Java Math ulp() Method

The ulp() method of Java Math class returns the size of an ulp of the argument.

Syntax:

1. public static double ulp(double x)
2. public static float ulp(float x)

Parameters:

The parameter ‘x’ represents the floating-point number whose ulp is to be determined.

Return Value:

The ulp() method returns the size of an ulp of the argument.

• It returns zero with same sign as argument, if the argument passed is zero.
• It returns positive infinity, if the argument is positive or negative infinity.
• It returns Double.MIN_VALUE, if the double at argument is negative or positive zero.
• It returns Float.MIN_VALUE, if the float argument is negative or positive zero.
• It returns a value equal to 2¹⁰⁴, if the argument is ±MAX_VALUE.
• It returns a value equal to 2⁹⁷¹, if the argument is ±MAX_VALUE

Example 1:

public class JavaMathUlpExample1 {
    public static void main(String[] args) {
        double a=90;
        //returns the size of an ulp of the argument
        System.out.println("Ulp value for "+a+" : "+Math.ulp(a));
    }
}

Output:

Ulp value for 90.0 : 1.4210854715202004E-14

Example 2:

public class JavaMathUlpExample2 {
    public static void main(String[] args) {
        double a=Double.NEGATIVE_INFINITY;
        //returns positive infinity, if the argument is positive or negative infinity
        System.out.println("Ulp value for "+a+" : "+Math.ulp(a));
    }
}

Output:

Ulp value for -Infinity : Infinity

Example 3:

public class JavaMathUlpExample3 {
    public static void main(String[] args) {
        Float a=0f;
        // returns Float.MIN_VALUE, if the float argument is negative or positive zero
        System.out.println("Float.MIN_VALUE : "+Float.MIN_VALUE);
        System.out.println("Ulp value for "+a+" : "+Math.ulp(a));
    }
}

Output:

Float.MIN_VALUE : 1.4E-45
Ulp value for 0.0 : 1.4E-45

Example 4:

public class JavaMathUlpExample4 {
    public static void main(String[] args) {
        Double a=Double.MAX_VALUE;
        //returns a value equal to 2 raise to power 971, if the argument is ±Double.MAX_VALUE
        System.out.println("2 raise to power 971 : "+Math.pow(2,971));
        System.out.println("Ulp value for "+a+" : "+Math.ulp(a));
    }
}

Output:

2 raise to power 971 : 1.9958403095347198E292
Ulp value for 1.7976931348623157E308 : 1.9958403095347198E292

Example 5:

public class JavaMathUlpExample5 {
    public static void main(String[] args) {
        Float a=Float.MAX_VALUE;
        //returns a value equal to 2 raise to power 104, if the argument is ±Float.MAX_VALUE
        System.out.println("2 raise to power 971 : "+Math.pow(2,104));
        System.out.println("Ulp value for "+a+" : "+Math.ulp(a));
    }
}

Output:

2 raise to power 971 : 2.028240960365167E31
Ulp value for 3.4028235E38 : 2.028241E31