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

Latest revision as of 19:02, 22 April 2023

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

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

• If std::is_same_v<std::decay_t<T>, std::decay_t<U>> is true:
  • std::strong_ordering(strong_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::strong_order,
  • otherwise, if T is a floating-point type:
    • if std::numeric_limits<T>::is_iec559 is true, performs the ISO/IEC/IEEE 60559 totalOrder comparison of floating-point values and returns that result as a value of type std::strong_ordering (note: this comparison can distinguish between the positive and negative zero and between the NaNs with different representations),
    • otherwise, yields a value of type std::strong_ordering that is consistent with the ordering observed by T's comparison operators,
  • otherwise, std::strong_ordering(std::compare_three_way()(t, u)) if it is well-formed.
• In all other cases, the expression is ill-formed, which can result in substitution failure when it appears in the immediate context of a template instantiation.

Customization point objects

The name std::strong_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 __strong_order_fn.

All instances of __strong_order_fn are equal. The effects of invoking different instances of type __strong_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::strong_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::strong_order above, __strong_order_fn models

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

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

[edit] Strict total order of IEEE floating-point types

Let x and y be values of same IEEE floating-point type, and total_order_less(x, y) be the boolean result indicating if x precedes y in the strict total order defined by totalOrder in ISO/IEC/IEEE 60559.

(total_order_less(x, y) || total_order_less(y, x)) == false if and only if x and y have the same bit pattern.

• if neither x nor y is NaN:
  • if x < y, then total_order_less(x, y) == true;
  • if x > y, then total_order_less(x, y) == false;
  • if x == y,
    • if x is negative zero and y is positive zero, total_order_less(x, y) == true,
    • if x is not zero and x's exponent field is less than y's, then total_order_less(x, y) == (x > 0) (only meaningful for decimal floating-point number);
• if either x or y is NaN:
  • if x is negative NaN and y is not negative NaN, then total_order_less(x, y) == true,
  • if x is not positive NaN and y is positive NaN, then total_order_less(x, y) == true,
  • if both x and y are NaNs with the same sign and x's mantissa field is less than y's, then total_order_less(x, y) == !std::signbit(x).

[edit] Example

[edit] See also