Counting down in for-loops

StackOverflow https://stackoverflow.com/questions/804777

  •  03-07-2019
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Question

I believe (from some research reading) that counting down in for-loops is actually more efficient and faster in runtime. My full software code is C++

I currently have this:

for (i=0; i<domain; ++i) {

my 'i' is unsigned resgister int, also 'domain' is unsigned int

in the for-loop i is used for going through an array, e.g.

array[i] = do stuff

converting this to count down messes up the expected/correct output of my routine.

I can imagine the answer being quite trivial, but I can't get my head round it.

UPDATE: 'do stuff' does not depend on previous or later iteration. The calculations within the for-loop are independant for that iteration of i. (I hope that makes sense).

UPDATE: To achieve a runtime speedup with my for-loop, do I count down and if so remove the unsigned part when delcaring my int, or what other method?

Please help.

Was it helpful?

Solution

I'm guessing your backward for loop looks like this:

for (i = domain - 1; i >= 0; --i) {

In that case, because i is unsigned, it will always be greater than or equal to zero. When you decrement an unsigned variable that is equal to zero, it will wrap around to a very large number. The solution is either to make i signed, or change the condition in the for loop like this:

for (i = domain - 1; i >= 0 && i < domain; --i) {

Or count from domain to 1 rather than from domain - 1 to 0:

for (i = domain; i >= 1; --i) {
    array[i - 1] = ...; // notice you have to subtract 1 from i inside the loop now
}

OTHER TIPS

There is only one correct method of looping backwards using an unsigned counter:

for( i = n; i-- > 0; )
{
    // Use i as normal here
}

There's a trick here, for the last loop iteration you will have i = 1 at the top of the loop, i-- > 0 passes because 1 > 0, then i = 0 in the loop body. On the next iteration i-- > 0 fails because i == 0, so it doesn't matter that the postfix decrement rolled over the counter.

Very non obvious I know.

This is not an answer to your problem, because you don't seem to have a problem.

This kind of optimization is completely irrelevant and should be left to the compiler (if done at all).

Have you profiled your program to check that your for-loop is a bottleneck? If not, then you do not need to spend time worrying about this. Even more so, having "i" as a "register" int, as you write, makes no real sense from a performance standpoint.

Even without knowing your problem domain, I can guarantee you that both the reverse-looping technique and the "register" int counter will have negligible impact on your program's performance. Remember, "Premature optimization is the root of all evil".

That said, better spent optimization time would be on thinking about the overall program structure, data structures and algorithms used, resource utilization, etc.

Checking to see if a number is zero can be quicker or more efficient than a comparison. But this is the sort of micro-optimization you really shouldn't worry about - a few clock cycles will be greatly dwarfed by just about any other perf issue.

On x86:

dec eax
jnz Foo

Instead of:

inc eax
cmp eax, 15
jl Foo

If you have a decent compiler, it will optimize "counting up" just as effectively as "counting down". Just try a few benchmarks and you'll see.

So you "read" that couting down is more efficient? I find this very difficult to believe unless you show me some profiler results and the code. I can buy it under some circumstances, but in the general case, no. Seems to me like this is a classic case of premature optimization.

Your comment about "register int i" is also very telling. Nowadays, the compiler always knows better than you how to allocate registers. Don't bother using using the register keyword unless you have profiled your code.

When you're looping through data structures of any sort, cache misses have a far bigger impact than the direction you're going. Concern yourself with the bigger picture of memory layout and algorithm structure instead of trivial micro-optimisations.

It has nothing to do with counting up or down. What can be faster is counting toward zero. Michael's answer shows why — x86 gives you a comparison with zero as an implicit side effect of many instructions, so after you adjust your counter, you just branch based on the result instead of doing an explicit comparison. (Maybe other architectures do that, too; I don't know.)

