/*******************************************************************************
 * This file is part of the "https://github.com/blackmatov/vmath.hpp"
 * For conditions of distribution and use, see copyright notice in LICENSE.md
 * Copyright (C) 2020-2021, by Matvey Cherevko (blackmatov@gmail.com)
 ******************************************************************************/

#include "vmath_tests.hpp"
#include "catch/catch.hpp"

#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>

namespace
{
    using namespace vmath_hpp;
    using namespace vmath_tests;

    constexpr float pi = radians(180.f);
    constexpr float pi_2 = radians(90.f);
    constexpr float pi_4 = radians(45.f);
}

TEST_CASE("vmath/ext") {
    SECTION("units") {
        STATIC_REQUIRE(zero2<int> == int2(0,0));
        STATIC_REQUIRE(zero3<int> == int3(0,0,0));
        STATIC_REQUIRE(zero4<int> == int4(0,0,0,0));

        STATIC_REQUIRE(unit2<int> == int2(1,1));
        STATIC_REQUIRE(unit2_x<int> == int2(1,0));
        STATIC_REQUIRE(unit2_y<int> == int2(0,1));

        STATIC_REQUIRE(unit3<int> == int3(1,1,1));
        STATIC_REQUIRE(unit3_x<int> == int3(1,0,0));
        STATIC_REQUIRE(unit3_y<int> == int3(0,1,0));
        STATIC_REQUIRE(unit3_z<int> == int3(0,0,1));

        STATIC_REQUIRE(unit4<int> == int4(1,1,1,1));
        STATIC_REQUIRE(unit4_x<int> == int4(1,0,0,0));
        STATIC_REQUIRE(unit4_y<int> == int4(0,1,0,0));
        STATIC_REQUIRE(unit4_z<int> == int4(0,0,1,0));
        STATIC_REQUIRE(unit4_w<int> == int4(0,0,0,1));

        STATIC_REQUIRE(zero2x2<int> == int2x2(0,0,0,0));
        STATIC_REQUIRE(zero3x3<int> == int3x3(0,0,0,0,0,0,0,0,0));
        STATIC_REQUIRE(zero4x4<int> == int4x4(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0));

        STATIC_REQUIRE(unit2x2<int> == int2x2(1,1,1,1));
        STATIC_REQUIRE(unit3x3<int> == int3x3(1,1,1,1,1,1,1,1,1));
        STATIC_REQUIRE(unit4x4<int> == int4x4(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1));

        STATIC_REQUIRE(identity2x2<int> == int2x2());
        STATIC_REQUIRE(identity3x3<int> == int3x3());
        STATIC_REQUIRE(identity4x4<int> == int4x4());
    }

    SECTION("vector hash") {
        REQUIRE(std::hash<int2>{}({1,2}) == std::hash<int2>{}({1,2}));
        REQUIRE_FALSE(std::hash<int2>{}({1,2}) == std::hash<int2>{}({2,1}));

        REQUIRE(std::hash<int3>{}({1,2,3}) == std::hash<int3>{}({1,2,3}));
        REQUIRE_FALSE(std::hash<int3>{}({1,2,3}) == std::hash<int3>{}({3,2,1}));

        REQUIRE(std::hash<int4>{}({1,2,3,4}) == std::hash<int4>{}({1,2,3,4}));
        REQUIRE_FALSE(std::hash<int4>{}({1,2,3,4}) == std::hash<int4>{}({3,2,1,4}));

        {
            std::set<int2> s;
            s.insert(int2(1,2));
            REQUIRE(s.count(int2(1,2)) > 0);
            REQUIRE_FALSE(s.count(int2(1,1)) > 0);
        }
        {
            std::map<int2, int> s;
            s.emplace(int2(1,2),3);
            s.emplace(int2(2,3),5);
            REQUIRE(s[int2(1,2)] == 3);
            REQUIRE(s[int2(2,3)] == 5);
        }
        {
            std::unordered_set<int2> s;
            s.insert(int2(1,2));
            REQUIRE(s.count(int2(1,2)) > 0);
            REQUIRE_FALSE(s.count(int2(1,1)) > 0);
        }
        {
            std::unordered_map<int2, int> s;
            s.emplace(int2(1,2),3);
            s.emplace(int2(2,3),5);
            REQUIRE(s[int2(1,2)] == 3);
            REQUIRE(s[int2(2,3)] == 5);
        }
    }

