log1p() Function

The log1p() function computes the natural logarithm of one plus a given value. It is particularly useful when working with very small values since it can provide greater accuracy compared to computing log(1+x) directly.

Syntax of log1p()

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double log1p(double x);
float  log1pf(float x);
long double log1pl(long double x);

Parameters

ParameterDescription
xThe value for which the logarithm of (1 + x) is computed. If x is less than -1, a domain error occurs.

It is worth noting that for very small values of x, log1p() is more accurate than computing log(1+x) directly. Furthermore, when x is less than -1 or equal to -1, errors such as domain or pole errors may occur. Depending on the error handling mode set (via math_errhandling), these errors will either set the global variable errno or raise floating-point exceptions.

Examples for log1p()

Example 1: Calculating the Natural Logarithm for a Positive Value

This example demonstrates how to use log1p() to calculate the natural logarithm of 1 plus a positive value.

Program

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

int main() {
    double value = 0.5;
    double result = log1p(value);
    
    printf("Natural logarithm of (1 + %.2f) is %.8f\n", value, result);
    return 0;
}

Explanation:

  1. The program initializes a variable with the value 0.5.
  2. It calls log1p() to compute the natural logarithm of 1 + 0.5.
  3. The result is printed with a precision of 8 decimal places.

Program Output:

Natural logarithm of (1 + 0.50) is 0.40546511

Example 2: Handling Small Magnitude Values for Enhanced Accuracy

This example demonstrates the use of log1p() when working with a very small value, ensuring enhanced precision compared to direct computation.

Program

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

int main() {
    double smallValue = 1e-8;
    double result = log1p(smallValue);
    
    printf("Natural logarithm of (1 + %.8f) is %.8f\n", smallValue, result);
    return 0;
}

Explanation:

  1. A very small value (1e-8) is assigned to a variable.
  2. log1p() is used to calculate the logarithm of 1 + 1e-8, ensuring better accuracy.
  3. The computed result is printed with high precision.

Program Output:

Natural logarithm of (1 + 0.00000001) is 0.00000001