17 Language support library [support]

17.11 Comparisons [cmp]

17.11.6 Comparison algorithms [cmp.alg]

The name strong_order denotes a customization point object ([customization.point.object]).

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

(1.1)
If the decayed types of E and F differ, strong_order(E, F) is ill-formed.
(1.2)
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]).
(1.3)
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.
(1.4)
Otherwise, strong_ordering(compare_three_way()(E, F)) if it is a well-formed expression.
(1.5)
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]

The name weak_order denotes a customization point object ([customization.point.object]).

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

(2.1)
If the decayed types of E and F differ, weak_order(E, F) is ill-formed.
(2.2)
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]).
(2.3)
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:
- (2.3.1)
  together, all negative NaN values;
- (2.3.2)
  negative infinity;
- (2.3.3)
  each normal negative value;
- (2.3.4)
  each subnormal negative value;
- (2.3.5)
  together, both zero values;
- (2.3.6)
  each subnormal positive value;
- (2.3.7)
  each normal positive value;
- (2.3.8)
  positive infinity;
- (2.3.9)
  together, all positive NaN values.
(2.4)
Otherwise, weak_ordering(compare_three_way()(E, F)) if it is a well-formed expression.
(2.5)
Otherwise, weak_ordering(strong_order(E, F)) if it is a well-formed expression.
(2.6)
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]

The name partial_order denotes a customization point object ([customization.point.object]).

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

(3.1)
If the decayed types of E and F differ, partial_order(E, F) is ill-formed.
(3.2)
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]).
(3.3)
Otherwise, partial_ordering(compare_three_way()(E, F)) if it is a well-formed expression.
(3.4)
Otherwise, partial_ordering(weak_order(E, F)) if it is a well-formed expression.
(3.5)
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]

The name compare_strong_order_fallback denotes a customization point object ([customization.point.object]).

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

(4.1)
If the decayed types of E and F differ, compare_strong_order_fallback(E, F) is ill-formed.
(4.2)
Otherwise, strong_order(E, F) if it is a well-formed expression.
(4.3)
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.
(4.4)
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]

The name compare_weak_order_fallback denotes a customization point object ([customization.point.object]).

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

(5.1)
If the decayed types of E and F differ, compare_weak_order_fallback(E, F) is ill-formed.
(5.2)
Otherwise, weak_order(E, F) if it is a well-formed expression.
(5.3)
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.
(5.4)
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]

The name compare_partial_order_fallback denotes a customization point object ([customization.point.object]).

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

(6.1)
If the decayed types of E and F differ, compare_partial_order_fallback(E, F) is ill-formed.
(6.2)
Otherwise, partial_order(E, F) if it is a well-formed expression.
(6.3)
Otherwise, if the expressions E == F, E < F, and F < E are all well-formed and each of decltype(E == F) and decltype(E < F) 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.
(6.4)
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]