The three-way comparison operator groups left-to-right.

compare-expression: shift-expression compare-expression <=> shift-expression

The expression p <=> q is a prvalue indicating whether
p is less than, equal to, greater than, or incomparable with
q.

If both operands have arithmetic types,
or one operand has integral type and
the other operand has unscoped enumeration type,
the usual arithmetic conversions are applied to the operands.

Then:

- If a narrowing conversion is required, other than from an integral type to a floating-point type, the program is ill-formed.
- Otherwise, if the operands have integral type, the result is of type std::strong_ordering.The result is std::strong_ordering::equal if both operands are arithmetically equal, std::strong_ordering::less if the first operand is arithmetically less than the second operand, and std::strong_ordering::greater otherwise.
- Otherwise, the operands have floating-point type, and the result is of type std::partial_ordering.The expression a <=> b yields std::partial_ordering::less if a is less than b, std::partial_ordering::greater if a is greater than b, std::partial_ordering::equivalent if a is equivalent to b, and std::partial_ordering::unordered otherwise.

If both operands have the same enumeration type E,
the operator yields the result of
converting the operands to the underlying type of E
and applying <=> to the converted operands.

If at least one of the operands is of pointer type,
array-to-pointer conversions,
pointer conversions,
function pointer conversions,
and
qualification conversions
are performed on both operands
to bring them to their composite pointer type.

If at least one of the operands is of pointer-to-member type,
pointer-to-member conversions
and
qualification conversions
are performed on both operands
to bring them to their composite pointer type.

If both operands are null pointer constants,
but not both of integer type,
pointer conversions
are performed on both operands
to bring them to their composite pointer type.

In all cases, after the conversions, the operands shall have the same type.

[ Note ]

If the composite pointer type is an object pointer type,
p <=> q is of type std::strong_ordering.

If two pointer operands p and q compare equal ([expr.eq]),
p <=> q yields std::strong_ordering::equal;
if p and q compare unequal,
p <=> q yields
std::strong_ordering::less
if q compares greater than p
and
std::strong_ordering::greater
if p compares greater than q ([expr.rel]).

Otherwise, the result is unspecified.

The three comparison category types ([cmp.categories])
(the types
std::strong_ordering,
std::weak_ordering, and
std::partial_ordering)
are not predefined;
if the header <compare> ([compare.syn])
is not imported or included prior to a use of such a class type –
even an implicit use in which the type is not named
(e.g., via the auto specifier
in a defaulted three-way comparison
or use of the built-in operator) – the program is ill-formed.