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

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016
              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
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    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 "Magnum/Math/Dual.h"
#include "Magnum/Math/Vector2.h"

namespace Magnum { namespace Math { namespace Test {

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

    void construct();
    void constructDefault();
    void constructNoInit();
    void constructConversion();
    void constructCopy();

    void compare();

    void addSubtract();
    void negated();
    void multiplyDivide();
    void multiplyDivideScalar();
    void multiplyDivideDifferentType();

    void conjugated();
    void sqrt();

    void sincos();
    void sincosWithBase();

    void subclassTypes();
    void subclass();

    void debug();
};

typedef Math::Dual<Float> Dual;
typedef Math::Vector2<Float> Vector2;
typedef Math::Dual<Vector2> DualVector2;
typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Constants<Float> Constants;

using namespace Literals;

DualTest::DualTest() {
    addTests({&DualTest::construct,
              &DualTest::constructDefault,
              &DualTest::constructNoInit,
              &DualTest::constructConversion,
              &DualTest::constructCopy,

              &DualTest::compare,

              &DualTest::addSubtract,
              &DualTest::negated,
              &DualTest::multiplyDivide,
              &DualTest::multiplyDivideScalar,
              &DualTest::multiplyDivideDifferentType,

              &DualTest::conjugated,
              &DualTest::sqrt,

              &DualTest::sincos,
              &DualTest::sincosWithBase,

              &DualTest::subclassTypes,
              &DualTest::subclass,

              &DualTest::debug});
}

void DualTest::construct() {
    constexpr Dual a = {2.0f, -7.5f};
    constexpr Float b = a.real();
    constexpr Float c = a.dual();
    CORRADE_COMPARE(b, 2.0f);
    CORRADE_COMPARE(c, -7.5f);

    constexpr Dual d(3.0f);
    CORRADE_COMPARE(d.real(), 3.0f);
    CORRADE_COMPARE(d.dual(), 0.0f);
}

void DualTest::constructDefault() {
    constexpr Dual a;
    CORRADE_COMPARE(a, Dual(0.0f, 0.0f));
}

void DualTest::constructNoInit() {
    Dual a{2.0f, -7.5f};
    new(&a) Dual{NoInit};
    CORRADE_COMPARE(a, Dual(2.0f, -7.5f));
}

void DualTest::constructConversion() {
    typedef Math::Dual<Int> Duali;

    constexpr Dual a{1.3f, 2.7f};
    constexpr Duali b{a};

    CORRADE_COMPARE(b, (Duali{1, 2}));

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

void DualTest::constructCopy() {
    constexpr Dual a(2.0f, 3.0f);
    constexpr Dual b(a);
    CORRADE_COMPARE(b, Dual(2.0f, 3.0f));
}

void DualTest::compare() {
    CORRADE_VERIFY(Dual(1.0f, 1.0f+TypeTraits<Float>::epsilon()/2) == Dual(1.0f, 1.0f));
    CORRADE_VERIFY(Dual(1.0f, 1.0f+TypeTraits<Float>::epsilon()*2) != Dual(1.0f, 1.0f));
    CORRADE_VERIFY(Dual(1.0f+TypeTraits<Float>::epsilon()/2, 1.0f) == Dual(1.0f, 1.0f));
    CORRADE_VERIFY(Dual(1.0f+TypeTraits<Float>::epsilon()*2, 1.0f) != Dual(1.0f, 1.0f));

    /* Compare to real part only */
    CORRADE_VERIFY(Dual(1.0f, 0.0f) == 1.0f);
    CORRADE_VERIFY(Dual(1.0f, 3.0f) != 1.0f);
}

void DualTest::addSubtract() {
    Dual a(2.0f, -7.5f);
    Dual b(-3.3f, 0.2f);
    Dual c(-1.3f, -7.3f);

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

void DualTest::negated() {
    CORRADE_COMPARE(-Dual(1.0f, -6.5f), Dual(-1.0f, 6.5f));
}

void DualTest::multiplyDivide() {
    Dual a(1.5f, -4.0f);
    Dual b(-2.0f, 0.5f);
    Dual c(-3.0f, 8.75f);

    CORRADE_COMPARE(a*b, c);
    CORRADE_COMPARE(c/b, a);
}

void DualTest::multiplyDivideScalar() {
    Dual a{1.5f, -4.0f};
    Dual b{-3.0f, 8.0f};

    CORRADE_COMPARE(a*-2.0f, b);
    CORRADE_COMPARE(-2.0f*a, b);
    CORRADE_COMPARE(b/-2.0f, a);
}

void DualTest::multiplyDivideDifferentType() {
    DualVector2 a{{1.5f, 2.0f}, {-4.0f, 1.3f}};
    Dual b{-2.0f, 0.5f};
    DualVector2 c{{-3.0f, -4.0f}, {8.75f, -1.6f}};
    DualVector2 d{{-2.0f/1.5f, -1.0f}, {-7.25f/2.25f, 3.6f/4.0f}};