    SECTION("matrix hash") {
        REQUIRE(std::hash<int2x2>{}({1,2,3,4}) == std::hash<int2x2>{}({1,2,3,4}));
        REQUIRE_FALSE(std::hash<int2x2>{}({1,2,3,4}) == std::hash<int2x2>{}({1,2,4,3}));

        {
            std::set<int2x2> s;
            s.insert(int2x2(1,2,3,4));
            REQUIRE(s.count(int2x2(1,2,3,4)) > 0);
            REQUIRE_FALSE(s.count(int2x2(1,1,1,1)) > 0);
        }
        {
            std::map<int2x2, int> s;
            s.emplace(int2x2(1,2,3,4),3);
            s.emplace(int2x2(2,3,4,5),5);
            REQUIRE(s[int2x2(1,2,3,4)] == 3);
            REQUIRE(s[int2x2(2,3,4,5)] == 5);
        }
        {
            std::unordered_set<int2x2> s;
            s.insert(int2x2(1,2,3,4));
            REQUIRE(s.count(int2x2(1,2,3,4)) > 0);
            REQUIRE_FALSE(s.count(int2x2(1,1,1,1)) > 0);
        }
        {
            std::unordered_map<int2x2, int> s;
            s.emplace(int2x2(1,2,3,4),3);
            s.emplace(int2x2(2,3,4,5),5);
            REQUIRE(s[int2x2(1,2,3,4)] == 3);
            REQUIRE(s[int2x2(2,3,4,5)] == 5);
        }
    }

    SECTION("quaternion hash") {
        REQUIRE(std::hash<fqua>{}({1,2,3,4}) == std::hash<fqua>{}({1,2,3,4}));
        REQUIRE_FALSE(std::hash<fqua>{}({1,2,3,4}) == std::hash<fqua>{}({3,2,1,4}));

        {
            std::set<qua<int>> s;
            s.insert(qua(1,2,3,4));
            REQUIRE(s.count(qua(1,2,3,4)) > 0);
            REQUIRE_FALSE(s.count(qua(1,1,1,1)) > 0);
        }
        {
            std::map<qua<int>, int> s;
            s.emplace(qua(1,2,3,4),3);
            s.emplace(qua(2,3,4,5),5);
            REQUIRE(s[qua(1,2,3,4)] == 3);
            REQUIRE(s[qua(2,3,4,5)] == 5);
        }
        {
            std::unordered_set<qua<int>> s;
            s.insert(qua(1,2,3,4));
            REQUIRE(s.count(qua(1,2,3,4)) > 0);
            REQUIRE_FALSE(s.count(qua(1,1,1,1)) > 0);
        }
        {
            std::unordered_map<qua<int>, int> s;
            s.emplace(qua(1,2,3,4),3);
            s.emplace(qua(2,3,4,5),5);
            REQUIRE(s[qua(1,2,3,4)] == 3);
            REQUIRE(s[qua(2,3,4,5)] == 5);
        }
    }

    SECTION("cast_to") {
        {
            constexpr auto i = cast_to<int>(1.5f);
            STATIC_REQUIRE(i == 1);
            STATIC_REQUIRE(std::is_same_v<decltype(i), const int>);
        }
        {
            constexpr auto v = cast_to<int>(float2{1.5f});
            STATIC_REQUIRE(v == int2(1));
            STATIC_REQUIRE(std::is_same_v<decltype(v)::component_type, int>);
        }
        {
            constexpr auto m = cast_to<int>(float2x2{1.5f});
            STATIC_REQUIRE(m == int2x2(1));
            STATIC_REQUIRE(std::is_same_v<decltype(m)::row_type, int2>);
        }
        {
            constexpr auto v = cast_to<int>(fqua{1.5f, 2.2f, 3.6f, 4.5f});
            STATIC_REQUIRE(v == qua(1,2,3,4));
            STATIC_REQUIRE(std::is_same_v<decltype(v)::component_type, int>);
        }
    }

