Undefined behavior

Renders the entire program meaningless if certain rules of the language are violated.

Explanation

The C++ standard precisely defines the observable behavior of every C++ program that does not fall into one of the following classes:

ill-formed - the program has syntax errors or diagnosable semantic errors. A conforming C++ compiler is required to issue a diagnostic, even if it defines a language extension that assigns meaning to such code (such as with variable-length arrays). The text of the standard uses shall, shall not, and ill-formed to indicate these requirements.
ill-formed no diagnostic required - the program has semantic errors which may not be diagnosable in general case (e.g. violations of the ODR or other errors that are only detectable at link time). The behavior is undefined if such program is executed.
implementation-defined behavior - the behavior of the program varies between implementations, and the conforming implementation must document the effects of each behavior. For example, the type of std::size_t or the number of bits in a byte, or the text of std::bad_alloc::what. A subset of implementation-defined behavior is locale-specific behavior, which depends on the implementation-supplied locale.
unspecified behavior - the behavior of the program varies between implementations and the conforming implementation is not required to document the effects of each behavior. For example, order of evaluation, whether identical string literals are distinct, the amount of array allocation overhead, etc. Each unspecified behavior results in one of a set of valid results.
undefined behavior - there are no restrictions on the behavior of the program. Examples of undefined behavior are memory accesses outside of array bounds, signed integer overflow, null pointer dereference, modification of the same scalar more than once in an expression without sequence points, access to an object through a pointer of a different type, etc. Compilers are not required to diagnose undefined behavior (although many simple situations are diagnosed), and the compiled program is not required to do anything meaningful.

UB and optimization

Because correct C++ programs are free of undefined behavior, compilers may produce unexpected results when a program that actually has UB is compiled with optimization enabled:

For example,

Signed overflow

int foo(int x) {
    return x+1 > x; // either true or UB due to signed overflow
}

may be compiled as (demo)

foo(int):
        movl    $1, %eax
        ret

Access out of bounds

int table[4] = {};
bool exists_in_table(int v)
{
    // return true in one of the first 4 iterations or UB due to out-of-bounds access
    for (int i = 0; i <= 4; i++) {
        if (table[i] == v) return true;
    }
    return false;
}

May be compiled as (demo)

exists_in_table(int):
        movl    $1, %eax
        ret

Uninitialized scalar

Run this code

std::size_t f(int x)
{
    std::size_t a;
    if(x) // either x nonzero or UB
        a = 42;
    return a; 
}

May be compiled as (demo)

f(int):
        mov     eax, 42
        ret

the output shown was observed on an older version of gcc

Run this code

bool p; // uninitialized local variable
if(p) // UB access to uninitialized scalar
    std::puts("p is true");
if(!p) // UB access to uninitialized scalar
    std::puts("p is false");

Possible output:

p is true
p is false

Access to pointer passed to realloc

Choose clang to observe the output shown

Run this code

#include <iostream>
#include <cstdlib>
int main() {
    int *p = (int*)std::malloc(sizeof(int));
    int *q = (int*)std::realloc(p, sizeof(int));
    *p = 1; // UB access to a pointer that was passed to realloc
    *q = 2;
    if (p == q) // UB access to a pointer that was passed to realloc
        std::cout << *p << *q << '\n';
}

Possible output:

Infinite loop without side-effects

Choose clang to observe the output shown

Run this code

#include <iostream>
 
int fermat() {
  const int MAX = 1000;
  int a=1,b=1,c=1;
  // Endless loop with no side effects is UB
  while (1) {
    if (((a*a*a) == ((b*b*b)+(c*c*c)))) return 1;
    a++;
    if (a>MAX) { a=1; b++; }
    if (b>MAX) { b=1; c++; }
    if (c>MAX) { c=1;}
  }
  return 0;
}
 
int main() {
  if (fermat())
    std::cout << "Fermat's Last Theorem has been disproved.\n";
  else
    std::cout << "Fermat's Last Theorem has not been disproved.\n";
}

Possible output:

Fermat's Last Theorem has been disproved.

External links

What Every C Programmer Should Know About Undefined Behavior #1/3
What Every C Programmer Should Know About Undefined Behavior #2/3
What Every C Programmer Should Know About Undefined Behavior #3/3
Undefined behavior can result in time travel (among other things, but time travel is the funkiest)
Understanding Integer Overflow in C/C++
Undefined Behavior and Fermat’s Last Theorem
Fun with NULL pointers, part 1 (local exploit in Linux 2.6.30 caused by UB due to null pointer dereference)

Language
Standard library headers
Concepts
Utilities library
Strings library
Containers library
Algorithms library
Iterators library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications