package hw4.test;

import static org.hamcrest.CoreMatchers.not;
import static org.junit.Assert.*;

import org.junit.Test;

import hw4.*;

/**
 * This class contains a <em>small</em> set of test cases that can be used to
 * test the implementation of the RatNum class. For a more complete test, see
 * <tt>RatNumTest</tt>. This class, <tt>RatNumSmallTest</tt>, deliberately
 * omits some of the tests from <tt>RatNumTest</tt>, to permit comparing the
 * effects of the two test suites.
 */
public final class RatNumSmallTest {

  // Naming convention used throughout class: spell out number in
  // variable as its constructive form. Unary minus is notated with
  // the prefix "neg", and the solidus ("/") is notated with an 'I'
  // character. Thus, "1 + 2/3" becomes "one_plus_two_I_three".

  // some simple base RatNums
  private RatNum zero = new RatNum(0);
  private RatNum one = new RatNum(1);
  private RatNum negOne = new RatNum(-1);
  private RatNum two = new RatNum(2);
  private RatNum three = new RatNum(3);
  private RatNum one_I_two = new RatNum(1, 2);
  private RatNum one_I_three = new RatNum(1, 3);
  private RatNum one_I_four = new RatNum(1, 4);
  private RatNum two_I_three = new RatNum(2, 3);
  private RatNum three_I_four = new RatNum(3, 4);
  private RatNum negOne_I_two = new RatNum(-1, 2);

  // improper fraction
  private RatNum three_I_two = new RatNum(3, 2);

  // NaNs
  private RatNum one_I_zero = new RatNum(1, 0);
  private RatNum negOne_I_zero = new RatNum(-1, 0);
  private RatNum hundred_I_zero = new RatNum(100, 0);

  /**
   * ratnums: Set of varied ratnums (includes NaNs) set is { 0, 1, -1, 2, 1/2,
   * 3/2, 1/0, -1/0, 100/0 }
   */
  private RatNum[] ratNums = new RatNum[] { zero, one, negOne, two,
      one_I_two, negOne_I_two, three_I_two,
      /* NaNs */one_I_zero, negOne_I_zero, hundred_I_zero };

  /**
   * ratnans: Set of varied NaNs set is { 1/0, -1/0, 100/0 }
   */
  private RatNum[] ratNaNs = new RatNum[] { one_I_zero, negOne_I_zero,
      hundred_I_zero };

  /**
   * ratNonNaNs: Set of varied non-NaN ratNums set is ratNums - ratNaNs
   */
  private RatNum[] ratNonNaNs = new RatNum[] { zero, one, negOne, two,
      one_I_two, three_I_two };

  /**
   * Asserts that RatNum.toString() is equal to rep. This method depends on the
   * implementation of RatNum's "toString" and "equals" methods. Therefore,
   * one should verify (test) those methods before using this method is in
   * tests.
   */
  private void eq(RatNum ratNum, String rep) {
    assertEquals(rep, ratNum.toString());
  }

  // The actual test cases are below.
  //
  // The order of the test cases is important for producing useful
  // output. If a test uses a method of RatNum, it should test that
  // method before hand. For example, suppose one of the test cases
  // for "negate" is:
  //
  // "(new RatNum(1)).negate().equals(new RatNum(-1))"
  //
  // In this case, the test case relies on RatNum's "equals" method
  // in addition to "negate"; therefore, one should test "equals"
  // before "negate". Otherwise, it will be unclear if failing the
  // "negate" test is due "negate" having a bug or "equals" having a
  // bug. (Furthermore, the test depends on RatNum's constructor,
  // so it should also be tested beforehand.)
  //
  // In general, it is best to have as few dependences in your test
  // cases as possible. Doing so, will reduce the number of methods
  // that could cause a test case to fail, making it easier to find
  // the faulty method. In practice, one will usually need to
  // depend on a few core methods such as the constructors and
  // "equals" methods. Also, some of the test cases below depend on
  // the "toString" method because it made the cases easier to write.
  //
  // As a secondary concern to above, if one has access to the
  // source code of a class (as under glass box testing) one should
  // order tests such that a method is tested after all the methods
  // it depends on are tested. For example, in RatNum, the "sub"
  // method calls the "negate" method; therefore, one should test
  // "negate" before "sub". Following this methodology will make it
  // more clear that one should fix bugs in "negate" before looking
  // at the results of "sub" test because, "sub" could be correctly
  // written and the "sub" test case fails only be "negate" is
  // broken.
  //
  // If one does not have access to the source code (as is the case
  // of RatTermTest and RatPolyTest, because you are proving the
  // implementations), one can still take an educated guess as to
  // which methods depend on other methods, but don't worry about
  // getting it perfect.

