exp in C/C++: calculating the exponent
ðŸ‘‹ Hi! This article will discuss the exp
function, which calculates the exponent of a number in C/C++. We will start by using this function with an example, then try to implement it ourselves. We will also understand how exp
is different from expl
and expf
. At the end of the article, there will be exercises for further practice.
Calculating the exponent of a number in C/C++
To calculate the exponent of a number in C/C++, the builtin exp
function can be used. This function is accessible after including the <math.h>
file. In C++, you can include <cmath>
. Below is the prototype of this function:
double exp (double x);
 The function takes a single argument: the number for which the exponent needs to be calculated.
 The function returns the exponent of the argument passed to it.
Here is an example:
#include <cmath>
#include <iostream>
using namespace std;
int main() {
cout << "exp(1) = " << exp(1) << endl;
cout << "exp(2) = " << exp(2) << endl;
cout << "exp(10) = " << exp(10) << endl;
cout << "exp(0) = " << exp(0) << endl;
cout << "exp(0.25) = " << exp(0.25) << endl;
cout << "exp(2) = " << exp(2) << endl;
cout << "exp(4.567) = " << exp(4.567) << endl;
return 0;
}
Program output:
exp(1) = 2.71828
exp(2) = 7.38906
exp(10) = 22026.5
exp(0) = 1
exp(0.25) = 1.28403
exp(2) = 0.135335
exp(4.567) = 0.0103891
What value will be displayed on the screen after executing the following code?
#include <cmath>
#include <iostream>
using namespace std;
int main() {
double x = 2.5;
cout << exp(x + 1) / exp(x) << endl;
return 0;
}
Implementing exp yourself
To compute the exponent ourselves, the Taylor series can be used. The exponent expanded into a Taylor series looks like this:
The program:
#include <cmath>
#include <iostream>
using namespace std;
// Function to compute the factorial of a number
double factorial(int n) {
if (n == 0) return 1.0;
double result = 1.0;
for (int i = 1; i <= n; ++i) {
result *= i;
}
return result;
}
// Function to compute e^x using the Taylor series
double my_exp(double x, int num_terms = 20) {
double result = 1.0; // Start with the first term of the Taylor series (1)
for (int n = 1; n <= num_terms; ++n) {
result += pow(x, n) / factorial(n);
}
return result;
}
int main() {
cout << "my_exp(1) = " << my_exp(1) << endl;
cout << "my_exp(2) = " << my_exp(2) << endl;
cout << "my_exp(10) = " << my_exp(10) << endl;
cout << "my_exp(0) = " << my_exp(0) << endl;
cout << "my_exp(0.25) = " << my_exp(0.25) << endl;
cout << "my_exp(2) = " << my_exp(2) << endl;
cout << "my_exp(4.567) = " << my_exp(4.567) << endl;
return 0;
}
Output:
my_exp(1) = 2.71828
my_exp(2) = 7.38906
my_exp(10) = 21991.5
my_exp(0) = 1
my_exp(0.25) = 1.28403
my_exp(2) = 0.135335
my_exp(4.567) = 0.0103902
In the program above, twenty iterations for exponent calculation are performed. The number of iterations can be changed to be larger or smaller by passing a second argument num_terms
(default is twenty), depending on the accuracy needed.
Functions expl and expf
The functions expl
and expf
, like exp
, compute the exponent of a number. The only difference is that they work with floatingpoint numbers of type long double
(expl
) and float
(expf
). Here is an example:
#include <cmath>
#include <iostream>
using namespace std;
int main() {
cout << "expl(234) = " << expl(234) << endl;
cout << "exp (234) = " << exp(234) << endl;
cout << "expf(234) = " << expf(234) << endl;
return 0;
}
Output:
expl(234) = 4.21608e+101
exp (234) = 4.21608e+101
expf(234) = inf
As you can see, they return the same number, just of a different type. In the case of expf
, the number overflowed, resulting in inf
.
Exercises

Using
exp
,expl
, andexpf
:
Write a C++ program that prompts the user for a number and the type of the number (double
,long double
,float
), then computes the exponent of this number using the corresponding function (exp
,expl
,expf
) and displays the result. Also, display the original number entered by the user. 
Comparing
exp
andmy_exp
:
Using the example provided in the article, compare the results of the standardexp
function and your version of themy_exp
function for different numbers. Write a program that demonstrates the differences in the results and displays them on the screen. 
Using
expf
with large numbers:
Write a program that demonstrates overflow when using theexpf
function with large numbers. Your program should use theexp
,expl
, andexpf
functions, and the results of their work should be displayed on the screen.
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