Save data in another external file name output.txt? - fortran

Question

The program can run, I am not sure how to use open() and save the data in another external file name output.txt. My questions are stated below - please have a look and help.
program start
implicit none
integer ::n
real(kind=8)::x,h,k
real(kind=8),external:: taylorq
x=1.0
n=20
h=exp(x)
k=taylorq(x,n)
open(10,'output.txt') ----------- *question1:(when should i put this open file?)*
write(*,*)"The exact value=",h
write(*,*)"The approximate value=",k
write(*,*)"The error=",h-k
end program start
function taylorq(x,n)
implicit none
integer::n,i
real(kind=8):: x,taylor,taylor2,taylorq,h
h=exp(x)
taylor=1.
taylor2=taylor
write(*,*)"i exact appro error"-----------question2:(actually I want to draw a table with subtitle i, exact, appro, error in each column, is there a nice way to arrange them like eg.we can use %5s)
do i=1,n
taylor=taylor*x/i
taylor2=taylor2+taylor
write(10,*)i,h,taylor2,taylor2-h --------question3:*(I want to save the data written here into file output.txt)*
end do
close(10)
taylorq=taylor2
end function taylorq

Answer 1

1. where to open
You should put open(10,...) so it executes before any write(10,...) -- or read(10,...) if this was input.
Since your writes occur in the function taylorq, you should open() before the statement that calls taylorq.
For programs that do very large computations, which Fortran is suited/famous for, it is often best to do
all file open's very near the beginning of the program, so that if there is a problem opening any file,
it is caught and fixed without wasting hours or days of work. But your program is much simpler than that.
2. formatting
Yes, Fortran can do formatted output -- and also formatted input. Instead of a text string with
interpolated specifiers (like C and the C part of C++, and Java, and awk and perl and shell) it uses specifiers
with optionally interpolated text values, and the specifiers are written with the format letter on
the left followed by the width (almost always) and other parameters (sometimes).
You can either put the format directly in the WRITE (or READ) statement, or in a separate FORMAT
statement referred to by its label in the I/O statement.
write (10, '(I4,F10.2,F10.2,F10.2)' ) i,h,taylor2,taylor2-h
or
write (10, 900) i,h,taylor2,taylor2-h
! this next line can be anywhere in the same program-unit
900 format (I4,F10.2,F10.2,F10.2)
Unlike C-family languages, Fortran will always output the specified width; if the value doesn't fit,
it prints asterisks ***** instead of forcing the field wider (and thus misaligned) (or truncating as
COBOL does!). Your series grows fast enough you might want to use scientific notation like E10.3.
(The format letters can be in either case, but I find them easier to read in upper. YMMV.)
There are many, MANY, more options. Any textbook or your compiler manual should cover this.