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

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
                2020, 2021, 2022 Vladimír Vondruš <mosra@centrum.cz>

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

#include <sstream>
#include <Corrade/TestSuite/Tester.h>
#include <Corrade/TestSuite/Compare/Numeric.h>
#include <Corrade/Utility/DebugStl.h>
#include <Corrade/Utility/TypeTraits.h> /* CORRADE_STD_IS_TRIVIALLY_TRAITS_SUPPORTED */

#include "Magnum/Math/Half.h"
#include "Magnum/Math/Vector.h"
#include "Magnum/Math/StrictWeakOrdering.h"

struct Vec3 {
    float x, y, z;
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct VectorConverter<3, Float, Vec3> {
    constexpr static Vector<3, Float> from(const Vec3& other) {
        return {other.x, other.y, other.z};
    }

    constexpr static Vec3 to(const Vector<3, Float>& other) {
        return {other[0], other[1], other[2]};
    }
};

}

namespace Test { namespace {

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

    void construct();
    void constructFromData();
    void constructPad();
    void constructPadDefaultHalf();
    void constructDefault();
    void constructNoInit();
    void constructOneValue();
    void constructOneComponent();
    void constructConversion();
    void constructCopy();
    void convert();

    void isZeroFloat();
    void isZeroInteger();
    void isNormalized();

    void data();

    void negative();
    void addSubtract();
    void multiplyDivide();
    void multiplyDivideIntegral();
    void multiplyDivideComponentWise();
    void multiplyDivideComponentWiseIntegral();
    void modulo();
    void bitwise();

    void compare();
    void compareComponentWise();

    void dot();
    void dotSelf();
    void length();
    void lengthInverted();
    void normalized();
    void resized();

    void sum();
    void product();
    void min();
    void max();
    void minmax();

    void nanIgnoring();

    void projected();
    void projectedOntoNormalized();
    void projectedOntoNormalizedNotNormalized();
    void flipped();

    void angle();
    void angleNormalizedButOver1();
    void angleNotNormalized();

    void subclassTypes();
    void subclass();

    void strictWeakOrdering();

    void debug();
    void debugPacked();
};

typedef Math::Constants<Float> Constants;
typedef Math::Rad<Float> Rad;
typedef Vector<2, Float> Vector2;
typedef Vector<2, Half> Vector2h;
typedef Vector<3, Float> Vector3;
typedef Vector<4, Float> Vector4;
typedef Vector<4, Half> Vector4h;
typedef Vector<4, Int> Vector4i;

using namespace Literals;

VectorTest::VectorTest() {
    addTests({&VectorTest::construct,
              &VectorTest::constructFromData,
              &VectorTest::constructPad,
              &VectorTest::constructPadDefaultHalf,
              &VectorTest::constructDefault,
              &VectorTest::constructNoInit,
              &VectorTest::constructOneValue,
              &VectorTest::constructOneComponent,
              &VectorTest::constructConversion,
              &VectorTest::constructCopy,
              &VectorTest::convert,

              &VectorTest::isZeroFloat,
              &VectorTest::isZeroInteger,
              &VectorTest::isNormalized,

              &VectorTest::data,

              &VectorTest::negative,
              &VectorTest::addSubtract,
              &VectorTest::multiplyDivide,
              &VectorTest::multiplyDivideIntegral,
              &VectorTest::multiplyDivideComponentWise,
              &VectorTest::multiplyDivideComponentWiseIntegral,
              &VectorTest::modulo,
              &VectorTest::bitwise,

              &VectorTest::compare,
              &VectorTest::compareComponentWise,

              &VectorTest::dot,
              &VectorTest::dotSelf,
              &VectorTest::length,
              &VectorTest::lengthInverted,
              &VectorTest::normalized,
              &VectorTest::resized,

              &VectorTest::sum,
              &VectorTest::product,
              &VectorTest::min,
              &VectorTest::max,
              &VectorTest::minmax,

              &VectorTest::nanIgnoring,

              &VectorTest::projected,
              &VectorTest::projectedOntoNormalized,
              &VectorTest::projectedOntoNormalizedNotNormalized,
              &VectorTest::flipped,

              &VectorTest::angle,
              &VectorTest::angleNormalizedButOver1,
              &VectorTest::angleNotNormalized,

              &VectorTest::subclassTypes,
              &VectorTest::subclass,

              &VectorTest::strictWeakOrdering,

              &VectorTest::debug,
              &VectorTest::debugPacked});
}

void VectorTest::construct() {
    constexpr Vector4 a = {1.0f, 2.0f, -3.0f, 4.5f};
    CORRADE_COMPARE(a, Vector4(1.0f, 2.0f, -3.0f, 4.5f));