Borland's Pascal compilers are notorious for performing that optimization. The compiler transforms this code:

for i := x to y do
  foo(i);

into an internal representation more akin to this:

tmp := Succ(y - x);
i := x;
while tmp > 0 do begin
  foo(i);
  Inc(i);
  Dec(tmp);
end;

(I say notorious not because the optimization affects the outcome of the loop, but because the debugger displays the counter variable incorrectly. When the programmer inspects i, the debugger may display the value of tmp instead, causing no end of confusion and panic for programmers who think their loops are running backward.)

The idea is that even with the extra Inc or Dec instruction, it's still a net win, in terms of running time, over doing an explicit comparison. Whether you can actually notice that difference is up for debate.

But note that the conversion is something the compiler would do automatically, based on whether it deemed the transformation worthwhile. The compiler is usually better at optimizing code than you are, so don't spend too much effort competing with it.

Anyway, you asked about C++, not Pascal. C++ "for" loops aren't quite as easy to apply that optimization to as Pascal "for" loops are because the bounds of Pascal's loops are always fully calculated before the loop runs, whereas C++ loops sometimes depend on the stopping condition and the loop contents. C++ compilers need to do some amount of static analysis to determine whether any given loop could fit the requirements for the kind of transformation Pascal loops qualify for unconditionally. If the C++ compiler does the analysis, then it could do a similar transformation.

There's nothing stopping you from writing your loops that way on your own:

for (unsigned i = 0, tmp = domain; tmp > 0; ++i, --tmp)
  array[i] = do stuff

Doing that might make your code run faster. Like I said before, though, you probably won't notice. The bigger cost you pay by manually arranging your loops like that is that your code no longer follows established idioms. Your loop is a perfectly ordinary "for" loop, but it no longer looks like one — it has two variables, they're counting in opposite directions, and one of them isn't even used in the loop body — so anyone reading your code (including you, a week, a month, or a year from now when you've forgotten the "optimization" you were hoping to achieve) will need to spend extra effort proving to himself or herself that the loop is indeed an ordinary loop in disguise.

(Did you notice that my code above used unsigned variables with no danger of wrapping around at zero? Using two separate variables allows that.)

Three things to take away from all this:

  1. Let the optimizer do its job; on the whole it's better at it than you are.
  2. Make ordinary code look ordinary so that the special code doesn't have to compete to get attention from people reviewing, debugging, or maintaining it.
  3. Don't do anything fancy in the name of performance until testing and profiling show it to be necessary.

You may try the following, which compiler will optimize very efficiently:

#define for_range(_type, _param, _A1, _B1) \
    for (_type _param = _A1, _finish = _B1,\
    _step = static_cast<_type>(2*(((int)_finish)>(int)_param)-1),\
    _stop = static_cast<_type>(((int)_finish)+(int)_step); _param != _stop; \
_param = static_cast<_type>(((int)_param)+(int)_step))

Now you can use it:

for_range (unsigned, i, 10,0)
{
    cout << "backwards i: " << i << endl;
}

for_range (char, c, 'z','a')
{
    cout << c << endl;
}

enum Count { zero, one, two, three }; 

for_range (Count, c, three, zero)
{
    cout << "backwards: " << c << endl;
}

You may iterate in any direction:

for_range (Count, c, zero, three)
{
    cout << "forward: " << c << endl;
}

The loop 

for_range (unsigned,i,b,a)
{
   // body of the loop
}

will produce the following code:

 mov esi,b
L1:
;    body of the loop
   dec esi
   cmp esi,a-1
   jne L1

Hard to say with information given but... reverse your array, and count down?

Jeremy Ruten rightly pointed out that using an unsigned loop counter is dangerous. It's also unnecessary, as far as I can tell.

Others have also pointed out the dangers of premature optimization. They're absolutely right.

With that said, here is a style I used when programming embedded systems many years ago, when every byte and every cycle did count for something. These forms were useful for me on the particular CPUs and compilers that I was using, but your mileage may vary.

// Start out pointing to the last elem in array
pointer_to_array_elem_type p = array + (domain - 1);
for (int i = domain - 1; --i >= 0 ; ) {
     *p-- = (... whatever ...)
}

This form takes advantage of the condition flag that is set on some processors after arithmetical operations -- on some architectures, the decrement and testing for the branch condition can be combined into a single instruction. Note that using predecrement (--i) is the key here -- using postdecrement (i--) would not have worked as well.

