Java gcd gcd(long u, long v)

Description

Returns the greatest common divisor of a pair of numbers.

License

GNU General Public License

Declaration

public static final long gcd(long u, long v) 

Method Source Code

//package com.java2s;
// Licensed under the terms of the GNU GPL; see COPYING for details.

public class Main {
    /** Lowest bit set in a byte. */
    static final byte bytelsb[] = { 0, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2,
            1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1,
            2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6,
            1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 1,
            3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2,
            1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1,
            2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3,
            1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1 };

    /** Returns the greatest common divisor of a pair of numbers. */
    public static final long gcd(long u, long v) { // long version.
        assert u > 0 && v > 0;
        int u2s = ffs(u) - 1, v2s = ffs(v) - 1;
        u >>= u2s;//from   w w  w . j a va2s.  c  om
        v >>= v2s; // cast out twos.
        // binary gcd algorithm; u and v must be odd at this point.
        while (u != v) {
            while (u < v) {
                v -= u;
                v >>= (ffs(v) - 1);
            }
            long t = u;
            u = v;
            v = t;
        }
        // u,v have gcd
        return u << Math.min(u2s, v2s); // restore cast out twos.
    }

    /** Returns the greatest common divisor of a pair of numbers. */
    public static final int gcd(int u, int v) { // integer version.
        assert u > 0 && v > 0;
        int u2s = ffs(u) - 1, v2s = ffs(v) - 1;
        u >>= u2s;
        v >>= v2s; // cast out twos.
        // binary gcd algorithm; u and v must be odd at this point.
        while (u != v) {
            while (u < v) {
                v -= u;
                v >>= (ffs(v) - 1);
            }
            int t = u;
            u = v;
            v = t;
        }
        // u,v have gcd
        return u << Math.min(u2s, v2s); // restore cast out twos.
    }

    /** Find first set (least significant bit).
     *  @return the first bit set in the argument.  
     *          <code>ffs(0)==0</code> and <code>ffs(1)==1</code>. */
    public static final int ffs(int v) {
        if ((v & 0x0000FFFF) != 0)
            if ((v & 0x000000FF) != 0)
                return bytelsb[v & 0xFF];
            else
                return 8 + bytelsb[(v >> 8) & 0xFF];
        else if ((v & 0x00FFFFFF) != 0)
            return 16 + bytelsb[(v >> 16) & 0xFF];
        else
            return 24 + bytelsb[(v >> 24) & 0xFF];
    }

    /** Find first set (least significant bit).
     *  @return the first bit set in the argument.  
     *          <code>ffs(0)==0</code> and <code>ffs(1)==1</code>. */
    public static final int ffs(long v) {
        if ((v & 0xFFFFFFFFL) != 0)
            return ffs((int) (v & 0xFFFFFFFFL));
        else
            return 32 + ffs((int) (v >> 32));
    }
}

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