238
votes

While I was trying to learn about C++ operators, I stumbled upon a strange comparison operator on cppreference.com,* in a table that looked like this:

enter image description here

"Well, if these are common operators in C++, I better learn them", I thought. But all my attempts to elucidate this mystery were unsuccessful. Even here, on Stack Overflow I had no luck in my search.

Is there a connection between <=> and C++?

And if there is, what does this operator do exactly?

* In the meantime cppreference.com updated that page and now contains information about the<=>operator.

5
@cubuspl42 bar< foo::operator<=> is an example of how it could be like the <-- operator.Yakk - Adam Nevraumont
@haccks: Right. Like C++11 is a tag about compilers that implement C++11. And C++14 is a tag about compilers that implement C++14. And C++17 is about compilers that implement C++17. No, the C++20 is the tag for stuff about C++20. And since this question is about C++20, there it is. The tag wiki that was wrong, not the tag itself.Nicol Bolas

5 Answers

192
votes

This is called the three-way comparison operator.

According to the P0515 paper proposal:

There’s a new three-way comparison operator, <=>. The expression a <=> b returns an object that compares <0 if a < b, compares >0 if a > b, and compares ==0 if a and b are equal/equivalent.

To write all comparisons for your type, just write operator<=> that returns the appropriate category type:

  • Return an _ordering if your type naturally supports <, and we’ll efficiently generate <, >, <=, >=, ==, and !=; otherwise return an _equality, and we’ll efficiently generate == and !=.

  • Return strong if for your type a == b implies f(a) == f(b) (substitutability, where f reads only comparison-salient state accessible using the nonprivate const interface), otherwise return weak.

The cppreference says:

The three-way comparison operator expressions have the form

lhs <=> rhs   (1)  

The expression returns an object that

  • compares <0 if lhs < rhs
  • compares >0 if lhs > rhs
  • and compares ==0 if lhs and rhs are equal/equivalent.
123
votes

On 2017-11-11, the ISO C++ committee adopted Herb Sutter's proposal for the <=> "spaceship" three-way comparison operator as one of the new features that were added to C++20. In the paper titled Consistent comparison Sutter, Maurer and Brown demonstrate the concepts of the new design. For an overview of the proposal, here's an excerpt from the article:

The expression a <=> b returns an object that compares <0 if a < b, compares >0 if a > b, and compares ==0 if a and b are equal/equivalent.

Common case: To write all comparisons for your type X with type Y, with memberwise semantics, just write:

auto X::operator<=>(const Y&) =default;

Advanced cases: To write all comparisons for your type X with type Y, just write operator<=> that takes a Y, can use =default to get memberwise semantics if desired, and returns the appropriate category type:

  • Return an _ordering if your type naturally supports <, and we’ll efficiently generate symmetric <, >, <=, >=, ==, and !=; otherwise return an _equality, and we’ll efficiently generate symmetric == and !=.
  • Return strong_ if for your type a == b implies f(a) == f(b) (substitutability, where f reads only comparison-salient state that is accessible using the public const members), otherwise return weak_.

Comparison Categories

Five comparison categories are defined as std:: types, each having the following predefined values:

+--------------------------------------------------------------------+
|                  |          Numeric  values          | Non-numeric |
|     Category     +-----------------------------------+             |
|                  | -1   | 0          | +1            |   values    |
+------------------+------+------------+---------------+-------------+
| strong_ordering  | less | equal      | greater       |             |
| weak_ordering    | less | equivalent | greater       |             |
| partial_ordering | less | equivalent | greater       | unordered   |
| strong_equality  |      | equal      | nonequal      |             |
| weak_equality    |      | equivalent | nonequivalent |             |
+------------------+------+------------+---------------+-------------+

Implicit conversions between these types are defined as follows:

  • strong_ordering with values {less, equal, greater} implicitly converts to:
    • weak_ordering with values {less, equivalent, greater}
    • partial_ordering with values {less, equivalent, greater}
    • strong_equality with values {unequal, equal, unequal}
    • weak_equality with values {nonequivalent, equivalent, nonequivalent}
  • weak_ordering with values {less, equivalent, greater} implicitly converts to:
    • partial_ordering with values {less, equivalent, greater}
    • weak_equality with values {nonequivalent, equivalent, nonequivalent}
  • partial_ordering with values {less, equivalent, greater, unordered} implicitly converts to:
    • weak_equality with values {nonequivalent, equivalent, nonequivalent, nonequivalent}
  • strong_equality with values {equal, unequal} implicitly converts to:
    • weak_equality with values {equivalent, nonequivalent}

Three-way comparison

The<=>token is introduced. The character sequence<=>tokenizes to<= >, in old source code. For example,X<&Y::operator<=>needs to add a space to retain its meaning.

The overloadable operator<=>is a three-way comparison function and has precedence higher than< and lower than<<. It returns a type that can be compared against literal0but other return types are allowed such as to support expression templates. All<=>operators defined in the language and in the standard library return one of the 5 aforementionedstd::comparison category types.

For language types, the following built-in<=>same-type comparisons are provided. All are constexpr, except where noted otherwise. These comparisons cannot be invoked heterogeneously using scalar promotions/conversions.