    SECTION("component") {
        STATIC_REQUIRE(component(int2{1,2}, 0) == 1);
        STATIC_REQUIRE(component(int2{1,2}, 1) == 2);

        STATIC_REQUIRE(component(int2{0,0}, 0, 1) == int2{1,0});
        STATIC_REQUIRE(component(int2{0,0}, 1, 2) == int2{0,2});
    }

    SECTION("row") {
        STATIC_REQUIRE(row(int2x2(1,2,3,4), 0) == int2(1,2));
        STATIC_REQUIRE(row(int2x2(1,2,3,4), 1) == int2(3,4));

        STATIC_REQUIRE(row(int2x2(), 0, {1,2}) == int2x2(1,2,0,1));
        STATIC_REQUIRE(row(int2x2(), 1, {3,4}) == int2x2(1,0,3,4));
    }

    SECTION("column") {
        STATIC_REQUIRE(column(int2x2(1,2,3,4), 0) == int2(1,3));
        STATIC_REQUIRE(column(int2x2(1,2,3,4), 1) == int2(2,4));

        STATIC_REQUIRE(column(int2x2(), 0, {2,3}) == int2x2(2,0,3,1));
        STATIC_REQUIRE(column(int2x2(), 1, {3,4}) == int2x2(1,3,0,4));
    }

    SECTION("real") {
        STATIC_REQUIRE(real(qua{1,2,3,4}) == 4);
        STATIC_REQUIRE(real(qua{1,2,3,4}, 5) == qua{1,2,3,5});
    }

    SECTION("imag") {
        STATIC_REQUIRE(imag(qua{1,2,3,4}) == vec{1,2,3});
        STATIC_REQUIRE(imag(qua{1,2,3,4}, {4,3,2}) == qua{4,3,2,4});
    }

    SECTION("matrix translate") {
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * translate(float2{1.f,2.f}) == uapprox3(3.f,5.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * translate(translate(float2{1.f,2.f}), float2{1.f,2.f}) == uapprox3(4.f,7.f,1.f));

        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * translate(float3{1.f,2.f,3.f}) == uapprox4(3.f,5.f,7.f,1.f));
        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * translate(translate(float3{1.f,2.f,3.f}), float3{1.f,2.f,3.f}) == uapprox4(4.f,7.f,10.f,1.f));
    }

    SECTION("matrix rotate") {
        REQUIRE(float4(0.f,1.f,0.f,1.f) * rotate_x(pi_2) == uapprox4(0.f,0.f,1.f,1.f));
        REQUIRE(float4(0.f,0.f,1.f,1.f) * rotate_y(pi_2) == uapprox4(1.f,0.f,0.f,1.f));
        REQUIRE(float4(1.f,0.f,0.f,1.f) * rotate_z(pi_2) == uapprox4(0.f,1.f,0.f,1.f));

        REQUIRE(float4(0.f,1.f,0.f,1.f) * rotate_x(rotate_x(pi_4),pi_4) == uapprox4(0.f,0.f,1.f,1.f));
        REQUIRE(float4(0.f,0.f,1.f,1.f) * rotate_y(rotate_y(pi_4),pi_4) == uapprox4(1.f,0.f,0.f,1.f));
        REQUIRE(float4(1.f,0.f,0.f,1.f) * rotate_z(rotate_z(pi_4),pi_4) == uapprox4(0.f,1.f,0.f,1.f));

        REQUIRE(float3(2.f,3.f,1.f) * rotate(pi) == uapprox3(-2.f,-3.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(pi,{0.f,0.f,1.f}) == uapprox4(-2.f,-3.f,4.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(pi,float3{0.f,0.f,1.f}) == uapprox4(-2.f,-3.f,4.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(qrotate(pi,float3{0.f,0.f,1.f})) == uapprox4(-2.f,-3.f,4.f,1.f));

