/*
 * GF.java - Implements Finite Field GF(p^m).
 *
 * ------------------------------------------------------------------
 *
 * @begin[license]
 * Copyright (C) 2003  Kai Chen, Caltech
 *
 * This program 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 2
 * of the License, or (at your option) any later version.
 *
 * This program 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 this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 *
 * @author: Kai Chen
 * @email{kchen@cs.caltech.edu}
 * @end[license]
 *
 */


public class GF
{
    /* 
     * default values for EE127 final project:
     *       GF(2^5), poly(x) = x^5 + x^2 + 1.
     */
    private static final int DEFAULT_P = 2;
    private static final int DEFAULT_M = 5;
    private static final int DEFAULT_POLY[] = {1, 0, 1, 0, 0, 1};

    /* field related data */
    protected int p, m, n;
    protected int poly[];
    
    /* power and log tables */
    protected int powerTable[], logTable[];

    
    /* 
     * post: construct default GF(2^5)
     */
    public GF()
    {
        this(DEFAULT_P, DEFAULT_M, DEFAULT_POLY);
    }


    /* 
     * pre: p is prime, poly is irreducible with degree m
     * post: construct GF(p^m) 
     */
    public GF(int p, int m, int poly[])
    {
        this.p = p;
        this.m = m;
        this.poly = poly;

        /* compute n = p^m */
        n = 1;
        for(int i=0; i<m; i++)
            n *= p;

        /* compute powerTable */
        powerTable = new int[n];
        
        /* compute entries 0 <= i < m */
        for(int i=0; i<m; i++)
            powerTable[i] = (i==0) ? 1 : p*powerTable[i-1];
        

        /* compute m-th entry */
        for(int i=0, mask=1; i<m; i++, mask*=p)
            powerTable[m] += mask * ((p - poly[i]) % p);

        /* compute entries: m < i < n-1 */
        for(int i=m+1; i<orderOfAlpha(); i++)
            if((powerTable[i] = p*powerTable[i-1]) >= n)
                powerTable[i] = add(powerTable[i]%n, powerTable[m]);
        
        
        /* build the logTable */
        logTable = new int[n];
        
        for(int i=0; i<orderOfAlpha(); i++)
            logTable[powerTable[i]] = i;
    }


    /*
     * pre: x is a value in GF(p^m)
     * post: returns vector representation of x
     */
    protected int[] toVector(int x)
    {
        int vector[] = new int[m];
        for(int i=0; i<m; i++){
            vector[i] = x % p;
            x /= p;
        }
        return vector;
    }


    /*
     * pre: vector is a vector representation of a value x in GF(p^m)
     * post: returns x
     */
    protected int toValue(int vector[])
    {
        int x = 0;
        for(int i=m-1; i>=0; i--)
            x = x*p + vector[i];

        return x;
    }


    /*
     * pre: x, y are two values in GF(p^m)
     * post: returns a value (x+y) in GF(p^m)
     */
    public int add(int x, int y)
    {
        /* optimization for p=2 case */
        if(p==2) return x^y;
        
        int xVector[] = toVector(x);
        int yVector[] = toVector(y);
        int resultVector[] = new int[m];
        
        /* do 'entry-wise' addition */
        for(int i=0; i<m; i++)
            resultVector[i] = (xVector[i]+yVector[i]) % p;

        return toValue(resultVector);
    }


    /*
     * pre: x, y are two values in GF(p^m)
     * post: returns a value (x-y) in GF(p^m)
     */
    public int sub(int x, int y)
    {
        /* optimization for p=2 case */
        if(p==2) return x^y;

        int xVector[] = toVector(x);
        int yVector[] = toVector(y);
        int resultVector[] = new int[m];

        /* do 'entry-wise' subtraction */
        for(int i=0; i<m; i++)
            resultVector[i] = (p+xVector[i]-yVector[i]) % p;

        return toValue(resultVector);
    }


    /* 
     * pre: x is a value in GF(p^m)
     * post: returns the additive inverse of x
     */
    public int neg(int x)
    {
        return sub(0, x);
    }


    /*
     * pre: x, y are two values in GF(p^m)
     * post: returns a value (x*y) in GF(p^m)
     */
    public int mul(int x, int y)
    {
        return (x==0 || y==0) ? 0 : power(log(x)+log(y));
    }

    
    /*
     * pre: x, y are two values in GF(p^m), y != 0.
     * post: returns a value z such that x = y*z in GF(p^m) 
     */
    public int div(int x, int y) throws RSException
    {
        if(y==0){
            throw new RSException("GF.div: Divide by zero error.");
        }
        return (x==0) ? 0 : power(log(x)-log(y));
    }


    /*
     * pre: x is a value in GF(p^m), x!=0
     * post: returns the multiplicative inverse of x
     */
    public int inv(int x) throws RSException
    {
        if(x==0){
            throw new RSException
                ("GF.inv: Zero has no multiplicative inverse.");
        }
        return div(1, x);
    }


    /*
     * post: returns alpha raised to k
     */
    public int power(int k)
    {
        return powerTable[((n-1)+k%(n-1)) % (n-1)];
    }


    /* 
     * pre: x is a value in GF(p^m)
     * post: find k such that p^k = x
     */
    public int log(int x)
    {
        return logTable[x];
    }


    /* 
     * post: returns the unity of the field
     */
    public int getUnity()
    {
        return power(0);
    }


    /*
     * post: returns the zero of the field
     */
    public int getZero()
    {
        return log(getUnity());
    }


    /* 
     * post: returns the size of the field
     */
    public int getFieldSize()
    {
        return n;
    }


    /* 
     * post: returns p
     */
    public int getP()
    {
        return p;
    }


    /*
     * post: returns the order of alpha - a primitive root 
     */
    public int orderOfAlpha()
    {
        return n-1;
    }

    
    /* 
     * A testdrive for GF
     */
    public static void main(String[] args)
    {
        GF gf = new GF();
        try{
            for(int i=0; i<gf.n-1; i++)
                System.out.println(gf.powerTable[i]+" "+ 
                    gf.inv(gf.powerTable[i]) +
                    " --- "+
                    gf.mul(gf.powerTable[i], gf.inv(gf.powerTable[i])));
        }catch(RSException ex){
            ex.printStackTrace();
        }

        
        System.out.println(gf.getUnity()+ "--------" +gf.getZero());
    }
}