I have recently seen several discussions on Twitter where people have been surprised/annoyed by what the compilers do to their branchless code. Here are some random comments on what the compilers do (and why).

Branches vs. conditional move

Branch misprediction is very expensive. But conditional moves are also costly (as they increase the length of dependency chains), so it is not obvious that a branch that sometimes mispredicts is slower than a conditional move. Agner Fog’s optimization manual says (for “a = b > c ? d : e;”):

As a rule of thumb, we can say that a conditional jump is faster than a conditional move if the code is part of a dependency chain and the prediction rate is better than 75%. A conditional jump is also preferred if we can avoid a lengthy calculation of d or e when the other operand is chosen.

Most I see written about branches and conditional moves focus on writing branchless code. But branch predictors are amazing¹ – they can easily find a pattern in how a branch is taken, and use correlated branches to improve the prediction rate. So it is often the case that branches that seem unpredictable predict better than 75% in reality, and doing it branchless makes the program slower.

The ternary operator

One way that seems natural to get the compiler to generate branchless code is to use the ternary operator, but that does not work. The reason is that

r = c ? a : b;

does evaluate a only when the condition c is true and b only when c is false, so the compiler front end must generate the same IR for this as for

if (c)
  r = a;
else
  r = b;

At least when a and b may have side effects.

Both GCC and Clang generate IR with branches for ternary operators (even with no side effects), so later optimization passes do not see any difference between source code using the ternary operator or branches.

Convincing GCC to make the right choice

Branches

GCC is rather aggressive in using conditional moves for x86_64, and it is common to find cases where using a branch instead would improve performance. It is often possible to make GCC emit a branch instruction by using __builtin_expect_with_probability to tell it that the branch is very likely.² For example, the function

int foo(int a, int b, int c)
{
  if (a == b)
    a &= c;
  return a;
}

is compiled to code using cmove while

#define VERY_LIKELY(x) __builtin_expect_with_probability(!!(x), 1, 0.999)

int foo(int a, int b, int c)
{
  if (VERY_LIKELY(a == b))
    a &= c;
  return a;
}

is compiled to code with branches. (godbolt)

Branchless

Many (most?) cases where GCC incorrectly decides to use a branch instead of emitting branchless code comes from optimization passes transforming the code to a form where the backend cannot change it to use conditional moves.

For example, the program in this blog post has a loop (godbolt)

while ((pos1 < size1) & (pos2 < size2)) {
  v1 = input1[pos1];
  v2 = input2[pos2];
  output_buffer[pos++] = (v1 <= v2) ? v1 : v2;
  pos1 = (v1 <= v2) ? pos1 + 1 : pos1;
  pos2 = (v1 >= v2) ? pos2 + 1 : pos2;
}

The comparisons are unpredictable, so the program runs faster if the loop body is generated as branchless code, but GCC emits branches for updating pos1 and pos2. The reason is that the sequence

  pos1 = (v1 <= v2) ? pos1 + 1 : pos1;
  pos2 = (v1 >= v2) ? pos2 + 1 : pos2;

has been optimized by jump threading to

  if (v1 <= v2) {
    pos1 = pos1 + 1;
    if (v2 == v1)
      goto skip;
  } else {
skip:
    pos2 = pos2 + 1;
  }

which is too complex for the backend to emit as branchless code.

We can get rid of the branches in this case by rewriting the loop to prevent jump threading from optimizing it:

while ((pos1 < size1) & (pos2 < size2)) {
  v1 = input1[pos1];
  v2 = input2[pos2];
  output_buffer[pos++] = (v1 <= v2) ? v1 : v2;
  pos1 += (v1 <= v2);
  pos2 += (v1 >= v2);
}

LLVM backend introducing branches

LLVM optimization passes are aggressive in changing branchy code to use the select IR instruction (that choose one value based on a condition, without IR-level branching) when possible. And select is typically generated as a cmove instruction, so it should be easy to get branchless code. But cmove is often slower than branches, so the backend can change select to branches when it believes it is better.

This can be seen in this example taken from Bug 39374 (godbolt)

#include <cstddef>
#include <cstdint>
#include <utility>

void downHeap(uint64_t* top, size_t size, size_t pos) {
  size_t parent = pos;
  size_t child;
  while ((child = 2 * parent + 2) < size) {
    auto left = child - 1;
    child = top[left] < top[child] ? child : left;  // <<-- Unpredictable, should be CMOV
    if (top[parent] < top[child]) {
      std::swap(top[parent], top[child]);
      parent = child;
    } else {
      return;
    }
  }
  if (--child < size && top[parent] < top[child]) {
    std::swap(top[parent], top[child]);
  }
}

Clang supports __builtin_unpredictable that tells the compiler that the branch condition is unpredictable and should therefore better be generated as branchless code. But this built-in only affects the middle-end passes, so it does not help the case above where it is the backend that is changing the select instruction to branches.

Straight-line code

Compilers may generate branches for straight-line code without ternary operators too.

Clang

The function below (taken from a blog post by Daan Sprenkels) tries to read an element from an array in a side-channel resistant way, but the generated code generated by clang contains branches that depend on the secret index. (godbolt)

#include <cstddef>
#include <cstdint>

// Select an element from an array in constant time.
uint64_t constant_time_lookup(const size_t secret_idx,
                              const uint64_t table[8]) {
  uint64_t result = 0;
  for (size_t i = 0; i < 8; i++) {
    const bool cond = i == secret_idx;
    const uint64_t mask = (-(int64_t)cond);
    result |= table[i] & mask;
  }
  return result;
}

Here, the LLVM instcombine pass has optimized the sequence

  %9 = icmp eq i64 %4, %0
  %11 = zext i1 %9 to i64
  %12 = sub nsw i64 0, %11
  %15 = and i64 %14, %12

to

  %9 = icmp eq i64 %4, %0
  %15 = select i1 %9, i64 %14, i64 0

and the select instruction is then changed to branches in the backend.

GCC

GCC can also introduce branches in straight-line code. For example, the front end generates IR for

unsigned r = ((a & 0xffff0000) != 0) << 4;

as³

unsigned r;
if (a > 65535)
  r = 16;
else
  r = 0;

This is typically turned back to straight-line code by later optimizations, but not always – it is easy to construct similar examples where the branches are present in the generated code: (godbolt)

unsigned foo(unsigned a, unsigned b)
{
  unsigned t = ((a > 2) != 0) << 1;
  t |= ((a < 10) != 0) << 2;
  return b >> t;
}

Conclusion

To summarize the main points made in this blog post:

• Branches are sometimes faster than cmove, and cmove is sometimes faster than branches.
• Sometimes compilers do the wrong thing:
  • __builtin_expect does not help convince GCC to use branches…
  • … but __builtin_expect_with_probability may help.
  • __builtin_unpredictable does not guarantee that LLVM generates branchless code.
• Compilers may insert branches in straight-line code.