Question

What of these two methods is in C more efficient? And how about:

pow(x,3)

vs.

x*x*x // etc?

Answer 1

UPDATE 2021

I’ve modified the benchmark code as follows:

• std::chrono used for timing measurements instead of boost
• C++11 <random> used instead of rand()
• Avoid repeated operations that can get hoisted out. The base parameter is ever-changing.

I get the following results with GCC 10 -O2 (in seconds):

exp     c++ pow     c pow       x*x*x...
2       0.204243    1.39962     0.0902527   
3       1.36162     1.38291     0.107679    
4       1.37717     1.38197     0.106103    
5       1.3815      1.39139     0.117097

GCC 10 -O3 is almost identical to GCC 10 -O2.

With GCC 10 -O2 -ffast-math:

exp     c++ pow     c pow       x*x*x...
2       0.203625    1.4056      0.0913414   
3       0.11094     1.39938     0.108027    
4       0.201593    1.38618     0.101585    
5       0.102141    1.38212     0.10662

With GCC 10 -O3 -ffast-math:

exp     c++ pow     c pow       x*x*x...
2       0.0451995   1.175       0.0450497   
3       0.0470842   1.20226     0.051399    
4       0.0475239   1.18033     0.0473844   
5       0.0522424   1.16817     0.0522291

With Clang 12 -O2:

exp     c++ pow     c pow       x*x*x...
2       0.106242    0.105435    0.105533    
3       1.45909     1.4425      0.102235    
4       1.45629     1.44262     0.108861    
5       1.45837     1.44483     0.1116

Clang 12 -O3 is almost identical to Clang 12 -O2.

With Clang 12 -O2 -ffast-math:

exp     c++ pow     c pow       x*x*x...
2       0.0233731   0.0232457   0.0231076   
3       0.0271074   0.0266663   0.0278415   
4       0.026897    0.0270698   0.0268115   
5       0.0312481   0.0296402   0.029811    

Clang 12 -O3 -ffast-math is almost identical to Clang 12 -O2 -ffast-math.

Machine is Intel Core i7-7700K on Linux 5.4.0-73-generic x86_64.

Conclusions:

• With GCC 10 (no -ffast-math), x*x*x... is always faster
• With GCC 10 -O2 -ffast-math, std::pow is as fast as x*x*x... for odd exponents
• With GCC 10 -O3 -ffast-math, std::pow is as fast as x*x*x... for all test cases, and is around twice as fast as -O2.
• With GCC 10, C’s pow(double, double) is always much slower
• With Clang 12 (no -ffast-math), x*x*x... is faster for exponents greater than 2
• With Clang 12 -ffast-math, all methods produce similar results
• With Clang 12, pow(double, double) is as fast as std::pow for integral exponents
• Writing benchmarks without having the compiler outsmart you is hard.

I’ll eventually get around to installing a more recent version of GCC on my machine and will update my results when I do so.

Here’s the updated benchmark code:

#include <cmath>
#include <chrono>
#include <iostream>
#include <random>

using Moment = std::chrono::high_resolution_clock::time_point;
using FloatSecs = std::chrono::duration<double>;

inline Moment now()
{
    return std::chrono::high_resolution_clock::now();
}

#define TEST(num, expression) \
double test##num(double b, long loops) \
{ \
    double x = 0.0; \
\
    auto startTime = now(); \
    for (long i=0; i<loops; ++i) \
    { \
        x += expression; \
        b += 1.0; \
    } \
    auto elapsed = now() - startTime; \
    auto seconds = std::chrono::duration_cast<FloatSecs>(elapsed); \
    std::cout << seconds.count() << "\t"; \
    return x; \
}

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 testCppPow(double base, long loops)
{
    double x = 0.0;

    auto startTime = now();
    for (long i=0; i<loops; ++i)
    {
        x += std::pow(base, exponent);
        base += 1.0;
    }
    auto elapsed = now() - startTime;

    auto seconds = std::chrono::duration_cast<FloatSecs>(elapsed); \
    std::cout << seconds.count() << "\t"; \

    return x;
}

double testCPow(double base, double exponent, long loops)
{
    double x = 0.0;

    auto startTime = now();
    for (long i=0; i<loops; ++i)
    {
        x += ::pow(base, exponent);
        base += 1.0;
    }
    auto elapsed = now() - startTime;

    auto seconds = std::chrono::duration_cast<FloatSecs>(elapsed); \
    std::cout << seconds.count() << "\t"; \

    return x;
}

int main()
{
    using std::cout;
    long loops = 100000000l;
    double x = 0;
    std::random_device rd;
    std::default_random_engine re(rd());
    std::uniform_real_distribution<double> dist(1.1, 1.2);
    cout << "exp\tc++ pow\tc pow\tx*x*x...";

    cout << "\n2\t";
    double b = dist(re);
    x += testCppPow<2>(b, loops);
    x += testCPow(b, 2.0, loops);
    x += test2(b, loops);

    cout << "\n3\t";
    b = dist(re);
    x += testCppPow<3>(b, loops);
    x += testCPow(b, 3.0, loops);
    x += test3(b, loops);

    cout << "\n4\t";
    b = dist(re);
    x += testCppPow<4>(b, loops);
    x += testCPow(b, 4.0, loops);
    x += test4(b, loops);

    cout << "\n5\t";
    b = dist(re);
    x += testCppPow<5>(b, loops);
    x += testCPow(b, 5.0, loops);
    x += test5(b, loops);

    std::cout << "\n" << x << "\n";
}

---

Old Answer, 2010

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.)

---

This is in response to the comment made by An Markm:

Even if a using namespace std directive was issued, if the second parameter to pow is an int, then the std::pow(double, int) overload from <cmath> will be called instead of ::pow(double, double) from <math.h>.

This test code confirms that behavior:

#include <iostream>

namespace foo
{

    double bar(double x, int i)
    {
        std::cout << "foo::bar\n";
        return x*i;
    }


}

double bar(double x, double y)
{
    std::cout << "::bar\n";
    return x*y;
}

using namespace foo;

int main()
{
    double a = bar(1.2, 3); // Prints "foo::bar"
    std::cout << a << "\n";
    return 0;
}