Procedure

     GCD ( Greatest Common Divisor )

     INTEGER FUNCTION GCD ( A, B )

Abstract

     Return the greatest common divisor of two integers.

Required_Reading

     None.

Keywords

     MATH
     NUMBERS

Declarations

     IMPLICIT NONE

     INTEGER          A
     INTEGER          B

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     A          I   Any integer
     B          I   Any integer

     The function returns the greatest common divisor of A and B.

Detailed_Input

     A        is any integer.

     B        is any integer.

Detailed_Output

     The function returns the greatest common divisor of A and B.

Parameters

     None.

Exceptions

     Error free.

     1)  If both A and B are zero, then GCD returns zero.

     2)  If exactly one of A and B is zero, then GCD is by definition
         the maximum of the absolute values of A and B.

Files

     None.

Particulars

     This routine uses Euclid's Algorithm to find the greatest common
     divisor (GCD) of the integers A and B. In other words the
     largest integer, G, such that A = k*G for some k and B = j*G for
     some G. Note if either A or B is zero, then we return the
     maximum of the two integers ABS(A) and ABS(B).  If one is
     non-zero we have just what the definition says. If both are zero
     the definition above does not give us a GCD, so we take the GCD
     of 0 and 0 to be 0.

Examples

     A      B            GCD
     -----  -----         -----
       8      4             4
      120    44             4
      15    135            15
     101     97             1
     119    221            17
     144     81             9
       0    111           111
       0      0             0

Restrictions

     None.

Literature_References

     [1]  D. Knuth, "The Art of Computer Programming Vol 1. --
          Fundamental Algorithms," 2nd Ed., Addison-Wesley, 1973

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 06-JUL-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WLT)