  // First, we test the constructors in isolation of (without
  // depending on) all other RatNum methods.
  //
  // Unfortunately, without using any of RatNum's methods, all we
  // can do is call the constructors and ensure that "checkRep"
  // passes. While this is useful, it does not catch many types of
  // errors. For example, the constructor could always return a
  // RatNum, r, where r.numer = 1 and r.denom = 1. Being a valid
  // RatNum, r would pass "checkRep" but would be the wrong RatNum
  // in most cases.
  //
  // Given that we are unable to fully test the constructors, when
  // any other test case fails, it could be due to an error in the
  // constructor instead of an error in method the test case is
  // testing.
  //
  // If RatNum had public fields, this problem would not exist,
  // because we could check if the fields were set to the correct
  // values. This problem is really a case of a more general
  // problem of being unable to test private fields and methods of
  // classes. For example, we are also unable to test the gcd
  // method because it is private. Solutions to this general
  // problem include:
  //
  // (1) Make the private fields and methods public. (For example,
  // make numer, denom, and gcd public.) This in not done in
  // general because private fields have many benefits as will
  // be discussed in class.
  //
  // (2) Move the test suite code into RatNum and, thus, it would
  // have access to private memebers. (Maybe as a static inner
  // class [Don't worry if you don't know what this means yet.])
  // This is not done in general because it clutters the class
  // being tested, making it harder to understand.
  //
  // In practice, while testing, you may find it necessary to do (1)
  // or (2) temporarily with a test case that accesses private
  // fields or methods to track down a bug. But after finding the
  // bug, remember to revert your code back. Also for future
  // problem sets where you will be writing your own test suites,
  // make sure that your test suite runs correctly without (1) or
  // (2) being true.

  // (Note, all of these objects were already constructed above as
  // fields of this class (RatNumTest); thus, one could argue that
  // this test case is redundant. We included this test case anyhow
  // to give you an example of such a test case and because the
  // implementation of this class could change eliminating the
  // fields above.)
  @Test
  public void testOneArgConstructor() {
    new RatNum(0);
    new RatNum(1);
    new RatNum(-1);
    new RatNum(2);
    new RatNum(3);
  }

  @Test
  public void testTwoArgConstructor() {
    new RatNum(1, 2);
    new RatNum(1, 3);
    new RatNum(1, 4);
    new RatNum(2, 3);
    new RatNum(3, 4);

    new RatNum(-1, 2);

    // improper fraction
    new RatNum(3, 2);

    // NaNs
    new RatNum(1, 0);
    new RatNum(-1, 0);
    new RatNum(100, 0);
  }

  // Next, we test isNaN because it can be tested in isolation from
  // everything except the constructors. (All instance method tests
  // will depend on a constructor.)
  @Test
  public void testIsNaN() {
    for (int i = 0; i < ratNaNs.length; i++) {
      assertTrue(ratNaNs[i].isNaN());
    }
    for (int i = 0; i < ratNonNaNs.length; i++) {
      assertFalse(ratNonNaNs[i].isNaN());
    }
  }

  // Next, we test isPos and isNeg because we can easily test these
  // methods without depending on any other methods (except the
  // constructors).
  private void assertPos(RatNum n) {
    assertTrue(n.isPositive());
    assertFalse(n.isNegative());
  }

  private void assertNeg(RatNum n) {
    assertTrue(n.isNegative());
    assertFalse(n.isPositive());
  }

