/*
* 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.
*/
package org.apache.commons.math4.fraction;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.exception.ConvergenceException;
import org.apache.commons.math4.exception.MathArithmeticException;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.fraction.Fraction;
import org.apache.commons.math4.fraction.FractionConversionException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
*/
public class FractionTest {
private void assertFraction(int expectedNumerator, int expectedDenominator, Fraction actual) {
Assert.assertEquals(expectedNumerator, actual.getNumerator());
Assert.assertEquals(expectedDenominator, actual.getDenominator());
}
@Test
public void testConstructor() {
assertFraction(0, 1, new Fraction(0, 1));
assertFraction(0, 1, new Fraction(0, 2));
assertFraction(0, 1, new Fraction(0, -1));
assertFraction(1, 2, new Fraction(1, 2));
assertFraction(1, 2, new Fraction(2, 4));
assertFraction(-1, 2, new Fraction(-1, 2));
assertFraction(-1, 2, new Fraction(1, -2));
assertFraction(-1, 2, new Fraction(-2, 4));
assertFraction(-1, 2, new Fraction(2, -4));
// overflow
try {
new Fraction(Integer.MIN_VALUE, -1);
Assert.fail();
} catch (MathArithmeticException ex) {
// success
}
try {
new Fraction(1, Integer.MIN_VALUE);
Assert.fail();
} catch (MathArithmeticException ex) {
// success
}
assertFraction(0, 1, new Fraction(0.00000000000001));
assertFraction(2, 5, new Fraction(0.40000000000001));
assertFraction(15, 1, new Fraction(15.0000000000001));
}
@Test(expected=ConvergenceException.class)
public void testGoldenRatio() {
// the golden ratio is notoriously a difficult number for continuous fraction
new Fraction((1 + FastMath.sqrt(5)) / 2, 1.0e-12, 25);
}
// MATH-179
@Test
public void testDoubleConstructor() throws ConvergenceException {
assertFraction(1, 2, new Fraction((double)1 / (double)2));
assertFraction(1, 3, new Fraction((double)1 / (double)3));
assertFraction(2, 3, new Fraction((double)2 / (double)3));
assertFraction(1, 4, new Fraction((double)1 / (double)4));
assertFraction(3, 4, new Fraction((double)3 / (double)4));
assertFraction(1, 5, new Fraction((double)1 / (double)5));
assertFraction(2, 5, new Fraction((double)2 / (double)5));
assertFraction(3, 5, new Fraction((double)3 / (double)5));
assertFraction(4, 5, new Fraction((double)4 / (double)5));
assertFraction(1, 6, new Fraction((double)1 / (double)6));
assertFraction(5, 6, new Fraction((double)5 / (double)6));
assertFraction(1, 7, new Fraction((double)1 / (double)7));
assertFraction(2, 7, new Fraction((double)2 / (double)7));
assertFraction(3, 7, new Fraction((double)3 / (double)7));
assertFraction(4, 7, new Fraction((double)4 / (double)7));
assertFraction(5, 7, new Fraction((double)5 / (double)7));
assertFraction(6, 7, new Fraction((double)6 / (double)7));
assertFraction(1, 8, new Fraction((double)1 / (double)8));
assertFraction(3, 8, new Fraction((double)3 / (double)8));
assertFraction(5, 8, new Fraction((double)5 / (double)8));
assertFraction(7, 8, new Fraction((double)7 / (double)8));
assertFraction(1, 9, new Fraction((double)1 / (double)9));
assertFraction(2, 9, new Fraction((double)2 / (double)9));
assertFraction(4, 9, new Fraction((double)4 / (double)9));
assertFraction(5, 9, new Fraction((double)5 / (double)9));
assertFraction(7, 9, new Fraction((double)7 / (double)9));
assertFraction(8, 9, new Fraction((double)8 / (double)9));
assertFraction(1, 10, new Fraction((double)1 / (double)10));
assertFraction(3, 10, new Fraction((double)3 / (double)10));
assertFraction(7, 10, new Fraction((double)7 / (double)10));
assertFraction(9, 10, new Fraction((double)9 / (double)10));
assertFraction(1, 11, new Fraction((double)1 / (double)11));
assertFraction(2, 11, new Fraction((double)2 / (double)11));
assertFraction(3, 11, new Fraction((double)3 / (double)11));
assertFraction(4, 11, new Fraction((double)4 / (double)11));
assertFraction(5, 11, new Fraction((double)5 / (double)11));
assertFraction(6, 11, new Fraction((double)6 / (double)11));
assertFraction(7, 11, new Fraction((double)7 / (double)11));
assertFraction(8, 11, new Fraction((double)8 / (double)11));
assertFraction(9, 11, new Fraction((double)9 / (double)11));
assertFraction(10, 11, new Fraction((double)10 / (double)11));
