/*
* 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.util.HashMap;
import java.util.List;
import java.util.Map;
import java.math.BigInteger;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.random.RandomDataImpl;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for the {@link ArithmeticUtils} class.
*
* @version $Id: ArithmeticUtilsTest.java 1371680 2012-08-10 12:15:23Z luc $
*/
public class ArithmeticUtilsTest {
/** cached binomial coefficients */
private static final List<Map<Integer, Long>> binomialCache = new ArrayList<Map<Integer, Long>>();
/** Verify that b(0,0) = 1 */
@Test
public void test0Choose0() {
Assert.assertEquals(ArithmeticUtils.binomialCoefficientDouble(0, 0), 1d, 0);
Assert.assertEquals(ArithmeticUtils.binomialCoefficientLog(0, 0), 0d, 0);
Assert.assertEquals(ArithmeticUtils.binomialCoefficient(0, 0), 1);
}
@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));
testAddAndCheckLongFailure(max, 1L);
testAddAndCheckLongFailure(min, -1L);
testAddAndCheckLongFailure(1L, max);
testAddAndCheckLongFailure(-1L, min);
}
@Test
public void testBinomialCoefficient() {
long[] bcoef5 = {
1,
5,
10,
10,
5,
1 };
long[] bcoef6 = {
1,
6,
15,
20,
15,
6,
1 };
for (int i = 0; i < 6; i++) {
Assert.assertEquals("5 choose " + i, bcoef5[i], ArithmeticUtils.binomialCoefficient(5, i));
}
for (int i = 0; i < 7; i++) {
Assert.assertEquals("6 choose " + i, bcoef6[i], ArithmeticUtils.binomialCoefficient(6, i));
}
for (int n = 1; n < 10; n++) {
for (int k = 0; k <= n; k++) {
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), ArithmeticUtils.binomialCoefficient(n, k));
Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), ArithmeticUtils.binomialCoefficientDouble(n, k), Double.MIN_VALUE);
Assert.assertEquals(n + " choose " + k, FastMath.log(binomialCoefficient(n, k)), ArithmeticUtils.binomialCoefficientLog(n, k), 10E-12);
}
}
int[] n = { 34, 66, 100, 1500, 1500 };
int[] k = { 17, 33, 10, 1500 - 4, 4 };
for (int i = 0; i < n.length; i++) {
long expected = binomialCoefficient(n[i], k[i]);
Assert.assertEquals(n[i] + " choose " + k[i], expected,
ArithmeticUtils.binomialCoefficient(n[i], k[i]));
Assert.assertEquals(n[i] + " choose " + k[i], expected,
ArithmeticUtils.binomialCoefficientDouble(n[i], k[i]), 0.0);
Assert.assertEquals("log(" + n[i] + " choose " + k[i] + ")", FastMath.log(expected),
ArithmeticUtils.binomialCoefficientLog(n[i], k[i]), 0.0);
}
}
@Test
public void testBinomialCoefficientFail() {
try {
ArithmeticUtils.binomialCoefficient(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientDouble(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientLog(4, 5);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientDouble(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficientLog(-1, -2);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(67, 30);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
try {
ArithmeticUtils.binomialCoefficient(67, 34);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
double x = ArithmeticUtils.binomialCoefficientDouble(1030, 515);
Assert.assertTrue("expecting infinite binomial coefficient", Double
.isInfinite(x));
}
/**
* Tests correctness for large n and sharpness of upper bound in API doc
* JIRA: MATH-241
*/
@Test
public void testBinomialCoefficientLarge() throws Exception {
// This tests all legal and illegal values for n <= 200.
for (int n = 0; n <= 200; n++) {
for (int k = 0; k <= n; k++) {
long ourResult = -1;
long exactResult = -1;
boolean shouldThrow = false;
boolean didThrow = false;
try {
ourResult = ArithmeticUtils.binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
didThrow = true;
}
try {
exactResult = binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
shouldThrow = true;
}
Assert.assertEquals(n + " choose " + k, exactResult, ourResult);
Assert.assertEquals(n + " choose " + k, shouldThrow, didThrow);
Assert.assertTrue(n + " choose " + k, (n > 66 || !didThrow));
if (!shouldThrow && exactResult > 1) {
Assert.assertEquals(n + " choose " + k, 1.,
ArithmeticUtils.binomialCoefficientDouble(n, k) / exactResult, 1e-10);
Assert.assertEquals(n + " choose " + k, 1,
ArithmeticUtils.binomialCoefficientLog(n, k) / FastMath.log(exactResult), 1e-10);
}
}
}
long ourResult = ArithmeticUtils.binomialCoefficient(300, 3);
long exactResult = binomialCoefficient(300, 3);
Assert.assertEquals(exactResult, ourResult);
ourResult = ArithmeticUtils.binomialCoefficient(700, 697);
exactResult = binomialCoefficient(700, 697);
Assert.assertEquals(exactResult, ourResult);
// This one should throw
try {
ArithmeticUtils.binomialCoefficient(700, 300);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// Expected
}
int n = 10000;
ourResult = ArithmeticUtils.binomialCoefficient(n, 3);
exactResult = binomialCoefficient(n, 3);
Assert.assertEquals(exactResult, ourResult);
Assert.assertEquals(1, ArithmeticUtils.binomialCoefficientDouble(n, 3) / exactResult, 1e-10);
Assert.assertEquals(1, ArithmeticUtils.binomialCoefficientLog(n, 3) / FastMath.log(exactResult), 1e-10);
