user/test/com/google/gwt/emultest/java/math/BigIntegerDivideTest.java

/*
 * Copyright 2009 Google Inc.
 * 
 * Licensed 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.
 */

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements. See the NOTICE file distributed with 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.
 * 
 * INCLUDES MODIFICATIONS BY GOOGLE.
 */
/**
 * author Elena Semukhina
 */
package com.google.gwt.emultest.java.math;

import com.google.gwt.emultest.java.util.EmulTestBase;

import java.math.BigInteger;

/**
 * Class: java.math.BigInteger Methods: divide, remainder, mod, and
 * divideAndRemainder.
 */
public class BigIntegerDivideTest extends EmulTestBase {
  /**
   * Divide by zero.
   */
  public void testCase1() {
    byte aBytes[] = {1, 2, 3, 4, 5, 6, 7};
    byte bBytes[] = {0};
    int aSign = 1;
    int bSign = 0;
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    try {
      aNumber.divide(bNumber);
      fail("ArithmeticException has not been caught");
    } catch (ArithmeticException e) {
      assertEquals("Improper exception message", "BigInteger divide by zero",
          e.getMessage());
    }
  }

  /**
   * Divide two negative numbers.
   */
  public void testCase10() {
    byte aBytes[] = {1, 100, 56, 7, 98, -1, 39, -128, 127, 5, 6, 7, 8, 9};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = -1;
    int bSign = -1;
    byte rBytes[] = {23, 115, 11, 78, 35, -11};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide zero by a negative number.
   */
  public void testCase11() {
    byte aBytes[] = {0};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = 0;
    int bSign = -1;
    byte rBytes[] = {0};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
  }

  /**
   * Divide ZERO by a negative number.
   */
  public void testCase12() {
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int bSign = -1;
    byte rBytes[] = {0};
    BigInteger aNumber = BigInteger.ZERO;
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
  }

  /**
   * Divide a positive number by ONE.
   */
  public void testCase13() {
    byte aBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = 1;
    byte rBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = BigInteger.ONE;
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide ONE by ONE.
   */
  public void testCase14() {
    byte rBytes[] = {1};
    BigInteger aNumber = BigInteger.ONE;
    BigInteger bNumber = BigInteger.ONE;
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Remainder of division by zero.
   */
  public void testCase15() {
    byte aBytes[] = {1, 2, 3, 4, 5, 6, 7};
    byte bBytes[] = {0};
    int aSign = 1;
    int bSign = 0;
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    try {
      aNumber.remainder(bNumber);
      fail("ArithmeticException has not been caught");
    } catch (ArithmeticException e) {
      assertEquals("Improper exception message", "BigInteger divide by zero",
          e.getMessage());
    }
  }

  /**
   * Remainder of division of equal numbers.
   */
  public void testCase16() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    byte bBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {0};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
  }

  /**
   * Remainder of division of two positive numbers.
   */
  public void testCase17() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {12, -21, 73, 56, 27};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Remainder of division of two negative numbers.
   */
  public void testCase18() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = -1;
    int bSign = -1;
    byte rBytes[] = {-13, 20, -74, -57, -27};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Remainder of division of two numbers of different signs. The first is
   * positive.
   */
  public void testCase19() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {12, -21, 73, 56, 27};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide by ZERO.
   */
  public void testCase2() {
    byte aBytes[] = {1, 2, 3, 4, 5, 6, 7};
    int aSign = 1;
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = BigInteger.ZERO;
    try {
      aNumber.divide(bNumber);
      fail("ArithmeticException has not been caught");
    } catch (ArithmeticException e) {
      assertEquals("Improper exception message", "BigInteger divide by zero",
          e.getMessage());
    }
  }

  /**
   * Remainder of division of two numbers of different signs. The first is
   * negative.
   */
  public void testCase20() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[] = {-13, 20, -74, -57, -27};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * divideAndRemainder of two numbers of different signs. The first is
   * negative.
   */
  public void testCase21() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[][] = { {-5, 94, -115, -74, -85, 84}, {-13, 20, -74, -57, -27}};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result[] = aNumber.divideAndRemainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result[0].toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      if (resBytes[i] != rBytes[0][i]) {
        fail("Incorrect quotation");
      }
    }
    assertEquals(-1, result[0].signum());
    resBytes = result[1].toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      if (resBytes[i] != rBytes[1][i]) {
        fail("Incorrect remainder");
      }
      assertEquals(-1, result[1].signum());
    }
  }

  /**
   * mod when modulus is negative.
   */
  public void testCase22() {
    byte aBytes[] = {1, 2, 3, 4, 5, 6, 7};
    byte bBytes[] = {1, 30, 40, 56, -1, 45};
    int aSign = 1;
    int bSign = -1;
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    try {
      aNumber.mod(bNumber);
      fail("ArithmeticException has not been caught");
    } catch (ArithmeticException e) {
      assertEquals("Improper exception message",
          "BigInteger: modulus not positive", e.getMessage());
    }
  }

