/*
* 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.math3.util;
import java.util.ArrayList;
import java.util.Arrays;
import java.math.BigInteger;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.random.RandomDataGenerator;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for the {@link ArithmeticUtils} class.
*
*/
public class ArithmeticUtilsTest {
@Test
public void testAddAndCheck() {
int big = Integer.MAX_VALUE;
int bigNeg = Integer.MIN_VALUE;
Assert.assertEquals(big, ArithmeticUtils.addAndCheck(big, 0));
try {
ArithmeticUtils.addAndCheck(big, 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
try {
ArithmeticUtils.addAndCheck(bigNeg, -1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
}
@Test
public void testAddAndCheckLong() {
long max = Long.MAX_VALUE;
long min = Long.MIN_VALUE;
Assert.assertEquals(max, ArithmeticUtils.addAndCheck(max, 0L));
Assert.assertEquals(min, ArithmeticUtils.addAndCheck(min, 0L));
Assert.assertEquals(max, ArithmeticUtils.addAndCheck(0L, max));
Assert.assertEquals(min, ArithmeticUtils.addAndCheck(0L, min));
Assert.assertEquals(1, ArithmeticUtils.addAndCheck(-1L, 2L));
Assert.assertEquals(1, ArithmeticUtils.addAndCheck(2L, -1L));
Assert.assertEquals(-3, ArithmeticUtils.addAndCheck(-2L, -1L));
Assert.assertEquals(min, ArithmeticUtils.addAndCheck(min + 1, -1L));
Assert.assertEquals(-1, ArithmeticUtils.addAndCheck(min, max));
testAddAndCheckLongFailure(max, 1L);
testAddAndCheckLongFailure(min, -1L);
testAddAndCheckLongFailure(1L, max);
testAddAndCheckLongFailure(-1L, min);
testAddAndCheckLongFailure(max, max);
testAddAndCheckLongFailure(min, min);
}
@Test
public void testGcd() {
int a = 30;
int b = 50;
int c = 77;
Assert.assertEquals(0, ArithmeticUtils.gcd(0, 0));
Assert.assertEquals(b, ArithmeticUtils.gcd(0, b));
Assert.assertEquals(a, ArithmeticUtils.gcd(a, 0));
Assert.assertEquals(b, ArithmeticUtils.gcd(0, -b));
Assert.assertEquals(a, ArithmeticUtils.gcd(-a, 0));
Assert.assertEquals(10, ArithmeticUtils.gcd(a, b));
Assert.assertEquals(10, ArithmeticUtils.gcd(-a, b));
Assert.assertEquals(10, ArithmeticUtils.gcd(a, -b));
Assert.assertEquals(10, ArithmeticUtils.gcd(-a, -b));
Assert.assertEquals(1, ArithmeticUtils.gcd(a, c));
Assert.assertEquals(1, ArithmeticUtils.gcd(-a, c));
Assert.assertEquals(1, ArithmeticUtils.gcd(a, -c));
Assert.assertEquals(1, ArithmeticUtils.gcd(-a, -c));
Assert.assertEquals(3 * (1<<15), ArithmeticUtils.gcd(3 * (1<<20), 9 * (1<<15)));
Assert.assertEquals(Integer.MAX_VALUE, ArithmeticUtils.gcd(Integer.MAX_VALUE, 0));
Assert.assertEquals(Integer.MAX_VALUE, ArithmeticUtils.gcd(-Integer.MAX_VALUE, 0));
Assert.assertEquals(1<<30, ArithmeticUtils.gcd(1<<30, -Integer.MIN_VALUE));
try {
// gcd(Integer.MIN_VALUE, 0) > Integer.MAX_VALUE
ArithmeticUtils.gcd(Integer.MIN_VALUE, 0);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// gcd(0, Integer.MIN_VALUE) > Integer.MAX_VALUE
ArithmeticUtils.gcd(0, Integer.MIN_VALUE);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// gcd(Integer.MIN_VALUE, Integer.MIN_VALUE) > Integer.MAX_VALUE
ArithmeticUtils.gcd(Integer.MIN_VALUE, Integer.MIN_VALUE);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
}
@Test
public void testGcdConsistency() {
