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This article will demonstrate various ways on how to use exponential functions in C language.

In C language, use powas the method of exponential function

powThe math function is part of the C math library and <math.h>is defined in the header. When using the C++ gcccompiler toolchain, the math library should be explicitly linked. -lmThe math flag should be passed when compiling, or included in the appropriate build system file as needed. powOnly floating point numbers are defined, so for best results it should not be used for integers.

In the following sample code, we demonstrate how to calculate doublethe nth power of a single variable. powtakes two arguments - a base to be exponentialized and the exponent itself. We can powchain the result of the function into printfa call to , since it returns the calculated number. Note, however, that there are multiple errors to watch out for with certain inputs, all of which are documented here .

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main() {
    double x = 10.0;
    printf("x: %f\n", x);
    printf("x^2: %f\n", pow(x, 2));

    exit(EXIT_SUCCESS);
}

Output:

x: 10.000000
x^2: 100.000000

Using custom functions for integer exponential calculations in C

Alternatively, we can also define our own custom function to calculate the exponent of an integer. First, we intimplement this function for the value of . The implementation of this function is very straight forward; forthe iterations of the loop multiply the base integer by itself ntimes. The function returns the calculated intvalue of . Note that it does not check for overflow of integer types, and users should be aware of this fact when using this function.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int exponentInt(const int base, int n)
{
    int i, p = base;
    for (i = 1; i < n; ++i)
        p *= base;
    return p;
}

int main() {
    int x2 = 10;
    printf("x2: %d\n", x2);
    printf("x2^4: %d\n", exponentInt(x2, 4));

    exit(EXIT_SUCCESS);
}

Output:

x2: 10
x2^4: 10000

The previous implementation of the exponential function is limited in that it can only compute up to 2 ³²int -1, since the type is limited to 32 bits of storage. We can unsigned longextend this limitation by using the type, which has 64 bits of storage on the appropriate system. Therefore, the exponential function can compute up to 2 ⁶⁴ -1. It should be noted that this function will overflow after a certain point, as demonstrated in the following example.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

unsigned long exponentInteger(const unsigned long base, unsigned n)
{
    unsigned long i, p = base;
    for (i = 1; i < n; ++i)
        p *= base;
    return p;
}

int main() {
    int x2 = 10;
    printf("x2: %d\n", x2);
    printf("x2^19: %lu\n", exponentInteger(x2, 19));
    printf("x2^20: %lu\n", exponentInteger(x2, 20));

    exit(EXIT_SUCCESS);
}

Output:

x2: 10
x2^19: 10000000000000000000
x2^20: 7766279631452241920