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

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 object pointer type and
the other operand is of object pointer or array type,
array-to-pointer conversions ([conv.array]),
pointer conversions ([conv.ptr]),
and
qualification conversions
are performed on both operands
to bring them to their composite pointer type ([expr.type]).

After the conversions, the operands shall have the same type.

[*Note 1*: *end note*]

If both of the operands are arrays,
array-to-pointer conversions are not applied.

—
In this case,
p <=> q is of type std::strong_ordering and
the result is defined by the following rules:

- If two pointer operands p and q compare equal ([expr.eq]), p <=> q yields std::strong_ordering::equal;
- otherwise, 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 a standard library declaration ([compare.syn], [std.modules])
of such a class type does not precede ([basic.lookup.general])
a use of that type —
even an implicit use in which the type is not named
(e.g., via the auto specifier ([dcl.spec.auto])
in a defaulted three-way comparison ([class.spaceship])
or use of the built-in operator) — the program is ill-formed.