java.math.Division Maven / Gradle / Ivy

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 *  this work for additional information regarding copyright ownership.
 *  The ASF licenses this file to You under the Apache License, Version 2.0
 *  (the "License"); you may not use this file except in compliance with
 *  the License.  You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

package java.math;

/**
 * Static library that provides all operations related with division and modular
 * arithmetic to {@link BigInteger}. Some methods are provided in both mutable
 * and immutable way. There are several variants provided listed below:
 *
 * 
 *  Division
 * 
 * {@link BigInteger} division and remainder by {@link BigInteger}.
 * {@link BigInteger} division and remainder by {@code int}.
 * gcd between {@link BigInteger} numbers.
 * 
 * 
 *  Modular arithmetic 
 * 
 * Modular exponentiation between {@link BigInteger} numbers.
 * Modular inverse of a {@link BigInteger} numbers.
 * 
 * 
 *
 */
class Division {

    /**
     * Divides an array by an integer value. Implements the Knuth's division
     * algorithm. See D. Knuth, The Art of Computer Programming, vol. 2.
     *
     * @return remainder
     */
    static int divideArrayByInt(int[] quotient, int[] dividend, final int dividendLength,
            final int divisor) {

        long rem = 0;
        long bLong = divisor & 0xffffffffL;

        for (int i = dividendLength - 1; i >= 0; i--) {
            long temp = (rem << 32) | (dividend[i] & 0xffffffffL);
            long quot;
            if (temp >= 0) {
                quot = (temp / bLong);
                rem = (temp % bLong);
            } else {
                /*
                 * make the dividend positive shifting it right by 1 bit then
                 * get the quotient an remainder and correct them properly
                 */
                long aPos = temp >>> 1;
                long bPos = divisor >>> 1;
                quot = aPos / bPos;
                rem = aPos % bPos;
                // double the remainder and add 1 if a is odd
                rem = (rem << 1) + (temp & 1);
                if ((divisor & 1) != 0) {
                    // the divisor is odd
                    if (quot <= rem) {
                        rem -= quot;
                    } else {
                        if (quot - rem <= bLong) {
                            rem += bLong - quot;
                            quot -= 1;
                        } else {
                            rem += (bLong << 1) - quot;
                            quot -= 2;
                        }
                    }
                }
            }
            quotient[i] = (int) (quot & 0xffffffffL);
        }
        return (int) rem;
    }
}