        REQUIRE(float3(2.f,3.f,1.f) * rotate(rotate(pi_2),pi_2) == uapprox3(-2.f,-3.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(rotate(pi_2,{0.f,0.f,1.f}),pi_2,{0.f,0.f,1.f}) == uapprox4(-2.f,-3.f,4.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(rotate(pi_2,float3{0.f,0.f,1.f}),pi_2,float3{0.f,0.f,1.f}) == uapprox4(-2.f,-3.f,4.f,1.f));
        REQUIRE(float4(2.f,3.f,4.f,1.f) * rotate(rotate(qrotate(pi_2,float3{0.f,0.f,1.f})),qrotate(pi_2,float3{0.f,0.f,1.f})) == uapprox4(-2.f,-3.f,4.f,1.f));
    }

    SECTION("matrix scale") {
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * scale(float2{2.f,3.f}) == uapprox3(4.f,9.f,1.f));
        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * scale(float3{2.f,3.f,4.f}) == uapprox4(4.f,9.f,16.f,1.f));
        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * scale(float3{2.f,3.f,4.f}) == uapprox4(4.f,9.f,16.f,1.f));

        STATIC_REQUIRE(float3(2.f,3.f,1.f) * scale(scale(float2{2.f,2.f}), {2.f,3.f}) == uapprox3(8.f,18.f,1.f));
        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * scale(scale(float3{2.f,2.f,2.f}), {2.f,3.f,4.f}) == uapprox4(8.f,18.f,32.f,1.f));
        STATIC_REQUIRE(float4(2.f,3.f,4.f,1.f) * scale(scale(float3{2.f,2.f,2.f}), float3{2.f,3.f,4.f}) == uapprox4(8.f,18.f,32.f,1.f));
    }

    SECTION("matrix shear") {
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_x(0.f) == uapprox3(2.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_x(1.f) == uapprox3(5.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_x(2.f) == uapprox3(8.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_x(shear_x(1.f),1.f) == uapprox3(8.f,3.f,1.f));

        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_y(0.f) == uapprox3(2.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_y(1.f) == uapprox3(2.f,5.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_y(2.f) == uapprox3(2.f,7.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear_y(shear_y(1.f),1.f) == uapprox3(2.f,7.f,1.f));

        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear(float2(0.f,0.f)) == uapprox3(2.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear(float2(2.f,0.f)) == uapprox3(8.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear(float2(0.f,2.f)) == uapprox3(2.f,7.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear(shear(float2(1.f,0.f)),float2(1.f,0.f)) == uapprox3(8.f,3.f,1.f));
        STATIC_REQUIRE(float3(2.f,3.f,1.f) * shear(shear(float2(0.f,1.f)),float2(0.f,1.f)) == uapprox3(2.f,7.f,1.f));
    }

    SECTION("matrix orthographic") {
        REQUIRE(all(approx(
            orthographic_lh(800.f, 600.f, 5.f, 10.f),
            scale(1.f,1.f,-1.f) * orthographic_rh(800.f, 600.f, 5.f, 10.f))));

        REQUIRE(all(approx(
            orthographic_lh(100.f, 800.f, 50.f, 640.f, 5.f, 10.f),
            scale(1.f,1.f,-1.f) * orthographic_rh(100.f, 800.f, 50.f, 640.f, 5.f, 10.f))));
    }


    SECTION("matrix perspective") {
        REQUIRE(all(approx(
            perspective_lh(800.f, 600.f, 5.f, 10.f),
            scale(1.f,1.f,-1.f) * perspective_rh(800.f, 600.f, 5.f, 10.f))));

        REQUIRE(all(approx(
            perspective_fov_lh(1.5f, 1.3f, 0.f, 10.f),
            scale(1.f,1.f,-1.f) * perspective_fov_rh(1.5f, 1.3f, 0.f, 10.f))));

        REQUIRE(all(approx(
            perspective_lh(100.f, 800.f, 50.f, 600.f, 5.f, 10.f),
            scale(1.f,1.f,-1.f) * perspective_rh(100.f, 800.f, 50.f, 600.f, 5.f, 10.f))));
    }

    SECTION("matrix look_at") {
        (void)look_at_lh(float3(1,2,3), float3(0,0,0), float3(0,2,0));
        (void)look_at_rh(float3(1,2,3), float3(0,0,0), float3(0,2,0));
    }

