Why does this loop produce "warning: iteration 3u invokes undefined behavior" and output more than 4 lines?

Signed integer overflow (as strictly speaking, there is no such thing as "unsigned integer overflow") means undefined behaviour. And this means anything can happen, and discussing why does it happen under the rules of C++ doesn't make sense.

C++11 draft N3337: §5.4:1

If during the evaluation of an expression, the result is not mathematically defined or not in the range of representable values for its type, the behavior is undefined. [ Note: most existing implementations of C++ ignore integer overflows. Treatment of division by zero, forming a remainder using a zero divisor, and all floating point exceptions vary among machines, and is usually adjustable by a library function. —end note ]

Your code compiled with g++ -O3 emits warning (even without -Wall)

a.cpp: In function 'int main()':
a.cpp:11:18: warning: iteration 3u invokes undefined behavior [-Waggressive-loop-optimizations]
   std::cout << i*1000000000 << std::endl;
                  ^
a.cpp:9:2: note: containing loop
  for (int i = 0; i < 4; ++i)
  ^

The only way we can analyze what the program is doing, is by reading the generated assembly code.

Here is the full assembly listing:

    .file   "a.cpp"
    .section    .text$_ZNKSt5ctypeIcE8do_widenEc,"x"
    .linkonce discard
    .align 2
LCOLDB0:
LHOTB0:
    .align 2
    .p2align 4,,15
    .globl  __ZNKSt5ctypeIcE8do_widenEc
    .def    __ZNKSt5ctypeIcE8do_widenEc;    .scl    2;  .type   32; .endef
__ZNKSt5ctypeIcE8do_widenEc:
LFB860:
    .cfi_startproc
    movzbl  4(%esp), %eax
    ret $4
    .cfi_endproc
LFE860:
LCOLDE0:
LHOTE0:
    .section    .text.unlikely,"x"
LCOLDB1:
    .text
LHOTB1:
    .p2align 4,,15
    .def    ___tcf_0;   .scl    3;  .type   32; .endef
___tcf_0:
LFB1091:
    .cfi_startproc
    movl    $__ZStL8__ioinit, %ecx
    jmp __ZNSt8ios_base4InitD1Ev
    .cfi_endproc
LFE1091:
    .section    .text.unlikely,"x"
LCOLDE1:
    .text
LHOTE1:
    .def    ___main;    .scl    2;  .type   32; .endef
    .section    .text.unlikely,"x"
LCOLDB2:
    .section    .text.startup,"x"
LHOTB2:
    .p2align 4,,15
    .globl  _main
    .def    _main;  .scl    2;  .type   32; .endef
_main:
LFB1084:
    .cfi_startproc
    leal    4(%esp), %ecx
    .cfi_def_cfa 1, 0
    andl    $-16, %esp
    pushl   -4(%ecx)
    pushl   %ebp
    .cfi_escape 0x10,0x5,0x2,0x75,0
    movl    %esp, %ebp
    pushl   %edi
    pushl   %esi
    pushl   %ebx
    pushl   %ecx
    .cfi_escape 0xf,0x3,0x75,0x70,0x6
    .cfi_escape 0x10,0x7,0x2,0x75,0x7c
    .cfi_escape 0x10,0x6,0x2,0x75,0x78
    .cfi_escape 0x10,0x3,0x2,0x75,0x74
    xorl    %edi, %edi
    subl    $24, %esp
    call    ___main
L4:
    movl    %edi, (%esp)
    movl    $__ZSt4cout, %ecx
    call    __ZNSolsEi
    movl    %eax, %esi
    movl    (%eax), %eax
    subl    $4, %esp
    movl    -12(%eax), %eax
    movl    124(%esi,%eax), %ebx
    testl   %ebx, %ebx
    je  L15
    cmpb    $0, 28(%ebx)
    je  L5
    movsbl  39(%ebx), %eax
L6:
    movl    %esi, %ecx
    movl    %eax, (%esp)
    addl    $1000000000, %edi
    call    __ZNSo3putEc
    subl    $4, %esp
    movl    %eax, %ecx
    call    __ZNSo5flushEv
    jmp L4
    .p2align 4,,10
L5:
    movl    %ebx, %ecx
    call    __ZNKSt5ctypeIcE13_M_widen_initEv
    movl    (%ebx), %eax
    movl    24(%eax), %edx
    movl    $10, %eax
    cmpl    $__ZNKSt5ctypeIcE8do_widenEc, %edx
    je  L6
    movl    $10, (%esp)
    movl    %ebx, %ecx
    call    *%edx
    movsbl  %al, %eax
    pushl   %edx
    jmp L6
L15:
    call    __ZSt16__throw_bad_castv
    .cfi_endproc
LFE1084:
    .section    .text.unlikely,"x"
LCOLDE2:
    .section    .text.startup,"x"
LHOTE2:
    .section    .text.unlikely,"x"
LCOLDB3:
    .section    .text.startup,"x"
LHOTB3:
    .p2align 4,,15
    .def    __GLOBAL__sub_I_main;   .scl    3;  .type   32; .endef
__GLOBAL__sub_I_main:
LFB1092:
    .cfi_startproc
    subl    $28, %esp
    .cfi_def_cfa_offset 32
    movl    $__ZStL8__ioinit, %ecx
    call    __ZNSt8ios_base4InitC1Ev
    movl    $___tcf_0, (%esp)
    call    _atexit
    addl    $28, %esp
    .cfi_def_cfa_offset 4
    ret
    .cfi_endproc
LFE1092:
    .section    .text.unlikely,"x"
LCOLDE3:
    .section    .text.startup,"x"
LHOTE3:
    .section    .ctors,"w"
    .align 4
    .long   __GLOBAL__sub_I_main
.lcomm __ZStL8__ioinit,1,1
    .ident  "GCC: (i686-posix-dwarf-rev1, Built by MinGW-W64 project) 4.9.0"
    .def    __ZNSt8ios_base4InitD1Ev;   .scl    2;  .type   32; .endef
    .def    __ZNSolsEi; .scl    2;  .type   32; .endef
    .def    __ZNSo3putEc;   .scl    2;  .type   32; .endef
    .def    __ZNSo5flushEv; .scl    2;  .type   32; .endef
    .def    __ZNKSt5ctypeIcE13_M_widen_initEv;  .scl    2;  .type   32; .endef
    .def    __ZSt16__throw_bad_castv;   .scl    2;  .type   32; .endef
    .def    __ZNSt8ios_base4InitC1Ev;   .scl    2;  .type   32; .endef
    .def    _atexit;    .scl    2;  .type   32; .endef

