Avoid stalling pipeline by calculating conditional early

Question

When talking about the performance of ifs, we usually talk about how mispredictions can stall the pipeline. The recommended solutions I see are:

1. Trust the branch predictor for conditions that usually have one result; or
2. Avoid branching with a little bit of bit-magic if reasonably possible; or
3. Conditional moves where possible.

What I couldn't find was whether or not we can calculate the condition early to help where possible. So, instead of:

... work
if (a > b) {
    ... more work
}

Do something like this:

bool aGreaterThanB = a > b;
... work
if (aGreaterThanB) {
    ... more work
}

Could something like this potentially avoid stalls on this conditional altogether (depending on the length of the pipeline and the amount of work we can put between the bool and the if)? It doesn't have to be as I've written it, but is there a way to evaluate conditionals early so the CPU doesn't have to try and predict branches?

Also, if that helps, is it something a compiler is likely to do anyway?

Answer 1

Yes, it can be beneficial to allow the the branch condition to calculated as early as possible, so that any misprediction can be resolved early and the front-end part of the pipeline can start re-filling early. In the best case, the mis-prediction can be free if there is enough work already in-flight to totally hide the front end bubble.

Unfortunately, on out-of-order CPUs, early has a somewhat subtle definition and so getting the branch to resolve early isn't as simple as just moving lines around in the source - you'll probably have to make a change to way the condition is calculated.

What doesn't work

Unfortunately, earlier doesn't refer to the position of the condition/branch in the source file, nor does it refer to the positions of the assembly instructions corresponding to the comparison or branch. So at a fundamental level, it mostly⁷ doesn't work as in your example.

Even if source level positioning mattered, it probably wouldn't work in your example because:

You've moved the evaluation of the condition up and assigned it to a bool, but it's not the test (the < operator) that can mispredict, it's the subsequent conditional branch: after all, it's a branch misprediction. In your example, the branch is in the same place in both places: its form has simply changed from if (a > b) to if (aGreaterThanB).

Beyond that, the way you've transformed the code isn't likely to fool most compilers. Optimizing compilers don't emit code line-by-line in the order you've written it, but rather schedule things as they see fit based on the source-level dependencies. Pulling the condition up earlier will likely just be ignored, since compilers will want to put the check where it would naturally go: approximately right before the branch on architectures with a flag register.

For example, consider the following two implementations of a simple function, which follow the pattern you suggested. The second function moves the condition up to the top of the function.

int test1(int a, int b) {
    int result = a * b;
    result *= result;
    if (a > b) {
        return result + a;
    }
    return result + b * 3;
}

int test2(int a, int b) {
    bool aGreaterThanB = a > b;
    int result = a * b;
    result *= result;
    if (aGreaterThanB) {
        return result + a;
    }
    return result + b * 3;
}

I checked gcc, clang² and MSVC, and all compiled both functions identically (the output differed between compilers, but for each compiler the output was the same for the two functions). For example, compiling test2 with gcc resulted in:

test2(int, int):
  mov eax, edi
  imul eax, esi
  imul eax, eax
  cmp edi, esi
  jg .L4
  lea edi, [rsi+rsi*2]
.L4:
  add eax, edi
  ret

The cmp instruction corresponds to the a > b condition, and gcc has moved it back down past all the "work" and put it right next to the jg which is the conditional branch.

What does work

So if we know that simple manipulation of the order of operations in the source doesn't work, what does work? As it turns out, anything you can do move the branch condition "up" in the data flow graph might improve performance by allowing the misprediction to be resolved earlier. I'm not going to get deep into how modern CPUs depend on dataflow, but you can find a brief overview here with pointers to further reading at the end.

Traversing a linked list

Here's a real-world example involving linked-list traversal.

Consider the the task of summing all values a null-terminated linked list which also stores its length¹ as a member of the list head structure. The linked list implemented as one list_head object and zero or more list nodes (with a single int value payload), defined like so:

struct list_node {
    int value;
    list_node* next;
};

struct list_head {
    int size;
    list_node *first;
};

The canonical search loop would use the node->next == nullptr sentinel in the last node to determine that is has reached the end of the list, like this:

long sum_sentinel(list_head list) {
    int sum = 0;
    for (list_node* cur = list.first; cur; cur = cur->next) {
        sum += cur->value;
    }
    return sum;
}

That's about as simple as you get.

However, this puts the branch that ends the summation (the one that first cur == null) at the end of the node-to-node pointer-chasing, which is the longest dependency in the data flow graph. If this branch mispredicts, the resolution of the mispredict will occur "late" and the front-end bubble will add directly to the runtime.

On the other hand, you could do the summation by explicitly counting nodes, like so:

long sum_counter(list_head list) {
    int sum = 0;
    list_node* cur = list.first;
    for (int i = 0; i < list.size; cur = cur->next, i++) {
        sum += cur->value;
    }
    return sum;
}

Comparing this to the sentinel solution, it seems like we have added extra work: we now need to initialize, track and decrement the count⁴. The key, however, is that this decrement dependency chain is very short and so it will "run ahead" of pointer-chasing work and the mis-prediction will occur early while there is still valid remaining pointer chasing work to do, possibly with a large improvement in runtime.