    CORRADE_VERIFY(std::is_nothrow_constructible<Vector4, Float, Float, Float, Float>::value);
}

void VectorTest::constructFromData() {
    Float data[] = { 1.0f, 2.0f, 3.0f, 4.0f };
    CORRADE_COMPARE(Vector4::from(data), Vector4(1.0f, 2.0f, 3.0f, 4.0f));
}

void VectorTest::constructPad() {
    constexpr Vector<2, Float> a{1.0f, -1.0f};
    constexpr Vector4 b = Vector4::pad(a);
    constexpr Vector4 c = Vector4::pad(a, 5.0f);
    CORRADE_COMPARE(b, Vector4(1.0f, -1.0f, 0.0f, 0.0f));
    CORRADE_COMPARE(c, Vector4(1.0f, -1.0f, 5.0f, 5.0f));

    constexpr Vector<5, Float> d{1.0f, -1.0f, 8.0f, 2.3f, -1.1f};
    constexpr Vector4 e = Vector4::pad(d);
    CORRADE_COMPARE(e, Vector4(1.0f, -1.0f, 8.0f, 2.3f));
}

void VectorTest::constructPadDefaultHalf() {
    using namespace Literals;
    /* The default pad value should work also for the Half type */
    Vector4h a = Vector4h::pad(Vector2h{1.0_h, -1.0_h});
    CORRADE_COMPARE(a, (Vector4h{1.0_h, -1.0_h, 0.0_h, 0.0_h}));
}

void VectorTest::constructDefault() {
    constexpr Vector4 a;
    constexpr Vector4 b{ZeroInit};
    CORRADE_COMPARE(a, Vector4(0.0f, 0.0f, 0.0f, 0.0f));
    CORRADE_COMPARE(b, Vector4(0.0f, 0.0f, 0.0f, 0.0f));

    CORRADE_VERIFY(std::is_nothrow_default_constructible<Vector4>::value);
    CORRADE_VERIFY(std::is_nothrow_constructible<Vector4, ZeroInitT>::value);

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!std::is_convertible<ZeroInitT, Vector4>::value);
}

void VectorTest::constructNoInit() {
    Vector4 a{1.0f, 2.0f, -3.0f, 4.5f};
    new(&a) Vector4{Magnum::NoInit};
    {
        /* Explicitly check we're not on Clang because certain Clang-based IDEs
           inherit __GNUC__ if GCC is used instead of leaving it at 4 like
           Clang itself does */
        #if defined(CORRADE_TARGET_GCC) && !defined(CORRADE_TARGET_CLANG) && __GNUC__*100 + __GNUC_MINOR__ >= 601 && __OPTIMIZE__
        CORRADE_EXPECT_FAIL("GCC 6.1+ misoptimizes and overwrites the value.");
        #endif
        CORRADE_COMPARE(a, (Vector4{1.0f, 2.0f, -3.0f, 4.5f}));
    }

    CORRADE_VERIFY(std::is_nothrow_constructible<Vector4, Magnum::NoInitT>::value);

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!std::is_convertible<Magnum::NoInitT, Vector4>::value);
}

void VectorTest::constructOneValue() {
    constexpr Vector4 a(7.25f);

    CORRADE_COMPARE(a, Vector4(7.25f, 7.25f, 7.25f, 7.25f));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!std::is_convertible<Float, Vector4>::value);

    CORRADE_VERIFY(std::is_nothrow_constructible<Vector4, Float>::value);
}

void VectorTest::constructOneComponent() {
    typedef Vector<1, Float> Vector1;

    /* Implicit constructor must work */
    constexpr Vector1 vec = 1.0f;
    CORRADE_COMPARE(vec, Vector1(1));

    CORRADE_VERIFY(std::is_nothrow_constructible<Vector1, Float>::value);
}

void VectorTest::constructConversion() {
    constexpr Vector4 a(1.3f, 2.7f, -15.0f, 7.0f);
    constexpr Vector4i b(a);

    CORRADE_COMPARE(b, Vector4i(1, 2, -15, 7));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!std::is_convertible<Vector4, Vector4i>::value);

    CORRADE_VERIFY(std::is_nothrow_constructible<Vector4, Vector4i>::value);
}

void VectorTest::constructCopy() {
    constexpr Vector4 a(1.0f, 3.5f, 4.0f, -2.7f);
    constexpr Vector4 b(a);
    CORRADE_COMPARE(b, Vector4(1.0f, 3.5f, 4.0f, -2.7f));