    SECTION("vector angle") {
        REQUIRE(angle(float2(2.f,0.f), float2(0.f,1.f)) == uapprox(radians(90.f)));
        REQUIRE(angle(float2(0.f,3.f), float2(1.f,0.f)) == uapprox(radians(90.f)));
        REQUIRE(angle(float2(0.5f,0.f), float2(-1.f,0.f)) == uapprox(radians(180.f)));
        REQUIRE(angle(float2(-0.2f,0.f), float2(1.f,0.f)) == uapprox(radians(180.f)));
        REQUIRE(angle(float3(0.f,2.f,0.f), float3(0.f,0.f,1.f)) == uapprox(radians(90.f)));
        REQUIRE(angle(float3(0.f,0.f,3.f), float3(0.f,1.f,0.f)) == uapprox(radians(90.f)));
    }

    SECTION("vector rotate") {
        REQUIRE(rotate(float2(2.f,0.f), radians(90.f)) == uapprox2(0.f,2.f));
        REQUIRE(rotate(float2(1.5f,0.f), radians(-90.f)) == uapprox2(0.f,-1.5f));

        REQUIRE(rotate_x(float3(0.f,1.5f,0.f), radians(90.f)) == uapprox3(0.f,0.f,1.5f));
        REQUIRE(rotate_y(float3(0.f,0.f,1.5f), radians(90.f)) == uapprox3(1.5f,0.f,0.f));
        REQUIRE(rotate_z(float3(1.5f,0.f,0.f), radians(90.f)) == uapprox3(0.f,1.5f,0.f));

        REQUIRE(rotate(float3(1.5f,0.f,0.f), qrotate_z(radians(90.f))) == uapprox3(0.f,1.5f,0.f));
        REQUIRE(rotate(float3(1.5f,0.f,0.f), radians(90.f), float3(0,0,1)) == uapprox3(0.f,1.5f,0.f));

        REQUIRE(rotate_x(float4(0.f,1.5f,0.f,2.f), radians(90.f)) == uapprox4(0.f,0.f,1.5f,2.f));
        REQUIRE(rotate_y(float4(0.f,0.f,1.5f,2.f), radians(90.f)) == uapprox4(1.5f,0.f,0.f,2.f));
        REQUIRE(rotate_z(float4(1.5f,0.f,0.f,2.f), radians(90.f)) == uapprox4(0.f,1.5f,0.f,2.f));

        REQUIRE(rotate(float4(1.5f,0.f,0.f,2.f), qrotate_z(radians(90.f))) == uapprox4(0.f,1.5f,0.f,2.f));
        REQUIRE(rotate(float4(1.5f,0.f,0.f,2.f), radians(90.f), float3(0,0,1)) == uapprox4(0.f,1.5f,0.f,2.f));
    }

    SECTION("vector project") {
        STATIC_REQUIRE(project(float2(2.f, 2.f), float2(0.f, 1.f)) == uapprox2(0.f, 2.f));
        STATIC_REQUIRE(project(float3(2.f, 2.f, 2.f), float3(0.f, 0.f, 1.f)) == uapprox3(0.f, 0.f, 2.f));
    }

    SECTION("vector perpendicular") {
        STATIC_REQUIRE(perpendicular(float2(2.f, 2.f), float2(0.f, 1.f)) == uapprox2(2.f, 0.f));
        STATIC_REQUIRE(perpendicular(float3(2.f, 2.f, 2.f), float3(0.f, 0.f, 1.f)) == uapprox3(2.f, 2.f, 0.f));
    }

    SECTION("quaternion/qrotate(m)") {
        REQUIRE(all(approx(
            vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(0.f, vec{1.f,2.f,3.f})))),
            vec{4.f,3.f,2.f,1.f} * rotate(0.f, vec{1.f,2.f,3.f}), 0.001f)));
        REQUIRE(all(approx(
            vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(radians(12.5f), vec{1.f,2.f,3.f})))),
            vec{4.f,3.f,2.f,1.f} * rotate(radians(12.5f), vec{1.f,2.f,3.f}), 0.001f)));
        REQUIRE(all(approx(
            vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(radians(-190.5f), vec{1.f,2.f,3.f})))),
            vec{4.f,3.f,2.f,1.f} * rotate(radians(-190.5f), vec{1.f,2.f,3.f}), 0.001f)));
    }

