Given subexpressions E and F, the expression strong_order(E, F) is expression-equivalent ([defns.expression.equivalent]) to the following:

• If the decayed types of E and F differ, strong_order(E, F) is ill-formed.

• Otherwise, strong_ordering(strong_order(E, F)) if it is a well-formed expression where the meaning of strong_order is established as-if by performing argument-dependent lookup only ([basic.lookup.argdep]).

• Otherwise, if the decayed type T of E is a floating-point type, yields a value of type strong_ordering that is consistent with the ordering observed by T's comparison operators, and if numeric_limits<T>​::​is_iec559 is true, is additionally consistent with the totalOrder operation as specified in ISO/IEC 60559.

• Otherwise, strong_ordering(compare_three_way()(E, F)) if it is a well-formed expression.

• Otherwise, strong_order(E, F) is ill-formed.

[Note 1:

Ill-formed cases above result in substitution failure when strong_order(E, F) appears in the immediate context of a template instantiation.

— end note]

Given subexpressions E and F, the expression weak_order(E, F) is expression-equivalent ([defns.expression.equivalent]) to the following:

• If the decayed types of E and F differ, weak_order(E, F) is ill-formed.

• Otherwise, weak_ordering(weak_order(E, F)) if it is a well-formed expression where the meaning of weak_order is established as-if by performing argument-dependent lookup only ([basic.lookup.argdep]).

• Otherwise, if the decayed type T of E is a floating-point type, yields a value of type weak_ordering that is consistent with the ordering observed by T's comparison operators and strong_order, and if numeric_limits<T>​::​is_iec559 is true, is additionally consistent with the following equivalence classes, ordered from lesser to greater:

  • together, all negative NaN values;
  • negative infinity;
  • each normal negative value;
  • each subnormal negative value;
  • together, both zero values;
  • each subnormal positive value;
  • each normal positive value;
  • positive infinity;
  • together, all positive NaN values.

• Otherwise, weak_ordering(compare_three_way()(E, F)) if it is a well-formed expression.

• Otherwise, weak_ordering(strong_order(E, F)) if it is a well-formed expression.

• Otherwise, weak_order(E, F) is ill-formed.

[Note 2:

Ill-formed cases above result in substitution failure when weak_order(E, F) appears in the immediate context of a template instantiation.

— end note]

Given subexpressions E and F, the expression partial_order(E, F) is expression-equivalent ([defns.expression.equivalent]) to the following:

• If the decayed types of E and F differ, partial_order(E, F) is ill-formed.

• Otherwise, partial_ordering(partial_order(E, F)) if it is a well-formed expression where the meaning of partial_order is established as-if by performing argument-dependent lookup only ([basic.lookup.argdep]).

• Otherwise, partial_ordering(compare_three_way()(E, F)) if it is a well-formed expression.

• Otherwise, partial_ordering(weak_order(E, F)) if it is a well-formed expression.

• Otherwise, partial_order(E, F) is ill-formed.

[Note 3:

Ill-formed cases above result in substitution failure when partial_order(E, F) appears in the immediate context of a template instantiation.

— end note]

Given subexpressions E and F, the expression compare_strong_order_fallback(E, F) is expression-equivalent ([defns.expression.equivalent]) to:

• If the decayed types of E and F differ, compare_strong_order_fallback(E, F) is ill-formed.

• Otherwise, strong_order(E, F) if it is a well-formed expression.

• Otherwise, if the expressions E == F and E < F are both well-formed and each of decltype(E == F) and decltype(E < F) models boolean-testable, E == F ? strong_ordering::equal : E < F ? strong_ordering::less : strong_ordering::greater except that E and F are evaluated only once.

• Otherwise, compare_strong_order_fallback(E, F) is ill-formed.

[Note 4:

Ill-formed cases above result in substitution failure when compare_strong_order_fallback(E, F) appears in the immediate context of a template instantiation.

— end note]

Given subexpressions E and F, the expression compare_weak_order_fallback(E, F) is expression-equivalent ([defns.expression.equivalent]) to:

• If the decayed types of E and F differ, compare_weak_order_fallback(E, F) is ill-formed.

• Otherwise, weak_order(E, F) if it is a well-formed expression.

• Otherwise, if the expressions E == F and E < F are both well-formed and each of decltype(E == F) and decltype(E < F) models boolean-testable, E == F ? weak_ordering::equivalent : E < F ? weak_ordering::less : weak_ordering::greater except that E and F are evaluated only once.

• Otherwise, compare_weak_order_fallback(E, F) is ill-formed.

[Note 5:

Ill-formed cases above result in substitution failure when compare_weak_order_fallback(E, F) appears in the immediate context of a template instantiation.

— end note]

Given subexpressions E and F, the expression compare_partial_order_fallback(E, F) is expression-equivalent ([defns.expression.equivalent]) to:

• If the decayed types of E and F differ, compare_partial_order_fallback(E, F) is ill-formed.

• Otherwise, partial_order(E, F) if it is a well-formed expression.

• Otherwise, if the expressions E == F, E < F, and F < E are all well-formed and each of decltype(E == F), decltype(E < F), and decltype(F < E) models boolean-testable, E == F ? partial_ordering::equivalent : E < F ? partial_ordering::less : F < E ? partial_ordering::greater : partial_ordering::unordered except that E and F are evaluated only once.

• Otherwise, compare_partial_order_fallback(E, F) is ill-formed.

[Note 6:

Ill-formed cases above result in substitution failure when compare_partial_order_fallback(E, F) appears in the immediate context of a template instantiation.

— end note]