  /**
   * mod when a divisor is positive.
   */
  public void testCase23() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {12, -21, 73, 56, 27};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.mod(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * mod when a divisor is negative.
   */
  public void testCase24() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 75};
    byte bBytes[] = {27, -15, 65, 39, 100};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[] = {15, 5, -9, -17, 73};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.mod(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide two equal positive numbers.
   */
  public void testCase3() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    byte bBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {1};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide two equal in absolute value numbers of different signs.
   */
  public void testCase4() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    byte bBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[] = {-1};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Divide two numbers of different length and different signs. The second is
   * longer.
   */
  public void testCase5() {
    byte aBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127};
    byte bBytes[] = {-127, 100, 56, 7, 98, -1, 39, -128, 127, 1, 2, 3, 4, 5};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[] = {0};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
  }

  /**
   * Divide two positive numbers of the same length. The second is greater.
   */
  public void testCase6() {
    byte aBytes[] = {1, 100, 56, 7, 98, -1, 39, -128, 127};
    byte bBytes[] = {15, 100, 56, 7, 98, -1, 39, -128, 127};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {0};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
  }

  /**
   * Divide two positive numbers.
   */
  public void testCase7() {
    byte aBytes[] = {1, 100, 56, 7, 98, -1, 39, -128, 127, 5, 6, 7, 8, 9};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {23, 115, 11, 78, 35, -11};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide a positive number by a negative one.
   */
  public void testCase8() {
    byte aBytes[] = {1, 100, 56, 7, 98, -1, 39, -128, 127, 5, 6, 7, 8, 9};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {-24, -116, -12, -79, -36, 11};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Divide a negative number by a positive one.
   */
  public void testCase9() {
    byte aBytes[] = {1, 100, 56, 7, 98, -1, 39, -128, 127, 5, 6, 7, 8, 9};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = -1;
    int bSign = 1;
    byte rBytes[] = {-24, -116, -12, -79, -36, 11};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Verifies the case when borrow != 0 in the private divide method.
   */
  public void testDivisionKnuth1() {
    byte aBytes[] = {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7};
    byte bBytes[] = {-3, -3, -3, -3};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {0, -5, -12, -33, -96, -36, -105, -56, 92, 15, 48, -109};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Verifies the case when the first digits of the dividend and divisor equal.
   */
  public void testDivisionKnuthFirstDigitsEqual() {
    byte aBytes[] = {2, -3, -4, -5, -1, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5};
    byte bBytes[] = {2, -3, -4, -5, -1, -1, -1, -1};
    int aSign = -1;
    int bSign = -1;
    byte rBytes[] = {0, -1, -1, -1, -1, -2, -88, -60, 41};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Verifies the case when the divisor is already normalized.
   */
  public void testDivisionKnuthIsNormalized() {
    byte aBytes[] = {-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5};
    byte bBytes[] = {-1, -1, -1, -1, -1, -1, -1, -1};
    int aSign = -1;
    int bSign = -1;
    byte rBytes[] = {0, -9, -8, -7, -6, -5, -4, -3};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide the number of multi digits by the number of one digit.
   */
  public void testDivisionKnuthMultiDigitsByOneDigit() {
    byte aBytes[] = {113, -83, 123, -5, 18, -34, 67, 39, -29};
    byte bBytes[] = {2, -3, -4, -5};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {-38, 2, 7, 30, 109, -43};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Divide the number of one digit by the number of one digit.
   */
  public void testDivisionKnuthOneDigitByOneDigit() {
    byte aBytes[] = {113, -83, 123, -5};
    byte bBytes[] = {2, -3, -4, -5};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {-37};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", -1, result.signum());
  }

  /**
   * Tests the step D6 from the Knuth algorithm.
   */
  public void testRemainderKnuth1() {
    byte aBytes[] = {-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1};
    byte bBytes[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
    int aSign = 1;
    int bSign = 1;
    byte rBytes[] = {1, 2, 3, 4, 5, 6, 7, 7, 18, -89};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide the number of multi digits by the number of one digit.
   */
  public void testRemainderKnuthMultiDigitsByOneDigit() {
    byte aBytes[] = {113, -83, 123, -5, 18, -34, 67, 39, -29};
    byte bBytes[] = {2, -3, -4, -50};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {2, -37, -60, 59};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }

  /**
   * Divide the number of one digit by the number of one digit.
   */
  public void testRemainderKnuthOneDigitByOneDigit() {
    byte aBytes[] = {113, -83, 123, -5};
    byte bBytes[] = {2, -3, -4, -50};
    int aSign = 1;
    int bSign = -1;
    byte rBytes[] = {2, -9, -14, 53};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.remainder(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for (int i = 0; i < resBytes.length; i++) {
      assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 1, result.signum());
  }
}