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What are "sequence points"?
What is the relation between undefined behaviour and sequence points?
I often use funny and convoluted expressions like a[++i] = i;, to make myself feel better. Why should I stop using them?
If you've read this, be sure to visit the follow-up question Undefined behavior and sequence points reloaded.
(Note: This is meant to be an entry to Stack Overflow's C++ FAQ. If you want to critique the idea of providing an FAQ in this form, then the posting on meta that started all this would be the place to do that. Answers to that question are monitored in the C++ chatroom, where the FAQ idea started out in the first place, so your answer is very likely to get read by those who came up with the idea.)
C++98 and C++03
This answer is for the older versions of the C++ standard. The C++11 and C++14 versions of the standard do not formally contain 'sequence points'; operations are 'sequenced before' or 'unsequenced' or 'indeterminately sequenced' instead. The net effect is essentially the same, but the terminology is different.
Disclaimer : Okay. This answer is a bit long. So have patience while reading it. If you already know these things, reading them again won't make you crazy.
Pre-requisites : An elementary knowledge of C++ Standard
What are Sequence Points?
The Standard says
At certain specified points in the execution sequence called sequence points, all side effects of previous evaluations
shall be complete and no side effects of subsequent evaluations shall have taken place. (§1.9/7)
Side effects? What are side effects?
Evaluation of an expression produces something and if in addition there is a change in the state of the execution environment it is said that the expression (its evaluation) has some side effect(s).
For example:
int x = y++; //where y is also an int
In addition to the initialization operation the value of y gets changed due to the side effect of ++ operator.
So far so good. Moving on to sequence points. An alternation definition of seq-points given by the comp.lang.c author Steve Summit:
Sequence point is a point in time at which the dust has settled and all side effects which have been seen so far are guaranteed to be complete.
What are the common sequence points listed in the C++ Standard?
Those are:
at the end of the evaluation of full expression (§1.9/16) (A full-expression is an expression that is not a subexpression of another expression.)1
Example :
int a = 5; // ; is a sequence point here
in the evaluation of each of the following expressions after the evaluation of the first expression (§1.9/18) 2
a && b (§5.14)
a || b (§5.15)
a ? b : c (§5.16)
a , b (§5.18) (here a , b is a comma operator; in func(a,a++) , is not a comma operator, it's merely a separator between the arguments a and a++. Thus the behaviour is undefined in that case (if a is considered to be a primitive type))
at a function call (whether or not the function is inline), after the evaluation of all function arguments (if any) which
takes place before execution of any expressions or statements in the function body (§1.9/17).
1 : Note : the evaluation of a full-expression can include the evaluation of subexpressions that are not lexically
part of the full-expression. For example, subexpressions involved in evaluating default argument expressions (8.3.6) are considered to be created in the expression that calls the function, not the expression that defines the default argument
2 : The operators indicated are the built-in operators, as described in clause 5. When one of these operators is overloaded (clause 13) in a valid context, thus designating a user-defined operator function, the expression designates a function invocation and the operands form an argument list, without an implied sequence point between them.
What is Undefined Behaviour?
The Standard defines Undefined Behaviour in Section §1.3.12 as
behavior, such as might arise upon use of an erroneous program construct or erroneous data, for which this International Standard imposes no requirements 3.
Undefined behavior may also be expected when this
International Standard omits the description of any explicit definition of behavior.
3 : permissible undefined behavior ranges from ignoring the situation completely with unpredictable results, to behaving during translation or program execution in a documented manner characteristic of the environment (with or with-
out the issuance of a diagnostic message), to terminating a translation or execution (with the issuance of a diagnostic message).
In short, undefined behaviour means anything can happen from daemons flying out of your nose to your girlfriend getting pregnant.
What is the relation between Undefined Behaviour and Sequence Points?
Before I get into that you must know the difference(s) between Undefined Behaviour, Unspecified Behaviour and Implementation Defined Behaviour.
You must also know that the order of evaluation of operands of individual operators and subexpressions of individual expressions, and the order in which side effects take place, is unspecified.
