How to calculate Euler constant or Euler powered in C++?

17
votes

I am trying to find the more 'natural' way to use the number e in C/C++. I am focused on calculating the function e^n.

I think that 'cmath', by default, does not provide support for both (function and constant). However, it can be enabled to include constants defined by the compiler, in this case, M_E. This can be done by including the statement #define _USE_MATH_DEFINES.

On the other hand, e can be defined as a constant:

#define E 2.71828182845904523536;

or

const double EULER = 2.71828182845904523536;

Said this. Which one is the most 'standard' way to approach to this mathematical constant? Is it any other library?

3
c++eulers-number
in calculcating e^n, is n an integer, real, or complex? Only if it's an integer, will std::pow(Euler,n) possibly be more efficient than simply std::exp(n). – Walter

3 Answers

22
votes

If you can avoid using a preprocessor symbol you should. It will cause you trouble when you least expect it. E is likely going to be a variable.

Proposed solution:

#include <cmath>
const double EulerConstant = std::exp(1.0);

The advantage of calculating the constant instead of assigning a floating point literal is that it will produce a result with precision that matches the precision of the double data type for your particular C++ implementation. And it removes the possibility of introducing an error by accidentally skipping a digit.

As illustrated above, <cmath> does declare std::exp, so there is no need for you to roll your own.

5
votes

C++20 std::numbers::e

C++20 has also added an e constant to the standard library: http://eel.is/c++draft/numbers

I expect the usage to be like:

#include <math>
#include <iostream>

int main() {
    std::cout << std::numbers::e << std::endl;
}

I'll give it a try when support arrives to GCC, GCC 9.1.0 with g++-9 -std=c++2a still doesn't support it.

The accepted proposal describes:

5.0. “Headers” [headers] In the table [tab:cpp.library.headers], a new header needs to be added.

[...]

namespace std {
namespace math { 
template<typename T > inline constexpr T e_v = unspecified;
inline constexpr double e = e_v<double>;

There is also a std::numbers::pi of course :-) How to use the PI constant in C++

These constants use the C++14 variable template feature: C++14 Variable Templates: what is their purpose? Any usage example?

In earlier versions of the draft, the constant was under std::math::e: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0631r7.pdf

0
votes

I am just facing this school problem as well, and figured out I'd have Euler's number calculated without cmath. So we need to calculate 1 + 1/1! + 1/2! + ... + 1/n!.

I use recursive functions to achieve so like this (the main is only for testing my solution about e) :

#include <iostream>
#include <iomanip>
using namespace std;

double Factorial(int n){    // Max n = 170
    if(n==1) return 1;
    else return n * Factorial(n-1);
}

double GetEuler(int n){
    if(n == 0) return 1;
    else return (1/Factorial(n) + GetEuler(n-1));
}

int main(){
    int n;
    double e;

    e = GetEuler(170);
    cout << setprecision(15) << e << endl;

    return 0;
}

Output : 2.71828182845905