source: mainline/uspace/lib/cpp/include/impl/functional.hpp@ 9c00022

/*
 * Copyright (c) 2018 Jaroslav Jindrak
 * 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.
 * - The name of the author may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``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 AUTHOR 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 LIBCPP_FUNCTIONAL
#define LIBCPP_FUNCTIONAL

#include <limits>
#include <memory>
#include <typeinfo>
#include <type_traits>
#include <utility>

namespace std
{
    namespace aux
    {
        /**
         * 20.9.2, requirements:
         */
        template<class R, class T, class T1, class... Ts>
        decltype(auto) invoke(R T::* f, T1&& t1, Ts&&... args)
        {
            if constexpr (is_member_function_pointer_v<decltype(f)>)
            {
                if constexpr (is_base_of_v<T, remove_reference_t<T1>>)
                    // (1.1)
                    return (t1.*f)(forward<Ts>(args)...);
                else
                    // (1.2)
                    return ((*t1).*f)(forward<Ts>(args)...);
            }
            else if constexpr (is_member_object_pointer_v<decltype(f)> && sizeof...(args) == 0)
            {
                /**
                 * Note: Standard requires to N be equal to 1, but we take t1 directly
                 *       so we need sizeof...(args) to be 0.
                 */
                if constexpr (is_base_of_v<T, remove_reference_t<T1>>)
                    // (1.3)
                    return t1.*f;
                else
                    // (1.4)
                    return (*t1).*f;
            }

            /**
             * Note: If this condition holds this will not be reachable,
             *       but a new addition to the standard (17.7 point (8.1))
             *       prohibits us from simply using false as the condition here,
             *       so we use this because we know it is false here.
             */
            static_assert(is_member_function_pointer_v<decltype(f)>, "invalid invoke");
        }

        template<class F, class... Args>
        decltype(auto) invoke(F&& f, Args&&... args)
        {
            // (1.5)
            return f(forward<Args>(args)...);
        }
    }

    /**
     * 20.9.3, invoke:
     */

    template<class F, class... Args>
    result_of_t<F&&(Args&&...)> invoke(F&& f, Args&&... args)
    {
        return aux::invoke(forward<F>(f)(forward<Args>(args)...));
    }

    /**
     * 20.9.4, reference_wrapper:
     */

    template<class T>
    class reference_wrapper
    {
        public:
            using type = T;
            // TODO: conditional typedefs

            reference_wrapper(type& val) noexcept
                : data_{&val}
            { /* DUMMY BODY */ }

            reference_wrapper(type&&) = delete;

            reference_wrapper(const reference_wrapper& other) noexcept
                : data_{other.data_}
            { /* DUMMY BODY */ }

            reference_wrapper& operator=(const reference_wrapper& other) noexcept
            {
                data_ = other.data_;

                return *this;
            }

            operator type&() const noexcept
            {
                return *data_;
            }

            type& get() const noexcept
            {
                return *data_;
            }

            template<class... Args>
            result_of_t<type&(Args&&...)> operator()(Args&&... args) const
            {
                return invoke(*data_, std::forward<Args>(args)...);
            }

        private:
            type* data_;
    };

    template<class T>
    reference_wrapper<T> ref(T& t) noexcept
    {
        return reference_wrapper<T>{t};
    }

    template<class T>
    reference_wrapper<const T> cref(const T& t) noexcept
    {
        return reference_wrapper<const T>{t};
    }

    template<class T>
    void ref(const T&&) = delete;

    template<class T>
    void cref(const T&&) = delete;

    template<class T>
    reference_wrapper<T> ref(reference_wrapper<T> t) noexcept
    {
        return ref(t.get());
    }

    template<class T>
    reference_wrapper<const T> cref(reference_wrapper<T> t) noexcept
    {
        return cref(t.get());
    }

