Help with Fortran: Calculate Cos(x) from Equation

[NicolasPan]

Hello I was assigned the following problem:Make a Fortran program which will be able to read a degree[0-360] checking validity range(not type) and it will be able to calculate and print the cos(x) from the following equation:
cos(x)=1-x^2/2! + x^4/4!-x^6/6!+x^8/8!-...,where x is in radiants.As a convergence criteria assume 10^(-5) using the absolute error between two successive repeats(I suppose it means do's).For the calculation of the ! the greatest possible kind of integer should be used.Finally the total number of repeats should be printed on screen.I have been trying really hard to make it run properly but I still have some questions,which I would be greatful would you be able to answer them.1)How can I measure the diffrence of two succesive repeats?
2)The command iostat will work only for the read it corresponds?

program askhsh6_ergasia2
implicit none
integer(kind=4)::i,fact,fact2
real,parameter::pi=3.14159265
real::degree,radiants,cosradiants,s
print*,'This program reads and calculates an angle`s co-sinus'
print*,'Please input the degrees of the angle'
read*,degree
do while(degree<0 .or. degree>360)
read*,degree
  print*,'Error input degree'
  cycle
  end do
  radiants=(degree*pi/180)
  fact=1
  fact2=1
  s=0
do i=2,100,2
      fact=fact*i
      fact2=fact2*(i+2)
      cosradiants=(-(radiants)**i/fact)+(((radiants)**(i+2))/fact2)
  s=s+cosradiants

end do
  print*,s+1.

end program

 

[Khashishi]

Your factorials are jumping over some numbers. Also, these numbers will get fairly large, so you may have some numerical problems.

For convergence, you should probably test if cosradiants lt 10^-5 and break out of the loop if true.

 

[bigfooted]

1)How can I measure the diffrence of two succesive repeats?

cosradiants = 0
do i=2,100,2
      fact=fact*i
      fact2=fact2*(i+2)
      oldcosradiants = cosradiants
      cosradiants=(-(radiants)**i/fact)+(((radiants)**(i+2))/fact2)
      difference = cosradiants - oldcosradiants
      s=s+cosradiants
end do

2)The command iostat will work only for the read it corresponds?

You mean you want to do something like this:

READ(*,*,IOSTAT=io) x

Then the value of io corresponds to x, each read will generate a new IOSTAT for that read that you will have to give to some variable.

Hope this helps.edit: of course you need to check your original code, as Khashishi mentioned, your factorials are wrong.

 

[Khashishi]

No, you don't need to calculate the difference in cosradiants. cosradiants is already the difference between pairwise terms in the series, since you are adding them all together into s.

 

[SteamKing]

A four-byte Fortran REAL data type has a max. magnitude of about 10^-38 to 10³⁸. This means that only about 33! can be represented in single-precision REAL data types. If you want to go higher than 33!, you'll need to use a DOUBLE PRECISION data type.

 

[NicolasPan]

Hello everyone ! Thank you very much for your help I really appreciate that! Could you please explain why my factorials are wrong? It's strange since I get correct answers only for some degrees e.x 45 and wrong for many others such as 90 degrees.Thanks in advance

 

[Khashishi]

You are skipping many numbers since your loop counts by 2. Also, you are using integer*4 which is much too small to store factorials larger than 12! or so. You should probably use real*8.

 

[SteamKing]

Hello everyone ! Thank you very much for your help I really appreciate that! Could you please explain why my factorials are wrong? It's strange since I get correct answers only for some degrees e.x 45 and wrong for many others such as 90 degrees.Thanks in advance

Even though you're using 2!, 4!, 6!, 8!, etc. 8! is still 1×2×3×4×5×6×7×8, so you can't skip over numbers in calculating the correct value of the factorial.

8! ≠ 6! × 8

8! = 6! × 7 × 8