    #ifdef CORRADE_STD_IS_TRIVIALLY_TRAITS_SUPPORTED
    CORRADE_VERIFY(std::is_trivially_copy_constructible<Vector4>::value);
    CORRADE_VERIFY(std::is_trivially_copy_assignable<Vector4>::value);
    #endif
    CORRADE_VERIFY(std::is_nothrow_copy_constructible<Vector4>::value);
    CORRADE_VERIFY(std::is_nothrow_copy_assignable<Vector4>::value);
}

void VectorTest::convert() {
    constexpr Vec3 a{1.5f, 2.0f, -3.5f};
    constexpr Vector3 b(1.5f, 2.0f, -3.5f);

    /* GCC 5.1 had a bug: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=66450
       Hopefully this does not reappear. */
    constexpr Vector3 c{a};
    CORRADE_COMPARE(c, b);

    constexpr Vec3 d(b);
    CORRADE_COMPARE(d.x, a.x);
    CORRADE_COMPARE(d.y, a.y);
    CORRADE_COMPARE(d.z, a.z);

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!std::is_convertible<Vec3, Vector3>::value);
    CORRADE_VERIFY(!std::is_convertible<Vector3, Vec3>::value);
}

void VectorTest::isZeroFloat() {
    CORRADE_VERIFY(!Vector3(0.01f, 0.0f, 0.0f).isZero());
    CORRADE_VERIFY(Vector3(0.0f, Math::TypeTraits<float>::epsilon()/2.0f, 0.0f).isZero());
    CORRADE_VERIFY(Vector3(0.0f, 0.0f, 0.0f).isZero());
}

void VectorTest::isZeroInteger() {
    CORRADE_VERIFY(!Math::Vector<3, Int>{0, 1, 0}.isZero());
    CORRADE_VERIFY(Math::Vector<3, Int>{0, 0, 0}.isZero());
}

void VectorTest::isNormalized() {
    CORRADE_VERIFY(!Vector3(1.0f, 2.0f, -1.0f).isNormalized());
    CORRADE_VERIFY(Vector3(0.0f, 1.0f, 0.0f).isNormalized());
}

void VectorTest::data() {
    Vector4 a(4.0f, 5.0f, 6.0f, 7.0f);
    a[2] = 1.0f;
    a[3] = 1.5f;

    CORRADE_COMPARE(a[2], 1.0f);
    CORRADE_COMPARE(a[3], 1.5f);
    CORRADE_COMPARE(a, Vector4(4.0f, 5.0f, 1.0f, 1.5f));

    constexpr Vector4 ca(1.0f, 2.0f, -3.0f, 4.5f);
    constexpr Float f = ca[3];
    CORRADE_COMPARE(f, 4.5f);

    /* Pointer chasings, i.e. *(b.data()[3]), are not possible */
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Apparently dereferencing a pointer is verboten */
    constexpr
    #endif
    Float g = *ca.data();
    CORRADE_COMPARE(a.data()[1], 5.0f);
    CORRADE_COMPARE(g, 1.0f);

    /* It actually returns an array */
    CORRADE_COMPARE(Corrade::Containers::arraySize(a.data()), 4);
    CORRADE_COMPARE(Corrade::Containers::arraySize(ca.data()), 4);
}

void VectorTest::compare() {
    CORRADE_VERIFY(Vector4(1.0f, -3.5f, 5.0f, -10.0f) == Vector4(1.0f + TypeTraits<Float>::epsilon()/2, -3.5f, 5.0f, -10.0f));
    CORRADE_VERIFY(Vector4(1.0f, -1.0f, 5.0f, -10.0f) != Vector4(1.0f, -1.0f + TypeTraits<Float>::epsilon()*2, 5.0f, -10.0f));

    CORRADE_VERIFY(Vector4i(1, -3, 5, -10) == Vector4i(1, -3, 5, -10));
    CORRADE_VERIFY(Vector4i(1, -3, 5, -10) != Vector4i(1, -2, 5, -10));
}

void VectorTest::compareComponentWise() {
    typedef BoolVector<3> BoolVector3;
    typedef BoolVector<4> BoolVector4;

    Vector4 a{1.0f, -3.5f, 5.0f, -10.0f};
    Vector4 b{1.0f + TypeTraits<Float>::epsilon()/2, -3.5f, 5.0f - TypeTraits<Float>::epsilon()*2, -10.0f};
    Vector4 c{1.0f + TypeTraits<Float>::epsilon()*2, -3.5f, 5.0f - TypeTraits<Float>::epsilon()*10, -10.0f};
    CORRADE_COMPARE(equal(a, b), BoolVector4{0xf});
    CORRADE_COMPARE(equal(a, c), BoolVector4{0xa});
    CORRADE_COMPARE(notEqual(a, b), BoolVector4{0x0});
    CORRADE_COMPARE(notEqual(a, c), BoolVector4{0x5});