int[] primeList = {19, 23, 53, 67, 73, 79, 101, 103, 111, 131};
ArrayList<Integer> primes = new ArrayList<Integer>();
for (int i = 0; i < primeList.length; i++) {
primes.add(Integer.valueOf(primeList[i]));
}
RandomDataGenerator randomData = new RandomDataGenerator();
for (int i = 0; i < 20; i++) {
Object[] sample = randomData.nextSample(primes, 4);
int p1 = ((Integer) sample[0]).intValue();
int p2 = ((Integer) sample[1]).intValue();
int p3 = ((Integer) sample[2]).intValue();
int p4 = ((Integer) sample[3]).intValue();
int i1 = p1 * p2 * p3;
int i2 = p1 * p2 * p4;
int gcd = p1 * p2;
Assert.assertEquals(gcd, ArithmeticUtils.gcd(i1, i2));
long l1 = i1;
long l2 = i2;
Assert.assertEquals(gcd, ArithmeticUtils.gcd(l1, l2));
}
}
@Test
public void testGcdLong(){
long a = 30;
long b = 50;
long c = 77;
Assert.assertEquals(0, ArithmeticUtils.gcd(0L, 0));
Assert.assertEquals(b, ArithmeticUtils.gcd(0, b));
Assert.assertEquals(a, ArithmeticUtils.gcd(a, 0));
Assert.assertEquals(b, ArithmeticUtils.gcd(0, -b));
Assert.assertEquals(a, ArithmeticUtils.gcd(-a, 0));
Assert.assertEquals(10, ArithmeticUtils.gcd(a, b));
Assert.assertEquals(10, ArithmeticUtils.gcd(-a, b));
Assert.assertEquals(10, ArithmeticUtils.gcd(a, -b));
Assert.assertEquals(10, ArithmeticUtils.gcd(-a, -b));
Assert.assertEquals(1, ArithmeticUtils.gcd(a, c));
Assert.assertEquals(1, ArithmeticUtils.gcd(-a, c));
Assert.assertEquals(1, ArithmeticUtils.gcd(a, -c));
Assert.assertEquals(1, ArithmeticUtils.gcd(-a, -c));
Assert.assertEquals(3L * (1L<<45), ArithmeticUtils.gcd(3L * (1L<<50), 9L * (1L<<45)));
Assert.assertEquals(1L<<45, ArithmeticUtils.gcd(1L<<45, Long.MIN_VALUE));
Assert.assertEquals(Long.MAX_VALUE, ArithmeticUtils.gcd(Long.MAX_VALUE, 0L));
Assert.assertEquals(Long.MAX_VALUE, ArithmeticUtils.gcd(-Long.MAX_VALUE, 0L));
Assert.assertEquals(1, ArithmeticUtils.gcd(60247241209L, 153092023L));
try {
// gcd(Long.MIN_VALUE, 0) > Long.MAX_VALUE
ArithmeticUtils.gcd(Long.MIN_VALUE, 0);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// gcd(0, Long.MIN_VALUE) > Long.MAX_VALUE
ArithmeticUtils.gcd(0, Long.MIN_VALUE);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// gcd(Long.MIN_VALUE, Long.MIN_VALUE) > Long.MAX_VALUE
ArithmeticUtils.gcd(Long.MIN_VALUE, Long.MIN_VALUE);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
}
@Test
public void testLcm() {
int a = 30;
int b = 50;
int c = 77;
Assert.assertEquals(0, ArithmeticUtils.lcm(0, b));
Assert.assertEquals(0, ArithmeticUtils.lcm(a, 0));
Assert.assertEquals(b, ArithmeticUtils.lcm(1, b));
Assert.assertEquals(a, ArithmeticUtils.lcm(a, 1));
Assert.assertEquals(150, ArithmeticUtils.lcm(a, b));
Assert.assertEquals(150, ArithmeticUtils.lcm(-a, b));
Assert.assertEquals(150, ArithmeticUtils.lcm(a, -b));
Assert.assertEquals(150, ArithmeticUtils.lcm(-a, -b));
Assert.assertEquals(2310, ArithmeticUtils.lcm(a, c));
// Assert that no intermediate value overflows:
// The naive implementation of lcm(a,b) would be (a*b)/gcd(a,b)
Assert.assertEquals((1<<20)*15, ArithmeticUtils.lcm((1<<20)*3, (1<<20)*5));
// Special case
Assert.assertEquals(0, ArithmeticUtils.lcm(0, 0));
try {
// lcm == abs(MIN_VALUE) cannot be represented as a nonnegative int
