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Showing content from https://timsong-cpp.github.io/cppwp/n4659/function.objects below:

[function.objects]

23 General utilities library [utilities] 23.14 Function objects [function.objects] 23.14.1 Header <functional> synopsis [functional.syn]

namespace std {
    template <class F, class... Args>
    invoke_result_t<F, Args...> invoke(F&& f, Args&&... args)
      noexcept(is_nothrow_invocable_v<F, Args...>);

    template <class T> class reference_wrapper;

  template <class T> reference_wrapper<T> ref(T&) noexcept;
  template <class T> reference_wrapper<const T> cref(const T&) noexcept;
  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>) noexcept;
  template <class T> reference_wrapper<const T> cref(reference_wrapper<T>) noexcept;

    template <class T = void> struct plus;
  template <class T = void> struct minus;
  template <class T = void> struct multiplies;
  template <class T = void> struct divides;
  template <class T = void> struct modulus;
  template <class T = void> struct negate;
  template <> struct plus<void>;
  template <> struct minus<void>;
  template <> struct multiplies<void>;
  template <> struct divides<void>;
  template <> struct modulus<void>;
  template <> struct negate<void>;

    template <class T = void> struct equal_to;
  template <class T = void> struct not_equal_to;
  template <class T = void> struct greater;
  template <class T = void> struct less;
  template <class T = void> struct greater_equal;
  template <class T = void> struct less_equal;
  template <> struct equal_to<void>;
  template <> struct not_equal_to<void>;
  template <> struct greater<void>;
  template <> struct less<void>;
  template <> struct greater_equal<void>;
  template <> struct less_equal<void>;

    template <class T = void> struct logical_and;
  template <class T = void> struct logical_or;
  template <class T = void> struct logical_not;
  template <> struct logical_and<void>;
  template <> struct logical_or<void>;
  template <> struct logical_not<void>;

    template <class T = void> struct bit_and;
  template <class T = void> struct bit_or;
  template <class T = void> struct bit_xor;
  template <class T = void> struct bit_not;
  template <> struct bit_and<void>;
  template <> struct bit_or<void>;
  template <> struct bit_xor<void>;
  template <> struct bit_not<void>;

    template <class F>
    unspecified not_fn(F&& f);

    template<class T> struct is_bind_expression;
  template<class T> struct is_placeholder;

  template<class F, class... BoundArgs>
    unspecified bind(F&&, BoundArgs&&...);
  template<class R, class F, class... BoundArgs>
    unspecified bind(F&&, BoundArgs&&...);

  namespace placeholders {
        see below _1;
    see below _2;
               .
               .
               .
    see below _M;
  }

    template<class R, class T>
    unspecified mem_fn(R T::*) noexcept;

    class bad_function_call;

  template<class> class function;   template<class R, class... ArgTypes> class function<R(ArgTypes...)>;

  template<class R, class... ArgTypes>
    void swap(function<R(ArgTypes...)>&, function<R(ArgTypes...)>&) noexcept;

  template<class R, class... ArgTypes>
    bool operator==(const function<R(ArgTypes...)>&, nullptr_t) noexcept;
  template<class R, class... ArgTypes>
    bool operator==(nullptr_t, const function<R(ArgTypes...)>&) noexcept;
  template<class R, class... ArgTypes>
    bool operator!=(const function<R(ArgTypes...)>&, nullptr_t) noexcept;
  template<class R, class... ArgTypes>
    bool operator!=(nullptr_t, const function<R(ArgTypes...)>&) noexcept;

    template<class ForwardIterator, class BinaryPredicate = equal_to<>>
    class default_searcher;

  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
    class boyer_moore_searcher;

  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
    class boyer_moore_horspool_searcher;

    template <class T>
    struct hash;

    template <class T>
    inline constexpr bool is_bind_expression_v = is_bind_expression<T>::value;
  template <class T>
    inline constexpr int is_placeholder_v = is_placeholder<T>::value;
}

[ Example: If a C++ program wants to have a by-element addition of two vectors a and b containing double and put the result into a, it can do:

transform(a.begin(), a.end(), b.begin(), a.begin(), plus<double>());

— end example ]

[ Example: To negate every element of a:

transform(a.begin(), a.end(), a.begin(), negate<double>());

— end example ]

23.14.2 Definitions [func.def]

The following definitions apply to this Clause:

A call signature is the name of a return type followed by a parenthesized comma-separated list of zero or more argument types.