    SECTION("quaternion/qrotate(q, m)") {
        REQUIRE(all(approx(
            vec{4.f,3.f,2.f} * qrotate(
                qrotate(float3x3(rotate(0.f, vec{1.f,2.f,3.f}))),
                float3x3(rotate(0.f, vec{3.f,2.f,1.f}))),
            vec{4.f,3.f,2.f} *
                float3x3(rotate(0.f, vec{1.f,2.f,3.f})) *
                float3x3(rotate(0.f, vec{3.f,2.f,1.f})))));
    }

    SECTION("quaternion/qrotate(from, to)") {
        REQUIRE(+unit3_x<float> * qrotate(-unit3_x<float>, +unit3_x<float>) == uapprox3(-unit3_x<float>));
        REQUIRE(-unit3_y<float> * qrotate(+unit3_y<float>, -unit3_y<float>) == uapprox3(+unit3_y<float>));
        REQUIRE(+unit3_z<float> * qrotate(-unit3_z<float>, +unit3_z<float>) == uapprox3(-unit3_z<float>));
        REQUIRE(vec{1.f,2.f,3.f} * qrotate(vec{1.f,2.f,3.f}, vec{-2.f,1.f,3.f}) == uapprox3(-2.f,1.f,3.f));
        REQUIRE(vec{-2.f,1.f,3.f} * qrotate(vec{-2.f,1.f,3.f}, vec{1.f,2.f,3.f}) == uapprox3(1.f,2.f,3.f));
    }

    SECTION("quaternion/qrotate(q, from, to)") {
        REQUIRE(vec{1.f,2.f,3.f} *
            inverse(qrotate(float3x3(rotate(radians(12.f), {2.f,2.f,2.f})))) *
            qrotate(
                qrotate(float3x3(rotate(radians(12.f), {2.f,2.f,2.f}))),
                vec{1.f,2.f,3.f},
                vec{-2.f,1.f,3.f}) == uapprox3(vec{-2.f,1.f,3.f}));
    }

    SECTION("quaternion/qrotate(angle, axis)") {
        REQUIRE(all(approx(
            rotate(12.3f, float3(1.f,2.f,3.f)),
            rotate(qrotate(12.3f, float3(1.f,2.f,3.f)) * 2.f))));

        REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(pi_2) == uapprox3(0.f,0.f,1.f));
        REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(pi_2) == uapprox3(1.f,0.f,0.f));
        REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(pi_2) == uapprox3(0.f,1.f,0.f));

        REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
        REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));

        REQUIRE(qrotate_x(12.3f) == qrotate(12.3f, unit3_x<float> * 2.f));
        REQUIRE(qrotate_y(12.3f) == qrotate(12.3f, unit3_y<float> * 2.f));
        REQUIRE(qrotate_z(12.3f) == qrotate(12.3f, unit3_z<float> * 2.f));
    }

    SECTION("quaternion/qrotate(q, angle, axis)") {
        REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(qrotate_x(pi_4),pi_4) == uapprox3(0.f,0.f,1.f));
        REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(qrotate_y(pi_4),pi_4) == uapprox3(1.f,0.f,0.f));
        REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(qrotate_z(pi_4),pi_4) == uapprox3(0.f,1.f,0.f));

        REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,{0.f,0.f,1.f}),pi_2,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
        REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,float3{0.f,0.f,1.f}),pi_2,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
    }

    SECTION("quaternion/qlook_at") {
        REQUIRE(all(approx(
            qlook_at_lh(float3(1.f,2.f,3.f), float3(0,1,0)),
            qrotate(float3x3(look_at_lh(float3(), float3(1.f,2.f,3.f), float3(0,1,0)))))));
        REQUIRE(all(approx(
            qlook_at_rh(float3(1.f,2.f,3.f), float3(0,1,0)),
            qrotate(float3x3(look_at_rh(float3(), float3(1.f,2.f,3.f), float3(0,1,0)))))));
    }
}