Java Programming Create a program to create a program that adds the numbers 1/2

Question

Java Programming

Create a program to create a program that adds the numbers 1/2 to itself and 1/3 to itself a large number of times using both types float and double. It is to then compare the values of adding the numbers to multiplying 1/2 and 1/3 times the number of times they were added.

The program must first add 1/2 and 1/3 using type float, and compare to the value obtain using multiplication instead of addition. It is to do this for the following values:

1.000

10,000

100,000

1,000,000

10,000,000

100,000,000

1,000,000,000

The program should do this using two nested loops. The outer loop determines the number of times to add and starts at a 1000 and increments by multiples of 10 up to a 1,000,000,000. The inner loop does the addition of the numbers 1/2 and 1/3. When the inner loop completes, output the two sums and the two products, and the differences between the sums and the products to check for rounding errors. Then continue the outer loop. Remember to clear your variables for the sums before the start of the inner loop.

Next the program repeats the above except that it uses type double instead of type float for the variables. This will require a second set of nested loops and different variables.

As always, have your name, the assignment number, and a brief description of the program in comments at the top, have comments in the program, use proper blocking, and make certain to test your program to verify that it is working properly.

Lastly, notice the values produced, do they make sense to you?

Explanation / Answer

public class ErrorCheck {
  
  
  
   public static void main(String args[]){
      
       float float_sum_1=0, float_sum_2=0;
       float float_mul_1=0, float_mul_2=0;
      
       double double_sum_1=0, double_sum_2=0;
       double double_mul_1=0, double_mul_2=0;
      
       System.out.println("FOR FLOATS:- ");
       for(long i=1000; i<=1000000000; i=i*10)
       {
           float_sum_1=0;
           float_sum_2=0;
           float_mul_1=0;
           float_mul_2=0;
          
           for(long j=1; j<=1000; j++)
           {
               float_sum_1 += (1/2.0);
               float_sum_2 += (1/3.0);
           }
          
           float_mul_1 = (float) ((1/2.0)*i);
           float_mul_2 = (float) ((1/3.0)*i);
          
           System.out.println("For "+i +"times:");
           System.out.println("Two sums are: "+float_sum_1+" and "+float_sum_2);
           System.out.println("Two muls are: "+float_mul_1+" and "+float_mul_2);
           System.out.println("Error as difference are: "+(float_mul_1 - float_sum_1)+ " and "+(float_mul_2 - float_sum_2));
           System.out.println(" ");
       }
      
       System.out.println(" FOR DOUBLES:- ");
       for(long i=1000; i<=1000000000; i=i*10)
       {
           double_sum_1=0;
           double_sum_2=0;
           double_mul_1=0;
           double_mul_2=0;
          
           for(long j=1; j<=1000; j++)
           {
               double_sum_1 += (1/2.0);
               double_sum_2 += (1/3.0);
           }
          
           double_mul_1 = (float) ((1/2.0)*i);
           double_mul_2 = (float) ((1/3.0)*i);
          
           System.out.println("For "+i +"times:");
           System.out.println("Two sums are: "+double_sum_1+" and "+double_sum_2);
           System.out.println("Two muls are: "+double_mul_1+" and "+double_mul_2);
           System.out.println("Error as difference are: "+(double_mul_1 - double_sum_1)+ " and "+(double_mul_2 - double_sum_2));
           System.out.println(" ");
       }
      
   }

}

---------------------------------------------------------------------------

OUTPUT

FOR FLOATS:-

For 1000times:
Two sums are: 500.0 and 333.3341
Two muls are: 500.0 and 333.33334
Error as difference are: 0.0 and -7.6293945E-4

For 10000times:
Two sums are: 500.0 and 333.3341
Two muls are: 5000.0 and 3333.3333
Error as difference are: 4500.0 and 2999.999

For 100000times:
Two sums are: 500.0 and 333.3341
Two muls are: 50000.0 and 33333.332
Error as difference are: 49500.0 and 32999.996

For 1000000times:
Two sums are: 500.0 and 333.3341
Two muls are: 500000.0 and 333333.34
Error as difference are: 499500.0 and 333000.0

For 10000000times:
Two sums are: 500.0 and 333.3341
Two muls are: 5000000.0 and 3333333.2
Error as difference are: 4999500.0 and 3333000.0

For 100000000times:
Two sums are: 500.0 and 333.3341
Two muls are: 5.0E7 and 3.3333334E7
Error as difference are: 4.99995E7 and 3.3333E7

For 1000000000times:
Two sums are: 500.0 and 333.3341
Two muls are: 5.0E8 and 3.33333344E8
Error as difference are: 4.99999488E8 and 3.33333024E8

FOR DOUBLES:-

For 1000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 500.0 and 333.3333435058594
Error as difference are: 0.0 and 1.0172527538543363E-5

For 10000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 5000.0 and 3333.333251953125
Error as difference are: 4500.0 and 2999.9999186197933

For 100000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 50000.0 and 33333.33203125
Error as difference are: 49500.0 and 32999.99869791667

For 1000000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 500000.0 and 333333.34375
Error as difference are: 499500.0 and 333000.0104166667

For 10000000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 5000000.0 and 3333333.25
Error as difference are: 4999500.0 and 3332999.9166666665

For 100000000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 5.0E7 and 3.3333334E7
Error as difference are: 4.99995E7 and 3.3333000666666668E7

For 1000000000times:
Two sums are: 500.0 and 333.33333333333184
Two muls are: 5.0E8 and 3.33333344E8
Error as difference are: 4.999995E8 and 3.333330106666667E8

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