}
// MATH-181
@Test
public void testDigitLimitConstructor() throws ConvergenceException {
assertFraction(2, 5, new Fraction(0.4, 9));
assertFraction(2, 5, new Fraction(0.4, 99));
assertFraction(2, 5, new Fraction(0.4, 999));
assertFraction(3, 5, new Fraction(0.6152, 9));
assertFraction(8, 13, new Fraction(0.6152, 99));
assertFraction(510, 829, new Fraction(0.6152, 999));
assertFraction(769, 1250, new Fraction(0.6152, 9999));
// MATH-996
assertFraction(1, 2, new Fraction(0.5000000001, 10));
}
@Test
public void testIntegerOverflow() {
checkIntegerOverflow(0.75000000001455192);
checkIntegerOverflow(1.0e10);
checkIntegerOverflow(-1.0e10);
checkIntegerOverflow(-43979.60679604749);
}
private void checkIntegerOverflow(double a) {
try {
@SuppressWarnings("unused")
Fraction f = new Fraction(a, 1.0e-12, 1000);
//System.out.println(f.getNumerator() + "/" + f.getDenominator());
Assert.fail("an exception should have been thrown");
} catch (ConvergenceException ce) {
// expected behavior
}
}
@Test
public void testEpsilonLimitConstructor() throws ConvergenceException {
assertFraction(2, 5, new Fraction(0.4, 1.0e-5, 100));
assertFraction(3, 5, new Fraction(0.6152, 0.02, 100));
assertFraction(8, 13, new Fraction(0.6152, 1.0e-3, 100));
assertFraction(251, 408, new Fraction(0.6152, 1.0e-4, 100));
assertFraction(251, 408, new Fraction(0.6152, 1.0e-5, 100));
assertFraction(510, 829, new Fraction(0.6152, 1.0e-6, 100));
assertFraction(769, 1250, new Fraction(0.6152, 1.0e-7, 100));
}
@Test
public void testCompareTo() {
Fraction first = new Fraction(1, 2);
Fraction second = new Fraction(1, 3);
Fraction third = new Fraction(1, 2);
Assert.assertEquals(0, first.compareTo(first));
Assert.assertEquals(0, first.compareTo(third));
Assert.assertEquals(1, first.compareTo(second));
Assert.assertEquals(-1, second.compareTo(first));
// these two values are different approximations of PI
// the first one is approximately PI - 3.07e-18
// the second one is approximately PI + 1.936e-17
Fraction pi1 = new Fraction(1068966896, 340262731);
Fraction pi2 = new Fraction( 411557987, 131002976);
Assert.assertEquals(-1, pi1.compareTo(pi2));
Assert.assertEquals( 1, pi2.compareTo(pi1));
Assert.assertEquals(0.0, pi1.doubleValue() - pi2.doubleValue(), 1.0e-20);
}
@Test
public void testDoubleValue() {
Fraction first = new Fraction(1, 2);
Fraction second = new Fraction(1, 3);
Assert.assertEquals(0.5, first.doubleValue(), 0.0);
Assert.assertEquals(1.0 / 3.0, second.doubleValue(), 0.0);
}
@Test
public void testFloatValue() {
Fraction first = new Fraction(1, 2);
Fraction second = new Fraction(1, 3);
Assert.assertEquals(0.5f, first.floatValue(), 0.0f);
Assert.assertEquals((float)(1.0 / 3.0), second.floatValue(), 0.0f);
}
@Test
public void testIntValue() {
Fraction first = new Fraction(1, 2);
Fraction second = new Fraction(3, 2);
Assert.assertEquals(0, first.intValue());
Assert.assertEquals(1, second.intValue());
}
@Test
public void testLongValue() {
Fraction first = new Fraction(1, 2);
Fraction second = new Fraction(3, 2);
Assert.assertEquals(0L, first.longValue());
Assert.assertEquals(1L, second.longValue());
}
@Test
public void testConstructorDouble() {
assertFraction(1, 2, new Fraction(0.5));
assertFraction(1, 3, new Fraction(1.0 / 3.0));
assertFraction(17, 100, new Fraction(17.0 / 100.0));
assertFraction(317, 100, new Fraction(317.0 / 100.0));
assertFraction(-1, 2, new Fraction(-0.5));
assertFraction(-1, 3, new Fraction(-1.0 / 3.0));
assertFraction(-17, 100, new Fraction(17.0 / -100.0));
assertFraction(-317, 100, new Fraction(-317.0 / 100.0));
}
@Test
public void testAbs() {
Fraction a = new Fraction(10, 21);
Fraction b = new Fraction(-10, 21);
Fraction c = new Fraction(10, -21);
assertFraction(10, 21, a.abs());
assertFraction(10, 21, b.abs());
assertFraction(10, 21, c.abs());
}
@Test
public void testPercentage() {
Assert.assertEquals(50.0, new Fraction(1, 2).percentageValue(), 1.0e-15);
}
@Test
public void testMath835() {
final int numer = Integer.MAX_VALUE / 99;
final int denom = 1;
final double percentage = 100 * ((double) numer) / denom;
final Fraction frac = new Fraction(numer, denom);
// With the implementation that preceded the fix suggested in MATH-835,
// this test was failing, due to overflow.
