Long ints in Fortran

Question

I'm trying to work with large numbers (~10^14), and I need to be able to store them and iterate over loops of that length, i.e.

n=SOME_BIG_NUMBER
do i=n,1,-1

I've tried the usual star notation, kind=8 etc. but nothing seems to work. Then I checked the huge intrinsic function, and the code:

program inttest

print *,huge(1)
print *,huge(2)
print *,huge(4)
print *,huge(8)
print *,huge(16)
print *,huge(32)

end program inttest

produces the number 2147483647 in all cases. Why is this? I'm using gfortran (f95) on a 64-bit machine.

If I'm going to need a bignum library, which one do people suggest?

Answer 1

The gfortran versions that I use, 4.3, 4.4 and 4.5 on a Mac, support 8-byte integers. The best way to select a variable type in Fortran >= 90 is to use an intrinsic function to specify the precision that you need. Try:

integer, parameter :: LargeInt_K = selected_int_kind (18)
integer (kind=LargeInt_K) :: i, n

to obtain at least 18 decimal digits, which will typically be a 8-byte integer.

With gfortran 4.3, huge (1_LargeInt_K) outputs 9223372036854775807. When you wrote huge (1), etc., by default the constant was a default integer, here evidently 4-bytes since huge returned 2147483647. So sometimes you need to specify the precision of constants, not just variables -- more commonly this trips people up when they lose significant figures on a real constant, which defaults to single precision.

Also see Fortran: integer*4 vs integer(4) vs integer(kind=4)

Usually gfortran has the command name gfortran. Could f95 be a different compiler? Try "gfortran -v" and "f95 -v".

Answer 2

You've misunderstood the precise definition of the HUGE function. HUGE(num) returns the largest number with the same kind and type as num. The value returned also has the same kind and type as num. Since all your input values are (default) integers HUGE, correctly, returns the largest default-size integer.

HUGE(num) does not return the largest integer with kind=num. Nor does HUGE(num) return the largest number representable in num bytes. While many compilers use integer(kind=4) and integer(kind=8) etc for 4- and 8-byte integers, this is not guaranteed by the language standard and cannot be relied upon to be portable.

@MSB's answer tells you how to do what you want, I'm just butting in with some clarification.