    CORRADE_COMPARE(Vector3(1.0f, -1.0f, 5.0f) < Vector3(1.1f, -1.0f, 3.0f), BoolVector3(0x1));
    CORRADE_COMPARE(Vector3(1.0f, -1.0f, 5.0f) <= Vector3(1.1f, -1.0f, 3.0f), BoolVector3(0x3));
    CORRADE_COMPARE(Vector3(1.0f, -1.0f, 5.0f) >= Vector3(1.1f, -1.0f, 3.0f), BoolVector3(0x6));
    CORRADE_COMPARE(Vector3(1.0f, -1.0f, 5.0f) > Vector3(1.1f, -1.0f, 3.0f), BoolVector3(0x4));
}

void VectorTest::negative() {
    CORRADE_COMPARE(-Vector4(1.0f, -3.0f, 5.0f, -10.0f), Vector4(-1.0f, 3.0f, -5.0f, 10.0f));
}

void VectorTest::addSubtract() {
    Vector4 a(1.0f, -3.0f, 5.0f, -10.0f);
    Vector4 b(7.5f, 33.0f, -15.0f, 0.0f);
    Vector4 c(8.5f, 30.0f, -10.0f, -10.0f);

    CORRADE_COMPARE(a + b, c);
    CORRADE_COMPARE(c - b, a);
}

void VectorTest::multiplyDivide() {
    Vector4 vector(1.0f, 2.0f, 3.0f, 4.0f);
    Vector4 multiplied(-1.5f, -3.0f, -4.5f, -6.0f);

    CORRADE_COMPARE(vector*-1.5f, multiplied);
    CORRADE_COMPARE(-1.5f*vector, multiplied);
    CORRADE_COMPARE(multiplied/-1.5f, vector);

    /* Divide vector with number and invert */
    Vector4 divisor(1.0f, 2.0f, -4.0f, 8.0f);
    Vector4 result(1.0f, 0.5f, -0.25f, 0.125f);
    CORRADE_COMPARE(1.0f/divisor, result);
}

void VectorTest::multiplyDivideIntegral() {
    Vector4i vector(32, 10, -6, 2);
    Vector4i multiplied(-48, -15, 9, -3);

    CORRADE_COMPARE(vector*-1.5f, multiplied);
    CORRADE_COMPARE(-1.5f*vector, multiplied);

    CORRADE_COMPARE(multiplied/-1.5f, vector);
    /* Using integer vector as divisor is not supported */
}

void VectorTest::multiplyDivideComponentWise() {
    Vector4 vec(1.0f, 2.0f, 3.0f, 4.0f);
    Vector4 multiplier(7.0f, -4.0f, -1.5f, 1.0f);
    Vector4 multiplied(7.0f, -8.0f, -4.5f, 4.0f);

    CORRADE_COMPARE(vec*multiplier, multiplied);
    CORRADE_COMPARE(multiplied/multiplier, vec);
}

void VectorTest::multiplyDivideComponentWiseIntegral() {
    Vector4i vec(7, 2, -16, -1);
    Vector4 multiplier(2.0f, -1.5f, 0.5f, 10.0f);
    Vector4i multiplied(14, -3, -8, -10);

    CORRADE_COMPARE(vec*multiplier, multiplied);
    CORRADE_COMPARE(multiplier*vec, multiplied);

    CORRADE_COMPARE(multiplied/multiplier, vec);
    /* Using integer vector as divisor is not supported */
}

void VectorTest::modulo() {
    typedef Math::Vector<2, Int> Vector2i;

    const Vector2i a(4, 13);
    const Vector2i b(2, 5);
    CORRADE_COMPARE(a % 2, Vector2i(0, 1));
    CORRADE_COMPARE(a % b, Vector2i(0, 3));
}

void VectorTest::bitwise() {
    typedef Math::Vector<2, Int> Vector2i;

    const Vector2i a(85, 240);
    const Vector2i b(170, 85);
    CORRADE_COMPARE(~a, Vector2i(-86, -241));
    CORRADE_COMPARE(a & b, Vector2i(0, 80));
    CORRADE_COMPARE(a | b, Vector2i(255, 245));
    CORRADE_COMPARE(a ^ b, Vector2i(255, 165));

    const Vector2i c(7, 32);
    CORRADE_COMPARE(c << 2, Vector2i(28, 128));
    CORRADE_COMPARE(c >> 2, Vector2i(1, 8));
}

void VectorTest::dot() {
    CORRADE_COMPARE(Math::dot(Vector4{1.0f, 0.5f, 0.75f, 1.5f}, {2.0f, 4.0f, 1.0f, 7.0f}), 15.25f);
}