A call wrapper type is a type that holds a callable object and supports a call operation that forwards to that object.

23.14.3 Requirements [func.require]

Define INVOKE(f, t1, t2, ..., tN) as follows:

(t1.*f)(t2, ..., tN) when f is a pointer to a member function of a class T and is_base_of_v<T, decay_t<decltype(t1)>> is true;
(t1.get().*f)(t2, ..., tN) when f is a pointer to a member function of a class T and decay_t<decltype(t1)> is a specialization of reference_wrapper;
((*t1).*f)(t2, ..., tN) when f is a pointer to a member function of a class T and t1 does not satisfy the previous two items;
t1.*f when N == 1 and f is a pointer to data member of a class T and is_base_of_v<T, decay_t<decltype(t1)>> is true;
t1.get().*f when N == 1 and f is a pointer to data member of a class T and decay_t<decltype(t1)> is a specialization of reference_wrapper;
(*t1).*f when N == 1 and f is a pointer to data member of a class T and t1 does not satisfy the previous two items;
f(t1, t2, ..., tN) in all other cases.

Define INVOKE<R>(f, t1, t2, ..., tN) as static_cast<void>(INVOKE(f, t1, t2, ..., tN)) if R is cv void, otherwise INVOKE(f, t1, t2, ..., tN) implicitly converted to R.

Every call wrapper shall be MoveConstructible. A forwarding call wrapper is a call wrapper that can be called with an arbitrary argument list and delivers the arguments to the wrapped callable object as references. This forwarding step shall ensure that rvalue arguments are delivered as rvalue references and lvalue arguments are delivered as lvalue references. A simple call wrapper is a forwarding call wrapper that is CopyConstructible and CopyAssignable and whose copy constructor, move constructor, and assignment operator do not throw exceptions. [ Note: In a typical implementation forwarding call wrappers have an overloaded function call operator of the form

template<class... UnBoundArgs>
R operator()(UnBoundArgs&&... unbound_args) cv-qual;

— end note ]

23.14.4 Function template invoke [func.invoke]

template <class F, class... Args> invoke_result_t<F, Args...> invoke(F&& f, Args&&... args) noexcept(is_nothrow_invocable_v<F, Args...>);

Returns: INVOKE(std::forward<F>(f), std::forward<Args>(args)...) ([func.require]).

23.14.5 Class template reference_wrapper [refwrap]

namespace std {
  template <class T> class reference_wrapper {
  public :
        using type = T;

        reference_wrapper(T&) noexcept;
    reference_wrapper(T&&) = delete;         reference_wrapper(const reference_wrapper& x) noexcept;

        reference_wrapper& operator=(const reference_wrapper& x) noexcept;

        operator T& () const noexcept;
    T& get() const noexcept;

        template <class... ArgTypes>
      invoke_result_t<T&, ArgTypes...>
      operator() (ArgTypes&&...) const;
  };

  template<class T>
    reference_wrapper(reference_wrapper<T>) -> reference_wrapper<T>;
}

reference_wrapper<T> is a CopyConstructible and CopyAssignable wrapper around a reference to an object or function of type T.

23.14.5.1 reference_wrapper construct/copy/destroy [refwrap.const]

reference_wrapper(T& t) noexcept;

Effects: Constructs a reference_wrapper object that stores a reference to t.

reference_wrapper(const reference_wrapper& x) noexcept;

Effects: Constructs a reference_wrapper object that stores a reference to x.get().

