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+/* gcd.c (greatest common divisor) */
+
+/***********************************************************************
+* This code is part of GLPK (GNU Linear Programming Kit).
+*
+* Copyright (C) 2000-2013 Andrew Makhorin, Department for Applied
+* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
+* reserved. E-mail: <mao@gnu.org>.
+*
+* GLPK is free software: you can redistribute it and/or modify it
+* under the terms of the GNU General Public License as published by
+* the Free Software Foundation, either version 3 of the License, or
+* (at your option) any later version.
+*
+* GLPK is distributed in the hope that it will be useful, but WITHOUT
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+* License for more details.
+*
+* You should have received a copy of the GNU General Public License
+* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
+***********************************************************************/
+
+#include "env.h"
+#include "misc.h"
+
+/***********************************************************************
+* NAME
+*
+* gcd - find greatest common divisor of two integers
+*
+* SYNOPSIS
+*
+* #include "misc.h"
+* int gcd(int x, int y);
+*
+* RETURNS
+*
+* The routine gcd returns gcd(x, y), the greatest common divisor of
+* the two positive integers given.
+*
+* ALGORITHM
+*
+* The routine gcd is based on Euclid's algorithm.
+*
+* REFERENCES
+*
+* Don Knuth, The Art of Computer Programming, Vol.2: Seminumerical
+* Algorithms, 3rd Edition, Addison-Wesley, 1997. Section 4.5.2: The
+* Greatest Common Divisor, pp. 333-56. */
+
+int gcd(int x, int y)
+{ int r;
+ xassert(x > 0 && y > 0);
+ while (y > 0)
+ r = x % y, x = y, y = r;
+ return x;
+}
+
+/***********************************************************************
+* NAME
+*
+* gcdn - find greatest common divisor of n integers
+*
+* SYNOPSIS
+*
+* #include "misc.h"
+* int gcdn(int n, int x[]);
+*
+* RETURNS
+*
+* The routine gcdn returns gcd(x[1], x[2], ..., x[n]), the greatest
+* common divisor of n positive integers given, n > 0.
+*
+* BACKGROUND
+*
+* The routine gcdn is based on the following identity:
+*
+* gcd(x, y, z) = gcd(gcd(x, y), z).
+*
+* REFERENCES
+*
+* Don Knuth, The Art of Computer Programming, Vol.2: Seminumerical
+* Algorithms, 3rd Edition, Addison-Wesley, 1997. Section 4.5.2: The
+* Greatest Common Divisor, pp. 333-56. */
+
+int gcdn(int n, int x[])
+{ int d, j;
+ xassert(n > 0);
+ for (j = 1; j <= n; j++)
+ { xassert(x[j] > 0);
+ if (j == 1)
+ d = x[1];
+ else
+ d = gcd(d, x[j]);
+ if (d == 1)
+ break;
+ }
+ return d;
+}
+
+/* eof */