@node gcd
@section gcd: greatest common divisor
@findex gcd

@c Copyright (C) 2006, 2009--2023 Free Software Foundation, Inc.

@c Permission is granted to copy, distribute and/or modify this document
@c under the terms of the GNU Free Documentation License, Version 1.3 or
@c any later version published by the Free Software Foundation; with no
@c Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A
@c copy of the license is at <https://www.gnu.org/licenses/fdl-1.3.en.html>.

The @code{gcd} function returns the greatest common divisor of two numbers
@code{a > 0} and @code{b > 0}.  It is the caller's responsibility to ensure
that the arguments are non-zero.

If you need a gcd function for an integer type larger than
@samp{unsigned long}, you can include the @file{gcd.c} implementation file
with parametrization.  The parameters are:

@itemize @bullet
@item WORD_T
Define this to the unsigned integer type that you need this function for.

@item GCD
Define this to the name of the function to be created.
@end itemize

The created function has the prototype
@smallexample
WORD_T GCD (WORD_T a, WORD_T b);
@end smallexample

If you need the least common multiple of two numbers, it can be computed
like this: @code{lcm(a,b) = (a / gcd(a,b)) * b} or
@code{lcm(a,b) = a * (b / gcd(a,b))}.
Avoid the formula @code{lcm(a,b) = (a * b) / gcd(a,b)} because---although
mathematically correct---it can yield a wrong result, due to integer overflow.

In some applications it is useful to have a function taking the gcd of two
signed numbers. In this case, the gcd function result is usually normalized
to be non-negative (so that two gcd results can be compared in magnitude
or compared against 1, etc.). Note that in this case the prototype of the
function has to be
@smallexample
unsigned long gcd (long a, long b);
@end smallexample
and not
@smallexample
long gcd (long a, long b);
@end smallexample
because @code{gcd(LONG_MIN,LONG_MIN) = -LONG_MIN = LONG_MAX + 1} does not
fit into a signed @samp{long}.