  @Test
  public void testIsPosAndIsNeg() {
    assertFalse(zero.isPositive());
    assertFalse(zero.isNegative());

    assertPos(one);
    assertNeg(negOne);
    assertPos(two);
    assertPos(three);

    assertPos(one_I_two);
    assertPos(one_I_three);
    assertPos(one_I_four);
    assertPos(two_I_three);
    assertPos(three_I_four);

    assertNeg(negOne_I_two);

    assertPos(three_I_two);

    assertPos(one_I_zero);
    assertPos(negOne_I_zero); // non-intuitive; see spec
    assertPos(hundred_I_zero);
  }

  // Next, we test doubleValue because the test does not require any
  // other RatNum methods (other than constructors).

  // asserts that two double's are within .0000001 of one another.
  // It is often impossible to assert that doubles are exactly equal
  // because of the idiosyncrasies of Java's floating point math.
  private void approxEq(double expected, double actual) {
    assertEquals(expected, actual, .0000001);
  }

  @Test
  public void testApprox() {
    approxEq(0.0, zero.doubleValue());
    approxEq(1.0, one.doubleValue());
    approxEq(-1.0, negOne.doubleValue());
    approxEq(2.0, two.doubleValue());
    approxEq(0.5, one_I_two.doubleValue());
    approxEq(2. / 3., two_I_three.doubleValue());
    approxEq(0.75, three_I_four.doubleValue());

    // To understand the use of "new Double(Double.NaN)" instead of
    // "Double.NaN", see the Javadoc for Double.equals().
    assertEquals(new Double(Double.NaN),
        new Double(one_I_zero.doubleValue()));

    // use left-shift operator "<<" to create integer for 2^30
    RatNum one_I_twoToThirty = new RatNum(1, (1 << 30));
    double quiteSmall = 1. / Math.pow(2, 30);
    approxEq(quiteSmall, one_I_twoToThirty.doubleValue());
  }

  // Next, we test the equals method because that can be tested in
  // isolation from everything except the constructor and maybe
  // isNaN, which we just tested.
  // Additionally, this method will be very useful for testing other
  // methods.

  /**
   * This test check is equals is reflexive. In other words that x.equals(x)
   * is always true.
   */
  @Test
  public void testEqualsReflexive() {
    for (int i = 0; i < ratNums.length; i++) {
      assertEquals(ratNums[i], ratNums[i]);
    }
  }

  @Test
  public void testEquals() {

    // Some simple cases.
    assertEquals(one, one);
    assertEquals(one.add(one), two);
    // including negitives:
    assertEquals(negOne, negOne);

    // Some simple cases where the objects are different but
    // represent the same rational number. That is, x != y but
    // x.equals(y).
    assertEquals(new RatNum(1, 1), new RatNum(1, 1));
    assertEquals(new RatNum(1, 2), new RatNum(1, 2));

    // Check that equals works on fractions that were not
    // constructed in reduced form.
    assertEquals(one, new RatNum(2, 2));
    assertEquals(new RatNum(2, 2), one);
    // including negitives:
    assertEquals(negOne, new RatNum(-9, 9));
    assertEquals(new RatNum(-9, 9), negOne);
    // including double negitives:
    assertEquals(one_I_two, new RatNum(-13, -26));
    assertEquals(new RatNum(-13, -26), one_I_two);

    // Check that all NaN's are equals to one another.
    assertEquals(one_I_zero, one_I_zero);
    assertEquals(one_I_zero, negOne_I_zero);
    assertEquals(one_I_zero, hundred_I_zero);

    // Some simple cases checking for false positives.
    assertThat(one, not(zero));
    assertThat(zero, not(one));
    assertThat(one, not(two));
    assertThat(two, not(one));

    // Check that equals does not neglect sign.
    assertThat(one, not(negOne));
    assertThat(negOne, not(one));

    // Check that equals does not return false positives on
    // fractions.
    assertThat(one, not(one_I_two));
    assertThat(one_I_two, not(one));
    assertThat(one, not(three_I_two));
    assertThat(three_I_two, not(one));
  }

  // Now that we have verified equals, we will use it in the
  // rest or our tests.