For example:
int x = 5, y = 6;
int z = x++ + y++; //it is unspecified whether x++ or y++ will be evaluated first.
Another example here.
Now the Standard in §5/4 says
Between the previous and next sequence point a scalar object shall have its stored value modified at most once by the evaluation of an expression.
What does it mean?
Informally it means that between two sequence points a variable must not be modified more than once.
In an expression statement, the next sequence point is usually at the terminating semicolon, and the previous sequence point is at the end of the previous statement. An expression may also contain intermediate sequence points.
From the above sentence the following expressions invoke Undefined Behaviour:
i++ * ++i; // UB, i is modified more than once btw two SPs
i = ++i; // UB, same as above
++i = 2; // UB, same as above
i = ++i + 1; // UB, same as above
++++++i; // UB, parsed as (++(++(++i)))
i = (i, ++i, ++i); // UB, there's no SP between `++i` (right most) and assignment to `i` (`i` is modified more than once btw two SPs)
But the following expressions are fine:
i = (i, ++i, 1) + 1; // well defined (AFAIK)
i = (++i, i++, i); // well defined
int j = i;
j = (++i, i++, j*i); // well defined
Furthermore, the prior value shall be accessed only to determine the value to be stored.
What does it mean? It means if an object is written to within a full expression, any and all accesses to it within the same expression must be directly involved in the computation of the value to be written.
For example in i = i + 1 all the access of i (in L.H.S and in R.H.S) are directly involved in computation of the value to be written. So it is fine.
This rule effectively constrains legal expressions to those in which the accesses demonstrably precede the modification.
Example 1:
std::printf("%d %d", i,++i); // invokes Undefined Behaviour because of Rule no 2
Example 2:
a[i] = i++ // or a[++i] = i or a[i++] = ++i etc
is disallowed because one of the accesses of i (the one in a[i]) has nothing to do with the value which ends up being stored in i (which happens over in i++), and so there's no good way to define--either for our understanding or the compiler's--whether the access should take place before or after the incremented value is stored. So the behaviour is undefined.
Example 3 :
int x = i + i++ ;// Similar to above
Follow up answer for C++11 here.
This is a follow up to my previous answer and contains C++11 related material..
Pre-requisites : An elementary knowledge of Relations (Mathematics).
Is it true that there are no Sequence Points in C++11?
Yes! This is very true.
Sequence Points have been replaced by Sequenced Before and Sequenced After (and Unsequenced and Indeterminately Sequenced) relations in C++11.
What exactly is this 'Sequenced before' thing?
Sequenced Before(§1.9/13) is a relation which is:
Asymmetric
Transitive
between evaluations executed by a single thread and induces a strict partial order1
Formally it means given any two evaluations(See below) A and B, if A is sequenced before B, then the execution of A shall precede the execution of B. If A is not sequenced before B and B is not sequenced before A, then A and B are unsequenced 2.
Evaluations A and B are indeterminately sequenced when either A is sequenced before B or B is sequenced before A, but it is unspecified which3.
[NOTES]
1 : A strict partial order is a binary relation "<" over a set P which is asymmetric, and transitive, i.e., for all a, b, and c in P, we have that:
........(i). if a < b then ¬ (b < a) (asymmetry);
........(ii). if a < b and b < c then a < c (transitivity).
2 : The execution of unsequenced evaluations can overlap.
3 : Indeterminately sequenced evaluations cannot overlap, but either could be executed first.
What is the meaning of the word 'evaluation' in context of C++11?
In C++11, evaluation of an expression (or a sub-expression) in general includes:
value computations (including determining the identity of an object for glvalue evaluation and fetching a value previously assigned to an object for prvalue evaluation) and
initiation of side effects.
Now (§1.9/14) says:
Every value computation and side effect associated with a full-expression is sequenced before every value computation and side effect associated with the next full-expression to be evaluated.