void VectorTest::dotSelf() {
    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).dot(), 30.0f);
}

void VectorTest::length() {
    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).length(), 5.4772256f);
}

void VectorTest::lengthInverted() {
    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).lengthInverted(), 0.182574f);
}

void VectorTest::normalized() {
    const auto vec = Vector4(1.0f, 1.0f, 1.0f, 1.0f).normalized();
    CORRADE_COMPARE(vec, Vector4(0.5f, 0.5f, 0.5f, 0.5f));
    CORRADE_COMPARE(vec.length(), 1.0f);
}

void VectorTest::resized() {
    const auto vec = Vector4(2.0f, 2.0f, 0.0f, 1.0f).resized(9.0f);
    CORRADE_COMPARE(vec, Vector4(6.0f, 6.0f, 0.0f, 3.0f));
    CORRADE_COMPARE(vec.length(), 9.0f);
}

void VectorTest::sum() {
    CORRADE_COMPARE(Vector3(1.0f, 2.0f, 4.0f).sum(), 7.0f);
}

void VectorTest::product() {
    CORRADE_COMPARE(Vector3(1.0f, 2.0f, 3.0f).product(), 6.0f);
}

void VectorTest::min() {
    /* Check also that initial value isn't initialized to 0 */
    CORRADE_COMPARE(Vector3(1.0f, -2.0f, 3.0f).min(), -2.0f);
}

void VectorTest::max() {
    /* Check also that initial value isn't initialized to 0 */
    CORRADE_COMPARE(Vector3(-1.0f, -2.0f, -3.0f).max(), -1.0f);
}

void VectorTest::minmax() {
    const auto expected = std::make_pair(-3.0f, 2.0f);
    CORRADE_COMPARE((Vector3{-1.0f, 2.0f, -3.0f}.minmax()), expected);
    CORRADE_COMPARE((Vector3{-1.0f, -3.0f, 2.0f}.minmax()), expected);
    CORRADE_COMPARE((Vector3{2.0f, -1.0f, -3.0f}.minmax()), expected);
    CORRADE_COMPARE((Vector3{2.0f, -3.0f, -1.0f}.minmax()), expected);
    CORRADE_COMPARE((Vector3{-3.0f, 2.0f, -1.0f}.minmax()), expected);
    CORRADE_COMPARE((Vector3{-3.0f, -1.0f, 2.0f}.minmax()), expected);
}

void VectorTest::nanIgnoring() {
    Vector3 oneNan{1.0f, Constants::nan(), -3.0f};
    Vector3 firstNan{Constants::nan(), 1.0f, -3.0f};
    Vector3 allNan{Constants::nan(), Constants::nan(), Constants::nan()};

    CORRADE_COMPARE(oneNan.min(), -3.0f);
    CORRADE_COMPARE(firstNan.min(), -3.0f);
    CORRADE_COMPARE(allNan.min(), Constants::nan());

    CORRADE_COMPARE(oneNan.max(), 1.0f);
    CORRADE_COMPARE(firstNan.max(), 1.0f);
    CORRADE_COMPARE(allNan.max(), Constants::nan());

    CORRADE_COMPARE(oneNan.minmax(), std::make_pair(-3.0f, 1.0f));
    CORRADE_COMPARE(firstNan.minmax(), std::make_pair(-3.0f, 1.0f));
    /* Need to compare this way because of NaNs */
    CORRADE_COMPARE(allNan.minmax().first, Constants::nan());
    CORRADE_COMPARE(allNan.minmax().second, Constants::nan());
}

void VectorTest::projected() {
    Vector3 line(1.0f, -1.0f, 0.5f);
    Vector3 projected = Vector3(1.0f, 2.0f, 3.0f).projected(line);

    CORRADE_COMPARE(projected, Vector3(0.222222f, -0.222222f, 0.111111f));
    CORRADE_COMPARE(projected.normalized(), line.normalized());
}

void VectorTest::projectedOntoNormalized() {
    Vector3 vector(1.0f, 2.0f, 3.0f);
    Vector3 line(1.0f, -1.0f, 0.5f);

