Essential Books

Named operators

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You can extend C++ with named operators that are “quoted” by standard C++ operators.

First we start with a dozen-line library: 

namespace named_operator {
  template<class D>struct make_operator{constexpr make_operator(){}};

  template<class T, char, class O> struct half_apply { T&& lhs; };

  template<class Lhs, class Op>
  half_apply<Lhs, '*', Op> operator*( Lhs&& lhs, make_operator<Op> ) {
    return {std::forward<Lhs>(lhs)};
  }

  template<class Lhs, class Op, class Rhs>
  auto operator*( half_apply<Lhs, '*', Op>&& lhs, Rhs&& rhs )
  -> decltype( named_invoke( std::forward<Lhs>(lhs.lhs), Op{}, std::forward<Rhs>(rhs) ) )
  {
    return named_invoke( std::forward<Lhs>(lhs.lhs), Op{}, std::forward<Rhs>(rhs) );
  }
}

this doesn’t do anything yet.

First, appending vectors 

namespace my_ns {
  struct append_t : named_operator::make_operator<append_t> {};
  constexpr append_t append{};
  
  template<class T, class A0, class A1>
  std::vector<T, A0> named_invoke( std::vector<T, A0> lhs, append_t, std::vector<T, A1> const& rhs ) {
      lhs.insert( lhs.end(), rhs.begin(), rhs.end() );
      return std::move(lhs);
  }
}
using my_ns::append;

std::vector<int> a {1,2,3};
std::vector<int> b {4,5,6};

auto c = a *append* b;

The core here is that we define an append object of type append_t:named_operator::make_operator<append_t>.

We then overload named_invoke( lhs, append_t, rhs ) for the types we want on the right and left.

The library overloads lhs*append_t, returning a temporary half_apply object. It also overloads half_apply*rhs to call named_invoke( lhs, append_t, rhs ).

We simply have to create the proper append_t token and do an ADL-friendly named_invoke of the proper signature, and everything hooks up and works.

For a more complex example, suppose you want to have element-wise multiplication of elements of a std::array: 

template<class=void, std::size_t...Is>
auto indexer( std::index_sequence<Is...> ) {
  return [](auto&& f) {
    return f( std::integral_constant<std::size_t, Is>{}... );
  };
}
template<std::size_t N>
auto indexer() { return indexer( std::make_index_sequence<N>{} ); }

namespace my_ns {
  struct e_times_t : named_operator::make_operator<e_times_t> {};
  constexpr e_times_t e_times{};

  template<class L, class R, std::size_t N,
    class Out=std::decay_t<decltype( std::declval<L const&>()*std::declval<R const&>() )>
  >
  std::array<Out, N> named_invoke( std::array<L, N> const& lhs, e_times_t, std::array<R, N> const& rhs ) {
    using result_type = std::array<Out, N>;
    auto index_over_N = indexer<N>();
    return index_over_N([&](auto...is)->result_type {
      return {{
        (lhs[is] * rhs[is])...
      }};
    });
  }
}

live example.

This element-wise array code can be extended to work on tuples or pairs or C-style arrays, or even variable length containers if you decide what to do if the lengths don’t match.

You could also an element-wise operator type and get lhs *element_wise<'+'>* rhs.

Writing a *dot* and *cross* product operators are also obvious uses.

The use of \* can be extended to support other delimiters, like \+. The delimeter precidence determines the precidence of the named operator, which may be important when translating physics equations over to C++ with minimal use of extra ()s.

With a slight change in the library above, we can support ->*then* operators and extend std::function prior to the standard being updated, or write monadic ->*bind*. It could also have a stateful named operator, where we carefully pass the Op down to the final invoke function, permitting: 

named_operator<'*'> append = [](auto lhs, auto&& rhs) {
  using std::begin; using std::end;
  lhs.insert( end(lhs), begin(rhs), end(rhs) );
  return std::move(lhs);
};

generating a named container-appending operator in C++17.

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Operator overloading:
* Operator Overloading
* Arithmetic operators
* Array subscript operator
* Conversion operators
* Complex Numbers Revisited
* Unary operators
* Comparison operators
* Assignment operator
* Named operators
* Function call operator
* Bitwise NOT operator
* Bit shift operators for IO
Table Of Contents
0 Getting started
1 Literals
2 Basic type keywords
3 Operator precedence
4 Floating point arithmetic
5 Bit operators
6 Bit manipulation
7 Bit fields
8 Arrays
9 Flow control
10 const keyword
11 Loops
12 mutable keyword
13 friend keyword
14 keywords
15 Variable declaration keywords
16 auto keyword
17 Pointers
18 Type keywords (class, enum, struct, union)
19 Classes / structs
20 std::string
21 Enumeration
22 std::atomic
23 std::vector
24 std::array
25 std::pair
26 std::map
27 std::unordered_map
28 std::set and std::multiset
29 std::any
30 std::variant
31 std::optional
32 std::integer_sequence
33 std::function
34 std::forward_list
35 std::iomanip
36 Iterators
37 Basic I/O
38 File I/O
39 Streams
40 Stream manipulators
41 Metaprogramming
42 Returning multiple values from a function
43 References
44 Polymorphism
45 Value and reference semantics
46 Function call by value vs. by reference
47 Copying vs assignment
48 Pointers to class / struct members
49 The this pointer
50 Smart pointers
51 Unions
52 Templates
53 Namespaces
54 Function overloading
55 Operator overloading
56 Lambdas
57 Threading
58 Value categories
59 Preprocessor
60 SFINAE
61 Rule of three, five and zero
62 RAII
63 Exceptions
64 Implementation-defined behavior
65 Special member functions
66 Random numbers
67 Sorting
68 Regular expressions
69 Perfect forwarding
70 Virtual member functions
71 Undefined behavior
72 Overload resolution
73 Move semantics
74 Pimpl idiom
75 Copy elision
76 Fold expressions
77 Unnamed types
78 Singleton
79 ISO C++ Standard
80 User-defined literals
81 Type erasure
82 Memory management
83 Explicit type conversions
84 RTTI
85 Standard library algorithms
86 Expression templates
87 Scopes
88 Atomic types
89 static assert
90 constexpr
91 Date and time with std::chrono
92 Trailing return type
93 Function template overloading
94 Common compile linker errors
95 Design patterns
96 Optimizations
97 Compiling and building
98 Type traits
99 One definition rule
100 Unspecified behavio
101 Argument dependent name lookup
102 Attributes
103 Internationalization
104 Profiling
105 Return type covariance
106 Non-static member functions
107 Recursion
108 Callable objects
109 Constant class member functions
110 C++ vs. C++ 11 vs C++ 17
111 Inline functions
112 Client server examples
113 Header files
114 Const correctness
115 Refactoring techniques
116 Parameter packs
117 Iteration
118 type deduction
119 C++ 11 memory model
120 Build systems
121 Concurrency with OpenMP
122 Type inference
123 Resource management
124 Storage class specifiers
125 Alignment
126 Inline variables
127 Linkage specifications
128 Curiusly recurring template pattern
129 Using declaration
130 Typedef and type aliases
131 Layout of object types
132 C incompatibilities
133 Optimization
134 Semaphore
135 Thread synchronization
136 Debugging
137 Futures and promises
138 More undefined behaviors
139 Mutexes
140 Recursive mutex
141 Unit testing
142 decltype
143 Digit separators
144 C++ Containers
145 Arithmetic meta-programming
146 Contributors