23.14.5.2 reference_wrapper assignment [refwrap.assign]

reference_wrapper& operator=(const reference_wrapper& x) noexcept;

Postconditions: *this stores a reference to x.get().

23.14.5.3 reference_wrapper access [refwrap.access]

operator T& () const noexcept;

Returns: The stored reference.

T& get() const noexcept;

Returns: The stored reference.

23.14.5.4 reference_wrapper invocation [refwrap.invoke]

template <class... ArgTypes> invoke_result_t<T&, ArgTypes...> operator()(ArgTypes&&... args) const;

Returns: INVOKE(get(), std::forward<ArgTypes>(args)...). ([func.require])

23.14.5.5 reference_wrapper helper functions [refwrap.helpers]

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

Returns: reference_wrapper<T>(t).

template <class T> reference_wrapper<T> ref(reference_wrapper<T> t) noexcept;

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

Returns: reference_wrapper <const T>(t).

template <class T> reference_wrapper<const T> cref(reference_wrapper<T> t) noexcept;

23.14.6 Arithmetic operations [arithmetic.operations]

The library provides basic function object classes for all of the arithmetic operators in the language ([expr.mul], [expr.add]).

23.14.6.1 Class template plus [arithmetic.operations.plus]

template <class T = void> struct plus { constexpr T operator()(const T& x, const T& y) const; };

constexpr T operator()(const T& x, const T& y) const;

template <> struct plus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) + std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) + std::forward(u));

Returns: std::forward<T>(t) + std::forward(u).

23.14.6.2 Class template minus [arithmetic.operations.minus]

template <class T = void> struct minus { constexpr T operator()(const T& x, const T& y) const; };

constexpr T operator()(const T& x, const T& y) const;

template <> struct minus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) - std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) - std::forward(u));

Returns: std::forward<T>(t) - std::forward(u).

23.14.6.3 Class template multiplies [arithmetic.operations.multiplies]

template <class T = void> struct multiplies { constexpr T operator()(const T& x, const T& y) const; };

constexpr T operator()(const T& x, const T& y) const;

template <> struct multiplies<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) * std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) * std::forward(u));

Returns: std::forward<T>(t) * std::forward(u).

23.14.6.4 Class template divides [arithmetic.operations.divides]

template <class T = void> struct divides { constexpr T operator()(const T& x, const T& y) const; };

constexpr T operator()(const T& x, const T& y) const;

template <> struct divides<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) / std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) / std::forward(u));

Returns: std::forward<T>(t) / std::forward(u).

23.14.6.5 Class template modulus [arithmetic.operations.modulus]

template <class T = void> struct modulus { constexpr T operator()(const T& x, const T& y) const; };

constexpr T operator()(const T& x, const T& y) const;

template <> struct modulus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) % std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) % std::forward(u));

Returns: std::forward<T>(t) % std::forward(u).

23.14.6.6 Class template negate [arithmetic.operations.negate]

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

constexpr T operator()(const T& x) const;

template <> struct negate<void> { template <class T> constexpr auto operator()(T&& t) const -> decltype(-std::forward<T>(t)); using is_transparent = unspecified; };

template <class T> constexpr auto operator()(T&& t) const -> decltype(-std::forward<T>(t));

Returns: -std::forward<T>(t).

23.14.7 Comparisons [comparisons]

The library provides basic function object classes for all of the comparison operators in the language ([expr.rel], [expr.eq]).

For templates less, greater, less_equal, and greater_equal, the specializations for any pointer type yield a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by the built-in operators <, >, <=, >=. [ Note: When a < b is well-defined for pointers a and b of type P, this implies (a < b) == less(a, b), (a > b) == greater(a, b), and so forth. — end note ] For template specializations less<void>, greater<void>, less_equal<void>, and greater_equal<void>, if the call operator calls a built-in operator comparing pointers, the call operator yields a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by those built-in operators.

23.14.7.1 Class template equal_to [comparisons.equal_to]

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