  // Next, we test the toString and valueOf methods because we can test
  // them isolation of everything except the constructor and equals,
  // and they will be useful methods to aid with testing other
  // methods. (In some cases, it is easier to use valueOf("1/2") than
  // new RatNum(1, 2) as you will see below.)

  // Note that "eq" calls "toString" on its first argument.
  @Test
  public void testToStringSimple() {
    eq(zero, "0");

    eq(one, "1");

    RatNum four = new RatNum(4);
    eq(four, "4");

    eq(negOne, "-1");

    RatNum negFive = new RatNum(-5);
    eq(negFive, "-5");

    RatNum negZero = new RatNum(-0);
    eq(negZero, "0");
  }

  @Test
  public void testToStringFractions() {
    RatNum one_I_two = new RatNum(1, 2);
    eq(one_I_two, "1/2");

    RatNum three_I_two = new RatNum(3, 2);
    eq(three_I_two, "3/2");

    RatNum negOne_I_thirteen = new RatNum(-1, 13);
    eq(negOne_I_thirteen, "-1/13");

    RatNum fiftyThree_I_seven = new RatNum(53, 7);
    eq(fiftyThree_I_seven, "53/7");
  }

  @Test
  public void testToStringNaN() {
    RatNum one_I_zero = new RatNum(1, 0);
    eq(one_I_zero, "NaN");

    RatNum two_I_zero = new RatNum(2, 0);
    eq(two_I_zero, "NaN");

    RatNum negOne_I_zero = new RatNum(-1, 0);
    eq(negOne_I_zero, "NaN");

    RatNum zero_I_zero = new RatNum(0, 0);
    eq(zero_I_zero, "NaN");

    RatNum negHundred_I_zero = new RatNum(-100, 0);
    eq(negHundred_I_zero, "NaN");

    RatNum two_I_one = new RatNum(2, 1);
    eq(two_I_one, "2");

    RatNum zero_I_one = new RatNum(0, 1);
    eq(zero_I_one, "0");

    RatNum negOne_I_negTwo = new RatNum(-1, -2);
    eq(negOne_I_negTwo, "1/2");

    RatNum two_I_four = new RatNum(2, 4);
    eq(two_I_four, "1/2");

    RatNum six_I_four = new RatNum(6, 4);
    eq(six_I_four, "3/2");

    RatNum twentySeven_I_thirteen = new RatNum(27, 13);
    eq(twentySeven_I_thirteen, "27/13");

    RatNum negHundred_I_negHundred = new RatNum(-100, -100);
    eq(negHundred_I_negHundred, "1");
  }

  // helper function, "decode-and-check"
  private void decChk(String s, RatNum expected) {
    RatNum.valueOf(s).equals(expected);
  }

  // Note that decChk calls valueOf.
  @Test
  public void testValueOf() {
    decChk("0", zero);

    decChk("1", one);
    decChk("1/1", one);
    decChk("2/2", one);
    decChk("-1/-1", one);

    decChk("-1", negOne);
    decChk("1/-1", negOne);
    decChk("-3/3", negOne);

    decChk("2", two);
    decChk("2/1", two);
    decChk("-4/-2", two);

    decChk("1/2", one_I_two);
    decChk("2/4", one_I_two);

    decChk("3/2", three_I_two);
    decChk("-6/-4", three_I_two);

    decChk("NaN", one_I_zero);
    decChk("NaN", negOne_I_zero);
  }

  // Next, we test the arithmetic operations.
  //
  // We test them in our best guess of increasing difficultly and
  // likelihood of having depend on a previous method. (For
  // example, add could use sub as a subroutine.
  //
  // Note that our tests depend on toString and
  // equals, which we have already tested.

