Difference between revisions of "cpp/utility/compare/weak order"

Revision as of 00:19, 6 September 2019

Compares two values using 3-way comparison and produces a result of type std::weak_ordering

Let t and u be expressions and T and U denote decltype((t)) and decltype((u)) respectively, std::weak_order(t, u) is expression-equivalent to:

• If std::is_same_v<std::decay_t<T>, std::decay_t<U>> == true:
  • std::weak_ordering(weak_order(t, u)), if it is a well-formed expression with overload resolution performed in a context that does not include a declaration of std​::​weak_order,
  • otherwise, if T is a floating-point type:
    • if std::numeric_limits<T>::is_iec559 is true, performs the weak ordering comparison of floating-point values (see below) and returns that result as a value of type std::weak_ordering,
    • otherwise, yields a value of type std::weak_ordering that is consistent with the ordering observed by T's comparison operators,
  • otherwise, std::weak_ordering(t <=> u) if it is well-formed,
  • other the expression is ill-formed, which can result in substitution failure when it appears in the immediate context of a template instantiation.
• Otherwise, std::weak_order(t, u) is ill-formed.

Expression-equivalent

Expression e is expression-equivalent to expression f, if

• e and f have the same effects, and
• either both are constant subexpressions or else neither is a constant subexpression, and
• either both are potentially-throwing or else neither is potentially-throwing (i.e. noexcept(e) == noexcept(f)).

Customization point objects

The name std::weak_order denotes a customization point object, which is a const function object of a literal semiregular class type. For exposition purposes, the cv-unqualified version of its type is denoted as __weak_order_fn.

All instances of __weak_order_fn are equal. The effects of invoking different instances of type __weak_order_fn on the same arguments are equivalent, regardless of whether the expression denoting the instance is an lvalue or rvalue, and is const-qualified or not (however, a volatile-qualified instance is not required to be invocable). Thus, std::weak_order can be copied freely and its copies can be used interchangeably.

Given a set of types Args..., if std::declval<Args>()... meet the requirements for arguments to std::weak_order above, __weak_order_fn models

• std::invocable<__weak_order_fn, Args...>,
• std::invocable<const __weak_order_fn, Args...>,
• std::invocable<__weak_order_fn&, Args...>, and
• std::invocable<const __weak_order_fn&, Args...>.
  

Otherwise, no function call operator of __weak_order_fn participates in overload resolution.

Notes

Weak order of IEEE floating-point types

Let x and y be values of same IEEE floating-point type, and weak_order_less(x, y) be the boolean result indicating if x precedes y in the strict weak order defined by the C++ standard.

• If neither x nor y is NaN, then weak_order_less(x, y) == true if and only if x < y, i.e. all representations of equal floating-point value are equivalent;
• If x is negative NaN and y is not negative NaN, then weak_order_less(x, y) == true;
• If x is not positive NaN and y is positive NaN, then weak_order_less(x, y) == true;
• If both x and y are NaNs with the same sign, then weak_order_less(x, y) || weak_order_less(y, x) == false, i.e. all NaNs with the same sign are equivalent.

Example

See also