expm1() Function

The expm1() function in C calculates the value of the exponential function minus one. It is especially useful for achieving higher precision when computing e raised to a small power, thereby avoiding significant numerical errors that can occur with direct calculations.

Syntax of expm1()

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double expm1(double x);
float  expm1f(float x);
long double expm1l(long double x);

Parameters

ParameterDescription
xThe exponent value for which the function computes ex – 1.

Return Value

The function returns the computed value of e raised to the power of x, minus one.

It is important to note that for small magnitude values, using expm1() can provide a more precise result compared to computing exp(x) - 1 directly, as it minimizes floating-point rounding errors.

Examples for expm1()

Example 1: Calculating expm1() for a Small Exponent Value

This example demonstrates the use of expm1() to compute the result for a small exponent, highlighting its accuracy.

Program

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

int main() {
    double x = 0.001;
    double result = expm1(x);
    
    printf("expm1(%.3f) = %.10f\n", x, result);
    return 0;
}

Explanation:

  1. The program defines a small exponent value 0.001.
  2. It computes e0.001 – 1 using expm1(), which is more accurate than using exp(0.001) - 1.
  3. The computed result is printed with high precision to demonstrate the function’s accuracy for small values.

Program Output:

expm1(0.001) = 0.0010005002

Example 2: Computing expm1() for a Larger Exponent Value

This example illustrates the use of expm1() for a larger exponent value, showing its behavior with higher magnitudes.

Program

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

int main() {
    double x = 2.0;
    double result = expm1(x);
    
    printf("expm1(%.1f) = %.10f\n", x, result);
    return 0;
}

Explanation:

  1. The program sets a larger exponent value of 2.0.
  2. It calculates e2.0 – 1 using expm1() to demonstrate the function’s capability with larger inputs.
  3. The result is printed to display the computed value.

Program Output:

expm1(2.0) = 6.3890560989