/*
* Copyright (C) 2011 The Guava Authors
*
* 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.
*/
package com.google.common.math;
import static com.google.common.math.MathTesting.ALL_INTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.ALL_LONG_CANDIDATES;
import static com.google.common.math.MathTesting.ALL_ROUNDING_MODES;
import static com.google.common.math.MathTesting.ALL_SAFE_ROUNDING_MODES;
import static com.google.common.math.MathTesting.EXPONENTS;
import static com.google.common.math.MathTesting.NEGATIVE_INTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.NEGATIVE_LONG_CANDIDATES;
import static com.google.common.math.MathTesting.NONZERO_LONG_CANDIDATES;
import static com.google.common.math.MathTesting.POSITIVE_INTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.POSITIVE_LONG_CANDIDATES;
import static java.math.BigInteger.valueOf;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.UNNECESSARY;
import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.testing.NullPointerTester;
import junit.framework.TestCase;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
/**
* Tests for LongMath.
*
* @author Louis Wasserman
*/
@GwtCompatible(emulated = true)
public class LongMathTest extends TestCase {
@GwtIncompatible("TODO")
public void testConstantMaxPowerOfSqrt2Unsigned() {
assertEquals(BigIntegerMath.sqrt(BigInteger.ZERO.setBit(2 * Long.SIZE - 1), FLOOR).longValue(),
LongMath.MAX_POWER_OF_SQRT2_UNSIGNED);
}
@GwtIncompatible("BigIntegerMath") // TODO(cpovirk): GWT-enable BigIntegerMath
public void testMaxLog10ForLeadingZeros() {
for (int i = 0; i < Long.SIZE; i++) {
assertEquals(
BigIntegerMath.log10(BigInteger.ONE.shiftLeft(Long.SIZE - i), FLOOR),
LongMath.maxLog10ForLeadingZeros[i]);
}
}
@GwtIncompatible("TODO")
public void testConstantsPowersOf10() {
for (int i = 0; i < LongMath.powersOf10.length; i++) {
assertEquals(LongMath.checkedPow(10, i), LongMath.powersOf10[i]);
}
try {
LongMath.checkedPow(10, LongMath.powersOf10.length);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
@GwtIncompatible("TODO")
public void testConstantsHalfPowersOf10() {
for (int i = 0; i < LongMath.halfPowersOf10.length; i++) {
assertEquals(BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * i + 1), FLOOR),
BigInteger.valueOf(LongMath.halfPowersOf10[i]));
}
BigInteger nextBigger =
BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * LongMath.halfPowersOf10.length + 1), FLOOR);
assertTrue(nextBigger.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0);
}
@GwtIncompatible("TODO")
public void testConstantsSqrtMaxLong() {
assertEquals(LongMath.sqrt(Long.MAX_VALUE, FLOOR), LongMath.FLOOR_SQRT_MAX_LONG);
}
@GwtIncompatible("TODO")
public void testConstantsFactorials() {
long expected = 1;
for (int i = 0; i < LongMath.factorials.length; i++, expected *= i) {
assertEquals(expected, LongMath.factorials[i]);
}
try {
LongMath.checkedMultiply(
LongMath.factorials[LongMath.factorials.length - 1], LongMath.factorials.length);
fail("Expected ArithmeticException");
} catch (ArithmeticException expect) {}
}
@GwtIncompatible("TODO")
public void testConstantsBiggestBinomials() {
for (int k = 0; k < LongMath.biggestBinomials.length; k++) {
assertTrue(fitsInLong(BigIntegerMath.binomial(LongMath.biggestBinomials[k], k)));
assertTrue(LongMath.biggestBinomials[k] == Integer.MAX_VALUE
|| !fitsInLong(BigIntegerMath.binomial(LongMath.biggestBinomials[k] + 1, k)));
// In the first case, any long is valid; in the second, we want to test that the next-bigger
// long overflows.
}
int k = LongMath.biggestBinomials.length;
assertFalse(fitsInLong(BigIntegerMath.binomial(2 * k, k)));
// 2 * k is the smallest value for which we don't replace k with (n-k).
