What is more efficient? Using pow to square or just multiply it with itself?

Question

What of these two methods is in C more efficient? And how about: pow(x,3) vs. x*x*x etc?

Answer 1

x*x or x*x*x will be faster than pow, since pow must deal with the general case, whereas x*x is specific. Also, you can ellide the function call and suchlike.

However, if you find yourself micro-optimizing like this, you need to get a profiler and do some serious profiling. The overwhelming probability is that you would never notice any difference between the two.

Answer 2

I do not know C very much, but I can give some general hints.

If x is a variable, then most likely x*x*x is faster than pow(x, 3), beucase the former is very direct and cannot be simplified. The latter might involve a function call, and is also more complex since the power is allowed to vary.

If, on the other hand, you want to compute (a + 2*b + sin(c)) * (a + 2*b + sin(c)) * (a + 2*b + sin(c)), then the pow method is faster, because if you do not use pow, you will need to compute the base three times.

Answer 3

If the exponent is constant and small, expand it out, minimizing the number of multiplications. (For example, x^4 is not optimally x*x*x*x, but y*y where y=x*x. And x^5 is y*y*x where y=x*x. And so on.) For constant integer exponents, just write out the optimized form already; with small exponents, this is a standard optimization that should be performed whether the code has been profiled or not. The optimized form will be quicker in so large a percentage of cases that it's basically always worth doing.

(If you use Visual C++, std::pow(float,int) performs the optimization I allude to, whereby the sequence of operations is related to the bit pattern of the exponent. I make no guarantee that the compiler will unroll the loop for you, though, so it's still worth doing it by hand.)

[edit] BTW pow has a (un)surprising tendency to crop up on the profiler results. If you don't absolutely need it (i.e., the exponent is large or not a constant), and you're at all concerned about performance, then best to write out the optimal code and wait for the profiler to tell you it's (surprisingly) wasting time before thinking further. (The alternative is to call pow and have the profiler tell you it's (unsurprisingly) wasting time -- you're cutting out this step by doing it intelligently.)

Answer 4

I tested the performance difference between x*x*... vs pow(x,i) for small i using this code:

#include <cstdlib>
#include <cmath>
#include <boost/date_time/posix_time/posix_time.hpp>

inline boost::posix_time::ptime now()
{
    return boost::posix_time::microsec_clock::local_time();
}

#define TEST(num, expression) \
double test##num(double b, long loops) \
{ \
    double x = 0.0; \
\
    boost::posix_time::ptime startTime = now(); \
    for (long i=0; i<loops; ++i) \
    { \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
        x += expression; \
    } \
    boost::posix_time::time_duration elapsed = now() - startTime; \
\
    std::cout << elapsed << " "; \
\
    return x; \
}

TEST(1, b)
TEST(2, b*b)
TEST(3, b*b*b)
TEST(4, b*b*b*b)
TEST(5, b*b*b*b*b)

template <int exponent>
double testpow(double base, long loops)
{
    double x = 0.0;

    boost::posix_time::ptime startTime = now();
    for (long i=0; i<loops; ++i)
    {
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
        x += std::pow(base, exponent);
    }
    boost::posix_time::time_duration elapsed = now() - startTime;

    std::cout << elapsed << " ";

    return x;
}

int main()
{
    using std::cout;
    long loops = 100000000l;
    double x = 0.0;
    cout << "1 ";
    x += testpow<1>(rand(), loops);
    x += test1(rand(), loops);

    cout << "\n2 ";
    x += testpow<2>(rand(), loops);
    x += test2(rand(), loops);

    cout << "\n3 ";
    x += testpow<3>(rand(), loops);
    x += test3(rand(), loops);

    cout << "\n4 ";
    x += testpow<4>(rand(), loops);
    x += test4(rand(), loops);

    cout << "\n5 ";
    x += testpow<5>(rand(), loops);
    x += test5(rand(), loops);
    cout << "\n" << x << "\n";
}

Results are:

1 00:00:01.126008 00:00:01.128338 
2 00:00:01.125832 00:00:01.127227 
3 00:00:01.125563 00:00:01.126590 
4 00:00:01.126289 00:00:01.126086 
5 00:00:01.126570 00:00:01.125930 
2.45829e+54

Note that I accumulate the result of every pow calculation to make sure the compiler doesn't optimize it away.

If I use the std::pow(double, double) version, and loops = 1000000l, I get:

1 00:00:00.011339 00:00:00.011262 
2 00:00:00.011259 00:00:00.011254 
3 00:00:00.975658 00:00:00.011254 
4 00:00:00.976427 00:00:00.011254 
5 00:00:00.973029 00:00:00.011254 
2.45829e+52

This is on an Intel Core Duo running Ubuntu 9.10 64bit. Compiled using gcc 4.4.1 with -o2 optimization.

So in C, yes x*x*x will be faster than pow(x, 3), because there is no pow(double, int) overload. In C++, it will be the roughly same. (Assuming the methodology in my testing is correct.)