0f, 2.5f));
    CORRADE_COMPARE(a.dual(), Complex(3.0f, -7.5f));

    constexpr DualComplex b(Complex(-1.0f, 2.5f));
    CORRADE_COMPARE(b, DualComplex({-1.0f, 2.5f}, {0.0f, 0.0f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, Complex, Complex>::value));
}

void DualComplexTest::constructIdentity() {
    constexpr DualComplex a;
    constexpr DualComplex b{IdentityInit};
    CORRADE_COMPARE(a, DualComplex({1.0f, 0.0f}, {0.0f, 0.0f}));
    CORRADE_COMPARE(b, DualComplex({1.0f, 0.0f}, {0.0f, 0.0f}));
    CORRADE_COMPARE(a.length(), 1.0f);
    CORRADE_COMPARE(b.length(), 1.0f);

    CORRADE_VERIFY(std::is_nothrow_default_constructible<DualComplex>::value);
    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, IdentityInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<IdentityInitT, DualComplex>::value));
}

void DualComplexTest::constructZero() {
    constexpr DualComplex a{ZeroInit};
    CORRADE_COMPARE(a, DualComplex({0.0f, 0.0f}, {0.0f, 0.0f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, ZeroInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<ZeroInitT, DualComplex>::value));
}

void DualComplexTest::constructNoInit() {
    DualComplex a{{-1.0f, 2.5f}, {3.0f, -7.5f}};
    new(&a) DualComplex{NoInit};
    {
        #if defined(__GNUC__) && __GNUC__*100 + __GNUC_MINOR__ >= 601 && __OPTIMIZE__
        CORRADE_EXPECT_FAIL("GCC 6.1+ misoptimizes and overwrites the value.");
        #endif
        CORRADE_COMPARE(a, DualComplex({-1.0f, 2.5f}, {3.0f, -7.5f}));
    }

    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, NoInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<NoInitT, DualComplex>::value));
}

void DualComplexTest::constructFromVector() {
    constexpr DualComplex a(Vector2(1.5f, -3.0f));
    CORRADE_COMPARE(a, DualComplex({1.0f, 0.0f}, {1.5f, -3.0f}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Vector2, DualComplex>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, Vector2>::value));
}

void DualComplexTest::constructConversion() {
    typedef Math::DualComplex<Int> DualComplexi;

    constexpr DualComplex a{{1.3f, 2.7f}, {-15.0f, 7.0f}};
    constexpr DualComplexi b{a};

    CORRADE_COMPARE(b, (DualComplexi{{1, 2}, {-15, 7}}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<DualComplex, DualComplexi>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<DualComplex, DualComplexi>::value));
}

void DualComplexTest::constructCopy() {
    constexpr Math::Dual<Complex> a({-1.0f, 2.5f}, {3.0f, -7.5f});
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Why can't be copy constexpr? */
    constexpr
    #endif
    DualComplex b(a);
    CORRADE_COMPARE(b, DualComplex({-1.0f, 2.5f}, {3.0f, -7.5f}));

    CORRADE_VERIFY(std::is_nothrow_copy_constructible<DualComplex>::value);
    CORRADE_VERIFY(std::is_nothrow_copy_assignable<DualComplex>::value);
}

void DualComplexTest::convert() {
    constexpr DualCmpl a{1.5f, -3.5f, 7.0f, -0.5f};
    constexpr DualComplex b{{1.5f, -3.5f}, {7.0f, -0.5f}};

    /* GCC 5.1 had a bug: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=66450
       Hopefully this does not reappear. */
    constexpr DualComplex c{a};
    CORRADE_COMPARE(c, b);

    constexpr DualCmpl d(b);
    CORRADE_COMPARE(d.re, a.re);
    CORRADE_COMPARE(d.im, a.im);
    CORRADE_COMPARE(d.x, a.x);
    CORRADE_COMPARE(d.y, a.y);

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<DualCmpl, DualComplex>::value));
    CORRADE_VERIFY(!(std::is_convertible<DualComplex, DualCmpl>::value));
}

void DualComplexTest::data() {
    constexpr DualComplex ca{{-1.0f, 2.5f}, {3.0f, -7.5f}};

    constexpr Complex b = ca.real();
    constexpr Complex c = ca.dual();
    CORRADE_COMPARE(b, Complex(-1.0f, 2.5f));
    CORRADE_COMPARE(c, Complex(3.0f, -7.5f));

    DualComplex a{{-1.0f, 2.5f}, {3.0f, -7.5f}};

    constexpr Float d = *ca.data();
    Float e = a.data()[3];
    CORRADE_COMPARE(d, -1.0f);
    CORRADE_COMPARE(e, -7.5f);
}

void DualComplexTest::isNormalized() {
    CORRADE_VERIFY(!DualComplex({2.0f, 1.0f}, {}).isNormalized());
    CORRADE_VERIFY((DualComplex::rotation(Deg(23.0f))*DualComplex::translation({6.0f, 3.0f})).isNormalized());
}

template<class T> void DualComplexTest::isNormalizedEpsilonRotation() {
    setTestCaseTemplateName(TypeTraits<T>::name());

