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Showing content from https://cplusplus.com/reference/utility/rel_ops/ below:

namespace

<utility>

std::rel_ops 
namespace rel_ops {  template <class T> bool operator!= (const T& x, const T& y);  template <class T> bool operator>  (const T& x, const T& y);  template <class T> bool operator<= (const T& x, const T& y);  template <class T> bool operator>= (const T& x, const T& y);}

Relational Operators

This namespace declares template functions for four relational operators (!=,>, <=, and >=), deriving their behavior from operator== (for !=) and from operator< (for >,<=, and >=): 

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namespace rel_ops {
  template <class T> bool operator!= (const T& x, const T& y) { return !(x==y); }
  template <class T> bool operator>  (const T& x, const T& y) { return y<x; }
  template <class T> bool operator<= (const T& x, const T& y) { return !(y<x); }
  template <class T> bool operator>= (const T& x, const T& y) { return !(x<y); }
}


This avoids the necessity to declare all six relational operators for every complete type; By defining just two: operator== and operator<, and importing this namespace, all six operators will be defined for the type (they will not be selected by argument-dependent lookup when not importing it, though).

Notice that using this namespace introduces these overloads for all types not defining their own. Still, because non-template functions take precedence over template functions, any of these operators may be defined with a different behavior for a specific type.



Template parameters
T
For operator!=, the type shall be EqualityComparable.
A type is EqualityComparable when it supports operator== operations that follow the typical reflexive, symmetric and transitive properties of equalities.

For operator>, operator<=, and operator>=, the type shall be LessThanComparable.


A type is LessThanComparable when it supports operator< operations that define a valid strict weak ordering relation.

Example 
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// rel_ops example:
#include <iostream>     // std::cout, std::boolalpha
#include <utility>      // std::rel_ops
#include <cmath>        // std::sqrt

class vector2d {
public:
  double x,y;
  vector2d (double px,double py): x(px), y(py) {}
  double length() const {return std::sqrt(x*x+y*y);}
  bool operator==(const vector2d& rhs) const {return length()==rhs.length();}
  bool operator< (const vector2d& rhs) const {return length()< rhs.length();}
};

int main () {
  using namespace std::rel_ops;
  vector2d a (10,10);	// length=14.14
  vector2d b (15,5);	// length=15.81
  std::cout << std::boolalpha;
  std::cout << "(a<b) is " << (a<b) << '\n';
  std::cout << "(a>b) is " << (a>b) << '\n';
  return 0;
}

Output: 
(a<b) is true
(a>b) is false

Because we used rel_ops, all types for which operator< is defined (like vector2d) also have operator>.



Data races The arguments are passed to the proper operator== or operator< overload, which can access them.
In any case, none of these functions can modify its arguments (const-qualified).

Exception safety If the type of the elements supports the appropriate operation with no-throw guarantee, the function never throws exceptions (no-throw guarantee).

See also
<utility>
Utility components (header)

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