    /**
     * 20.9.5, arithmetic operations:
     */

    template<class T = void>
    struct plus
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs + rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct minus
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs - rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct multiplies
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs * rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct divides
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs / rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct modulus
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs % rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct negate
    {
        constexpr T operator()(const T& x) const
        {
            return -x;
        }

        using argument_type = T;
        using result_type   = T;
    };

    namespace aux
    {
        /**
         * Used by some functions like std::set::find to determine
         * whether a functor is transparent.
         */
        struct transparent_t;

        template<class T, class = void>
        struct is_transparent: false_type
        { /* DUMMY BODY */ };

        template<class T>
        struct is_transparent<T, void_t<typename T::is_transparent>>
            : true_type
        { /* DUMMY BODY */ };

        template<class T>
        inline constexpr bool is_transparent_v = is_transparent<T>::value;
    }

    template<>
    struct plus<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) + forward<U>(rhs))
        {
            return forward<T>(lhs) + forward<T>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct minus<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) - forward<U>(rhs))
        {
            return forward<T>(lhs) - forward<T>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct multiplies<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) * forward<U>(rhs))
        {
            return forward<T>(lhs) * forward<T>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct divides<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) / forward<U>(rhs))
        {
            return forward<T>(lhs) / forward<T>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct modulus<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) % forward<U>(rhs))
        {
            return forward<T>(lhs) % forward<T>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct negate<void>
    {
        template<class T>
        constexpr auto operator()(T&& x) const
            -> decltype(-forward<T>(x))
        {
            return -forward<T>(x);
        }

        using is_transparent = aux::transparent_t;
    };

    /**
     * 20.9.6, comparisons:
     */

    template<class T = void>
    struct equal_to
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs == rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct not_equal_to
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs != rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct greater
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs > rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct less
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs < rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct greater_equal
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs >= rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct less_equal
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs <= rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<>
    struct equal_to<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) == forward<U>(rhs))
        {
            return forward<T>(lhs) == forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct not_equal_to<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) != forward<U>(rhs))
        {
            return forward<T>(lhs) != forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct greater<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) > forward<U>(rhs))
        {
            return forward<T>(lhs) > forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct less<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) < forward<U>(rhs))
        {
            return forward<T>(lhs) < forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct greater_equal<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) >= forward<U>(rhs))
        {
            return forward<T>(lhs) >= forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct less_equal<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) <= forward<U>(rhs))
        {
            return forward<T>(lhs) <= forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    /**
     * 20.9.7, logical operations:
     */

    template<class T = void>
    struct logical_and
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs && rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct logical_or
    {
        constexpr bool operator()(const T& lhs, const T& rhs) const
        {
            return lhs || rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = bool;
    };

    template<class T = void>
    struct logical_not
    {
        constexpr bool operator()(const T& x) const
        {
            return !x;
        }

        using argument_type = T;
        using result_type   = bool;
    };

    template<>
    struct logical_and<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) && forward<U>(rhs))
        {
            return forward<T>(lhs) && forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct logical_or<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) || forward<U>(rhs))
        {
            return forward<T>(lhs) || forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct logical_not<void>
    {
        template<class T>
        constexpr auto operator()(T&& x) const
            -> decltype(!forward<T>(x))
        {
            return !forward<T>(x);
        }

        using is_transparent = aux::transparent_t;
    };

    /**
     * 20.9.8, bitwise operations:
     */

    template<class T = void>
    struct bit_and
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs & rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct bit_or
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs | rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct bit_xor
    {
        constexpr T operator()(const T& lhs, const T& rhs) const
        {
            return lhs ^ rhs;
        }

        using first_argument_type  = T;
        using second_argument_type = T;
        using result_type          = T;
    };

    template<class T = void>
    struct bit_not
    {
        constexpr bool operator()(const T& x) const
        {
            return ~x;
        }

        using argument_type = T;
        using result_type   = T;
    };

    template<>
    struct bit_and<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) & forward<U>(rhs))
        {
            return forward<T>(lhs) & forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct bit_or<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) | forward<U>(rhs))
        {
            return forward<T>(lhs) | forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct bit_xor<void>
    {
        template<class T, class U>
        constexpr auto operator()(T&& lhs, U&& rhs) const
            -> decltype(forward<T>(lhs) ^ forward<U>(rhs))
        {
            return forward<T>(lhs) ^ forward<U>(rhs);
        }

        using is_transparent = aux::transparent_t;
    };

    template<>
    struct bit_not<void>
    {
        template<class T>
        constexpr auto operator()(T&& x) const
            -> decltype(~forward<T>(x))
        {
            return ~forward<T>(x);
        }

        using is_transparent = aux::transparent_t;
    };