    CORRADE_VERIFY((Math::DualComplex<T>{{T(0.801775644243754) + TypeTraits<T>::epsilon()/T(2.0), T(0.597625146975521)}, {T(8018055.25501103), T(5975850.58193309)}}.isNormalized()));
    CORRADE_VERIFY(!(Math::DualComplex<T>{{T(0.801775644243754) + TypeTraits<T>::epsilon()*T(2.0), T(0.597625146975521)}, {T(8018055.25501103), T(5975850.58193309)}}.isNormalized()));
}

template<class T> void DualComplexTest::isNormalizedEpsilonTranslation() {
    setTestCaseTemplateName(TypeTraits<T>::name());

    /* Translation does not affect normalization */
    CORRADE_VERIFY((Math::DualComplex<T>{{T(0.801775644243754), T(0.597625146975521)}, {T(8018055.25501103), T(20.5)}}.isNormalized()));
    CORRADE_VERIFY((Math::DualComplex<T>{{T(0.801775644243754), T(0.597625146975521)}, {T(8018055.25501103), T(-200000000.0)}}.isNormalized()));
}

void DualComplexTest::multiply() {
    DualComplex a({-1.5f,  2.0f}, { 3.0f, -6.5f});
    DualComplex b({ 2.0f, -7.5f}, {-0.5f,  1.0f});;
    CORRADE_COMPARE(a*b, DualComplex({12.0f, 15.25f}, {1.75f, -9.0f}));
}

void DualComplexTest::lengthSquared() {
    DualComplex a({-1.0f, 3.0f}, {0.5f, -2.0f});
    CORRADE_COMPARE(a.lengthSquared(), 10.0f);
}

void DualComplexTest::length() {
    DualComplex a({-1.0f, 3.0f}, {0.5f, -2.0f});
    CORRADE_COMPARE(a.length(), 3.162278f);
}

void DualComplexTest::normalized() {
    DualComplex a({-1.0f, 3.0f}, {0.5f, -2.0f});
    DualComplex b({-0.316228f, 0.948683f}, {0.5f, -2.0f});
    CORRADE_COMPARE(a.normalized().length(), 1.0f);
    CORRADE_COMPARE(a.normalized(), b);
}

template<class> struct NormalizedIterativeData;
template<> struct NormalizedIterativeData<Float> {
    static Math::Vector2<Float> translation() { return {10000.0f, -50.0f}; }
};
template<> struct NormalizedIterativeData<Double> {
    static Math::Vector2<Double> translation() { return {10000000.0, -500.0}; }
};

template<class T> void DualComplexTest::normalizedIterative() {
    setTestCaseTemplateName(TypeTraits<T>::name());

    auto a = Math::DualComplex<T>::rotation(Math::Deg<T>{T(36.7)})*Math::DualComplex<T>::translation(NormalizedIterativeData<T>::translation());
    for(std::size_t i = 0; i != testCaseRepeatId(); ++i) {
        a = Math::DualComplex<T>::rotation(Math::Deg<T>{T(87.1)})*a;
        a = a.normalized();
    }

    CORRADE_VERIFY(a.isNormalized());
}

void DualComplexTest::complexConjugated() {
    DualComplex a({-1.0f,  2.5f}, {3.0f, -7.5f});
    DualComplex b({-1.0f, -2.5f}, {3.0f,  7.5f});
    CORRADE_COMPARE(a.complexConjugated(), b);
}

void DualComplexTest::dualConjugated() {
    DualComplex a({-1.0f, 2.5f}, { 3.0f, -7.5f});
    DualComplex b({-1.0f, 2.5f}, {-3.0f,  7.5f});
    CORRADE_COMPARE(a.dualConjugated(), b);
}

void DualComplexTest::conjugated() {
    DualComplex a({-1.0f,  2.5f}, { 3.0f, -7.5f});
    DualComplex b({-1.0f, -2.5f}, {-3.0f, -7.5f});
    CORRADE_COMPARE(a.conjugated(), b);
}

void DualComplexTest::inverted() {
    DualComplex a({-1.0f, 1.5f}, {3.0f, -7.5f});
    DualComplex b({-0.307692f, -0.461538f}, {4.384616f, -0.923077f});
    CORRADE_COMPARE(a*a.inverted(), DualComplex());
    CORRADE_COMPARE(a.inverted(), b);
}

void DualComplexTest::invertedNormalized() {
    DualComplex a({-0.316228f,  0.9486831f}, {     3.0f,    -2.5f});
    DualComplex b({-0.316228f, -0.9486831f}, {3.320391f, 2.05548f});

    DualComplex inverted = a.invertedNormalized();
    CORRADE_COMPARE(a*inverted, DualComplex());
    CORRADE_COMPARE(inverted*a, DualComplex());
    CORRADE_COMPARE(inverted, b);
}

void DualComplexTest::invertedNormalizedNotNormalized() {
    std::ostringstream out;
    Error redirectError{&out};

