How to Handle Floating Point Errors in Fortran90 Real Number Calculations

[abdulsulo]

Hello guys I am trying to write a code which is below;

But my results seems to be fairly wrong.

I noticed some of my real numbers are not what I assigned them. For example Ks shows on the watch window as 9.9999999E-5.

How can I fix such situation?

program hw1
  
    REAL:: G,DVIS,Ks, EPS,LENGTH,D,Vs,Re,Vi,V0,FFACT,DELt,I,Vi1,H,T,PHO
  
    G=9.81
    D=0.3
    H=8
    Ks=1E-4
    T=60
    DVIS=0.001
    PHO=1000
    EPS=0.01
    DELt=0.02
    write(*,*) Ks
    write(*,*) G
    write(*,*) H
    write(*,*) T
    write(*,*) DVIS
    write(*,*) PHO
    write(*,*) EPS
    write(*,*) DELt
    WRITE(*,*) 'INPUT CYLINDER DIAMETER'
    READ(*,*) D
    WRITE(*,*) 'LENGTH'
    READ(*,*) LENGTH
  
    IF (LENGTH==50) THEN
        Vs=6.586
    ELSE IF (LENGTH==100) THEN
        Vs=5.00
    ELSE IF (LENGTH==200) THEN
        Vs=3.669
    ELSE IF (LENGTH==500) THEN
        Vs=2.36
    END IF
    write(*,*) Ks
    Re=PHO*Vs*D/DVIS
    write(*,*) Re
    FFACT=0.25/((log((Ks/(3.7*D))+(5.74/Re**0.9)))**2)   
    write(*,*) FFACT
    Vi=0
    write(*,*) Vi
    DO I=0.02, 200, 0.02
        if (I==0.02) THEN
            Vi1=Vi+(DELt*(H)*G/LENGTH)
            Vi=Vi1
            write(*,*) Vi1
        ELSE
        Re=PHO*Vi*D/DVIS
        FFACT=0.25/((log((Ks/(3.7*D))+(5.74/Re**0.9)))**2)
        Vi1=Vi+(DELt*(H-((1+(FFACT*LENGTH/D))*((Vi**2)/(2*G))))*G/LENGTH)
        Vi=Vi1
        write(*,*) Vi1
        end if
    end do
  
    pause
  
end program

<<Moderator's note: added code tags>>

 

[DrClaude]

You need to get familiar with floating point representation. See https://www.physicsforums.com/insights/cant-computer-simple-arithmetic/

 

[abdulsulo]

I read and tried to understand. But it seems there are no solutions for this? Am I wrong?

 

[DrClaude]

If you want higher precision, then use

REAL(KIND(1d0)) :: G,DVIS,Ks, EPS,LENGTH,D,Vs,Re,Vi,V0,FFACT,DELt,I,Vi1,H,T,PHO

to get double precision. On modern computer, single precision should not be used anyway.

 

[jedishrfu]

You could write the values using a formatted write which should "round" the number to be 1E-4 but written as 0.0001

http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/chap05/format.html

 

[FactChecker]

Notice that the printed values of K are actually very close to the number you set it to. 1E-4 and 9.9999999E-5 only differ by 0.000000000001 = 1E-12.
Number fractions on the computer are stored in binary and will not be exactly as you set them in base 10. The formats mentioned by others above will make them appear the same. If you need more accuracy, you should use a variable type for K that will keep more significant digits.

 

[Mark44]

Number fractions on the computer are stored in binary and will not be exactly as you set them in base 10.

... and some will not be exactly as you set them.

Fractions that are linear combinations of 1/2, 1/4, 1/8, 1/16, and so on, are stored in exact form. Fractions such as 1/5 and 1/10, that have nice, compact forms in base-10 (i.e., 1/5 = .2, 1/10 = .1), but their representations as binary fractions have patterns that repeat endlessly, and so they are not stored in exact form.

 

[Mark44]

I wrote an Insights article about this problem - Why Can’t My Computer Do Simple Arithmetic?

 

[abdulsulo]

Thank you all for kind insights. Now I got to read through articles that you linked and try to find solution to my problem.

 

[abdulsulo]

I am trying to make simple calculation of below;
Vi= 6.586542
Vs=6.586000

The program finds a as 6.554608 from below equation. How is this possible?
a=ABS(Vi-Vs)

EDİT: I found my error. Thank you for your interest.