Calculate log2 of a number in Java

This post will discuss how to calculate log₂(x) for a number x in Java.

1. Using `Math.log()` method

The logarithmic identity log_ba = log₁₀(a)/log₁₀(b) is commonly used to derive log₂ for a number x. i.e. log₂x = log₁₀(x)/log₁₀(2).

The idea is to use the Math.log() method to find the natural logarithm of a number and then use above logarithmic identity to derive log₂(x). Note that for negative numbers, the Math.log() method returns NaN and for zero value, it returns negative infinity.

public class Main {

public static double log2(int x) {

return Math.log(x) / Math.log(2);

}

public static void main(String[] args) {

int x = 10;

double log2x = log2(x);

System.out.println(log2x); // 3.3219280948873626

}

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2. Using Guava Library

Guava provides the LongMath.log2() method that returns the base-2 logarithm of a number, rounded according to the specified rounding mode.

Its usage is demonstrated below. Note that for non-positive numbers, LongMath.log2() throws java.lang.IllegalArgumentException.

import com.google.common.math.LongMath;

import java.math.RoundingMode;

public class Main {

public static int log2(int x) {

return LongMath.log2(x, RoundingMode.FLOOR);

}

public static void main(String[] args) {

int x = 10;

int log2x = log2(x);

System.out.println(log2x); // 3

}

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3. Using `Integer.numberOfLeadingZeros()` method

The idea here is to use the Integer.numberOfLeadingZeros() method to get the count of zero bits preceding the most significant set bit in the binary representation of a number. Then you can get the log₂(x) for a number x using the formula: 31 - Integer.numberOfLeadingZeros(x).

This is demonstrated below. Note that for non-positive numbers, the code explicitly throws java.lang.IllegalArgumentException exception.

public class Main {

public static int log2(int x) {

if (x <= 0) {

throw new IllegalArgumentException("x (" + x + ") must be positive");

}

return 31 - Integer.numberOfLeadingZeros(x);

}

public static void main(String[] args) {

int x = 10;

int log2x = log2(x);

System.out.println(log2x); // 3

}

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That’s all about calculating log₂(x) for a number x in Java.

Calculate log2 of a number in Java

1. Using Math.log() method

2. Using Guava Library

3. Using Integer.numberOfLeadingZeros() method

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1. Using `Math.log()` method

3. Using `Integer.numberOfLeadingZeros()` method