Alternatively,

// Start out pointing *beyond* the last elem in array
pointer_to_array_elem_type p = array + domain;
for (pointer_to_array_type p = array + domain; p - domain > 0 ; ) {
     *(--p) = (... whatever ...)
}

This second form takes advantage of pointer (address) arithmetic. I rarely see the form (pointer - int) these days (for good reason), but the language guarantees that when you subtract an int from a pointer, the pointer is decremented by (int * sizeof (*pointer)).

I'll emphasize again that whether these forms are a win for you depends on the CPU and compiler that you're using. They served me well on Motorola 6809 and 68000 architectures.

In some later arm cores, decrement and compare takes only a single instruction. This makes decrementing loops more efficient than incrementing ones.

I don't know why there isn't an increment-compare instruction also.

I'm surprised that this post was voted -1 when it's a true issue.

Everyone here is focusing on performance. There is actually a logical reason to iterate towards zero that can result in cleaner code.

Iterating over the last element first is convenient when you delete invalid elements by swapping with the end of the array. For bad elements not adjacent to the end we can swap into the end position, decrease the end bound of the array, and keep iterating. If you were to iterate toward the end then swapping with the end could result in swapping bad for bad. By iterating end to 0 we know that the element at the end of the array has already been proven valid for this iteration.

For further explanation...

If:

  1. You delete bad elements by swapping with one end of the array and changing the array bounds to exclude the bad elements.

Then obviously:

  1. You would swap with a good element i.e. one that has already been tested in this iteration.

So this implies:

  1. If we iterate away from the variable bound then elements between the variable bound and the current iteration pointer have been proven good. Whether the iteration pointer gets ++ or -- doesn't matter. What matters is that we're iterating away from the variable bound so we know that the elements adjacent to it are good.

So finally:

  1. Iterating towards 0 allows us to use only one variable to represent the array bounds. Whether this matters is a personal decision between you and your compiler.

What matters much more than whether you're increasing or decreasing your counter is whether or not you're going up memory or down memory. Most caches are optimized for going up memory, not down memory. Since memory access time is the bottleneck that most programs today face, this means that changing your program so that you go up memory can result in a performance boost even if this requires comparing your counter to a non-zero value. In some of my programs, I saw a significant improvement in performance by changing my code to go up memory instead of down it.

Skeptical? Here's the output that I got:

sum up   = 705046256
sum down = 705046256
Ave. Up Memory   = 4839 mus
Ave. Down Memory =  5552 mus
sum up   = inf
sum down = inf
Ave. Up Memory   = 18638 mus
Ave. Down Memory =  19053 mus

from running this program:

#include <chrono>
#include <iostream>
#include <random>
#include <vector>

template<class Iterator, typename T>
void FillWithRandomNumbers(Iterator start, Iterator one_past_end, T a, T b) {
  std::random_device rnd_device;
  std::mt19937 generator(rnd_device());
  std::uniform_int_distribution<T> dist(a, b);
  for (auto it = start; it != one_past_end; it++)
    *it = dist(generator);
  return ;
}

template<class Iterator>
void FillWithRandomNumbers(Iterator start, Iterator one_past_end, double a, double b) {
  std::random_device rnd_device;
  std::mt19937_64 generator(rnd_device());
  std::uniform_real_distribution<double> dist(a, b);
  for (auto it = start; it != one_past_end; it++)
    *it = dist(generator);
  return ;
}

template<class RAI, class T>
inline void sum_abs_up(RAI first, RAI one_past_last, T &total) {
  T sum = 0;
  auto it = first;
  do {
    sum += *it;
    it++;
  } while (it != one_past_last);
  total += sum;
}

template<class RAI, class T>
inline void sum_abs_down(RAI first, RAI one_past_last, T &total) {
  T sum = 0;
  auto it = one_past_last;
  do {
    it--;
    sum += *it;
  } while (it != first);
  total += sum;
}

