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Write a short program to compute the double factorial,
N !! = N (N-2) (N-4) (N-6) ... 2 or 1, depending if N is even or odd. You may do this either in the body of the program or in a subroutine.
Both N and N !! should be a regular integer (so declared integer, not integer*8).
Now write a loop over N and find out when machine precision makes N !! unreliable. This can be recognized when you increase N by 1 but the result for N !! is smaller. This is because of overrun.
Your assignment is to write a program to automatically find the maximal value of N before machine precision kills your routine. That is, it should loop over increasing N until the value of N !! actually decreases. Hint: you will have to store your previous value of N !! from the previous loop. You will also have to initially this “old” value to 1 before you start your loop.
If you can finish this successfully in under 1 hour, then you have good programming skills.
If you can finish this project successfully, but it takes you significantly longer than 1 hours, you need more practice.
If you cannot solve this problem at all, you have serious deficiencies and need to work much harder to improve your programming skills.
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