Trivial example:
int x;
x = 10;
++x;
Value computation and side effect associated with ++x is sequenced after the value computation and side effect of x = 10;
So there must be some relation between Undefined Behaviour and the above-mentioned things, right?
Yes! Right.
In (§1.9/15) it has been mentioned that
Except where noted, evaluations of operands of individual operators and of subexpressions of individual expressions are unsequenced4.
For example :
int main()
{
int num = 19 ;
num = (num << 3) + (num >> 3);
}
Evaluation of operands of + operator are unsequenced relative to each other.
Evaluation of operands of << and >> operators are unsequenced relative to each other.
4: In an expression that is evaluated more than once during the execution
of a program, unsequenced and indeterminately sequenced evaluations of its subexpressions need not be performed consistently in different evaluations.
(§1.9/15)
The value computations of the operands of an
operator are sequenced before the value computation of the result of the operator.
That means in x + y the value computation of x and y are sequenced before the value computation of (x + y).
More importantly
(§1.9/15) If a side effect on a scalar object is unsequenced relative to either
(a) another side effect on the same scalar object
or
(b) a value computation using the value of the same scalar object.
the behaviour is undefined.
Examples:
int i = 5, v[10] = { };
void f(int, int);
i = i++ * ++i; // Undefined Behaviour
i = ++i + i++; // Undefined Behaviour
i = ++i + ++i; // Undefined Behaviour
i = v[i++]; // Undefined Behaviour
i = v[++i]: // Well-defined Behavior
i = i++ + 1; // Undefined Behaviour
i = ++i + 1; // Well-defined Behaviour
++++i; // Well-defined Behaviour
f(i = -1, i = -1); // Undefined Behaviour (see below)
When calling a function (whether or not the function is inline), every value computation and side effect associated with any argument expression, or with the postfix expression designating the called function, is sequenced before execution of every expression or statement in the body of the called function. [Note: Value computations and side effects associated with different argument expressions are unsequenced. — end note]
Expressions (5), (7) and (8) do not invoke undefined behaviour. Check out the following answers for a more detailed explanation.
Multiple preincrement operations on a variable in C++0x
Unsequenced Value Computations
Final Note :
If you find any flaw in the post please leave a comment. Power-users (With rep >20000) please do not hesitate to edit the post for correcting typos and other mistakes.
C++17 (N4659) includes a proposal Refining Expression Evaluation Order for Idiomatic C++
which defines a stricter order of expression evaluation.
In particular, the following sentence
8.18 Assignment and compound assignment operators:....
In all cases, the assignment is sequenced after the value
computation of the right and left operands, and before the value computation of the assignment expression.
The right operand is sequenced before the left operand.
together with the following clarification
An expression X is said to be sequenced before an expression Y if every
value computation and every side effect associated with the expression X is sequenced before every value
computation and every side effect associated with the expression Y.
make several cases of previously undefined behavior valid, including the one in question:
a[++i] = i;
However several other similar cases still lead to undefined behavior.
In N4140:
i = i++ + 1; // the behavior is undefined
But in N4659
i = i++ + 1; // the value of i is incremented
i = i++ + i; // the behavior is undefined
Of course, using a C++17 compliant compiler does not necessarily mean that one should start writing such expressions.
I am guessing there is a fundamental reason for the change, it isn't merely cosmetic to make the old interpretation clearer: that reason is concurrency. Unspecified order of elaboration is merely selection of one of several possible serial orderings, this is quite different to before and after orderings, because if there is no specified ordering, concurrent evaluation is possible: not so with the old rules. For example in:
f (a,b)
previously either a then b, or, b then a. Now, a and b can be evaluated with instructions interleaved or even on different cores.
In C99(ISO/IEC 9899:TC3) which seems absent from this discussion thus far the following steteents are made regarding order of evaluaiton.