    /**
     * 20.9.9, negators:
     */

    template<class Predicate>
    class unary_negate;

    template<class Predicate>
    constexpr unary_negate<Predicate> not1(const Predicate& pred);

    template<class Predicate>
    class binary_negate;

    template<class Predicate>
    constexpr binary_negate<Predicate> not2(const Predicate& pred);

    /**
     * 20.9.10, bind:
     */

    template<class T>
    struct is_bind_expression;

    template<class T>
    struct is_placeholder;

    // TODO: void should be /unspecified/
    template<class F, class... Args>
    void bind(F&& f, Args&&... args);

    template<class R, class F, class... Args>
    void bind(F&& f, Args&&... args);

    namespace placeholders
    {
        /**
         * TODO: for X from 1 to implementation defined M
         * extern /unspecified/ _X;
         */
    }

    /**
     * 20.9.11, member function adaptors:
     */

    // TODO: void should be /unspecified/
    template<class R, class T>
    void mem_fn(R T::* f);

    /**
     * 20.9.12, polymorphic function adaptors:
     */

    namespace aux
    {
        // TODO: fix this
        /* template<class, class T, class... Args> */
        /* struct is_callable_impl: false_type */
        /* { /1* DUMMY BODY *1/ }; */

        /* template<class, class R, class... Args> */
        /* struct is_callable_impl< */
        /*     void_t<decltype(aux::invoke(declval<R(Args...)>(), declval<Args>()..., R))>, */
        /*     R, Args... */
        /* > : true_type */
        /* { /1* DUMMY BODY *1/ }; */

        /* template<class T> */
        /* struct is_callable: is_callable_impl<void_t<>, T> */
        /* { /1* DUMMY BODY *1/ }; */

        template<class Callable, class R, class... Args>
        R invoke_callable(Callable* clbl, Args&&... args)
        {
            return (*clbl)(forward<Args>(args)...);
        }

        template<class Callable>
        void copy_callable(Callable* to, Callable* from)
        {
            new(to) Callable{*from};
        }

        template<class Callable>
        void destroy_callable(Callable* clbl)
        {
            if (clbl)
                clbl->~Callable();
        }
    }

    class bad_function_call;

    template<class>
    class function; // undefined

    /**
     * Note: Ideally, this implementation wouldn't
     *       copy the target if it was a pointer to
     *       a function, but for the simplicity of the
     *       implementation, we do copy even in that
     *       case for now. It would be a nice optimization
     *       if this was changed in the future.
     */
    template<class R, class... Args>
    class function<R(Args...)>
    {
        public:
            using result_type = R;
            // TODO: conditional typedefs

            /**
             * 20.9.12.2.1, construct/copy/destroy:
             */

            function() noexcept
                : callable_{}, callable_size_{}, call_{},
                  copy_{}, dest_{}
            { /* DUMMY BODY */ }

            function(nullptr_t) noexcept
                : function{}
            { /* DUMMY BODY */ }

            function(const function& other)
                : callable_{}, callable_size_{other.callable_size_},
                  call_{other.call_}, copy_{other.copy_}, dest_{other.dest_}
            {
                callable_ = new uint8_t[callable_size_];
                (*copy_)(callable_, other.callable_);
            }

            function(function&& other)
                : callable_{other.callable_}, callable_size_{other.callable_size_},
                  call_{other.call_}, copy_{other.copy_}, dest_{other.dest_}
            {
                other.callable_ = nullptr;
                other.callable_size_ = size_t{};
                other.call_ = nullptr;
                other.copy_ = nullptr;
                other.dest_ = nullptr;
            }

            // TODO: shall not participate in overloading unless aux::is_callable<F>
            template<class F>
            function(F f)
                : callable_{}, callable_size_{sizeof(F)},
                  call_{(call_t)aux::invoke_callable<F, R, Args...>},
                  copy_{(copy_t)aux::copy_callable<F>},
                  dest_{(dest_t)aux::destroy_callable<F>}
            {
                callable_ = new uint8_t[callable_size_];
                (*copy_)(callable_, (uint8_t*)&f);
            }

