July 20, 2018

nullprogram.com/blog/2018/07/20/

In several places, the C and C++ language specifications use a curious, and fairly controversial, phrase: undefined behavior. For certain program constructs, the specification prescribes no specific behavior, instead allowing anything to happen. Such constructs are considered erroneous, and so the result depends on the particulars of the platform and implementation. The original purpose of undefined behavior was for implementation flexibility. In other words, it’s slack that allows a compiler to produce appropriate and efficient code for its target platform.

Specifying a particular behavior would have put unnecessary burden on implementations — especially in the earlier days of computing — making for inefficient programs on some platforms. For example, if the result of dereferencing a null pointer was defined to trap — to cause the program to halt with an error — then platforms that do not have hardware trapping, such as those without virtual memory, would be required to instrument, in software, each pointer dereference.

In the 21st century, undefined behavior has taken on a somewhat different meaning. Optimizers use it — or abuse it depending on your point of view — to lift constraints that would otherwise inhibit more aggressive optimizations. It’s not so much a fundamentally different application of undefined behavior, but it does take the concept to an extreme.

The reasoning works like this: A program that evaluates a construct whose behavior is undefined cannot, by definition, have any meaningful behavior, and so that program would be useless. As a result, compilers assume programs never invoke undefined behavior and use those assumptions to prove its optimizations.

Under this newer interpretation, mistakes involving undefined behavior are more punishing and surprising than before. Programs that seem to make some sense when run on a particular architecture may actually compile into a binary with a security vulnerability due to conclusions reached from an analysis of its undefined behavior.

This can be frustrating if your programs are intended to run on a very specific platform. In this situation, all behavior really could be locked down and specified in a reasonable, predictable way. Such a language would be like an extended, less portable version of C or C++. But your toolchain still insists on running your program on the abstract machine rather than the hardware you actually care about. However, even in this situation undefined behavior can still be desirable. I will provide a couple of examples in this article.

Signed integer overflow

To start things off, let’s look at one of my all time favorite examples of useful undefined behavior, a situation involving signed integer overflow. The result of a signed integer overflow isn’t just unspecified, it’s undefined behavior. Full stop.

This goes beyond a simple matter of whether or not the underlying machine uses a two’s complement representation. From the perspective of the abstract machine, just the act a signed integer overflowing is enough to throw everything out the window, even if the overflowed result is never actually used in the program.

On the other hand, unsigned integer overflow is defined — or, more accurately, defined to wrap, not overflow. Both the undefined signed overflow and defined unsigned overflow are useful in different situations.

For example, here’s a fairly common situation, much like what actually happened in bzip2. Consider this function that does substring comparison:

int cmp_signed ( int i1 , int i2 , unsigned char * buf ) { for (;;) { int c1 = buf [ i1 ]; int c2 = buf [ i2 ]; if ( c1 != c2 ) return c1 - c2 ; i1 ++ ; i2 ++ ; } } int cmp_unsigned ( unsigned i1 , unsigned i2 , unsigned char * buf ) { for (;;) { int c1 = buf [ i1 ]; int c2 = buf [ i2 ]; if ( c1 != c2 ) return c1 - c2 ; i1 ++ ; i2 ++ ; } }

In this function, the indices i1 and i2 will always be some small, non-negative value. Since it’s non-negative, it should be unsigned , right? Not necessarily. That puts an extra constraint on code generation and, at least on x86-64, makes for a less efficient function. Most of the time you actually don’t want overflow to be defined, and instead allow the compiler to assume it just doesn’t happen.

The constraint is that the behavior of i1 or i2 overflowing as an unsigned integer is defined, and the compiler is obligated to implement that behavior. On x86-64, where int is 32 bits, the result of the operation must be truncated to 32 bits one way or another, requiring extra instructions inside the loop.

In the signed case, incrementing the integers cannot overflow since that would be undefined behavior. This permits the compiler to perform the increment only in 64-bit precision without truncation if it would be more efficient, which, in this case, it is.

Here’s the output of Clang 6.0.0 with -Os on x86-64. Pay close attention to the main loop, which I named .loop :

cmp_signed: movsxd rdi , edi ; use i1 as a 64-bit integer mov al , [ rdx + rdi ] movsxd rsi , esi ; use i2 as a 64-bit integer mov cl , [ rdx + rsi ] jmp .check .loop: mov al , [ rdx + rdi + 1 ] mov cl , [ rdx + rsi + 1 ] inc rdx ; increment only the base pointer .check: cmp al , cl je .loop movzx eax , al movzx ecx , cl sub eax , ecx ; return c1 - c2 ret cmp_unsigned: mov eax , edi mov al , [ rdx + rax ] mov ecx , esi mov cl , [ rdx + rcx ] cmp al , cl jne .ret inc edi inc esi .loop: mov eax , edi ; truncated i1 overflow mov al , [ rdx + rax ] mov ecx , esi ; truncated i2 overflow mov cl , [ rdx + rcx ] inc edi ; increment i1 inc esi ; increment i2 cmp al , cl je .loop .ret: movzx eax , al movzx ecx , cl sub eax , ecx ret

As unsigned values, i1 and i2 can overflow independently, so they have to be handled as independent 32-bit unsigned integers. As signed values they can’t overflow, so they’re treated as if they were 64-bit integers and, instead, the pointer, buf , is incremented without concern for overflow. The signed loop is much more efficient (5 instructions versus 8).

