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Floating-Point Numbers - Exercises

Module by: Charles Severance, Kevin Dowd. E-mail the authors

Exercise 1

Run the following code to count the number of inverses that are not perfectly accurate:



      REAL*4 X,Y,Z 
      INTEGER I
      I = 0 
      DO X=1.0,1000.0,1.0
        Y = 1.0 / X
        Z = Y * X 
        IF ( Z .NE. 1.0 ) THEN 
          I = I + 1 
        ENDIF 
      ENDDO
      PRINT *,’Found ’,I 
      END

Exercise 2

Change the type of the variables to REAL*8 and repeat. Make sure to keep the optimization at a sufficiently low level (-00) to keep the compiler from eliminating the computations.

Exercise 3

Write a program to determine the number of digits of precision for REAL*4 and REAL*8.

Exercise 4

Write a program to demonstrate how summing an array forward to backward and backward to forward can yield a different result.

Exercise 5

Assuming your compiler supports varying levels of IEEE compliance, take a significant computational code and test its overall performance under the various IEEE compliance options. Do the results of the program change?

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