    Vector3 projected = vector.projectedOntoNormalized(line.normalized());
    CORRADE_COMPARE(projected, Vector3(0.222222f, -0.222222f, 0.111111f));
    CORRADE_COMPARE(projected.normalized(), line.normalized());
    CORRADE_COMPARE(projected, vector.projected(line));
}

void VectorTest::projectedOntoNormalizedNotNormalized() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    Vector3 vector(1.0f, 2.0f, 3.0f);
    Vector3 line(1.0f, -1.0f, 0.5f);

    std::ostringstream out;
    Error redirectError{&out};
    vector.projectedOntoNormalized(line);
    CORRADE_COMPARE(out.str(), "Math::Vector::projectedOntoNormalized(): line Vector(1, -1, 0.5) is not normalized\n");
}

void VectorTest::flipped() {
    constexpr Vector4 vector{1.0f, -3.5f, 2.1f, 0.5f};
    constexpr Vector4 flipped = vector.flipped();
    CORRADE_COMPARE(flipped, (Vector4{0.5f, 2.1f, -3.5f, 1.0f}));
}

void VectorTest::angle() {
    auto a = Vector3{2.0f,  3.0f, 4.0f}.normalized();
    auto b = Vector3{1.0f, -2.0f, 3.0f}.normalized();
    CORRADE_COMPARE(Math::angle(a, b), 1.162514_radf);
    CORRADE_COMPARE(Math::angle(-a, -b), 1.162514_radf);
    CORRADE_COMPARE(Math::angle(-a, b), Rad(180.0_degf) - 1.162514_radf);
    CORRADE_COMPARE(Math::angle(a, -b), Rad(180.0_degf) - 1.162514_radf);

    /* Same / opposite. Well, almost. It's interesting how imprecise
       normalization can get. */
    CORRADE_COMPARE_WITH(Math::angle(a, a), 0.0_radf,
        Corrade::TestSuite::Compare::around(0.0005_radf));
    CORRADE_COMPARE_WITH(Math::angle(a, -a), 180.0_degf,
        Corrade::TestSuite::Compare::around(0.0005_radf));
}

void VectorTest::angleNormalizedButOver1() {
    /* This vector *is* normalized, but its length is larger than 1, which
       would cause acos() to return a NaN. Ensure it's clamped to correct range
       before passing it there. */
    Vector3 a{1.0f + Math::TypeTraits<Float>::epsilon()/2,  0.0f, 0.0f};
    CORRADE_VERIFY(a.isNormalized());

    CORRADE_COMPARE(Math::angle(a, a), 0.0_radf);
    CORRADE_COMPARE(Math::angle(a, -a), 180.0_degf);
}

void VectorTest::angleNotNormalized() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};
    Math::angle(Vector3(2.0f, 3.0f, 4.0f).normalized(), {1.0f, -2.0f, 3.0f});
    Math::angle({2.0f, 3.0f, 4.0f}, Vector3(1.0f, -2.0f, 3.0f).normalized());

    CORRADE_COMPARE(out.str(),
        "Math::angle(): vectors Vector(0.371391, 0.557086, 0.742781) and Vector(1, -2, 3) are not normalized\n"
        "Math::angle(): vectors Vector(2, 3, 4) and Vector(0.267261, -0.534522, 0.801784) are not normalized\n");
}

template<class T> class BasicVec2: public Math::Vector<2, T> {
    public:
        template<class ...U> constexpr BasicVec2(U&&... args): Math::Vector<2, T>{args...} {}

        MAGNUM_VECTOR_SUBCLASS_IMPLEMENTATION(2, BasicVec2)
};

MAGNUM_VECTORn_OPERATOR_IMPLEMENTATION(2, BasicVec2)

typedef BasicVec2<Float> Vec2;
typedef BasicVec2<Int> Vec2i;

void VectorTest::subclassTypes() {
    Float* const data = nullptr;
    const Float* const cdata = nullptr;
    CORRADE_VERIFY(std::is_same<decltype(Vec2::from(data)), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(Vec2::from(cdata)), const Vec2&>::value);

    Vector<1, Float> one;
    CORRADE_VERIFY(std::is_same<decltype(Vec2::pad(one)), Vec2>::value);

    /* Const operators */
    const Vec2 c;
    const Vec2 c2;
    CORRADE_VERIFY(std::is_same<decltype(-c), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c + c), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c*1.0f), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(1.0f*c), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c/1.0f), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(1.0f/c), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c*c2), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c/c2), Vec2>::value);

    /* Assignment operators */
    Vec2 a;
    CORRADE_VERIFY(std::is_same<decltype(a = c), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a += c), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a -= c), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a *= 1.0f), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a /= 1.0f), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a *= c), Vec2&>::value);
    CORRADE_VERIFY(std::is_same<decltype(a /= c), Vec2&>::value);

    /* Modulo operations */
    const Vec2i ci;
    Vec2i i;
    const Int j = {};
    CORRADE_VERIFY(std::is_same<decltype(ci % j), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(i %= j), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci % ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(i %= ci), Vec2i&>::value);