ArithmeticUtils.lcm(Integer.MIN_VALUE, 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// lcm == abs(MIN_VALUE) cannot be represented as a nonnegative int
ArithmeticUtils.lcm(Integer.MIN_VALUE, 1<<20);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
ArithmeticUtils.lcm(Integer.MAX_VALUE, Integer.MAX_VALUE - 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
}
@Test
public void testLcmLong() {
long a = 30;
long b = 50;
long c = 77;
Assert.assertEquals(0, ArithmeticUtils.lcm(0, b));
Assert.assertEquals(0, ArithmeticUtils.lcm(a, 0));
Assert.assertEquals(b, ArithmeticUtils.lcm(1, b));
Assert.assertEquals(a, ArithmeticUtils.lcm(a, 1));
Assert.assertEquals(150, ArithmeticUtils.lcm(a, b));
Assert.assertEquals(150, ArithmeticUtils.lcm(-a, b));
Assert.assertEquals(150, ArithmeticUtils.lcm(a, -b));
Assert.assertEquals(150, ArithmeticUtils.lcm(-a, -b));
Assert.assertEquals(2310, ArithmeticUtils.lcm(a, c));
Assert.assertEquals(Long.MAX_VALUE, ArithmeticUtils.lcm(60247241209L, 153092023L));
// Assert that no intermediate value overflows:
// The naive implementation of lcm(a,b) would be (a*b)/gcd(a,b)
Assert.assertEquals((1L<<50)*15, ArithmeticUtils.lcm((1L<<45)*3, (1L<<50)*5));
// Special case
Assert.assertEquals(0L, ArithmeticUtils.lcm(0L, 0L));
try {
// lcm == abs(MIN_VALUE) cannot be represented as a nonnegative int
ArithmeticUtils.lcm(Long.MIN_VALUE, 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
try {
// lcm == abs(MIN_VALUE) cannot be represented as a nonnegative int
ArithmeticUtils.lcm(Long.MIN_VALUE, 1<<20);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
Assert.assertEquals((long) Integer.MAX_VALUE * (Integer.MAX_VALUE - 1),
ArithmeticUtils.lcm((long)Integer.MAX_VALUE, Integer.MAX_VALUE - 1));
try {
ArithmeticUtils.lcm(Long.MAX_VALUE, Long.MAX_VALUE - 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException expected) {
// expected
}
}
@Test
public void testMulAndCheck() {
int big = Integer.MAX_VALUE;
int bigNeg = Integer.MIN_VALUE;
Assert.assertEquals(big, ArithmeticUtils.mulAndCheck(big, 1));
try {
ArithmeticUtils.mulAndCheck(big, 2);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
try {
ArithmeticUtils.mulAndCheck(bigNeg, 2);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
}
@Test
public void testMulAndCheckLong() {
long max = Long.MAX_VALUE;
long min = Long.MIN_VALUE;
Assert.assertEquals(max, ArithmeticUtils.mulAndCheck(max, 1L));
Assert.assertEquals(min, ArithmeticUtils.mulAndCheck(min, 1L));
Assert.assertEquals(0L, ArithmeticUtils.mulAndCheck(max, 0L));
Assert.assertEquals(0L, ArithmeticUtils.mulAndCheck(min, 0L));
Assert.assertEquals(max, ArithmeticUtils.mulAndCheck(1L, max));
Assert.assertEquals(min, ArithmeticUtils.mulAndCheck(1L, min));
Assert.assertEquals(0L, ArithmeticUtils.mulAndCheck(0L, max));
Assert.assertEquals(0L, ArithmeticUtils.mulAndCheck(0L, min));
Assert.assertEquals(1L, ArithmeticUtils.mulAndCheck(-1L, -1L));
Assert.assertEquals(min, ArithmeticUtils.mulAndCheck(min / 2, 2));
testMulAndCheckLongFailure(max, 2L);
testMulAndCheckLongFailure(2L, max);
testMulAndCheckLongFailure(min, 2L);
testMulAndCheckLongFailure(2L, min);
testMulAndCheckLongFailure(min, -1L);
testMulAndCheckLongFailure(-1L, min);
}
@Test