Let's actually try this. First we examine the assembly for the two solutions, so we can verify there isn't anything unexpected going on:

<sum_sentinel(list_head)>:
test   rsi,rsi
je     1fe <sum_sentinel(list_head)+0x1e>
xor    eax,eax
loop:
add    eax,DWORD PTR [rsi]
mov    rsi,QWORD PTR [rsi+0x8]
test   rsi,rsi
jne    loop
cdqe   
ret    


<sum_counter(list_head)>:
test   edi,edi
jle    1d0 <sum_counter(list_head)+0x20>
xor    edx,edx
xor    eax,eax
loop:
add    edx,0x1
add    eax,DWORD PTR [rsi]
mov    rsi,QWORD PTR [rsi+0x8]
cmp    edi,edx
jne    loop:
cdqe   
ret    

As expected, the sentinel approach is slightly simpler: one less instruction during setup, and one less instruction in the loop⁵, but overall the key pointer chasing and addition steps are identical and we expect this loop to be dominated by the latency of successive node pointers.

Indeed, the loops perform virtually identically when summing short or long lists when the prediction impact is negligible. For long lists the branch prediction impact is automatically small since the single mis-prediction when the end of the list is reached is amortized across many nodes, and the runtime asymptotically reaches almost exactly 4 cycles per node for lists contained in L1, which is what we expect with Intel's best-case 4 cycle load-to-use latency.

For short lists, branch misprediction is neglible if the pattern of lists is predictable: either always the same or cycling with some moderate period (which can be 1000 or more with good prediction!). In this case the time per node can be less than 4 cycles when summing many short lists since multiple lists can be in flight at once (e.g., if summary an array of lists). In any case, both implementations perform almost identically. For example, when lists always have 5 nodes, the time to sum one list is about 12 cycles with either implementation:

** Running benchmark group Tests written in C++ **
                     Benchmark   Cycles   BR_MIS
       Linked-list w/ Sentinel    12.19     0.00
          Linked-list w/ count    12.40     0.00

Let's add branch prediction to the mix, by changing the list generation code to create lists with an average a length of 5, but with actual length uniformly distributed in [0, 10]. The summation code is unchanged: only the input differs. The results with random list lengths:

** Running benchmark group Tests written in C++ **
                     Benchmark   Cycles   BR_MIS
       Linked-list w/ Sentinel    43.87     0.88
          Linked-list w/ count    27.48     0.89

The BR_MIS column shows that we get nearly one branch misprediction per list⁶, as expected, since the loop exit is unpredictable.

However, the sentinel algorithm now takes ~44 cycles versus the ~27.5 cycles of the count algorithm. The count algorithm is about 16.5 cycles faster. You can play with the list lengths and other factors, and change the absolute timings, but the delta is almost always around 16-17 cycles, which not coincidentally is about the same as the branch misprediction penalty on recent Intel! By resolving the branch condition early, we are avoiding the front end bubble, where nothing would be happening at all.

Calculating iteration count ahead of time

Another example would be something like a loop which calculates a floating point value, say a Taylor series approximation, where the termination condition depends on some function of the calculated value. This has the same effect as above: the termination condition depends on the slow loop carried dependency, so it is just as slow to resolve as the calculation of the value itself. If the exit is unpredictable, you'll suffer a stall on exit.

If you could change that to calculate the iteration count up front, you could use a decoupled integer counter as the termination condition, avoiding the bubble. Even if the up-front calculation adds some time, it could still provide an overall speedup (and the calculation can run in parallel with the first iterations of the loop, anyways, so it may be much less costly what you'd expect by looking at its latency).

---

¹ MIPS is an interesting exception here having no flag registers - test results are stored directly into general purpose registers.

² Clang compiled this and many other variants in a branch-free manner, but it still interesting because you still have the same structure of a test instruction and a conditional move (taking the place of the branch).

³ Like the C++11 std::list.

⁴ As it turns out, on x86, the per-node work is actually very similar between the two approaches because of the way that dec implicitly set the zero flag, so we don't need an extra test instruction, while the mov used in pointer chasing doesn't, so the counter approach has an extra dec while the sentinel approach has an extra test, making it about a wash.

⁵ Although this part is just because gcc didn't manage to transform the incrementing for-loop to a decrementing one to take advantage of dec setting the zero flag, avoiding the cmp. Maybe newer gcc versions do better. See also footnote 4.

⁶ I guess this is closer to 0.9 than to 1.0 since perhaps the branch predictors still get the length = 10 case correct, since once you've looped 9 times the next iteration will always exit. A less synthetic/exact distribution wouldn't exhibit that.

⁷ I say mostly because in some cases you might save a cycle or two via such source or assembly-level re-orderings, because such things can have a minor effect on the execution order in out-of-order processors, execution order is also affected by assembly order, but only within the constraints of the data-flow graph. See also this comment.

Answer 2

The main problem with branch misprediction is not the few cycles it incurs as penalty while flushing younger operations (which is relatively fast), but the fact that it may occur very late along the pipe if there are data dependencies the branch condition has to resolve first.

With branches based on prior calculations, the dependency works just like with other operations. Additionally, the branch passes through prediction very early along the pipe so that the machine can go on fetching and allocating further operations. If the prediction was incorrect (which is more often the case with data-dependent branches, unlike loop controls that usually exhibit more predictable patterns), than the flush would occur only when the dependency was resolved and the prediction was proven to be wrong. The later that happens, the bigger the penalty.

Since out-of-order execution schedules operations as soon as dependency is resolved (assuming no port stress), moving the operation ahead is probably not going to help as it does not change the dependency chain and would not affect the scheduling time too much. The only potential benefit is if you move it far enough up so that the OOO window can see it much earlier, but modern CPUs usually run hundreds of instructions ahead, and hoisting instructions that far without breaking the program is hard. If you're running some loop though, it might be simple to compute the conditions of future iterations ahead, if possible.

None of this is going to change the prediction process which is completely orthogonal, but once the branch reaches the OOO part of the machine, it will get resolved immediately, clear if needed, and incur minimal penalty.