The signed integer helps to communicate the narrow contract of the function — the limited range of i1 and i2 — to the compiler. In a variant of C where signed integer overflow is defined (i.e. -fwrapv ), this capability is lost. In fact, using -fwrapv deoptimizes the signed version of this function.

Side note: Using size_t (an unsigned integer) is even better on x86-64 for this example since it’s already 64 bits and the function doesn’t need the initial sign/zero extension. However, this might simply move the sign extension out to the caller.

Strict aliasing

Another controversial undefined behavior is strict aliasing. This particular term doesn’t actually appear anywhere in the C specification, but it’s the popular name for C’s aliasing rules. In short, variables with types that aren’t compatible are not allowed to alias through pointers.

Here’s the classic example:

int foo ( int * a , int * b ) { * b = 0 ; // store * a = 1 ; // store return * b ; // load }

Naively one might assume the return *b could be optimized to a simple return 0 . However, since a and b have the same type, the compiler must consider the possibility that they alias — that they point to the same place in memory — and must generate code that works correctly under these conditions.

If foo has a narrow contract that forbids a and b to alias, we have a couple of options for helping our compiler.

First, we could manually resolve the aliasing issue by returning 0 explicitly. In more complicated functions this might mean making local copies of values, working only with those local copies, then storing the results back before returning. Then aliasing would no longer matter.

int foo ( int * a , int * b ) { * b = 0 ; * a = 1 ; return 0 ; }

Second, C99 introduced a restrict qualifier to communicate to the compiler that pointers passed to functions cannot alias. For example, the pointers to memcpy() are qualified with restrict as of C99. Passing aliasing pointers through restrict parameters is undefined behavior, e.g. this doesn’t ever happen as far as a compiler is concerned.

int foo ( int * restrict a , int * restrict b );

The third option is to design an interface that uses incompatible types, exploiting strict aliasing. This happens all the time, usually by accident. For example, int and long are never compatible even when they have the same representation.

int foo ( int * a , long * b );

If you use an extended or modified version of C without strict aliasing ( -fno-strict-aliasing ), then the compiler must assume everything aliases all the time, generating a lot more precautionary loads than necessary.

What irritates a lot of people is that compilers will still apply the strict aliasing rule even when it’s trivial for the compiler to prove that aliasing is occurring:

/* note: forbidden */ long a ; int * b = ( int * ) & a ;

It’s not just a simple matter of making exceptions for these cases. The language specification would need to define all the rules about when and where incompatible types are permitted to alias, and developers would have to understand all these rules if they wanted to take advantage of the exceptions. It can’t just come down to trusting that the compiler is smart enough to see the aliasing when it’s sufficiently simple. It would need to be carefully defined.

Besides, there are probably conforming, portable solutions that, with contemporary compilers, will safely compile to the efficient code you actually want anyway.

There is one special exception for strict aliasing: char * is allowed to alias with anything. This is important to keep in mind both when you intentionally want aliasing, but also when you want to avoid it. Writing through a char * pointer could force the compiler to generate additional, unnecessary loads.

In fact, there’s a whole dimension to strict aliasing that, even today, no compiler yet exploits: uint8_t is not necessarily unsigned char . That’s just one possible typedef definition for it. It could instead typedef to, say, some internal __byte type.

In other words, technically speaking, uint8_t does not have the strict aliasing exemption. If you wanted to write bytes to a buffer without worrying the compiler about aliasing issues with other pointers, this would be the tool to accomplish it. Unfortunately there’s far too much existing code that violates this part of strict aliasing that no toolchain is willing to exploit it for optimization purposes.

Other undefined behaviors

Some kinds of undefined behavior don’t have performance or portability benefits. They’re only there to make the compiler’s job a little simpler. Today, most of these are caught trivially at compile time as syntax or semantic issues (i.e. a pointer cast to a float).

Some others are obvious about their performance benefits and don’t require much explanation. For example, it’s undefined behavior to index out of bounds (with some special exceptions for one past the end), meaning compilers are not obligated to generate those checks, instead relying on the programmer to arrange, by whatever means, that it doesn’t happen.

Undefined behavior is like nitro, a dangerous, volatile substance that makes things go really, really fast. You could argue that it’s too dangerous to use in practice, but the aggressive use of undefined behavior is not without merit.