  @Test
  public void testNegate() {
    eq(zero.negate(), "0");
    eq(one.negate(), "-1");
    eq(negOne.negate(), "1");
    eq(two.negate(), "-2");
    eq(three.negate(), "-3");

    eq(one_I_two.negate(), "-1/2");
    eq(one_I_three.negate(), "-1/3");
    eq(one_I_four.negate(), "-1/4");
    eq(two_I_three.negate(), "-2/3");
    eq(three_I_four.negate(), "-3/4");

    eq(three_I_two.negate(), "-3/2");

    eq(one_I_zero.negate(), "NaN");
    eq(negOne_I_zero.negate(), "NaN");
    eq(hundred_I_zero.negate(), "NaN");
  }

  @Test
  public void testAddSimple() {
    eq(zero.add(zero), "0");
    eq(zero.add(one), "1");
    eq(one.add(zero), "1");
    eq(one.add(one), "2");
    eq(one.add(negOne), "0");
    eq(one.add(two), "3");
    eq(two.add(two), "4");
  }

  @Test
  public void testAddComplex() {
    eq(one_I_two.add(zero), "1/2");
    eq(one_I_two.add(one), "3/2");
    eq(one_I_two.add(one_I_two), "1");
    eq(one_I_two.add(one_I_three), "5/6");
    eq(one_I_two.add(negOne), "-1/2");
    eq(one_I_two.add(two), "5/2");
    eq(one_I_two.add(two_I_three), "7/6");
    eq(one_I_two.add(three_I_four), "5/4");

    eq(one_I_three.add(zero), "1/3");
    eq(one_I_three.add(two_I_three), "1");
    eq(one_I_three.add(three_I_four), "13/12");
  }

  @Test
  public void testAddImproper() {
    eq(three_I_two.add(one_I_two), "2");
    eq(three_I_two.add(one_I_three), "11/6");
    eq(three_I_four.add(three_I_four), "3/2");

    eq(three_I_two.add(three_I_two), "3");
  }

  @Test
  public void testAddOnNaN() {
    // each test case (addend, augend) drawn from the set
    // ratNums x ratNaNs

    for (int i = 0; i < ratNums.length; i++) {
      for (int j = 0; j < ratNaNs.length; j++) {
        eq(ratNums[i].add(ratNaNs[j]), "NaN");
        eq(ratNaNs[j].add(ratNums[i]), "NaN");
      }
    }

  }

  @Test
  public void testAddTransitively() {
    eq(one.add(one).add(one), "3");
    eq(one.add(one.add(one)), "3");
    eq(zero.add(zero).add(zero), "0");
    eq(zero.add(zero.add(zero)), "0");
    eq(one.add(two).add(three), "6");
    eq(one.add(two.add(three)), "6");

    eq(one_I_three.add(one_I_three).add(one_I_three), "1");
    eq(one_I_three.add(one_I_three.add(one_I_three)), "1");

    eq(one_I_zero.add(one_I_zero).add(one_I_zero), "NaN");
    eq(one_I_zero.add(one_I_zero.add(one_I_zero)), "NaN");

    eq(one_I_two.add(one_I_three).add(one_I_four), "13/12");
    eq(one_I_two.add(one_I_three.add(one_I_four)), "13/12");
  }

  @Test
  public void testSubSimple() {
    eq(zero.sub(one), "-1");
    eq(zero.sub(zero), "0");
    eq(one.sub(zero), "1");
    eq(one.sub(one), "0");
    eq(two.sub(one), "1");
    eq(one.sub(negOne), "2");
    eq(one.sub(two), "-1");
    eq(one.sub(three), "-2");
  }

  @Test
  public void testSubComplex() {
    eq(one.sub(one_I_two), "1/2");
    eq(one_I_two.sub(one), "-1/2");
    eq(one_I_two.sub(zero), "1/2");
    eq(one_I_two.sub(two_I_three), "-1/6");
    eq(one_I_two.sub(three_I_four), "-1/4");
  }

  @Test
  public void testSubImproper() {
    eq(three_I_two.sub(one_I_two), "1");
    eq(three_I_two.sub(one_I_three), "7/6");
  }