I can barely even read assembly, but even I can see the addl $1000000000, %edi line. The resulting code looks more like

for(int i = 0; /* nothing, that is - infinite loop */; i += 1000000000)
    std::cout << i << std::endl;

This comment of @T.C.:

I suspect that it's something like: (1) because every iteration with i of any value larger than 2 has undefined behavior -> (2) we can assume that i <= 2 for optimization purposes -> (3) the loop condition is always true -> (4) it's optimized away into an infinite loop.

gave me idea to compare the assembly code of the OP's code to the assembly code of the following code, with no undefined behaviour.

#include <iostream>

int main()
{
    // changed the termination condition
    for (int i = 0; i < 3; ++i)
        std::cout << i*1000000000 << std::endl;
}

And, in fact, the correct code has termination condition.

    ; ...snip...
L6:
    mov ecx, edi
    mov DWORD PTR [esp], eax
    add esi, 1000000000
    call    __ZNSo3putEc
    sub esp, 4
    mov ecx, eax
    call    __ZNSo5flushEv
    cmp esi, -1294967296 // here it is
    jne L7
    lea esp, [ebp-16]
    xor eax, eax
    pop ecx
    ; ...snip...

Unfortunately this is the consequences of writing buggy code.

Fortunately you can make use of better diagnostics and better debugging tools - that's what they are for:

enable all warnings

-Wall is the gcc option that enables all useful warnings with no false positives. This is a bare minimum that you should always use.

gcc has many other warning options, however, they are not enabled with -Wall as they may warn on false positives

Visual C++ unfortunately is lagging behind with the ability to give useful warnings. At least the IDE enables some by default.

use debug flags for debugging for integer overflow -ftrapv traps the program on overflow, Clang compiler is excellent for this: -fcatch-undefined-behavior catches a lot of instances of undefined behaviour (note: "a lot of" != "all of them")

for integer overflow -ftrapv traps the program on overflow,

Clang compiler is excellent for this: -fcatch-undefined-behavior catches a lot of instances of undefined behaviour (note: "a lot of" != "all of them")

I have a spaghetti mess of a program not written by me that needs to be shipped tomorrow! HELP!!!!!!111oneone

Use gcc's -fwrapv

This option instructs the compiler to assume that signed arithmetic overflow of addition, subtraction and multiplication wraps around using twos-complement representation.