Assert.assertEquals(percentage, frac.percentageValue(), Math.ulp(percentage));
}
@Test
public void testMath1261() {
final Fraction a = new Fraction(Integer.MAX_VALUE, 2);
final Fraction b = a.multiply(2);
Assert.assertTrue(b.equals(new Fraction(Integer.MAX_VALUE)));
final Fraction c = new Fraction(2, Integer.MAX_VALUE);
final Fraction d = c.divide(2);
Assert.assertTrue(d.equals(new Fraction(1, Integer.MAX_VALUE)));
}
@Test
public void testReciprocal() {
Fraction f = null;
f = new Fraction(50, 75);
f = f.reciprocal();
Assert.assertEquals(3, f.getNumerator());
Assert.assertEquals(2, f.getDenominator());
f = new Fraction(4, 3);
f = f.reciprocal();
Assert.assertEquals(3, f.getNumerator());
Assert.assertEquals(4, f.getDenominator());
f = new Fraction(-15, 47);
f = f.reciprocal();
Assert.assertEquals(-47, f.getNumerator());
Assert.assertEquals(15, f.getDenominator());
f = new Fraction(0, 3);
try {
f = f.reciprocal();
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {}
// large values
f = new Fraction(Integer.MAX_VALUE, 1);
f = f.reciprocal();
Assert.assertEquals(1, f.getNumerator());
Assert.assertEquals(Integer.MAX_VALUE, f.getDenominator());
}
@Test
public void testNegate() {
Fraction f = null;
f = new Fraction(50, 75);
f = f.negate();
Assert.assertEquals(-2, f.getNumerator());
Assert.assertEquals(3, f.getDenominator());
f = new Fraction(-50, 75);
f = f.negate();
Assert.assertEquals(2, f.getNumerator());
Assert.assertEquals(3, f.getDenominator());
// large values
f = new Fraction(Integer.MAX_VALUE-1, Integer.MAX_VALUE);
f = f.negate();
Assert.assertEquals(Integer.MIN_VALUE+2, f.getNumerator());
Assert.assertEquals(Integer.MAX_VALUE, f.getDenominator());
f = new Fraction(Integer.MIN_VALUE, 1);
try {
f = f.negate();
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {}
}
@Test
public void testAdd() {
Fraction a = new Fraction(1, 2);
Fraction b = new Fraction(2, 3);
assertFraction(1, 1, a.add(a));
assertFraction(7, 6, a.add(b));
assertFraction(7, 6, b.add(a));
assertFraction(4, 3, b.add(b));
Fraction f1 = new Fraction(Integer.MAX_VALUE - 1, 1);
Fraction f2 = Fraction.ONE;
Fraction f = f1.add(f2);
Assert.assertEquals(Integer.MAX_VALUE, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
f = f1.add(1);
Assert.assertEquals(Integer.MAX_VALUE, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
f1 = new Fraction(-1, 13*13*2*2);
f2 = new Fraction(-2, 13*17*2);
f = f1.add(f2);
Assert.assertEquals(13*13*17*2*2, f.getDenominator());
Assert.assertEquals(-17 - 2*13*2, f.getNumerator());
try {
f.add(null);
Assert.fail("expecting NullArgumentException");
} catch (NullArgumentException ex) {}
// if this fraction is added naively, it will overflow.