[...]the order of evaluation of subexpressions and the order in which
side effects take place are both unspecified. (Section 6.5 pp 67)
The order of evaluation of the operands is unspecified. If an attempt
is made to modify the result of an assignment operator or to access it
after the next sequence point, the behavior[sic] is undefined.(Section
6.5.16 pp 91)
In this answer there're some examples of well-defined and undefined expressions. I'm particularly interested in two of them:
(6) i = i++ + 1; // Undefined Behaviour
(7) i = ++i + 1; // Well-defined Behaviour
This means that there's a difference between pre-increment and post-increment in terms of sequence points and well defined /unspecified/undefined behavior, but I don't understand where this difference comes from.
In standard draft (N4618) there's an example of code ([intro.execution], pt 18)
i = i++ + 1; // the value of i is incremented
i = i++ + i; // the behavior is undefined
Which, as far as I understand, means that expression i = i++ + 1 should be well-defined and the value of a variable i should increase by 1 as the result of this expression. However, this code run in MSVS 2015 increases i by 2.
So, what happens in the expression i = i++ + 1? Is it well-defined, undefined, implementation-defined or unspecified behavior? And is there any difference between pre-increment and post-increment in this and similar expressions in terms of sequence points and UB, as stated in the original answer? And why Visual Studio shows the behavior which is different from written in standard?
Please also note that I'm primarily interested in modern c++ (14/17).
What happens in the expression i = i++ + 1? Is it well-defined, undefined, implementation defined or unspecified behaviour?
This exact example is given in the standard, how lucky are we?
N4296 1.9.15 [intro.execution]
i = i++ + 1; // the behavior is undefined
Of course, we'd like to know why too. The following standard quote appears to be relevant here:
N4296 1.9.15 [intro.execution]
[ ... ] The value computations of the operands of an operator are sequenced
before the value computation of the result of the operator. [ ... ]
This tells us that the sum will occur before the assignment (duh, how else does it know what to assign!), but it doesn't guarantee that the increment will occur before or after the assignment, now we're in murky water...
N4296 1.9.15 [intro.execution]
[ ... ] If a side effect on a scalar object is unsequenced relative to either
another side effect on the same scalar object or a value computation
using the value of the same scalar object, and they are not
potentially concurrent (1.10), the behavior is undefined. [ ... ]
The assignment operator has a side effect on the value of i, which means we have two side effects (the other is the assignment performed by i++) on the same scalar object, which are unsequenced, which is undefined.
Why does Visual Studio show the behavior which is different from written in standard?
It doesn't. The standard says it's undefined, which means it can do anything from what you wanted to something completely different, it just so happens that this is the behaviour that got spat out by the compiler!
i = ++i + 1; // Well-defined Behaviour
This means that there's a difference between preincrement and postincrement in terms of sequence points and well defined / unspecified / undefined behavior, but I don't understand where this difference comes from.
I believe that post is incorrect in several ways. Quoting the same section as they do, emphasis mine:
C++11 1.9/15
The value computations of the operands of an
operator are sequenced before the value computation of the result of the operator. If a side effect on a scalar
object is unsequenced relative to either another side effect on the same scalar object or a value computation
using the value of the same scalar object, the behavior is undefined.
Then the assignment operator:
C++11 5.17
In all cases, the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression.
Notable, the value computation or the right and left operands is not sequenced. (This has been explicitly spelled out in C11 1), which otherwise has a completely identical text as C++11.)
Meaning that in the expression i = ++i + 1; the side effect of ++i is unsequenced in relation to the value computation of the left operand i. Thus it is undefined behavior as per 1.9/15. And the UB has nothing to do with the assignment side-effect at all.
As for the expression i = i++ + 1;, the side-effect of assignment is, as per C++11, explicitly sequenced after the value computations, but before the value computation of the expression as whole. The value computation of i++ is not an issue as per 5.2.6 "The value computation of the ++ expression is sequenced before the modification of the operand object". As per the nature of the postfix ++, the side effect of updating i++ must be sequenced after the value computation of the whole expression. It is well-defined behavior, as far as I can tell.
Correct text should therefore be
(6) i = i++ + 1; // Well-defined Behaviour
(7) i = ++i + 1; // Undefined Behaviour
Apparently there was an incorrect example in C++11 1.9/15 i = i++ + 1; // the behavior is undefined which has been corrected in later versions of the standard.