1 - this rule does not apply to "unsigned integer overflow", as §3.9.1.4 says that

Unsigned integers, declared unsigned, shall obey the laws of arithmetic modulo 2n where n is the number of bits in the value representation of that particular size of integer.

and e.g. result of UINT_MAX + 1 is mathematically defined - by the rules of arithmetic modulo 2ⁿ

---

Short answer, gcc specifically has documented this problem, we can see that in the gcc 4.8 release notes which says (emphasis mine going forward):

GCC now uses a more aggressive analysis to derive an upper bound for the number of iterations of loops using constraints imposed by language standards. This may cause non-conforming programs to no longer work as expected, such as SPEC CPU 2006 464.h264ref and 416.gamess. A new option, -fno-aggressive-loop-optimizations, was added to disable this aggressive analysis. In some loops that have known constant number of iterations, but undefined behavior is known to occur in the loop before reaching or during the last iteration, GCC will warn about the undefined behavior in the loop instead of deriving lower upper bound of the number of iterations for the loop. The warning can be disabled with -Wno-aggressive-loop-optimizations.

and indeed if we use -fno-aggressive-loop-optimizations the infinite loop behavior should cease and it does in all the cases I have tested.

The long answer starts with knowing that signed integer overflow is undefined behavior by looking at the draft C++ standard section 5 Expressions paragraph 4 which says:

If during the evaluation of an expression, the result is not mathematically defined or not in the range of representable values for its type, the behavior is undefined. [ Note: most existing implementations of C++ ignore integer overflows. Treatment of division by zero, forming a remainder using a zero divisor, and all floating point exceptions vary among machines, and is usually adjustable by a library function. —end note

We know that the standard says undefined behavior is unpredictable from the note that come with the definition which says:

[ Note: Undefined behavior may be expected when this International Standard omits any explicit definition of behavior or when a program uses an erroneous construct or erroneous data. 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 without the issuance of a diagnostic message), to terminating a translation or execution (with the issuance of a diagnostic message). Many erroneous program constructs do not engender undefined behavior; they are required to be diagnosed. —end note ]

But what in the world can the gcc optimizer be doing to turn this into an infinite loop? It sounds completely wacky. But thankfully gcc gives us a clue to figuring it out in the warning:

warning: iteration 3u invokes undefined behavior [-Waggressive-loop-optimizations]
   std::cout << i*1000000000 << std::endl;
                  ^

The clue is the Waggressive-loop-optimizations, what does that mean? Fortunately for us this is not the first time this optimization has broken code in this way and we are lucky because John Regehr has documented a case in the article GCC pre-4.8 Breaks Broken SPEC 2006 Benchmarks which shows the following code:

int d[16];

int SATD (void)
{
  int satd = 0, dd, k;
  for (dd=d[k=0]; k<16; dd=d[++k]) {
    satd += (dd < 0 ? -dd : dd);
  }
  return satd;
}

the article says:

The undefined behavior is accessing d[16] just before exiting the loop. In C99 it is legal to create a pointer to an element one position past the end of the array, but that pointer must not be dereferenced.

and later on says:

In detail, here is what’s going on. A C compiler, upon seeing d[++k], is permitted to assume that the incremented value of k is within the array bounds, since otherwise undefined behavior occurs. For the code here, GCC can infer that k is in the range 0..15. A bit later, when GCC sees k<16, it says to itself: “Aha– that expression is always true, so we have an infinite loop.” The situation here, where the compiler uses the assumption of well-definedness to infer a useful dataflow fact,

So what the compiler must be doing in some cases is assuming since signed integer overflow is undefined behavior then i must always be less than 4 and thus we have an infinite loop.

He explains this is very similar to the infamous Linux kernel null pointer check removal where in seeing this code:

struct foo *s = ...;
int x = s->f;
if (!s) return ERROR;

gcc inferred that since s was deferenced in s->f; and since dereferencing a null pointer is undefined behavior then s must not be null and therefore optimizes away the if (!s) check on the next line.

The lesson here is that modern optimizers are very aggressive about exploiting undefined behavior and most likely will only get more aggressive. Clearly with just a few examples we can see the optimizer does things that seem completely unreasonable to a programmer but in retrospect from the optimizers perspective make sense.

---

tl;dr The code generates a test that integer + positive integer == negative integer. Usually the optimizer does not optimize this out, but in the specific case of std::endl being used next, the compiler does optimize this test out. I haven't figured out what's special about endl yet.

From the assembly code at -O1 and higher levels, it is clear that gcc refactors the loop to:

i = 0;
do {
    cout << i << endl;
    i += NUMBER;
} 
while (i != NUMBER * 4)

The biggest value that works correctly is 715827882, i.e. floor(INT_MAX/3). The assembly snippet at -O1 is:

L4:
movsbl  %al, %eax
movl    %eax, 4(%esp)
movl    $__ZSt4cout, (%esp)
call    __ZNSo3putEc
movl    %eax, (%esp)
call    __ZNSo5flushEv
addl    $715827882, %esi
cmpl    $-1431655768, %esi
jne L6
    // fallthrough to "return" code

Note, the -1431655768 is 4 * 715827882 in 2's complement.