public void testSubAndCheck() {
int big = Integer.MAX_VALUE;
int bigNeg = Integer.MIN_VALUE;
Assert.assertEquals(big, ArithmeticUtils.subAndCheck(big, 0));
Assert.assertEquals(bigNeg + 1, ArithmeticUtils.subAndCheck(bigNeg, -1));
Assert.assertEquals(-1, ArithmeticUtils.subAndCheck(bigNeg, -big));
try {
ArithmeticUtils.subAndCheck(big, -1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
try {
ArithmeticUtils.subAndCheck(bigNeg, 1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
}
}
@Test
public void testSubAndCheckErrorMessage() {
int big = Integer.MAX_VALUE;
try {
ArithmeticUtils.subAndCheck(big, -1);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
Assert.assertTrue(ex.getMessage().length() > 1);
}
}
@Test
public void testSubAndCheckLong() {
long max = Long.MAX_VALUE;
long min = Long.MIN_VALUE;
Assert.assertEquals(max, ArithmeticUtils.subAndCheck(max, 0));
Assert.assertEquals(min, ArithmeticUtils.subAndCheck(min, 0));
Assert.assertEquals(-max, ArithmeticUtils.subAndCheck(0, max));
Assert.assertEquals(min + 1, ArithmeticUtils.subAndCheck(min, -1));
// min == -1-max
Assert.assertEquals(-1, ArithmeticUtils.subAndCheck(-max - 1, -max));
Assert.assertEquals(max, ArithmeticUtils.subAndCheck(-1, -1 - max));
testSubAndCheckLongFailure(0L, min);
testSubAndCheckLongFailure(max, -1L);
testSubAndCheckLongFailure(min, 1L);
}
@Test
public void testPow() {
Assert.assertEquals(1801088541, ArithmeticUtils.pow(21, 7));
Assert.assertEquals(1, ArithmeticUtils.pow(21, 0));
try {
ArithmeticUtils.pow(21, -7);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
Assert.assertEquals(1801088541, ArithmeticUtils.pow(21, 7));
Assert.assertEquals(1, ArithmeticUtils.pow(21, 0));
try {
ArithmeticUtils.pow(21, -7);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
Assert.assertEquals(1801088541l, ArithmeticUtils.pow(21l, 7));
Assert.assertEquals(1l, ArithmeticUtils.pow(21l, 0));
try {
ArithmeticUtils.pow(21l, -7);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
Assert.assertEquals(1801088541l, ArithmeticUtils.pow(21l, 7l));
Assert.assertEquals(1l, ArithmeticUtils.pow(21l, 0l));
try {
ArithmeticUtils.pow(21l, -7l);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
BigInteger twentyOne = BigInteger.valueOf(21l);
Assert.assertEquals(BigInteger.valueOf(1801088541l), ArithmeticUtils.pow(twentyOne, 7));
Assert.assertEquals(BigInteger.ONE, ArithmeticUtils.pow(twentyOne, 0));
try {
ArithmeticUtils.pow(twentyOne, -7);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
Assert.assertEquals(BigInteger.valueOf(1801088541l), ArithmeticUtils.pow(twentyOne, 7l));
Assert.assertEquals(BigInteger.ONE, ArithmeticUtils.pow(twentyOne, 0l));
try {
ArithmeticUtils.pow(twentyOne, -7l);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
Assert.assertEquals(BigInteger.valueOf(1801088541l), ArithmeticUtils.pow(twentyOne, BigInteger.valueOf(7l)));
Assert.assertEquals(BigInteger.ONE, ArithmeticUtils.pow(twentyOne, BigInteger.ZERO));
try {
ArithmeticUtils.pow(twentyOne, BigInteger.valueOf(-7l));
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException e) {
// expected behavior
}
BigInteger bigOne =
new BigInteger("1543786922199448028351389769265814882661837148" +