  /*
   * public void testSubOnNaN() { // analogous to testAddOnNaN()
   *
   * for (int i=0; i<ratNums.length; i++) { for ( int j=0; j<ratNaNs.length;
   * j++) { eq( ratNums[i].sub(ratNaNs[j]), "NaN" ); eq(
   * ratNaNs[j].sub(ratNums[i]), "NaN" ); } } }
   */
  @Test
  public void testSubTransitively() {
    // subtraction is not transitive; testing that operation is
    // correct when *applied transitivitely*, not that it obeys
    // the transitive property

    eq(one.sub(one).sub(one), "-1");
    eq(one.sub(one.sub(one)), "1");
    eq(zero.sub(zero).sub(zero), "0");
    eq(zero.sub(zero.sub(zero)), "0");
    eq(one.sub(two).sub(three), "-4");
    eq(one.sub(two.sub(three)), "2");

    eq(one_I_three.sub(one_I_three).sub(one_I_three), "-1/3");
    eq(one_I_three.sub(one_I_three.sub(one_I_three)), "1/3");

    // eq( one_I_zero.sub(one_I_zero).sub(one_I_zero), "NaN" );
    // eq( one_I_zero.sub(one_I_zero.sub(one_I_zero)), "NaN" );

    eq(one_I_two.sub(one_I_three).sub(one_I_four), "-1/12");
    eq(one_I_two.sub(one_I_three.sub(one_I_four)), "5/12");
  }

  @Test
  public void testMulProperties() {
    // zero property
    for (int i = 0; i < ratNonNaNs.length; i++) {
      eq(zero.mul(ratNonNaNs[i]), "0");
      eq(ratNonNaNs[i].mul(zero), "0");
    }

    // one property
    for (int i = 0; i < ratNonNaNs.length; i++) {
      eq(one.mul(ratNonNaNs[i]), ratNonNaNs[i].toString());
      eq(ratNonNaNs[i].mul(one), ratNonNaNs[i].toString());
    }

    // negOne property
    for (int i = 0; i < ratNonNaNs.length; i++) {
      eq(negOne.mul(ratNonNaNs[i]), ratNonNaNs[i].negate().toString());
      eq(ratNonNaNs[i].mul(negOne), ratNonNaNs[i].negate().toString());
    }
  }

  @Test
  public void testMulSimple() {
    eq(two.mul(two), "4");
    eq(two.mul(three), "6");
    eq(three.mul(two), "6");
  }

  @Test
  public void testMulComplex() {
    eq(one_I_two.mul(two), "1");
    eq(two.mul(one_I_two), "1");
    eq(one_I_two.mul(one_I_two), "1/4");
    eq(one_I_two.mul(one_I_three), "1/6");
    eq(one_I_three.mul(one_I_two), "1/6");
  }

  @Test
  public void testMulImproper() {
    eq(three_I_two.mul(one_I_two), "3/4");
    eq(three_I_two.mul(one_I_three), "1/2");
    eq(three_I_two.mul(three_I_four), "9/8");
    eq(three_I_two.mul(three_I_two), "9/4");
  }

  @Test
  public void testMulOnNaN() {
    // analogous to testAddOnNaN()

    for (int i = 0; i < ratNums.length; i++) {
      for (int j = 0; j < ratNaNs.length; j++) {
        eq(ratNums[i].mul(ratNaNs[j]), "NaN");
        eq(ratNaNs[j].mul(ratNums[i]), "NaN");
      }
    }
  }

  @Test
  public void testMulTransitively() {
    eq(one.mul(one).mul(one), "1");
    eq(one.mul(one.mul(one)), "1");
    eq(zero.mul(zero).mul(zero), "0");
    eq(zero.mul(zero.mul(zero)), "0");
    eq(one.mul(two).mul(three), "6");
    eq(one.mul(two.mul(three)), "6");

    eq(one_I_three.mul(one_I_three).mul(one_I_three), "1/27");
    eq(one_I_three.mul(one_I_three.mul(one_I_three)), "1/27");

    eq(one_I_zero.mul(one_I_zero).mul(one_I_zero), "NaN");
    eq(one_I_zero.mul(one_I_zero.mul(one_I_zero)), "NaN");

    eq(one_I_two.mul(one_I_three).mul(one_I_four), "1/24");
    eq(one_I_two.mul(one_I_three.mul(one_I_four)), "1/24");
  }

