exp2() Function

The exp2() function computes the binary exponential, returning the result of 2 raised to the power of the provided value. It is useful for applications requiring fast computations of powers of 2, and it supports various floating-point types through its different versions.

Syntax of exp2()

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double exp2(double x);
float exp2f(float x);
long double exp2l(long double x);

Parameters

ParameterDescription
xThe exponent value for which 2 raised to that power is computed.

It is important to note that if the computed value exceeds the representable range of the return type, the function returns HUGE_VAL (or its float or long double equivalent) and sets an overflow error. This behavior should be considered when working with very large exponents.

Examples for exp2()

Example 1: Basic Calculation with a Positive Exponent

This example demonstrates the basic usage of exp2() with a positive exponent.

Program

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

int main() {
    double exponent = 3.0;
    double result = exp2(exponent);

    printf("2 raised to the power %.1f is %.2f\n", exponent, result);
    return 0;
}

Explanation:

  1. The program includes the necessary headers, stdio.h for input/output and math.h for the exp2() function.
  2. A variable exponent is set to 3.0.
  3. exp2() is called to compute 2 raised to the power 3.0, which equals 8.00.
  4. The result is printed using printf().

Program Output:

2 raised to the power 3.0 is 8.00

Example 2: Calculation with a Negative Exponent

This example shows how exp2() can be used with a negative exponent to compute a fractional result.

Program

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

int main() {
    double exponent = -2.0;
    double result = exp2(exponent);

    printf("2 raised to the power %.1f is %.4f\n", exponent, result);
    return 0;
}

Explanation:

  1. The necessary headers are included for standard input/output and mathematical functions.
  2. A variable exponent is set to -2.0.
  3. exp2() computes 2 raised to the power -2.0, yielding 0.2500.
  4. The result is printed with formatting to display four decimal places.

Program Output:

2 raised to the power -2.0 is 0.2500

Example 3: Handling Large Exponents with Overflow Consideration

This example illustrates how the function behaves when a very large exponent is used, potentially causing an overflow.

Program

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

int main() {
    double exponent = 1024.0;
    errno = 0;
    double result = exp2(exponent);

    if (errno == ERANGE) {
        printf("Overflow occurred when computing 2 raised to the power %.1f\n", exponent);
    } else {
        printf("2 raised to the power %.1f is %.2e\n", exponent, result);
    }
    return 0;
}

Explanation:

  1. The program includes headers for input/output, mathematical functions, and error handling.
  2. A large exponent value (1024.0) is assigned to the variable exponent.
  3. exp2() is used to compute the result, and errno is checked to determine if an overflow has occurred.
  4. If an overflow is detected, a message indicating the overflow is printed; otherwise, the result is displayed in scientific notation.

Program Output:

Overflow occurred when computing 2 raised to the power 1024.0