NOTE: None of this has the slightest to do with the change of wording about sequence points!
1) C11 6.5.16/3
The side effect of updating the stored value of the
left operand is sequenced after the value computations of the left and
right operands. The evaluations of the operands are unsequenced.
There was a debate today among some of my colleagues and I wanted to clarify it. It is about the evaluation order and the sequence point in an expression. It is clearly stated in the standard that C/C++ does not have a left-to-right evaluation in an expression unlike languages like Java which is guaranteed to have a sequencial left-to-right order. So, in the below expression, the evaluation of the leftmost operand(B) in the binary operation is sequenced before the evaluation of the rightmost operand(C):
A = B B_OP C
The following expression according, to CPPReference under the subsection Sequenced-before rules(Undefined Behaviour) and Bjarne's TCPPL 3rd ed, is an UB
x = x++ + 1;
It could be interpreted as the compilers like BUT the expression below is said to be clearly a well defined behaviour in C++11
x = ++x + 1;
So, if the above expression is well defined, what is the "fate" of this?
array[x] = ++x;
It seems the evaluation of a post-increment and post-decrement is not defined but the pre-increment and the pre-decrement is defined.
NOTE: This is not used in a real-life code. Clang 3.4 and GCC 4.8 clearly warns about both the pre- and post-increment sequence point.
Lets see what the standard says about sequencing:
C++11 5.17/1: the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression.
So the evaluation of the operands array[x] and ++x are not sequenced with respect to each other. Both use the value of x, and one modifies it, giving undefined behaviour.
(The second example differs by not using the value of x in the left operand; it remains an lvalue).
In array[x] = ++x;, there are two value computations on the scalar object x, and one side effect on x.
The value computation of ++x is sequenced relative to its side effect, but the value computation of x in array[x] is not sequenced relative to the side effect of ++x.
So the behavior is undefined.
The difference between x = ++x and array[x] = ++x is that in the former the appearance of x on the LHS is subject to side effect, while in the latter the x on the LHS is subject to value computation.
With the new college year upon us.
We have started to receive the standard why does ++ i ++ not work as expected questions.
After just answering one of these type of questions I was told that the new C++11 standard has changed and this is no longer undefined behavior. I have heard that sequence points have been replaced by sequenced before and sequenced after but have not read deep (or at all) into the subject.
So the question I was just answering had:
int i = 12;
k = ++ (++ i);
So the question is:
How has the sequence points changes in C++11 and how does it affect questions like the above. Is it still undefined behavior or is this now well defined?
The UB in those cases is based on [intro.execution]/15
Except where noted, evaluations of operands of individual operators and of subexpressions of individual expressions are unsequenced. [...] The value computations of the operands of an operator are sequenced before the value computation of the result of the operator. If a side effect on a scalar object is unsequenced relative to either another side effect on the same scalar object or a value computation using the value of the same scalar object, the behavior is undefined.
For ++(++i): [expr.pre.incr]/1 states that ++i is defined as i+=1. This leads to [expr.ass]/1, which says
In all cases, the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression.
Therefore, for ++(++i), equivalent to (i+=1)+=1, the inner assignment is sequenced before the outer assignment, and we have no UB.
[intro.execution]/15 has an example of UB:
i = i++ + 1; // the behavior is undefined
The case here is a bit different (thanks to Oktalist for pointing out a pre/postfix mistake here). [expr.post.incr]/1 describes the effects of postfix increment. It states:
The value computation of the ++ expression is sequenced before the modification of the operand object.
However, there is no requirement on the sequencing of the side effect (the modification of i). Such a requirement could also be imposed by the assignment-expression. But the assignment-expression only requires the value computations (but not the side effects) of the operands to be sequenced before the assignment. Therefore, the two modifications via i = .. and i++ are unsequenced, and we get undefined behaviour.