// check that it doesn't.
f1 = new Fraction(1,32768*3);
f2 = new Fraction(1,59049);
f = f1.add(f2);
Assert.assertEquals(52451, f.getNumerator());
Assert.assertEquals(1934917632, f.getDenominator());
f1 = new Fraction(Integer.MIN_VALUE, 3);
f2 = new Fraction(1,3);
f = f1.add(f2);
Assert.assertEquals(Integer.MIN_VALUE+1, f.getNumerator());
Assert.assertEquals(3, f.getDenominator());
f1 = new Fraction(Integer.MAX_VALUE - 1, 1);
f2 = Fraction.ONE;
f = f1.add(f2);
Assert.assertEquals(Integer.MAX_VALUE, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
try {
f = f.add(Fraction.ONE); // should overflow
Assert.fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
// denominator should not be a multiple of 2 or 3 to trigger overflow
f1 = new Fraction(Integer.MIN_VALUE, 5);
f2 = new Fraction(-1,5);
try {
f = f1.add(f2); // should overflow
Assert.fail("expecting MathArithmeticException but got: " + f.toString());
} catch (MathArithmeticException ex) {}
try {
f= new Fraction(-Integer.MAX_VALUE, 1);
f = f.add(f);
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f= new Fraction(-Integer.MAX_VALUE, 1);
f = f.add(f);
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f1 = new Fraction(3,327680);
f2 = new Fraction(2,59049);
try {
f = f1.add(f2); // should overflow
Assert.fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
}
@Test
public void testDivide() {
Fraction a = new Fraction(1, 2);
Fraction b = new Fraction(2, 3);
assertFraction(1, 1, a.divide(a));
assertFraction(3, 4, a.divide(b));
assertFraction(4, 3, b.divide(a));
assertFraction(1, 1, b.divide(b));
Fraction f1 = new Fraction(3, 5);
Fraction f2 = Fraction.ZERO;
try {
f1.divide(f2);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {}
f1 = new Fraction(0, 5);
f2 = new Fraction(2, 7);
Fraction f = f1.divide(f2);
Assert.assertSame(Fraction.ZERO, f);
f1 = new Fraction(2, 7);
f2 = Fraction.ONE;
f = f1.divide(f2);
Assert.assertEquals(2, f.getNumerator());
Assert.assertEquals(7, f.getDenominator());
f1 = new Fraction(1, Integer.MAX_VALUE);
f = f1.divide(f1);
Assert.assertEquals(1, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
f1 = new Fraction(Integer.MIN_VALUE, Integer.MAX_VALUE);
f2 = new Fraction(1, Integer.MAX_VALUE);
f = f1.divide(f2);
Assert.assertEquals(Integer.MIN_VALUE, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
try {
f.divide(null);
Assert.fail("NullArgumentException");
} catch (NullArgumentException ex) {}
try {
f1 = new Fraction(1, Integer.MAX_VALUE);
f = f1.divide(f1.reciprocal()); // should overflow
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f1 = new Fraction(1, -Integer.MAX_VALUE);
f = f1.divide(f1.reciprocal()); // should overflow
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f1 = new Fraction(6, 35);
f = f1.divide(15);
Assert.assertEquals(2, f.getNumerator());
Assert.assertEquals(175, f.getDenominator());
}
@Test
public void testMultiply() {
Fraction a = new Fraction(1, 2);
Fraction b = new Fraction(2, 3);
assertFraction(1, 4, a.multiply(a));
assertFraction(1, 3, a.multiply(b));
assertFraction(1, 3, b.multiply(a));
assertFraction(4, 9, b.multiply(b));
Fraction f1 = new Fraction(Integer.MAX_VALUE, 1);
Fraction f2 = new Fraction(Integer.MIN_VALUE, Integer.MAX_VALUE);
Fraction f = f1.multiply(f2);
Assert.assertEquals(Integer.MIN_VALUE, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
try {
f.multiply(null);
Assert.fail("expecting NullArgumentException");
} catch (NullArgumentException ex) {}
f1 = new Fraction(6, 35);
f = f1.multiply(15);
Assert.assertEquals(18, f.getNumerator());
Assert.assertEquals(7, f.getDenominator());
}
@Test
public void testSubtract() {
Fraction a = new Fraction(1, 2);
Fraction b = new Fraction(2, 3);
assertFraction(0, 1, a.subtract(a));
assertFraction(-1, 6, a.subtract(b));
assertFraction(1, 6, b.subtract(a));
assertFraction(0, 1, b.subtract(b));
Fraction f = new Fraction(1,1);
try {
f.subtract(null);
Assert.fail("expecting NullArgumentException");
} catch (NullArgumentException ex) {}
// if this fraction is subtracted naively, it will overflow.