    /* Bitwise operations */
    CORRADE_VERIFY(std::is_same<decltype(~ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci & ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci | ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci ^ ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci << 1), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci >> 1), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(i &= ci), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(i |= ci), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(i ^= ci), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(i <<= 1), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(i >>= 1), Vec2i&>::value);

    /* Integer multiplication/division */
    CORRADE_VERIFY(std::is_same<decltype(ci*1.0f), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(1.0f*ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(c*ci), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci*c), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(ci/c), Vec2i>::value);
    CORRADE_VERIFY(std::is_same<decltype(i *= c), Vec2i&>::value);
    CORRADE_VERIFY(std::is_same<decltype(i /= c), Vec2i&>::value);

    /* Functions */
    CORRADE_VERIFY(std::is_same<decltype(c.normalized()), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c.resized(1.0f)), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c.projected(c2)), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c.projectedOntoNormalized(c2)), Vec2>::value);
    CORRADE_VERIFY(std::is_same<decltype(c.flipped()), Vec2>::value);
}

void VectorTest::subclass() {
    Float data[] = {1.0f, -2.0f};
    CORRADE_COMPARE(Vec2::from(data), Vec2(1.0f, -2.0f));

    const Float cdata[] = {1.0f, -2.0f};
    CORRADE_COMPARE(Vec2::from(cdata), Vec2(1.0f, -2.0f));

    {
        constexpr Vector<1, Float> a = 5.0f;
        #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
        constexpr
        #endif
        Vec2 b = Vec2::pad(a);
        #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
        constexpr
        #endif
        Vec2 c = Vec2::pad(a, -1.0f);
        CORRADE_COMPARE(b, Vec2(5.0f, 0.0f));
        CORRADE_COMPARE(c, Vec2(5.0f, -1.0f));
    }

    /* Constexpr constructor */
    constexpr const Vec2 a{-2.0f, 5.0f};
    CORRADE_COMPARE(a[0], -2.0f);

    CORRADE_COMPARE(-Vec2(-2.0f, 5.0f), Vec2(2.0f, -5.0f));
    CORRADE_COMPARE(Vec2(-2.0f, 5.0f) + Vec2(1.0f, -3.0f), Vec2(-1.0f, 2.0f));
    CORRADE_COMPARE(Vec2(-2.0f, 5.0f) - Vec2(1.0f, -3.0f), Vec2(-3.0f, 8.0f));

    CORRADE_COMPARE(Vec2(-2.0f, 5.0f)*2.0f, Vec2(-4.0f, 10.0f));
    CORRADE_COMPARE(2.0f*Vec2(-2.0f, 5.0f), Vec2(-4.0f, 10.0f));
    CORRADE_COMPARE(Vec2(-2.0f, 5.0f)/0.5f, Vec2(-4.0f, 10.0f));
    CORRADE_COMPARE(2.0f/Vec2(-2.0f, 5.0f), Vec2(-1.0f, 0.4f));

    CORRADE_COMPARE(Vec2(-2.0f, 5.0f)*Vec2(1.5f, -2.0f), Vec2(-3.0f, -10.0f));
    CORRADE_COMPARE(Vec2(-2.0f, 5.0f)/Vec2(2.0f/3.0f, -0.5f), Vec2(-3.0f, -10.0f));

    /* No need to test in-place operators as the other ones are implemented
       using them */

    /* Modulo operations */
    CORRADE_COMPARE(Vec2i(4, 13) % 2, Vec2i(0, 1));
    CORRADE_COMPARE(Vec2i(4, 13) % Vec2i(2, 5), Vec2i(0, 3));

    /* Bitwise operations */
    CORRADE_COMPARE(~Vec2i(85, 240), Vec2i(-86, -241));
    CORRADE_COMPARE(Vec2i(85, 240) & Vec2i(170, 85), Vec2i(0, 80));
    CORRADE_COMPARE(Vec2i(85, 240) | Vec2i(170, 85), Vec2i(255, 245));
    CORRADE_COMPARE(Vec2i(85, 240) ^ Vec2i(170, 85), Vec2i(255, 165));

    CORRADE_COMPARE(Vec2i(7, 32) << 2, Vec2i(28, 128));
    CORRADE_COMPARE(Vec2i(7, 32) >> 2, Vec2i(1, 8));

    /* Integral multiplication/division */
    CORRADE_COMPARE(Vec2i(2, 4)*1.5f, Vec2i(3, 6));
    CORRADE_COMPARE(1.5f*Vec2i(2, 4), Vec2i(3, 6));
    {
        #ifdef CORRADE_TARGET_EMSCRIPTEN
        CORRADE_EXPECT_FAIL_IF(Vec2i(2, 4)/(2.0f/3.0f) == Vec2i(2, 5),
            "Emscripten -O1 misoptimizes the following (-O2 works).");
        #endif
        CORRADE_COMPARE(Vec2i(2, 4)/(2.0f/3.0f), Vec2i(3, 6));
    }

