atanh() Function

The atanh() function in C computes the area hyperbolic tangent of a given value. It performs the inverse operation of the hyperbolic tangent and is widely used in mathematical computations involving hyperbolic functions.

Syntax of atanh()

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double atanh(double x);

Parameters

ParameterDescription
xValue whose area hyperbolic tangent is to be computed. The value must lie within the interval [-1, +1].

The function computes the inverse hyperbolic tangent. If the provided value is outside the interval [-1, +1], a domain error occurs. Additionally, for the boundary values of -1 and +1, a pole error may be signaled.

Examples for atanh()

Example 1: Computing the Area Hyperbolic Tangent for a Valid Positive Value

This example demonstrates how to compute the area hyperbolic tangent for a valid positive input using atanh().

Program

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

int main() {
    double value = 0.5;
    double result = atanh(value);

    printf("The area hyperbolic tangent of %.2f is %.5f\n", value, result);
    return 0;
}

Explanation:

  1. A variable is declared and initialized with a valid positive value.
  2. The atanh() function is called with this value to compute its area hyperbolic tangent.
  3. The result is printed to the console using printf().

Program Output:

The area hyperbolic tangent of 0.50 is 0.54931

Example 2: Demonstrating Domain Error Handling with an Out-of-Range Input

This example illustrates how atanh() behaves when the input value is outside the allowed interval, triggering a domain error.

Program

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#include <stdio.h>
#include <math.h>
#include <errno.h>
#include <string.h>

int main() {
    errno = 0; // Reset errno before function call
    double value = 2.0;  // Out-of-range value for atanh()
    double result = atanh(value);

    if (errno != 0) {
        perror("Error computing atanh");
    } else {
        printf("The area hyperbolic tangent is %.5f\n", result);
    }
    return 0;
}

Explanation:

  1. The program initializes a variable with a value outside the acceptable interval.
  2. errno is reset to detect any errors that may occur during the function call.
  3. The atanh() function is invoked with the out-of-range value.
  4. An error message is printed if a domain error occurs; otherwise, the computed result is displayed.

Program Output:

Error computing atanh: Numerical argument out of domain