Fortran's warning on a program for evaluating elliptic integrals - fortran

Question

On internet, I found this program that demonstrate Evaluating elliptic integrals of first and second kinds (complete)
implicit none
real*8 e,e1,e2,xk
integer i, n
e=1.d-7
print *,' K K(K) E(K) STEPS '
print *,'------------------------------------------'
xk=0.d0
do i = 1, 20
call CElliptic(e,xk,e1,e2,n)
write(*,50) xk,e1,e2,n
xk = xk + 0.05d0
end do
print *,'1.00 INFINITY 1.0000000 0'
stop
50 format(' ',f4.2,' ',f9.7,' ',f9.7,' ',i2)
end
Complete elliptic integral of the first and second kind. The input parameter is xk, which should be between 0 and 1. Technique uses Gauss' formula for the arithmogeometrical mean. e is a measure of the convergence accuracy. The returned values are e1, the elliptic integral of the first kind, and e2, the elliptic integral of the second kind.
Subroutine CElliptic(e,xk,e1,e2,n)
! Label: et
real*8 e,xk,e1,e2,pi
real*8 A(0:99), B(0:99)
integer j,m,n
pi = 4.d0*datan(1.d0)
A(0)=1.d0+xk ; B(0)=1.d0-xk
n=0
if (xk < 0.d0) return
if (xk > 1.d0) return
if (e <= 0.d0) return
et n = n + 1
! Generate improved values
A(n)=(A(n-1)+B(n-1))/2.d0
B(n)=dsqrt(A(n-1)*B(n-1))
if (dabs(A(n)-B(n)) > e) goto et
e1=pi/2.d0/A(n)
e2=2.d0
m=1
do j = 1, n
e2=e2-m*(A(j)*A(j)-B(j)*B(j))
m=m*2
end do
e2 = e2*e1/2.d0
return
end
I have compiled it but I have received the following errors:
gfortran -Wall -c "gauss.f" (nel direttorio: /home/pierluigi/Scrivania)
gauss.f:53.9:
50 format(' ',f4.2,' ',f9.7,' ',f9.7,' ',i2)
1
Error: Invalid character in name at (1)
gauss.f:83.72:
if (dabs(A(n)-B(n)) > e) goto et
1
Warning: Deleted feature: Assigned GOTO statement at (1)
gauss.f:83.35:
if (dabs(A(n)-B(n)) > e) goto et
1
Error: ASSIGNED GOTO statement at (1) requires an INTEGER variable
gauss.f:48.18:
write(*,50) xk,e1,e2,n
1
Error: FORMAT label 50 at (1) not defined
Compilation failed.
Any suggestions please?
EDIT
I have read all your answers and thanks to you I managed to compile the program. I also have another curiosity and I do not know whether to write another question. In the meantime I modify this question. In my program, xk is increased by 0.05. Now I will that the program to read data from a file containing: the minimum value of xk; the maximum value of xk; the number of intervals. I thought:
open (10,file='data/test')
read (10,*) xkmi, xkma
read (10,*) nk
close (10)
lkmi = dlog(xkmi)
lkma = dlog(xkma)
ldk = (lkma-lkmi)/dfloat(nk-1)
In addition, the program must be modified in such a way that the result is written to another file. How can I change the rest of the program? Thank you very much.

Answer 1

Your source code file extension is f which, I think (check the documentation), tells gfortran that the file contains fixed source form. Until Fortran 90 Fortran was still written as if onto punched cards and the location of various bits and pieces of a line is confined to certain columns. A statement label, such as 50 in the first of the error messages, had to be in columns 1 - 6. Two solutions:
Make sure the label is in (some of) those columns. Or, better
Move to free source form, perhaps by changing the file extension to f90, perhaps by using a compilation option (check your documentation).
The error raised by the goto et phrase is, as your compiler has told you, an example of a deleted feature, in which the goto jumps to a statement whose label is provided at run-time, ie the value of et. Either tell your compiler (check ...) to conform to an old standard, or modernise your source.
Fix those errors and, I suspect, the other error messages will disappear. They are probably raised as a consequence of the compiler not correctly parsing the source after the errors.

Answer 2

Because the file has type ".f" gfortan is interpreting it as fixed-source layout. Trying compiling with the free-form layout by using compiler option -ffree-form and see if that works. This probably explains the error about the "invalid character". That statement not being recognized explains the "format not defined error". The "computed goto" is obsolete but valid Fortran. You can ignore that warning. If you wish, later you can modernize the code. For the remaining error, for the "assigned goto", declare "et" as an integer.

Answer 3

I would just do this
10 n = n + 1
! Generate improved values
A(n)=(A(n-1)+B(n-1))/2.d0
B(n)=dsqrt(A(n-1)*B(n-1))
if (dabs(A(n)-B(n)) > e) goto 10
and possibly compile as free form source as others have shown. The label et seems weird and non-standard, possibly a rare vendor extension.
You could also change the lines above to a do-loop with an exit statement (Fortran 90).
(The program compiled for me after the change).

Answer 4

I tested the subroutine and compared with matlab and it was not the same. It is very similar to the algorithm used in Abramowitz's book. Here is the one I wrote that works well, just for comparing.
subroutine CElliptic(m,K,E)
implicit none
real*8 m,alpha,E,K,A,B,C,A_p,B_p,C_0,pi,suma
integer j,N
N=100
alpha=asin(sqrt(m))
pi = 4.d0*datan(1.d0)
A_p=1.0
B_p=cos(alpha)
C_0=sin(alpha)
suma=0.0
do j=1,N
A=(A_p+B_p)/2.0d0
B=dsqrt(A_p*B_p)
C=(A_p-B_p)/2.0d0
suma=suma+2**(j)*C**2
A_p=A
B_p=B
end do
K=pi/(2*A)
E=(1-1.d0/2.d0*(C_0**2+suma))*K
end Subroutine CElliptic
best regards
Ed.