What people refer to when they say "branchless code" is something very particular, and it refers to not triggering the CPU's branch prediction. That is, don't make the CPU have to guess which fork in the code you're going to take. This is usually accomplished in one of two ways: either bit twiddling hacks or specialized instructions that do not affect the CPU's branch prediction, such as the 'cmov' family in x86. If you search for `examples of branchless code using conditional moves` using your search engine of choice, you'll find numerous examples.

A trivial example is actually written with a branch in C/C++, but relies on compiler optimizations to kick in. If you compile a ternary operator in C/C++ (and probably rust, C# and other languages) such as in:

   int min_branchless(int a, int b) {
        return a < b ? a : b; // Often emits cmov with -O2
   }

With gcc/clang a -O2, one would expect the compiler to emit the following assembly:

    cmp edi, esi
    cmovle eax, edi   ; select a if a <= b
    ret

There's numerical tricks for other operations/comparisons, and compilers know a lot of them. But, I just suggest compiling your code and configuring your compiler to emit the generated assembly with references to the code it was generated from (you should be able to get it to emit source line references in the assembly). You'll likely be surprised at the optimizations applied at -02, and utterly confused by what you find at -03.

edit: Also, it doesn't mean to never branch, but to minimize branching, especially in tight loops. Branch outside loops, not inside, for instance.

e.g. don't do:

    for (...) {
        if (condition independent of loop variable) { 
          ...
        } else {
          ...
        }
    }

do:

    if (condition independent of loop variable) { 
        for (...) {
          ...
        }
    } else {
        for (...) {
          ...
        }
    }