  @Test
  public void testDivSimple() {
    eq(zero.div(zero), "NaN");
    eq(zero.div(one), "0");
    eq(one.div(zero), "NaN");
    eq(one.div(one), "1");
    eq(one.div(negOne), "-1");
    eq(one.div(two), "1/2");
    eq(two.div(two), "1");
  }

  @Test
  public void testDivComplex() {
    eq(one_I_two.div(zero), "NaN");
    eq(one_I_two.div(one), "1/2");
    eq(one_I_two.div(one_I_two), "1");
    eq(one_I_two.div(one_I_three), "3/2");
    eq(one_I_two.div(negOne), "-1/2");
    eq(one_I_two.div(two), "1/4");
    eq(one_I_two.div(two_I_three), "3/4");
    eq(one_I_two.div(three_I_four), "2/3");

    eq(one_I_three.div(zero), "NaN");
    eq(one_I_three.div(two_I_three), "1/2");
    eq(one_I_three.div(three_I_four), "4/9");
  }

  @Test
  public void testDivImproper() {
    eq(three_I_two.div(one_I_two), "3");
    eq(three_I_two.div(one_I_three), "9/2");
    eq(three_I_two.div(three_I_two), "1");
  }

  @Test
  public void testDivOnNaN() {
    // each test case (addend, augend) drawn from the set
    // ratNums x ratNaNs

    for (int i = 0; i < ratNums.length; i++) {
      for (int j = 0; j < ratNaNs.length; j++) {
        eq(ratNums[i].div(ratNaNs[j]), "NaN");
        eq(ratNaNs[j].div(ratNums[i]), "NaN");
      }
    }

  }

  @Test
  public void testDivTransitively() {
    // (same note as in testSubTransitively re: transitivity property)

    eq(one.div(one).div(one), "1");
    eq(one.div(one.div(one)), "1");
    eq(zero.div(zero).div(zero), "NaN");
    eq(zero.div(zero.div(zero)), "NaN");
    eq(one.div(two).div(three), "1/6");
    eq(one.div(two.div(three)), "3/2");

    eq(one_I_three.div(one_I_three).div(one_I_three), "3");
    eq(one_I_three.div(one_I_three.div(one_I_three)), "1/3");

    eq(one_I_zero.div(one_I_zero).div(one_I_zero), "NaN");
    eq(one_I_zero.div(one_I_zero.div(one_I_zero)), "NaN");

    eq(one_I_two.div(one_I_three).div(one_I_four), "6");
    eq(one_I_two.div(one_I_three.div(one_I_four)), "3/8");

  }

  // Finally, we test compare. We do so last, because compare may
  // depend on sub, isNaN, and/or equals, so we want to test those
  // methods first.

  private void assertGreater(RatNum larger, RatNum smaller) {
    assertTrue(larger.compareTo(smaller) > 0);
    assertTrue(smaller.compareTo(larger) < 0);
  }

  @Test
  public void testCompareToReflexive() {
    // reflexivitiy: x.compare(x) == 0.
    for (int i = 0; i < ratNums.length; i++) {
      assertEquals(ratNums[i], ratNums[i]);
    }
  }

  @Test
  public void testCompareToNonFract() {
    assertGreater(one, zero);
    assertGreater(one, negOne);
    assertGreater(two, one);
    assertGreater(two, zero);
    assertGreater(zero, negOne);
  }

  @Test
  public void testCompareToFract() {
    assertGreater(one, one_I_two);
    assertGreater(two, one_I_three);
    assertGreater(one, two_I_three);
    assertGreater(two, two_I_three);
    assertGreater(one_I_two, zero);
    assertGreater(one_I_two, negOne);
    assertGreater(one_I_two, negOne_I_two);
    assertGreater(zero, negOne_I_two);
  }

  @Test
  public void testCompareToNaNs() {
    for (int i = 0; i < ratNaNs.length; i++) {
      for (int j = 0; j < ratNaNs.length; j++) {
        assertEquals(ratNaNs[i], ratNaNs[j]);
      }
      for (int j = 0; j < ratNonNaNs.length; j++) {
        assertGreater(ratNaNs[i], ratNonNaNs[j]);
      }
    }
  }

}