            /**
             * Note: For the moment we're ignoring the allocator
             *       for simplicity of the implementation.
             */

            template<class A>
            function(allocator_arg_t, const A& a) noexcept
                : function{}
            { /* DUMMY BODY */ }

            template<class A>
            function(allocator_arg_t, const A& a, nullptr_t) noexcept
                : function{}
            { /* DUMMY BODY */ }

            template<class A>
            function(allocator_arg_t, const A& a, const function& other)
                : function{other}
            { /* DUMMY BODY */ }

            template<class A>
            function(allocator_arg_t, const A& a, function&& other)
                : function{move(other)}
            { /* DUMMY BODY */ }

            // TODO: shall not participate in overloading unless aux::is_callable<F>
            template<class F, class A>
            function(allocator_arg_t, const A& a, F f)
                : function{f}
            { /* DUMMY BODY */ }

            function& operator=(const function& rhs)
            {
                function{rhs}.swap(*this);

                return *this;
            }

            /**
             * Note: We have to copy call_, copy_
             *       and dest_ because they can be templated
             *       by a type F we don't know.
             */
            function& operator=(function&& rhs)
            {
                clear_();

                callable_ = rhs.callable_;
                callable_size_ = rhs.callable_size_;
                call_ = rhs.call_;
                copy_ = rhs.copy_;
                dest_ = rhs.dest_;

                rhs.callable_ = nullptr;
                rhs.callable_size_ = size_t{};
                rhs.call_ = nullptr;
                rhs.copy_ = nullptr;
                rhs.dest_ = nullptr;

                return *this;
            }

            function& operator=(nullptr_t) noexcept
            {
                clear_();

                return *this;
            }

            // TODO: shall not participate in overloading unless aux::is_callable<F>
            template<class F>
            function& operator=(F&& f)
            {
                callable_size_ = sizeof(F);
                callable_ = new uint8_t[callable_size_];
                call_ = aux::invoke_callable<F, R, Args...>;
                copy_ = aux::copy_callable<F>;
                dest_ = aux::destroy_callable<F>;

                (*copy_)(callable_, (uint8_t*)&f);
            }

            template<class F>
            function& operator=(reference_wrapper<F> ref) noexcept
            {
                return (*this) = ref.get();
            }

            ~function()
            {
                if (callable_)
                {
                    (*dest_)(callable_);
                    delete[] callable_;
                }
            }

            /**
             * 20.9.12.2.2, function modifiers:
             */

            void swap(function& other) noexcept
            {
                std::swap(callable_, other.callable_);
                std::swap(callable_size_, other.callable_size_);
                std::swap(call_, other.call_);
                std::swap(copy_, other.copy_);
                std::swap(dest_, other.dest_);
            }

            template<class F, class A>
            void assign(F&& f, const A& a)
            {
                function{allocator_arg, a, forward<F>(f)}.swap(*this);
            }

            /**
             * 20.9.12.2.3, function capacity:
             */

            explicit operator bool() const noexcept
            {
                return callable_ != nullptr;
            }

            /**
             * 20.9.12.2.4, function invocation:
             */

            result_type operator()(Args... args) const
            {
                // TODO: throw bad_function_call if !callable_ || !call_
                if constexpr (is_same_v<R, void>)
                    (*call_)(callable_, forward<Args>(args)...);
                else
                    return (*call_)(callable_, forward<Args>(args)...);
            }

            /**
             * 20.9.12.2.5, function target access:
             */

            const type_info& target_type() const noexcept
            {
                return typeid(*callable_);
            }

            template<class T>
            T* target() noexcept
            {
                if (target_type() == typeid(T))
                    return (T*)callable_;
                else
                    return nullptr;
            }

            template<class T>
            const T* target() const noexcept
            {
                if (target_type() == typeid(T))
                    return (T*)callable_;
                else
                    return nullptr;
            }

        private:
            using call_t = R(*)(uint8_t*, Args&&...);
            using copy_t = void (*)(uint8_t*, uint8_t*);
            using dest_t = void (*)(uint8_t*);

            uint8_t* callable_;
            size_t callable_size_;
            call_t call_;
            copy_t copy_;
            dest_t dest_;

            void clear_()
            {
                if (callable_)
                {
                    (*dest_)(callable_);
                    delete[] callable_;
                    callable_ = nullptr;
                }
            }
    };

    /**
     * 20.9.12.2.7, specialized algorithms:
     */

    template<class R, class... Args>
    void swap(function<R(Args...)>& f1, function<R(Args...)>& f2)
    {
        f1.swap(f2);
    }