    CORRADE_COMPARE(Vec2i(2, 4)*Vec2(-1.5f, 0.5f), Vec2i(-3, 2));
    CORRADE_COMPARE(Vec2(-1.5f, 0.5f)*Vec2i(2, 4), Vec2i(-3, 2));
    {
        #ifdef CORRADE_TARGET_EMSCRIPTEN
        CORRADE_EXPECT_FAIL_IF(Vec2i(2, 4)/Vec2(-2.0f/3.0f, 2.0f) == Vec2i(-2, 2),
            "Emscripten -O1 misoptimizes the following (-O2 works).");
        #endif
        CORRADE_COMPARE(Vec2i(2, 4)/Vec2(-2.0f/3.0f, 2.0f), Vec2i(-3, 2));
    }

    /* Functions */
    CORRADE_COMPARE(Vec2(3.0f, 0.0f).normalized(), Vec2(1.0f, 0.0f));
    CORRADE_COMPARE(Vec2(3.0f, 0.0f).resized(6.0f), Vec2(6.0f, 0.0f));
    CORRADE_COMPARE(Vec2(1.0f, 1.0f).projected({0.0f, 2.0f}), Vec2(0.0f, 1.0f));
    CORRADE_COMPARE(Vec2(1.0f, 1.0f).projectedOntoNormalized({0.0f, 1.0f}), Vec2(0.0f, 1.0f));
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vec2 flipped = Vec2{1.0f, 0.4f}.flipped();
    CORRADE_COMPARE(flipped, (Vec2{0.4f, 1.0f}));
}

void VectorTest::strictWeakOrdering() {
    StrictWeakOrdering o;

    const Vector2 v2a{1.0f, 2.0f};
    const Vector2 v2b{2.0f, 3.0f};
    const Vector2 v2c{1.0f, 3.0f};

    CORRADE_VERIFY( o(v2a, v2b));
    CORRADE_VERIFY(!o(v2b, v2a));
    CORRADE_VERIFY( o(v2a, v2c));
    CORRADE_VERIFY(!o(v2c, v2a));
    CORRADE_VERIFY( o(v2c, v2b));
    CORRADE_VERIFY(!o(v2b, v2c));

    CORRADE_VERIFY(!o(v2a, v2a));

    const Vector3 v3a{1.0f, 2.0f, 3.0f};
    const Vector3 v3b{2.0f, 3.0f, 4.0f};
    const Vector3 v3c{1.0f, 2.0f, 4.0f};

    CORRADE_VERIFY( o(v3a, v3b));
    CORRADE_VERIFY(!o(v3b, v3a));
    CORRADE_VERIFY( o(v3a, v3c));
    CORRADE_VERIFY(!o(v3c, v3a));
    CORRADE_VERIFY( o(v3c, v3b));
    CORRADE_VERIFY(!o(v3b, v3c));

    CORRADE_VERIFY(!o(v3a, v3a));

    const Vector4 v4a{1.0f, 2.0f, 3.0f, 4.0f};
    const Vector4 v4b{2.0f, 3.0f, 4.0f, 5.0f};
    const Vector4 v4c{1.0f, 2.0f, 3.0f, 5.0f};

    CORRADE_VERIFY( o(v4a, v4b));
    CORRADE_VERIFY(!o(v4b, v4a));
    CORRADE_VERIFY( o(v4a, v4c));
    CORRADE_VERIFY(!o(v4c, v4a));
    CORRADE_VERIFY( o(v4c, v4b));
    CORRADE_VERIFY(!o(v4b, v4c));

    CORRADE_VERIFY(!o(v4a, v4a));
}

void VectorTest::debug() {
    std::ostringstream o;
    Debug(&o) << Vector4(0.5f, 15.0f, 1.0f, 1.0f);
    CORRADE_COMPARE(o.str(), "Vector(0.5, 15, 1, 1)\n");

    o.str({});
    Debug(&o) << "a" << Vector4() << "b" << Vector4();
    CORRADE_COMPARE(o.str(), "a Vector(0, 0, 0, 0) b Vector(0, 0, 0, 0)\n");
}

void VectorTest::debugPacked() {
    std::ostringstream out;
    /* Second is not packed, the first should not make any flags persistent */
    Debug{&out} << Debug::packed << Vector4(0.5f, 15.0f, 1.0f, 1.0f) << Vector4();
    CORRADE_COMPARE(out.str(), "{0.5, 15, 1, 1} Vector(0, 0, 0, 0)\n");
}

}}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::VectorTest)