Java Long Number Mod modularReciprocal(long a, long mod)

Description

Computes the reciprocal or multiplicative inverse of a (modulo mod).

License

BSD License

Exception

Parameter	Description
ArithmeticException	if a is not invertible (modulo mod)

Return

the multiplicative inverse of a (modulo mod), if it exists, and throws an exception otherwise.

Declaration

public static long modularReciprocal(long a, long mod) 

Method Source Code

//package com.java2s;
/*/*from w w w .  j a v a 2s . c  o  m*/
 * =============================================================================
 * Simplified BSD License, see http://www.opensource.org/licenses/
 * -----------------------------------------------------------------------------
 * Copyright (c) 2008-2009, Marco Terzer, Zurich, Switzerland
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are met:
 * 
 *     * Redistributions of source code must retain the above copyright notice, 
 *       this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright 
 *       notice, this list of conditions and the following disclaimer in the 
 *       documentation and/or other materials provided with the distribution.
 *     * Neither the name of the Swiss Federal Institute of Technology Zurich 
 *       nor the names of its contributors may be used to endorse or promote 
 *       products derived from this software without specific prior written 
 *       permission.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
 * POSSIBILITY OF SUCH DAMAGE.
 * =============================================================================
 */

public class Main {
    /**
     * Computes the reciprocal or multiplicative inverse of a (modulo mod). Note
     * that a is only invertible if a and mod are coprime. If this is not the
     * case, an {@link ArithmeticException} is thrown.
     * <p>
     * The returned value <tt>inv(a)</tt> meets the following equality:
     * <tt>inv(a) * a = 1 (modulo mod)</tt>.
     * 
     * @return    the multiplicative inverse of a (modulo mod), if it exists, and 
     *          throws an exception otherwise.
     * @throws ArithmeticException if a is not invertible (modulo mod)  
     */
    public static int modularReciprocal(int a, int mod) {
        final int origA = a;
        final int origMod = mod;
        int x = 0;
        int y = 1;
        int lastx = 1;
        int lasty = 0;
        while (mod != 0) {
            int temp = mod;
            final int quotient = a / mod;
            mod = a % mod;
            a = temp;

            temp = x;
            x = lastx - quotient * x;
            lastx = temp;

            temp = y;
            y = lasty - quotient * y;
            lasty = temp;
        }
        if (a != 1 && a != -1) {
            throw new ArithmeticException(origA + " is not invertible (mod " + origMod + ") " + "since gcd(" + origA
                    + ", " + origMod + ") = " + a + " != 1");
        }
        return lastx;
    }

    /**
     * Computes the reciprocal or multiplicative inverse of a (modulo mod). Note
     * that a is only invertible if a and mod are coprime. If this is not the
     * case, an {@link ArithmeticException} is thrown.
     * <p>
     * The returned value <tt>inv(a)</tt> meets the following equality:
     * <tt>inv(a) * a = 1 (modulo mod)</tt>.
     * 
     * @return    the multiplicative inverse of a (modulo mod), if it exists, and 
     *          throws an exception otherwise. 
     * @throws ArithmeticException if a is not invertible (modulo mod)  
     */
    public static long modularReciprocal(long a, long mod) {
        final long origA = a;
        final long origMod = mod;
        long x = 0;
        long y = 1;
        long lastx = 1;
        long lasty = 0;
        while (mod != 0) {
            long temp = mod;
            final long quotient = a / mod;
            mod = a % mod;
            a = temp;

            temp = x;
            x = lastx - quotient * x;
            lastx = temp;

            temp = y;
            y = lasty - quotient * y;
            lasty = temp;
        }
        if (a != 1L && a != -1L) {
            throw new ArithmeticException(origA + " is not invertible (mod " + origMod + ") " + "since gcd(" + origA
                    + ", " + origMod + ") = " + a + " != 1");
        }
        return lastx;
    }
}

Related

1. mod(long x, long y)
2. modDivide(long a, long b, long m)
3. modifiedCalcElementOffset(long index, long mask)
4. modifyValue(long value, char op, long modifier, long max, long min)
5. mods(long v, long m)
6. modulo(final long x, final long y)
7. modulo(long a, long n)