"4763915343722775611762713982220306372888519211" +
"560905579993523402015636025177602059044911261");
Assert.assertEquals(bigOne, ArithmeticUtils.pow(twentyOne, 103));
Assert.assertEquals(bigOne, ArithmeticUtils.pow(twentyOne, 103l));
Assert.assertEquals(bigOne, ArithmeticUtils.pow(twentyOne, BigInteger.valueOf(103l)));
}
@Test(expected=MathArithmeticException.class)
public void testPowIntOverflow() {
ArithmeticUtils.pow(21, 8);
}
@Test
public void testPowInt() {
final int base = 21;
Assert.assertEquals(85766121L,
ArithmeticUtils.pow(base, 6));
Assert.assertEquals(1801088541L,
ArithmeticUtils.pow(base, 7));
}
@Test(expected=MathArithmeticException.class)
public void testPowNegativeIntOverflow() {
ArithmeticUtils.pow(-21, 8);
}
@Test
public void testPowNegativeInt() {
final int base = -21;
Assert.assertEquals(85766121,
ArithmeticUtils.pow(base, 6));
Assert.assertEquals(-1801088541,
ArithmeticUtils.pow(base, 7));
}
@Test
public void testPowMinusOneInt() {
final int base = -1;
for (int i = 0; i < 100; i++) {
final int pow = ArithmeticUtils.pow(base, i);
Assert.assertEquals("i: " + i, i % 2 == 0 ? 1 : -1, pow);
}
}
@Test
public void testPowOneInt() {
final int base = 1;
for (int i = 0; i < 100; i++) {
final int pow = ArithmeticUtils.pow(base, i);
Assert.assertEquals("i: " + i, 1, pow);
}
}
@Test(expected=MathArithmeticException.class)
public void testPowLongOverflow() {
ArithmeticUtils.pow(21, 15);
}
@Test
public void testPowLong() {
final long base = 21;
Assert.assertEquals(154472377739119461L,
ArithmeticUtils.pow(base, 13));
Assert.assertEquals(3243919932521508681L,
ArithmeticUtils.pow(base, 14));
}
@Test(expected=MathArithmeticException.class)
public void testPowNegativeLongOverflow() {
ArithmeticUtils.pow(-21L, 15);
}
@Test
public void testPowNegativeLong() {
final long base = -21;
Assert.assertEquals(-154472377739119461L,
ArithmeticUtils.pow(base, 13));
Assert.assertEquals(3243919932521508681L,
ArithmeticUtils.pow(base, 14));
}
@Test
public void testPowMinusOneLong() {
final long base = -1;
for (int i = 0; i < 100; i++) {
final long pow = ArithmeticUtils.pow(base, i);
Assert.assertEquals("i: " + i, i % 2 == 0 ? 1 : -1, pow);
}
}
@Test
public void testPowOneLong() {
final long base = 1;
for (int i = 0; i < 100; i++) {
final long pow = ArithmeticUtils.pow(base, i);
Assert.assertEquals("i: " + i, 1, pow);
}
}
@Test
public void testIsPowerOfTwo() {
final int n = 1025;
final boolean[] expected = new boolean[n];
Arrays.fill(expected, false);
for (int i = 1; i < expected.length; i *= 2) {
expected[i] = true;
}
for (int i = 0; i < expected.length; i++) {
final boolean actual = ArithmeticUtils.isPowerOfTwo(i);
Assert.assertTrue(Integer.toString(i), actual == expected[i]);
}
}
private void testAddAndCheckLongFailure(long a, long b) {
try {
ArithmeticUtils.addAndCheck(a, b);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// success
}
}
private void testMulAndCheckLongFailure(long a, long b) {
try {
ArithmeticUtils.mulAndCheck(a, b);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// success
}
}
private void testSubAndCheckLongFailure(long a, long b) {
try {
ArithmeticUtils.subAndCheck(a, b);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// success
}
}
}