    /**
     * 20.9.12.2.6, null pointer comparisons:
     */

    template<class R, class... Args>
    bool operator==(const function<R(Args...)>& f, nullptr_t) noexcept
    {
        return !f;
    }

    template<class R, class... Args>
    bool operator==(nullptr_t, const function<R(Args...)>& f) noexcept
    {
        return !f;
    }

    template<class R, class... Args>
    bool operator!=(const function<R(Args...)>& f, nullptr_t) noexcept
    {
        return (bool)f;
    }

    template<class R, class... Args>
    bool operator!=(nullptr_t, const function<R(Args...)>& f) noexcept
    {
        return (bool)f;
    }

    /**
     * 20.9.13, hash function primary template:
     */

    namespace aux
    {
        template<class T>
        union converter
        {
            T value;
            uint64_t converted;
        };

        template<class T>
        T hash_(uint64_t x) noexcept
        {
            /**
             * Note: std::hash is used for indexing in
             *       unordered containers, not for cryptography.
             *       Because of this, we decided to simply convert
             *       the value to uin64_t, which will help us
             *       with testing (since in order to create
             *       a collision in a multiset or multimap
             *       we simply need 2 values that congruent
             *       by the size of the table.
             */
            return static_cast<T>(x);
        }

        template<class T>
        size_t hash(T x) noexcept
        {
            static_assert(is_arithmetic_v<T> || is_pointer_v<T>,
                          "invalid type passed to aux::hash");

            converter<T> conv;
            conv.value = x;

            return hash_<size_t>(conv.converted);
        }
    }

    template<class T>
    struct hash
    { /* DUMMY BODY */ };

    template<>
    struct hash<bool>
    {
        size_t operator()(bool x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = bool;
        using result_type   = size_t;
    };

    template<>
    struct hash<char>
    {
        size_t operator()(char x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = char;
        using result_type   = size_t;
    };

    template<>
    struct hash<signed char>
    {
        size_t operator()(signed char x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = signed char;
        using result_type   = size_t;
    };

    template<>
    struct hash<unsigned char>
    {
        size_t operator()(unsigned char x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = unsigned char;
        using result_type   = size_t;
    };

    template<>
    struct hash<char16_t>
    {
        size_t operator()(char16_t x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = char16_t;
        using result_type   = size_t;
    };

    template<>
    struct hash<char32_t>
    {
        size_t operator()(char32_t x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = char32_t;
        using result_type   = size_t;
    };

    template<>
    struct hash<wchar_t>
    {
        size_t operator()(wchar_t x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = wchar_t;
        using result_type   = size_t;
    };

    template<>
    struct hash<short>
    {
        size_t operator()(short x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = short;
        using result_type   = size_t;
    };

    template<>
    struct hash<unsigned short>
    {
        size_t operator()(unsigned short x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = unsigned short;
        using result_type   = size_t;
    };

    template<>
    struct hash<int>
    {
        size_t operator()(int x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = int;
        using result_type   = size_t;
    };

    template<>
    struct hash<unsigned int>
    {
        size_t operator()(unsigned int x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = unsigned int;
        using result_type   = size_t;
    };

    template<>
    struct hash<long>
    {
        size_t operator()(long x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = long;
        using result_type   = size_t;
    };

    template<>
    struct hash<long long>
    {
        size_t operator()(long long x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = long long;
        using result_type   = size_t;
    };

    template<>
    struct hash<unsigned long>
    {
        size_t operator()(unsigned long x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = unsigned long;
        using result_type   = size_t;
    };

    template<>
    struct hash<unsigned long long>
    {
        size_t operator()(unsigned long long x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = unsigned long long;
        using result_type   = size_t;
    };

    template<>
    struct hash<float>
    {
        size_t operator()(float x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = float;
        using result_type   = size_t;
    };

    template<>
    struct hash<double>
    {
        size_t operator()(double x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = double;
        using result_type   = size_t;
    };

    template<>
    struct hash<long double>
    {
        size_t operator()(long double x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = long double;
        using result_type   = size_t;
    };

    template<class T>
    struct hash<T*>
    {
        size_t operator()(T* x) const noexcept
        {
            return aux::hash(x);
        }

        using argument_type = T*;
        using result_type   = size_t;
    };
}

#endif