template<class T> std::chrono::nanoseconds TimeDown(
                      std::vector<T> &vec, const std::vector<T> &vec_original,
                      std::size_t num_repititions, T &running_sum) {
  std::chrono::nanoseconds total{0};
  for (std::size_t i = 0; i < num_repititions; i++) {
    auto start_time = std::chrono::high_resolution_clock::now();
    sum_abs_down(vec.begin(), vec.end(), running_sum);
    total += std::chrono::high_resolution_clock::now() - start_time;
    vec = vec_original;
  }
  return total;
}

template<class T> std::chrono::nanoseconds TimeUp(
                      std::vector<T> &vec, const std::vector<T> &vec_original,
                      std::size_t num_repititions, T &running_sum) {
  std::chrono::nanoseconds total{0};
  for (std::size_t i = 0; i < num_repititions; i++) {
    auto start_time = std::chrono::high_resolution_clock::now();
    sum_abs_up(vec.begin(), vec.end(), running_sum);
    total += std::chrono::high_resolution_clock::now() - start_time;
    vec = vec_original;
  }
  return total;
}

int main() {
  std::size_t num_repititions = 1 << 10;
  {
  typedef int ValueType;
  auto lower = std::numeric_limits<ValueType>::min();
  auto upper = std::numeric_limits<ValueType>::max();
  std::vector<ValueType> vec(1 << 24);

  FillWithRandomNumbers(vec.begin(), vec.end(), lower, upper);
  const auto vec_original = vec;
  ValueType sum_up = 0, sum_down = 0;

  auto time_up = TimeUp(vec, vec_original, num_repititions, sum_up).count();
  auto time_down = TimeDown(vec, vec_original, num_repititions, sum_down).count();
  std::cout << "sum up   = " << sum_up   << '\n';
  std::cout << "sum down = " << sum_down << '\n';
  std::cout << "Ave. Up Memory   = " << time_up/(num_repititions * 1000) << " mus\n";
  std::cout << "Ave. Down Memory =  "<< time_down/(num_repititions * 1000) << " mus"
            << std::endl;
  }
  {
  typedef double ValueType;
  auto lower = std::numeric_limits<ValueType>::min();
  auto upper = std::numeric_limits<ValueType>::max();
  std::vector<ValueType> vec(1 << 24);

  FillWithRandomNumbers(vec.begin(), vec.end(), lower, upper);
  const auto vec_original = vec;
  ValueType sum_up = 0, sum_down = 0;

  auto time_up = TimeUp(vec, vec_original, num_repititions, sum_up).count();
  auto time_down = TimeDown(vec, vec_original, num_repititions, sum_down).count();
  std::cout << "sum up   = " << sum_up   << '\n';
  std::cout << "sum down = " << sum_down << '\n';
  std::cout << "Ave. Up Memory   = " << time_up/(num_repititions * 1000) << " mus\n";
  std::cout << "Ave. Down Memory =  "<< time_down/(num_repititions * 1000) << " mus"
            << std::endl;
  }
  return 0;
}

Both sum_abs_up and sum_abs_down do the same thing and are timed they same way with the only difference being that sum_abs_up goes up memory while sum_abs_down goes down memory. I even pass vec by reference so that both functions access the same memory locations. Nevertheless, sum_abs_up is consistently faster than sum_abs_down. Give it a run yourself (I compiled it with g++ -O3).

FYI vec_original is there for experimentation, to make it easy for me to change sum_abs_up and sum_abs_down in a way that makes them alter vec while not allowing these changes to affect future timings.

It's important to note how tight the loop that I'm timing is. If a loop's body is large then it likely won't matter whether its iterator goes up or down memory since the time it takes to execute the loop's body will likely completely dominate. Also, it's important to mention that with some rare loops, going down memory is sometimes faster than going up it. But even with such loops it's rarely ever the case that going up was always slower than going down (unlike loops that go up memory, which are very often always faster than the equivalent down-memory loops; a small handful of times they were even 40+% faster).

The point is, as a rule of thumb, if you have the option, if the loop's body is small, and if there's little difference between having your loop go up memory instead of down it, then you should go up memory.

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