}
@GwtIncompatible("TODO")
public void testConstantsBiggestSimpleBinomials() {
for (int k = 0; k < LongMath.biggestSimpleBinomials.length; k++) {
assertTrue(LongMath.biggestSimpleBinomials[k] <= LongMath.biggestBinomials[k]);
simpleBinomial(LongMath.biggestSimpleBinomials[k], k); // mustn't throw
if (LongMath.biggestSimpleBinomials[k] < Integer.MAX_VALUE) {
// unless all n are fair game with this k
try {
simpleBinomial(LongMath.biggestSimpleBinomials[k] + 1, k);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
}
try {
int k = LongMath.biggestSimpleBinomials.length;
simpleBinomial(2 * k, k);
// 2 * k is the smallest value for which we don't replace k with (n-k).
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
public void testLessThanBranchFree() {
for (long x : ALL_LONG_CANDIDATES) {
for (long y : ALL_LONG_CANDIDATES) {
BigInteger difference = BigInteger.valueOf(x).subtract(BigInteger.valueOf(y));
if (fitsInLong(difference)) {
int expected = (x < y) ? 1 : 0;
int actual = LongMath.lessThanBranchFree(x, y);
assertEquals(expected, actual);
}
}
}
}
// Throws an ArithmeticException if "the simple implementation" of binomial coefficients overflows
@GwtIncompatible("TODO")
private long simpleBinomial(int n, int k) {
long accum = 1;
for (int i = 0; i < k; i++) {
accum = LongMath.checkedMultiply(accum, n - i);
accum /= i + 1;
}
return accum;
}
@GwtIncompatible("java.math.BigInteger")
public void testIsPowerOfTwo() {
for (long x : ALL_LONG_CANDIDATES) {
// Checks for a single bit set.
BigInteger bigX = BigInteger.valueOf(x);
boolean expected = (bigX.signum() > 0) && (bigX.bitCount() == 1);
assertEquals(expected, LongMath.isPowerOfTwo(x));
}
}
public void testLog2ZeroAlwaysThrows() {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.log2(0L, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
public void testLog2NegativeAlwaysThrows() {
for (long x : NEGATIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.log2(x, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
/* Relies on the correctness of BigIntegerMath.log2 for all modes except UNNECESSARY. */
public void testLog2MatchesBigInteger() {
for (long x : POSITIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
// The BigInteger implementation is tested separately, use it as the reference.
assertEquals(BigIntegerMath.log2(valueOf(x), mode), LongMath.log2(x, mode));
}
}
}
/* Relies on the correctness of isPowerOfTwo(long). */
public void testLog2Exact() {
for (long x : POSITIVE_LONG_CANDIDATES) {
// We only expect an exception if x was not a power of 2.
boolean isPowerOf2 = LongMath.isPowerOfTwo(x);
try {
assertEquals(x, 1L << LongMath.log2(x, UNNECESSARY));
assertTrue(isPowerOf2);
} catch (ArithmeticException e) {
assertFalse(isPowerOf2);
}
}
}
@GwtIncompatible("TODO")
public void testLog10ZeroAlwaysThrows() {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.log10(0L, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("TODO")
public void testLog10NegativeAlwaysThrows() {
for (long x : NEGATIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.log10(x, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
// Relies on the correctness of BigIntegerMath.log10 for all modes except UNNECESSARY.
@GwtIncompatible("TODO")
public void testLog10MatchesBigInteger() {
for (long x : POSITIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
assertEquals(BigIntegerMath.log10(valueOf(x), mode), LongMath.log10(x, mode));
}
}
}
// Relies on the correctness of log10(long, FLOOR) and of pow(long, int).