// check that it doesn't.
Fraction f1 = new Fraction(1,32768*3);
Fraction f2 = new Fraction(1,59049);
f = f1.subtract(f2);
Assert.assertEquals(-13085, f.getNumerator());
Assert.assertEquals(1934917632, f.getDenominator());
f1 = new Fraction(Integer.MIN_VALUE, 3);
f2 = new Fraction(1,3).negate();
f = f1.subtract(f2);
Assert.assertEquals(Integer.MIN_VALUE+1, f.getNumerator());
Assert.assertEquals(3, f.getDenominator());
f1 = new Fraction(Integer.MAX_VALUE, 1);
f2 = Fraction.ONE;
f = f1.subtract(f2);
Assert.assertEquals(Integer.MAX_VALUE-1, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
f = f1.subtract(1);
Assert.assertEquals(Integer.MAX_VALUE-1, f.getNumerator());
Assert.assertEquals(1, f.getDenominator());
try {
f1 = new Fraction(1, Integer.MAX_VALUE);
f2 = new Fraction(1, Integer.MAX_VALUE - 1);
f = f1.subtract(f2);
Assert.fail("expecting ArithmeticException"); //should overflow
} catch (ArithmeticException ex) {}
// denominator should not be a multiple of 2 or 3 to trigger overflow
f1 = new Fraction(Integer.MIN_VALUE, 5);
f2 = new Fraction(1,5);
try {
f = f1.subtract(f2); // should overflow
Assert.fail("expecting MathArithmeticException but got: " + f.toString());
} catch (MathArithmeticException ex) {}
try {
f= new Fraction(Integer.MIN_VALUE, 1);
f = f.subtract(Fraction.ONE);
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f= new Fraction(Integer.MAX_VALUE, 1);
f = f.subtract(Fraction.ONE.negate());
Assert.fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f1 = new Fraction(3,327680);
f2 = new Fraction(2,59049);
try {
f = f1.subtract(f2); // should overflow
Assert.fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
}
@Test
public void testEqualsAndHashCode() {
Fraction zero = new Fraction(0,1);
Fraction nullFraction = null;
Assert.assertTrue( zero.equals(zero));
Assert.assertFalse(zero.equals(nullFraction));
Assert.assertFalse(zero.equals(Double.valueOf(0)));
Fraction zero2 = new Fraction(0,2);
Assert.assertTrue(zero.equals(zero2));
Assert.assertEquals(zero.hashCode(), zero2.hashCode());
Fraction one = new Fraction(1,1);
Assert.assertFalse((one.equals(zero) ||zero.equals(one)));
}
@Test
public void testGetReducedFraction() {
Fraction threeFourths = new Fraction(3, 4);
Assert.assertTrue(threeFourths.equals(Fraction.getReducedFraction(6, 8)));
Assert.assertTrue(Fraction.ZERO.equals(Fraction.getReducedFraction(0, -1)));
try {
Fraction.getReducedFraction(1, 0);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// expected
}
Assert.assertEquals(Fraction.getReducedFraction
(2, Integer.MIN_VALUE).getNumerator(),-1);
Assert.assertEquals(Fraction.getReducedFraction
(1, -1).getNumerator(), -1);
}
@Test
public void testToString() {
Assert.assertEquals("0", new Fraction(0, 3).toString());
Assert.assertEquals("3", new Fraction(6, 2).toString());
Assert.assertEquals("2 / 3", new Fraction(18, 27).toString());
}
@Test
public void testSerial() throws FractionConversionException {
Fraction[] fractions = {
new Fraction(3, 4), Fraction.ONE, Fraction.ZERO,
new Fraction(17), new Fraction(FastMath.PI, 1000),
new Fraction(-5, 2)
};
for (Fraction fraction : fractions) {
Assert.assertEquals(fraction, TestUtils.serializeAndRecover(fraction));
}
}
}