  • Forbool, integral, and pointer types,<=>returnsstrong_ordering.
  • For pointer types, the different cv-qualifications and derived-to-base conversions are allowed to invoke a homogeneous built-in<=>, and there are built-in heterogeneousoperator<=>(T*, nullptr_t). Only comparisons of pointers to the same object/allocation are constant expressions.
  • For fundamental floating point types,<=> returnspartial_ordering, and can be invoked heterogeneously by widening arguments to a larger floating point type.
  • For enumerations,<=> returns the same as the enumeration's underlying type's<=>.
  • Fornullptr_t,<=> returnsstrong_orderingand always yieldsequal.
  • For copyable arrays,T[N] <=> T[N]returns the same type asT's<=>and performs lexicographical elementwise comparison. There is no<=>for other arrays.
  • Forvoidthere is no<=>.

To better understand the inner workings of this operator, please read the original paper. This is just what I've found out using search engines.

12
votes

This answer has become irrelevant since the referenced web page has changed

The web page you are referencing was broken. It was being edited a lot that day and different parts was not in sync. The status when I was looking at it was:

At the top of the page it lists the currently existing comparison operators (in C++14). There is no <=>there.

At the bottom of the page, they should have listed the same operators, but they goofed and added this future suggestion.

gcc doesn't know about <=>yet (and with -std=c++14, never will), so it thinks you meant a <= > b. This is explains the error message.

If you try the same thing five years from now you will probably get a better error message, something like <=> not part of C++14.

7
votes

Defaulting <=> automatically gives ==, !=, <, >, <=, >= for free

C++20 has a new "default comparison" feature setup so that defaulting <=> gives all the others for free. I believe that this has been the major motivation behind the addition of operator<=>.

Adapted from https://en.cppreference.com/w/cpp/language/default_comparisons:

main.cpp

#include <cassert>
#include <compare>
#include <set>

struct Point {
    int x;
    int y;
    auto operator<=>(const Point&) const = default;
};

int main() {
    Point pt1{1, 1}, pt2{1, 2};

    // Just to show it Is enough for `std::set`.
    std::set<Point> s;
    s.insert(pt1);

    // All of these are automatically defined for us!
    assert(!(pt1 == pt2));
    assert( (pt1 != pt2));
    assert( (pt1 <  pt2));
    assert( (pt1 <= pt2));
    assert(!(pt1 >  pt2));
    assert(!(pt1 >= pt2));
}

compile and run:

sudo apt install g++-10
g++-10 -ggdb3 -O0 -std=c++20 -Wall -Wextra -pedantic -o main.out main.cpp
./main.out

An equivalent more explicit version of the above would be:

struct Point {
    int x;
    int y;
    auto operator<=>(const Point& other) const {
        if (x < other.x) return -1;
        if (x > other.x) return 1;
        if (y < other.y) return -1;
        if (y > other.y) return 1;
        return 0;
    }
    bool operator==(const Point& other) const = default;
};

In this case, we need to explicitly set bool operator==(const Point& other) const = default; because if operator<=> is not defaulted (e.g. as given explicitly above), then operator== is not automatically defaulted:

Per the rules for any operator<=> overload, a defaulted <=> overload will also allow the type to be compared with <, <=, >, and >=.

If operator<=> is defaulted and operator== is not declared at all, then operator== is implicitly defaulted.

The above example uses the same algorithm as the default operator<=>, as explained by cppreference as:

The default operator<=> performs lexicographical comparison by successively comparing the base (left-to-right depth-first) and then non-static member (in declaration order) subobjects of T to compute <=>, recursively expanding array members (in order of increasing subscript), and stopping early when a not-equal result is found

Before C++20, you could not do something like operator== = default, and defining one operator would not lead to the others being defined, e.g. the following fails to compile with -std=c++17:

#include <cassert>

struct Point {
    int x;
    int y;
    auto operator==(const Point& other) const {
        return x == other.x && y == other.y;
    };
};

int main() {
    Point pt1{1, 1}, pt2{1, 2};

    // Do some checks.
    assert(!(pt1 == pt2));
    assert( (pt1 != pt2));
}

with error:

main.cpp:16:18: error: no match for ‘operator!=’ (operand types are ‘Point’ and ‘Point’)
   16 |     assert( (pt1 != pt2));
      |              ~~~ ^~ ~~~
      |              |      |
      |              Point  Point

The above does compile under -std=c++20 however.

Related: Are any C++ operator overloads provided automatically based on others?

Tested on Ubuntu 20.04, GCC 10.2.0.

0
votes

Three-Way Comparison operator (<=>) is introduced in C++ 20.

This expression returns the object as below;

auto cmp  = a <=> b;

cmp > 0 if a > b
cmp = 0 if a == b
cmp < 0 if a < b  

Example Program

#include <iostream>

using namespace std;

int main()
{
        int lhs = 10, rhs = 20;
        auto result = lhs <=> rhs;

        if (result < 0) {
                cout << "lhs is less than rhs" << endl;
        }
        else if (result > 0) {
                cout << "lhs is greater than rhs" << endl;
        }
        else {
                cout << "lhs and rhs are equal" << endl;
        }

}

How to compile and run?

g++-10 threewaycmp.cpp -std=c++20
./a.out

Result

lhs is less than rhs

Please refer to below link for more details https://en.cppreference.com/w/cpp/language/operator_comparison