@GwtIncompatible("TODO")
public void testLog10Exact() {
for (long x : POSITIVE_LONG_CANDIDATES) {
int floor = LongMath.log10(x, FLOOR);
boolean expectSuccess = LongMath.pow(10, floor) == x;
try {
assertEquals(floor, LongMath.log10(x, UNNECESSARY));
assertTrue(expectSuccess);
} catch (ArithmeticException e) {
assertFalse(expectSuccess);
}
}
}
@GwtIncompatible("TODO")
public void testLog10TrivialOnPowerOf10() {
long x = 1000000000000L;
for (RoundingMode mode : ALL_ROUNDING_MODES) {
assertEquals(12, LongMath.log10(x, mode));
}
}
@GwtIncompatible("TODO")
public void testSqrtNegativeAlwaysThrows() {
for (long x : NEGATIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.sqrt(x, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
// Relies on the correctness of BigIntegerMath.sqrt for all modes except UNNECESSARY.
@GwtIncompatible("TODO")
public void testSqrtMatchesBigInteger() {
for (long x : POSITIVE_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
// Promote the long value (rather than using longValue() on the expected value) to avoid
// any risk of truncation which could lead to a false positive.
assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
}
}
}
/* Relies on the correctness of sqrt(long, FLOOR). */
@GwtIncompatible("TODO")
public void testSqrtExactMatchesFloorOrThrows() {
for (long x : POSITIVE_LONG_CANDIDATES) {
long sqrtFloor = LongMath.sqrt(x, FLOOR);
// We only expect an exception if x was not a perfect square.
boolean isPerfectSquare = (sqrtFloor * sqrtFloor == x);
try {
assertEquals(sqrtFloor, LongMath.sqrt(x, UNNECESSARY));
assertTrue(isPerfectSquare);
} catch (ArithmeticException e) {
assertFalse(isPerfectSquare);
}
}
}
@GwtIncompatible("TODO")
public void testPow() {
for (long i : ALL_LONG_CANDIDATES) {
for (int exp : EXPONENTS) {
assertEquals(LongMath.pow(i, exp), valueOf(i)
.pow(exp)
.longValue());
}
}
}
@GwtIncompatible("TODO")
public void testDivNonZero() {
for (long p : NONZERO_LONG_CANDIDATES) {
for (long q : NONZERO_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
long expected =
new BigDecimal(valueOf(p)).divide(new BigDecimal(valueOf(q)), 0, mode).longValue();
assertEquals(expected, LongMath.divide(p, q, mode));
}
}
}
}
@GwtIncompatible("TODO")
public void testDivNonZeroExact() {
for (long p : NONZERO_LONG_CANDIDATES) {
for (long q : NONZERO_LONG_CANDIDATES) {
boolean dividesEvenly = (p % q) == 0L;
try {
assertEquals(p, LongMath.divide(p, q, UNNECESSARY) * q);
assertTrue(dividesEvenly);
} catch (ArithmeticException e) {
assertFalse(dividesEvenly);
}
}
}
}
@GwtIncompatible("TODO")
public void testZeroDivIsAlwaysZero() {
for (long q : NONZERO_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
assertEquals(0L, LongMath.divide(0L, q, mode));
}
}
}
@GwtIncompatible("TODO")
public void testDivByZeroAlwaysFails() {
for (long p : ALL_LONG_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
LongMath.divide(p, 0L, mode);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
}
}
@GwtIncompatible("TODO")
public void testIntMod() {
for (long x : ALL_LONG_CANDIDATES) {
for (int m : POSITIVE_INTEGER_CANDIDATES) {
assertEquals(valueOf(x)
.mod(valueOf(m))
.intValue(), LongMath.mod(x, m));
}
}
}
@GwtIncompatible("TODO")
public void testIntModNegativeModulusFails() {
for (long x : ALL_LONG_CANDIDATES) {
for (int m : NEGATIVE_INTEGER_CANDIDATES) {
try {
LongMath.mod(x, m);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