N.B. i = (i = 1); does not have the same problem: The inner assignment guarantees the side effect of i = 1 is sequenced before the value computation of the same expression. And the value is required for the outer assignment, which guarantees that it (the value computation of the right operand (i = 1)) is sequenced before the side effect of the outer assignment. Similarly, i = ++i + 1; (equivalent to i = (i+=1) + 1;) has defined behaviour.
The comma operator is an example where the side effects are sequenced; [expr.comma]/1
Every value computation and side effect associated with the left expression is sequenced before every value computation and side effect associated with the right expression.
[intro.execution]/15 includes the example i = 7, i++, i++; (read: (i=7), i++, i++;), which is defined behaviour (i becomes 9).
I don't think sequencing is relevant to your situation. The expression ++i++ is grouped as ++(i++), so:
If i is a built-in type, then this is invalid, since i++ is an rvalue.
If i is of user-defined type and the operators are overloaded, this is a nested function call, such as T::operator++(T::operator++(i), 0), and function arguments are evaluated before the function call is evaluated.
Sorry for opening this topic again, but thinking about this topic itself has started giving me an Undefined Behavior. Want to move into the zone of well-defined behavior.
Given
int i = 0;
int v[10];
i = ++i; //Expr1
i = i++; //Expr2
++ ++i; //Expr3
i = v[i++]; //Expr4
I think of the above expressions (in that order) as
operator=(i, operator++(i)) ; //Expr1 equivalent
operator=(i, operator++(i, 0)) ; //Expr2 equivalent
operator++(operator++(i)) ; //Expr3 equivalent
operator=(i, operator[](operator++(i, 0)); //Expr4 equivalent
Now coming to behaviors here are the important quotes from C++ 0x.
$1.9/12- "Evaluation of an expression
(or a sub-expression) in general
includes both value computations
(including determining the identity of
an object for lvalue evaluation and
fetchinga value previously assigned to
an object for rvalue evaluation) and
initiation of side effects."
$1.9/15- "If a side effect on a scalar
object is unsequenced relative to
either another side effect on the same
scalar object or a value
computation using the value of the
same scalar object, the behavior is
undefined."
[ Note: Value computations and side
effects associated with different
argument expressions are unsequenced.
—end note ]
$3.9/9- "Arithmetic types (3.9.1),
enumeration types, pointer types,
pointer to member types (3.9.2),
std::nullptr_t, and cv-qualified
versions of these types (3.9.3) are
collectively called scalar types."
In Expr1, the evaluation of the expression i (first argument), is unsequenced with respect to the evaluation of the expession operator++(i) (which has a side effect).
Hence Expr1 has undefined behavior.
In Expr2, the evaluation of the expression i (first argument), is unsequenced with respect to the evaluation of the expession operator++(i, 0) (which has a side effect)'.
Hence Expr2 has undefined behavior.
In Expr3, the evaluation of the lone argument operator++(i) is required to be complete before the outer operator++ is called.
Hence Expr3 has well defined behavior.
In Expr4, the evaluation of the expression i (first argument) is unsequenced with respect to the evaluation of the operator[](operator++(i, 0) (which has a side effect).
Hence Expr4 has undefined behavior.
Is this understanding correct?
P.S. The method of analyzing the expressions as in OP is not correct. This is because, as #Potatoswatter, notes - "clause 13.6 does not apply. See the disclaimer in 13.6/1, "These candidate functions participate in the operator overload resolution process as described in 13.3.1.2 and are used for no other purpose." They are just dummy declarations; no function-call semantics exist with respect to built-in operators."
Native operator expressions are not equivalent to overloaded operator expressions. There is a sequence point at the binding of values to function arguments, which makes the operator++() versions well-defined. But that doesn't exist for the native-type case.
In all four cases, i changes twice within the full-expression. Since no ,, ||, or && appear in the expressions, that's instant UB.
§5/4:
Between the previous and next sequence point a scalar object shall have its stored value modified at most once by the evaluation of an expression.
