The following algorithm (attributed to Clever Moler) estimates machine precision

Question

The following algorithm (attributed to Clever Moler) estimates machine precision (eps): a = 4.0/3.0; b = a 1.0; c = b + b + b; eps = abs(c 1.0). Implement the program in C++, Java, or Python twice with single and double precision variable types and report the value of eps for both single and double precision.

2. (10 points) The following algorithm (attributed to Clever Moler) estimates machine precision (eps): a 4.0/3.0; ba-1.0 epsabs(c-1.0). Implement the program twice with single and double precision variable types and report the value of eps for both single and double precision

Explanation / Answer

Here is the required code for this problem in Java. Comments are included, go through it, learn how things work and let me know if you have any doubts. Thanks

// EPS.java

public class EPS {

      public static void main(String[] args) {

            // finding eps using single precision (float) variables

            float a = (float) (4.0 / 3.0);

            float b = (float) (a - 1.0);

            float c = b + b + b;

            float result = (float) (c - 1.0);

            float eps1 = Math.abs(result);

            System.out.println("eps for single precision variables: " + eps1);

            // finding eps using double precision (float) variables

            double x = 4.0 / 3.0;

            double y = x - 1.0;

            double z = y + y + y;

            double eps2 = Math.abs(z - 1.0);

            System.out.println("eps for double precision variables: " + eps2);

      }

}

/*OUTPUT*/

eps for single precision variables: 1.1920929E-7

eps for double precision variables: 2.220446049250313E-16

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