    DualComplex({-1.0f, -2.5f}, {}).invertedNormalized();
    CORRADE_COMPARE(out.str(), "Math::Complex::invertedNormalized(): Complex(-1, -2.5) is not normalized\n");
}

void DualComplexTest::rotation() {
    DualComplex a = DualComplex::rotation(Deg(120.0f));
    CORRADE_COMPARE(a.length(), 1.0f);
    CORRADE_COMPARE(a, DualComplex({-0.5f, 0.8660254f}, {0.0f, 0.0f}));
    CORRADE_COMPARE_AS(a.rotation().angle(), Deg(120.0f), Rad);

    /* Constexpr access to rotation */
    constexpr DualComplex b({-1.0f, 2.0f}, {});
    constexpr Complex c = b.rotation();
    CORRADE_COMPARE(c, Complex(-1.0f, 2.0f));

    /* Conversion from a rotation complex should give the same result */
    CORRADE_COMPARE(DualComplex{Complex::rotation(120.0_degf)}, a);
}

void DualComplexTest::translation() {
    Vector2 vec(1.5f, -3.5f);
    DualComplex a = DualComplex::translation(vec);
    CORRADE_COMPARE(a.length(), 1.0f);
    CORRADE_COMPARE(a, DualComplex({}, {1.5f, -3.5f}));
    CORRADE_COMPARE(a.translation(), vec);
}

void DualComplexTest::combinedTransformParts() {
    Vector2 translation = Vector2(-1.5f, 2.75f);
    DualComplex a = DualComplex::translation(translation)*DualComplex::rotation(Deg(23.0f));
    DualComplex b = DualComplex::rotation(Deg(23.0f))*DualComplex::translation(translation);

    CORRADE_COMPARE_AS(a.rotation().angle(), Deg(23.0f), Rad);
    CORRADE_COMPARE_AS(b.rotation().angle(), Deg(23.0f), Rad);
    CORRADE_COMPARE(a.translation(), translation);
    CORRADE_COMPARE(b.translation(), Complex::rotation(Deg(23.0f)).transformVector(translation));
}

void DualComplexTest::matrix() {
    DualComplex a = DualComplex::rotation(Deg(23.0f))*DualComplex::translation({2.0f, 3.0f});
    Matrix3 m = Matrix3::rotation(Deg(23.0f))*Matrix3::translation({2.0f, 3.0f});

    CORRADE_COMPARE(a.toMatrix(), m);
    CORRADE_COMPARE(DualComplex::fromMatrix(m), a);
}

void DualComplexTest::matrixNotOrthogonal() {
    std::ostringstream o;
    Error redirectError{&o};

    DualComplex::fromMatrix(Matrix3::rotation(23.0_degf)*Matrix3::translation({2.0f, 3.0f})*2);
    CORRADE_COMPARE(o.str(),
        "Math::DualComplex::fromMatrix(): the matrix doesn't represent rigid transformation:\n"
        "Matrix(1.84101, -0.781462, 1.33763,\n"
        "       0.781462, 1.84101, 7.08595,\n"
        "       0, 0, 2)\n");
}

void DualComplexTest::transformPoint() {
    DualComplex a = DualComplex::translation({2.0f, 3.0f})*DualComplex::rotation(Deg(23.0f));
    DualComplex b = DualComplex::rotation(Deg(23.0f))*DualComplex::translation({2.0f, 3.0f});
    Matrix3 m = Matrix3::translation({2.0f, 3.0f})*Matrix3::rotation(Deg(23.0f));
    Matrix3 n = Matrix3::rotation(Deg(23.0f))*Matrix3::translation({2.0f, 3.0f});
    Vector2 v(-3.6f, 0.7f);

    Vector2 transformedA = a.transformPoint(v);
    CORRADE_COMPARE(transformedA, m.transformPoint(v));
    CORRADE_COMPARE(transformedA, Vector2(-1.58733f, 2.237721f));

    Vector2 transformedB = b.transformPoint(v);
    CORRADE_COMPARE(transformedB, n.transformPoint(v));
    CORRADE_COMPARE(transformedB, Vector2(-2.918512f, 2.780698f));
}

void DualComplexTest::strictWeakOrdering() {
    StrictWeakOrdering o;
    const DualComplex a{{1.0f, 0.0f}, {1.0f, 3.0f}};
    const DualComplex b{{1.0f, 2.0f}, {3.0f, 4.0f}};
    const DualComplex c{{1.0f, 0.0f}, {1.0f, 4.0f}};

    CORRADE_VERIFY( o(a, b));
    CORRADE_VERIFY(!o(b, a));
    CORRADE_VERIFY( o(a, c));
    CORRADE_VERIFY(!o(c, a));
    CORRADE_VERIFY( o(c, b));
    CORRADE_VERIFY(!o(b, c));
    CORRADE_VERIFY(!o(a, a));
}

void DualComplexTest::debug() {
    std::ostringstream o;

    Debug(&o) << DualComplex({-1.0f, -2.5f}, {-3.0f, -7.5f});
    CORRADE_COMPARE(o.str(), "DualComplex({-1, -2.5}, {-3, -7.5})\n");
}

}}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::DualComplexTest)