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[cmp.alg]
# 17 Language support library [[support]](./#support)
## 17.12 Comparisons [[cmp]](cmp#alg)
### 17.12.6 Comparison algorithms [cmp.alg]
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5480)
The name strong_order denotes
a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#1.sentence-1)
Given subexpressions E and F,
the expression strong_order(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to the following:
- [(1.1)](#1.1)
If the decayed types of E and F differ, strong_order(E, F) is ill-formed[.](#1.1.sentence-1)
- [(1.2)](#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]](basic.lookup.argdep "6.5.4 Argument-dependent name lookup"))[.](#1.2.sentence-1)
- [(1.3)](#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[.](#1.3.sentence-1)
- [(1.4)](#1.4)
Otherwise, strong_ordering(compare_three_way()(E, F)) if it is a well-formed expression[.](#1.4.sentence-1)
- [(1.5)](#1.5)
Otherwise, strong_order(E, F) is ill-formed[.](#1.5.sentence-1)
[*Note [1](#note-1)*:
Ill-formed cases above result in substitution failure
when strong_order(E, F) appears in the immediate context
of a template instantiation[.](#1.sentence-3)
— *end note*]
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5518)
The name weak_order denotes
a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#2.sentence-1)
Given subexpressions E and F,
the expression weak_order(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to the following:
- [(2.1)](#2.1)
If the decayed types of E and F differ, weak_order(E, F) is ill-formed[.](#2.1.sentence-1)
- [(2.2)](#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]](basic.lookup.argdep "6.5.4 Argument-dependent name lookup"))[.](#2.2.sentence-1)
- [(2.3)](#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)](#2.3.1)
together, all negative NaN values;
* [(2.3.2)](#2.3.2)
negative infinity;
* [(2.3.3)](#2.3.3)
each normal negative value;
* [(2.3.4)](#2.3.4)
each subnormal negative value;
* [(2.3.5)](#2.3.5)
together, both zero values;
* [(2.3.6)](#2.3.6)
each subnormal positive value;
* [(2.3.7)](#2.3.7)
each normal positive value;
* [(2.3.8)](#2.3.8)
positive infinity;
* [(2.3.9)](#2.3.9)
together, all positive NaN values[.](#2.3.sentence-1)
- [(2.4)](#2.4)
Otherwise, weak_ordering(compare_three_way()(E, F)) if it is a well-formed expression[.](#2.4.sentence-1)
- [(2.5)](#2.5)
Otherwise, weak_ordering(strong_order(E, F)) if it is a well-formed expression[.](#2.5.sentence-1)
- [(2.6)](#2.6)
Otherwise, weak_order(E, F) is ill-formed[.](#2.6.sentence-1)
[*Note [2](#note-2)*:
Ill-formed cases above result in substitution failure
when weak_order(E, F) appears in the immediate context
of a template instantiation[.](#2.sentence-3)
— *end note*]
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5570)
The name partial_order denotes
a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#3.sentence-1)
Given subexpressions E and F,
the expression partial_order(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to the following:
- [(3.1)](#3.1)
If the decayed types of E and F differ, partial_order(E, F) is ill-formed[.](#3.1.sentence-1)
- [(3.2)](#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]](basic.lookup.argdep "6.5.4 Argument-dependent name lookup"))[.](#3.2.sentence-1)
- [(3.3)](#3.3)
Otherwise, partial_ordering(compare_three_way()(E, F)) if it is a well-formed expression[.](#3.3.sentence-1)
- [(3.4)](#3.4)
Otherwise, partial_ordering(weak_order(E, F)) if it is a well-formed expression[.](#3.4.sentence-1)
- [(3.5)](#3.5)
Otherwise, partial_order(E, F) is ill-formed[.](#3.5.sentence-1)
[*Note [3](#note-3)*:
Ill-formed cases above result in substitution failure
when partial_order(E, F) appears in the immediate context
of a template instantiation[.](#3.sentence-3)
— *end note*]
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5602)
The name compare_strong_order_fallback denotes a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#4.sentence-1)
Given subexpressions E and F,
the expression compare_strong_order_fallback(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to:
- [(4.1)](#4.1)
If the decayed types of E and F differ, compare_strong_order_fallback(E, F) is ill-formed[.](#4.1.sentence-1)
- [(4.2)](#4.2)
Otherwise, strong_order(E, F) if it is a well-formed expression[.](#4.2.sentence-1)
- [(4.3)](#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*](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]"),E == F ? strong_ordering::equal : E < F ? strong_ordering::less : strong_ordering::greater except that E and F are evaluated only once[.](#4.3.sentence-1)
- [(4.4)](#4.4)
Otherwise, compare_strong_order_fallback(E, F) is ill-formed[.](#4.4.sentence-1)
[*Note [4](#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[.](#4.sentence-3)
— *end note*]
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5636)
The name compare_weak_order_fallback denotes
a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#5.sentence-1)
Given subexpressions E and F,
the expression compare_weak_order_fallback(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to:
- [(5.1)](#5.1)
If the decayed types of E and F differ, compare_weak_order_fallback(E, F) is ill-formed[.](#5.1.sentence-1)
- [(5.2)](#5.2)
Otherwise, weak_order(E, F) if it is a well-formed expression[.](#5.2.sentence-1)
- [(5.3)](#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*](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]"),E == F ? weak_ordering::equivalent : E < F ? weak_ordering::less : weak_ordering::greater except that E and F are evaluated only once[.](#5.3.sentence-1)
- [(5.4)](#5.4)
Otherwise, compare_weak_order_fallback(E, F) is ill-formed[.](#5.4.sentence-1)
[*Note [5](#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[.](#5.sentence-3)
— *end note*]
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/support.tex#L5670)
The name compare_partial_order_fallback denotes
a customization point object ([[customization.point.object]](customization.point.object "16.3.3.3.5 Customization Point Object types"))[.](#6.sentence-1)
Given subexpressions E and F,
the expression compare_partial_order_fallback(E, F) is expression-equivalent ([[defns.expression.equivalent]](defns.expression.equivalent "3.22 expression-equivalent")) to:
- [(6.1)](#6.1)
If the decayed types of E and F differ, compare_partial_order_fallback(E, F) is ill-formed[.](#6.1.sentence-1)
- [(6.2)](#6.2)
Otherwise, partial_order(E, F) if it is a well-formed expression[.](#6.2.sentence-1)
- [(6.3)](#6.3)
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*](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]"),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[.](#6.3.sentence-1)
- [(6.4)](#6.4)
Otherwise, compare_partial_order_fallback(E, F) is ill-formed[.](#6.4.sentence-1)
[*Note [6](#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[.](#6.sentence-3)
— *end note*]