Hitting -O2 optimizes that to the following:

L4:
movsbl  %al, %eax
addl    $715827882, %esi
movl    %eax, 4(%esp)
movl    $__ZSt4cout, (%esp)
call    __ZNSo3putEc
movl    %eax, (%esp)
call    __ZNSo5flushEv
cmpl    $-1431655768, %esi
jne L6
leal    -8(%ebp), %esp
jne L6 
   // fallthrough to "return" code

So the optimization that has been made is merely that the addl was moved higher up.

If we recompile with 715827883 instead then the -O1 version is identical apart from the changed number and test value. However, -O2 then makes a change:

L4:
movsbl  %al, %eax
addl    $715827883, %esi
movl    %eax, 4(%esp)
movl    $__ZSt4cout, (%esp)
call    __ZNSo3putEc
movl    %eax, (%esp)
call    __ZNSo5flushEv
jmp L2

Where there was cmpl $-1431655764, %esi at -O1, that line has been removed for -O2. The optimizer must have decided that adding 715827883 to %esi can never equal -1431655764.

This is pretty puzzling. Adding that to INT_MIN+1 does generate the expected result, so the optimizer must have decided that %esi can never be INT_MIN+1 and I'm not sure why it would decide that.

In the working example it seems it'd be equally valid to conclude that adding 715827882 to a number cannot equal INT_MIN + 715827882 - 2 ! (this is only possible if wraparound does actually occur), yet it does not optimize the line out in that example.

The code I was using is:

#include <iostream>
#include <cstdio>

int main()
{
    for (int i = 0; i < 4; ++i)
    {
        //volatile int j = i*715827883;
        volatile int j = i*715827882;
        printf("%d\n", j);

        std::endl(std::cout);
    }
}

If the std::endl(std::cout) is removed then the optimization no longer occurs. In fact replacing it with std::cout.put('\n'); std::flush(std::cout); also causes the optimization to not happen, even though std::endl is inlined.

The inlining of std::endl seems to affect the earlier part of the loop structure (which I don't quite understand what it is doing but I'll post it here in case someone else does):

With original code and -O2:

L2:
movl    %esi, 28(%esp)
movl    28(%esp), %eax
movl    $LC0, (%esp)
movl    %eax, 4(%esp)
call    _printf
movl    __ZSt4cout, %eax
movl    -12(%eax), %eax
movl    __ZSt4cout+124(%eax), %ebx
testl   %ebx, %ebx
je  L10
cmpb    $0, 28(%ebx)
je  L3
movzbl  39(%ebx), %eax
L4:
movsbl  %al, %eax
addl    $715827883, %esi
movl    %eax, 4(%esp)
movl    $__ZSt4cout, (%esp)
call    __ZNSo3putEc
movl    %eax, (%esp)
call    __ZNSo5flushEv
jmp L2                  // no test

With mymanual inlining of std::endl, -O2:

L3:
movl    %ebx, 28(%esp)
movl    28(%esp), %eax
addl    $715827883, %ebx
movl    $LC0, (%esp)
movl    %eax, 4(%esp)
call    _printf
movl    $10, 4(%esp)
movl    $__ZSt4cout, (%esp)
call    __ZNSo3putEc
movl    $__ZSt4cout, (%esp)
call    __ZNSo5flushEv
cmpl    $-1431655764, %ebx
jne L3
xorl    %eax, %eax

One difference between these two is that %esi is used in the original , and %ebx in the second version; is there any difference in semantics defined between %esi and %ebx in general? (I don't know much about x86 assembly).

---

Another example of this error being reported in gcc is when you have a loop that executes for a constant number of iterations, but you are using the counter variable as an index into an array that has less than that number of items, such as:

int a[50], x;

for( i=0; i < 1000; i++) x = a[i];

The compiler can determine that this loop will try to access memory outside of the array 'a'. The compiler complains about this with this rather cryptic message:

iteration xxu invokes undefined behavior [-Werror=aggressive-loop-optimizations]

---

What I cannot get is why i value is broken by that overflow operation?

It seems that integer overflow occurs in 4th iteration (for i = 3). signed integer overflow invokes undefined behavior. In this case nothing can be predicted. The loop may iterate only 4 times or it may go to infinite or anything else!
Result may vary compiler to compiler or even for different versions of same compiler.

C11: 1.3.24 undefined behavior:

behavior for which this International Standard imposes no requirements [ Note: Undefined behavior may be expected when this International Standard omits any explicit definition of behavior or when a program uses an erroneous construct or erroneous data. 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 without the issuance of a diagnostic message), to terminating a translation or execution (with the issuance of a diagnostic message). Many erroneous program constructs do not engender undefined behavior; they are required to be diagnosed. —end note ]

---