    CORRADE_COMPARE(a*b, c);
    CORRADE_COMPARE(b*a, c);
    CORRADE_COMPARE(c/b, a);
    CORRADE_COMPARE(b/a, d);
}

void DualTest::conjugated() {
    CORRADE_COMPARE(Dual(1.0f, -6.5f).conjugated(), Dual(1.0f, 6.5f));
}

void DualTest::sqrt() {
    CORRADE_COMPARE(Math::sqrt(Dual(16.0f, 2.0f)), Dual(4.0f, 0.25f));
}

void DualTest::sincos() {
    const auto result = std::make_pair(
        Dual(0.5f, 0.8660254037844386f*Constants::pi()/2),
        Dual(0.8660254037844386f, -0.5f*Constants::pi()/2));
    CORRADE_COMPARE(Math::sincos(Math::Dual<Deg>(30.0_degf, 90.0_degf)), result);
    CORRADE_COMPARE(Math::sincos(Math::Dual<Rad>(Rad(Constants::pi()/6), Rad(Constants::pi()/2))), result);
}

void DualTest::sincosWithBase() {
    /* Verify that the functions can be called with Dual<Unit<Deg, T>> and Dual<Unit<Rad, T>> */
    CORRADE_VERIFY((std::is_same<decltype(2*Math::Dual<Deg>{15.0_degf}), Math::Dual<Unit<Math::Deg, Float>>>::value));
    CORRADE_VERIFY((std::is_same<decltype(2*Math::Dual<Rad>{Rad{Constants::pi()/12}}), Math::Dual<Unit<Math::Rad, Float>>>::value));

    const auto result = std::make_pair(
        Dual(0.5f, 0.8660254037844386f*Constants::pi()/2),
        Dual(0.8660254037844386f, -0.5f*Constants::pi()/2));
    CORRADE_COMPARE(Math::sincos(2*Math::Dual<Deg>(15.0_degf, 45.0_degf)), result);
    CORRADE_COMPARE(Math::sincos(2*Math::Dual<Rad>(Rad(Constants::pi()/12), Rad(Constants::pi()/4))), result);
}

namespace {

template<class T> class BasicDualVec2: public Math::Dual<Math::Vector2<T>> {
    public:
        /* MSVC 2015 can't handle {} here */
        template<class ...U> constexpr BasicDualVec2(U&&... args): Math::Dual<Math::Vector2<T>>(args...) {}

        MAGNUM_DUAL_SUBCLASS_IMPLEMENTATION(BasicDualVec2, Math::Vector2, T)
        MAGNUM_DUAL_SUBCLASS_MULTIPLICATION_IMPLEMENTATION(BasicDualVec2, Math::Vector2)
};

MAGNUM_DUAL_OPERATOR_IMPLEMENTATION(BasicDualVec2, Math::Vector2, T)

typedef BasicDualVec2<Float> DualVec2;

}

void DualTest::subclassTypes() {
    const DualVec2 a;
    CORRADE_VERIFY((std::is_same<decltype(-a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a + a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a - a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a*a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a/a), DualVec2>::value));

    DualVec2 b;
    CORRADE_VERIFY((std::is_same<decltype(b += a), DualVec2&>::value));
    CORRADE_VERIFY((std::is_same<decltype(b -= a), DualVec2&>::value));

    const Dual c;
    CORRADE_VERIFY((std::is_same<decltype(a*c), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c*a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a/c), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c/a), DualVec2>::value));

    CORRADE_VERIFY((std::is_same<decltype(a*5.0f), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(5.0f*a), DualVec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a/5.0f), DualVec2>::value));
}

void DualTest::subclass() {
    const DualVec2 a{Vector2{1.5f,  2.0f}, Vector2{-4.0f,  1.3f}};
    const DualVec2 b{Vector2{3.0f, -1.2f}, Vector2{ 0.2f, -1.0f}};
    const DualVec2 c{Vector2{4.5f,  0.8f}, Vector2{-3.8f,  0.3f}};
    const DualVec2 d{Vector2{4.5f, -2.4f}, Vector2{-11.7f, -3.56f}};

    CORRADE_COMPARE(-a, (DualVec2{Vector2{-1.5f, -2.0f}, Vector2{4.0f, -1.3f}}));
    CORRADE_COMPARE(a + b, c);
    CORRADE_COMPARE(c - b, a);
    CORRADE_COMPARE(a*b, d);
    CORRADE_COMPARE(d/b, a);

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

    const Dual e{-2.0f, 0.5f};
    const DualVec2 f{Vector2{-3.0f, -4.0f}, Vector2{8.75f, -1.6f}};
    const DualVec2 g{Vector2{-2.0f/1.5f, -1.0f}, Vector2{-7.25f/2.25f, 3.6f/4.0f}};
    CORRADE_COMPARE(a*e, f);
    CORRADE_COMPARE(e*a, f);
    CORRADE_COMPARE(f/e, a);
    CORRADE_COMPARE(e/a, g);

    const DualVec2 h{Vector2{-3.0f, -4.0f}, Vector2{8.0f, -2.6f}};
    CORRADE_COMPARE(a*-2.0f, h);
    CORRADE_COMPARE(-2.0f*a, h);
    CORRADE_COMPARE(h/-2.0f, a);
}

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

    Debug(&o) << Dual(2.5f, -0.3f);
    CORRADE_COMPARE(o.str(), "Dual(2.5, -0.3)\n");
}

}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::DualTest)