}
@Test
public void testFactorial() {
for (int i = 1; i < 21; i++) {
Assert.assertEquals(i + "! ", factorial(i), ArithmeticUtils.factorial(i));
Assert.assertEquals(i + "! ", factorial(i), ArithmeticUtils.factorialDouble(i), Double.MIN_VALUE);
Assert.assertEquals(i + "! ", FastMath.log(factorial(i)), ArithmeticUtils.factorialLog(i), 10E-12);
}
Assert.assertEquals("0", 1, ArithmeticUtils.factorial(0));
Assert.assertEquals("0", 1.0d, ArithmeticUtils.factorialDouble(0), 1E-14);
Assert.assertEquals("0", 0.0d, ArithmeticUtils.factorialLog(0), 1E-14);
}
@Test
public void testFactorialFail() {
try {
ArithmeticUtils.factorial(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorialDouble(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorialLog(-1);
Assert.fail("expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// ignored
}
try {
ArithmeticUtils.factorial(21);
Assert.fail("expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// ignored
}
Assert.assertTrue("expecting infinite factorial value", Double.isInfinite(ArithmeticUtils.factorialDouble(171)));
}
@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]));
}
RandomDataImpl randomData = new RandomDataImpl();
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, 7l));
Assert.assertEquals(1, ArithmeticUtils.pow(21, 0l));
try {
ArithmeticUtils.pow(21, -7l);
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
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]);
}
}
@Test
public void testStirlingS2() {
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(0, 0));
for (int n = 1; n < 30; ++n) {
Assert.assertEquals(0, ArithmeticUtils.stirlingS2(n, 0));
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(n, 1));
if (n > 2) {
Assert.assertEquals((1l << (n - 1)) - 1l, ArithmeticUtils.stirlingS2(n, 2));
Assert.assertEquals(ArithmeticUtils.binomialCoefficient(n, 2),
ArithmeticUtils.stirlingS2(n, n - 1));
}
Assert.assertEquals(1, ArithmeticUtils.stirlingS2(n, n));
}
Assert.assertEquals(536870911l, ArithmeticUtils.stirlingS2(30, 2));
Assert.assertEquals(576460752303423487l, ArithmeticUtils.stirlingS2(60, 2));
Assert.assertEquals( 25, ArithmeticUtils.stirlingS2( 5, 3));
Assert.assertEquals( 90, ArithmeticUtils.stirlingS2( 6, 3));
Assert.assertEquals( 65, ArithmeticUtils.stirlingS2( 6, 4));
Assert.assertEquals( 301, ArithmeticUtils.stirlingS2( 7, 3));
Assert.assertEquals( 350, ArithmeticUtils.stirlingS2( 7, 4));
Assert.assertEquals( 140, ArithmeticUtils.stirlingS2( 7, 5));
Assert.assertEquals( 966, ArithmeticUtils.stirlingS2( 8, 3));
Assert.assertEquals( 1701, ArithmeticUtils.stirlingS2( 8, 4));
Assert.assertEquals( 1050, ArithmeticUtils.stirlingS2( 8, 5));
Assert.assertEquals( 266, ArithmeticUtils.stirlingS2( 8, 6));
Assert.assertEquals( 3025, ArithmeticUtils.stirlingS2( 9, 3));
Assert.assertEquals( 7770, ArithmeticUtils.stirlingS2( 9, 4));
Assert.assertEquals( 6951, ArithmeticUtils.stirlingS2( 9, 5));
Assert.assertEquals( 2646, ArithmeticUtils.stirlingS2( 9, 6));
Assert.assertEquals( 462, ArithmeticUtils.stirlingS2( 9, 7));
Assert.assertEquals( 9330, ArithmeticUtils.stirlingS2(10, 3));
Assert.assertEquals(34105, ArithmeticUtils.stirlingS2(10, 4));
Assert.assertEquals(42525, ArithmeticUtils.stirlingS2(10, 5));
Assert.assertEquals(22827, ArithmeticUtils.stirlingS2(10, 6));
Assert.assertEquals( 5880, ArithmeticUtils.stirlingS2(10, 7));
Assert.assertEquals( 750, ArithmeticUtils.stirlingS2(10, 8));
}
@Test(expected=NotPositiveException.class)
public void testStirlingS2NegativeN() {
ArithmeticUtils.stirlingS2(3, -1);
}
@Test(expected=NumberIsTooLargeException.class)
public void testStirlingS2LargeK() {
ArithmeticUtils.stirlingS2(3, 4);
}
@Test(expected=MathArithmeticException.class)
public void testStirlingS2Overflow() {
ArithmeticUtils.stirlingS2(26, 9);
}
/**
* Exact (caching) recursive implementation to test against
*/
private long binomialCoefficient(int n, int k) throws MathArithmeticException {
if (binomialCache.size() > n) {
Long cachedResult = binomialCache.get(n).get(Integer.valueOf(k));
if (cachedResult != null) {
return cachedResult.longValue();
}
}
long result = -1;
if ((n == k) || (k == 0)) {
result = 1;
} else if ((k == 1) || (k == n - 1)) {
result = n;
} else {
// Reduce stack depth for larger values of n
if (k < n - 100) {
binomialCoefficient(n - 100, k);
}
if (k > 100) {
binomialCoefficient(n - 100, k - 100);
}
result = ArithmeticUtils.addAndCheck(binomialCoefficient(n - 1, k - 1),
binomialCoefficient(n - 1, k));
}
if (result == -1) {
throw new MathArithmeticException();
}
for (int i = binomialCache.size(); i < n + 1; i++) {
binomialCache.add(new HashMap<Integer, Long>());
}
binomialCache.get(n).put(Integer.valueOf(k), Long.valueOf(result));
return result;
}
/**
* Exact direct multiplication implementation to test against
*/
private long factorial(int n) {
long result = 1;
for (int i = 2; i <= n; i++) {
result *= i;
}
return result;
}
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
}
}
}