How to implement exponential function in C language

The implementation method of exponential function in C language requires specific code examples

The exponential function is a common function in mathematics, and its definition is f(x) = e^x, where e is the base of the natural logarithm. In C language, we need to implement the exponential function ourselves. Two implementation methods will be introduced below, and specific code examples will be given.

Method 1: Taylor series expansion
The exponential function can be approximated using Taylor series expansion. The Taylor series expansion formula is as follows:
e^x = 1 x x^2/2! x^ 3/3! … x^n/n! …

We can write a loop based on the Taylor series expansion formula to calculate the approximate value of the exponential function. The following is a specific code example:

#include <stdio.h>

double power(double x, int n) // 计算 x 的 n 次方
{
    double result = 1.0;
    for (int i = 0; i < n; i++)
    {
        result *= x;
    }
    return result;
}

double factorial(int n) // 计算 n 的阶乘
{
    double result = 1.0;
    for (int i = 1; i <= n; i++)
    {
        result *= i;
    }
    return result;
}

double exponential(double x, int n) // 使用泰勒级数展开计算指数函数的近似值
{
    double result = 0.0;
    for (int i = 0; i <= n; i++)
    {
        result += power(x, i) / factorial(i);
    }
    return result;
}

int main()
{
    double x = 1.0; // 指数函数的自变量
    int n = 10; // 近似的级数项数

    double result = exponential(x, n);
    printf("e^%f = %f
", x, result);

    return 0;
}

Method 2: Power series expansion
Another way to implement an exponential function is to use the power series expansion formula. The power series expansion formula is as follows:
e^x = 1 x/1! x^2/2! x^3/3! … Write a loop to compute an approximation of an exponential function. The following is a specific code example:

#include <stdio.h>

double power(double x, int n) // 计算 x 的 n 次方
{
    double result = 1.0;
    for (int i = 0; i < n; i++)
    {
        result *= x;
    }
    return result;
}

double factorial(int n) // 计算 n 的阶乘
{
    double result = 1.0;
    for (int i = 1; i <= n; i++)
    {
        result *= i;
    }
    return result;
}

double exponential(double x, int n) // 使用幂级数展开计算指数函数的近似值
{
    double result = 0.0;
    for (int i = 0; i <= n; i++)
    {
        result += power(x, i) / factorial(i);
    }
    return result;
}

int main()
{
    double x = 1.0; // 指数函数的自变量
    int n = 10; // 近似的级数项数

    double result = exponential(x, n);
    printf("e^%f = %f
", x, result);

    return 0;
}

In the above code example, we define two auxiliary functions power and factorial, which are used to calculate power and factorial respectively. Then, we define the exponential function, which computes an approximation of an exponential function. Finally, in the main function, we use the exponential function to calculate an approximation of e^1 and print the result.

Through the above two implementation methods, we can implement the exponential function ourselves in C language. Both methods approximate the value of the exponential function through series expansion, and within a given number of iterations, a certain accuracy can be obtained. The appropriate method and number of iterations can be selected as needed to obtain an approximation of the exponential function that meets the requirements.

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