Edit for C++0x (updated)
§1.9/15:
The value computations of the operands of an operator are sequenced before the value computation of the result of the operator. If a side effect on a scalar object is unsequenced relative to either another side effect on the same scalar object or a value computation using the value of the same scalar object, the behavior is undefined.
Note however that a value computation and a side effect are two distinct things. If ++i is equivalent to i = i+1, then + is the value computation and = is the side effect. From 1.9/12:
Evaluation of an expression (or a sub-expression) in general includes both value computations (including determining the identity of an object for glvalue evaluation and fetching a value previously assigned to an object for prvalue evaluation) and initiation of side effects.
So although the value computations are more strongly sequenced in C++0x than C++03, the side effects are not. Two side effects in the same expression, unless otherwise sequenced, produce UB.
Value computations are ordered by their data dependencies anyway and, side effects absent, their order of evaluation is unobservable, so I'm not sure why C++0x goes to the trouble of saying anything, but that just means I need to read more of the papers by Boehm and friends wrote.
Edit #3:
Thanks Johannes for coping with my laziness to type "sequenced" into my PDF reader search bar. I was going to bed and getting up on the last two edits anyway… right ;v) .
§5.17/1 defining the assignment operators says
In all cases, the assignment is sequenced after the value computation of the right and left operands, and before the value computation of the assignment expression.
Also §5.3.2/1 on the preincrement operator says
If x is not of type bool, the expression ++x is equivalent to x+=1 [Note: see … addition (5.7) and assignment operators (5.17) …].
By this identity, ++ ++ x is shorthand for (x +=1) +=1. So, let's interpret that.
Evaluate the 1 on the far RHS and descend into the parens.
Evaluate the inner 1 and the value (prvalue) and address (glvalue) of x.
Now we need the value of the += subexpression.
We're done with the value computations for that subexpression.
The assignment side effect must be sequenced before the value of assignment is available!
Assign the new value to x, which is identical to the glvalue and prvalue result of the subexpression.
We're out of the woods now. The whole expression has now been reduced to x +=1.
So, then 1 and 3 are well-defined and 2 and 4 are undefined behavior, which you would expect.
The only other surprise I found by searching for "sequenced" in N3126 was 5.3.4/16, where the implementation is allowed to call operator new before evaluating constructor arguments. That's cool.
Edit #4: (Oh, what a tangled web we weave)
Johannes notes again that in i == ++i; the glvalue (a.k.a. the address) of i is ambiguously dependent on ++i. The glvalue is certainly a value of i, but I don't think 1.9/15 is intended to include it for the simple reason that the glvalue of a named object is constant, and cannot actually have dependencies.
For an informative strawman, consider
( i % 2? i : j ) = ++ i; // certainly undefined
Here, the glvalue of the LHS of = is dependent on a side-effect on the prvalue of i. The address of i is not in question; the outcome of the ?: is.
Perhaps a good counterexample is
int i = 3, &j = i;
j = ++ i;
Here j has a glvalue distinct from (but identical to) i. Is this well-defined, yet i = ++i is not? This represents a trivial transformation that a compiler could apply to any case.
1.9/15 should say
If a side effect on a scalar object is unsequenced relative to either another side effect on the same scalar object or a value computation using the prvalue of the same scalar object, the behavior is undefined.
In thinking about expressions like those mentioned, I find it useful to imagine a machine where memory has interlocks so that reading a memory location as part of a read-modify-write sequence will cause any attempted read or write, other than the concluding write of the sequence, to be stalled until the sequence completes. Such a machine would hardly be an absurd concept; indeed, such a design could simplify many multi-threaded code scenarios. On the other hand, an expression like "x=y++;" could fail on such a machine if 'x' and 'y' were references to the same variable, and the compiler's generated code did something like read-and-lock reg1=y; reg2=reg1+1; write x=reg1; write-and-unlock y=reg2. That would be a very reasonable code sequence on processors where writing a newly-computed value would impose a pipeline delay, but the write to x would lock up the processor if y were aliased to the same variable.