}
}
@GwtIncompatible("TODO")
public void testIntModZeroModulusFails() {
for (long x : ALL_LONG_CANDIDATES) {
try {
LongMath.mod(x, 0);
fail("Expected AE");
} catch (ArithmeticException expected) {}
}
}
@GwtIncompatible("TODO")
public void testMod() {
for (long x : ALL_LONG_CANDIDATES) {
for (long m : POSITIVE_LONG_CANDIDATES) {
assertEquals(valueOf(x)
.mod(valueOf(m))
.longValue(), LongMath.mod(x, m));
}
}
}
@GwtIncompatible("TODO")
public void testModNegativeModulusFails() {
for (long x : ALL_LONG_CANDIDATES) {
for (long m : NEGATIVE_LONG_CANDIDATES) {
try {
LongMath.mod(x, m);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
}
}
public void testGCDExhaustive() {
for (long a : POSITIVE_LONG_CANDIDATES) {
for (long b : POSITIVE_LONG_CANDIDATES) {
assertEquals(valueOf(a).gcd(valueOf(b)), valueOf(LongMath.gcd(a, b)));
}
}
}
@GwtIncompatible("TODO")
public void testGCDZero() {
for (long a : POSITIVE_LONG_CANDIDATES) {
assertEquals(a, LongMath.gcd(a, 0));
assertEquals(a, LongMath.gcd(0, a));
}
assertEquals(0, LongMath.gcd(0, 0));
}
@GwtIncompatible("TODO")
public void testGCDNegativePositiveThrows() {
for (long a : NEGATIVE_LONG_CANDIDATES) {
try {
LongMath.gcd(a, 3);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
try {
LongMath.gcd(3, a);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("TODO")
public void testGCDNegativeZeroThrows() {
for (long a : NEGATIVE_LONG_CANDIDATES) {
try {
LongMath.gcd(a, 0);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
try {
LongMath.gcd(0, a);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("TODO")
public void testCheckedAdd() {
for (long a : ALL_INTEGER_CANDIDATES) {
for (long b : ALL_INTEGER_CANDIDATES) {
BigInteger expectedResult = valueOf(a).add(valueOf(b));
boolean expectedSuccess = fitsInLong(expectedResult);
try {
assertEquals(a + b, LongMath.checkedAdd(a, b));
assertTrue(expectedSuccess);
} catch (ArithmeticException e) {
assertFalse(expectedSuccess);
}
}
}
}
@GwtIncompatible("TODO")
public void testCheckedSubtract() {
for (long a : ALL_INTEGER_CANDIDATES) {
for (long b : ALL_INTEGER_CANDIDATES) {
BigInteger expectedResult = valueOf(a).subtract(valueOf(b));
boolean expectedSuccess = fitsInLong(expectedResult);
try {
assertEquals(a - b, LongMath.checkedSubtract(a, b));
assertTrue(expectedSuccess);
} catch (ArithmeticException e) {
assertFalse(expectedSuccess);
}
}
}
}
@GwtIncompatible("TODO")
public void testCheckedMultiply() {
for (long a : ALL_INTEGER_CANDIDATES) {
for (long b : ALL_INTEGER_CANDIDATES) {
BigInteger expectedResult = valueOf(a).multiply(valueOf(b));
boolean expectedSuccess = fitsInLong(expectedResult);
try {
assertEquals(a * b, LongMath.checkedMultiply(a, b));
assertTrue(expectedSuccess);
} catch (ArithmeticException e) {
assertFalse(expectedSuccess);
}
}
}
}
@GwtIncompatible("TODO")
public void testCheckedPow() {
for (long b : ALL_INTEGER_CANDIDATES) {
for (int exp : EXPONENTS) {
BigInteger expectedResult = valueOf(b).pow(exp);
boolean expectedSuccess = fitsInLong(expectedResult);
try {
assertEquals(expectedResult.longValue(), LongMath.checkedPow(b, exp));
assertTrue(expectedSuccess);
} catch (ArithmeticException e) {
assertFalse(expectedSuccess);
}
}
}
}
// Depends on the correctness of BigIntegerMath.factorial.
@GwtIncompatible("TODO")
public void testFactorial() {
for (int n = 0; n <= 50; n++) {
BigInteger expectedBig = BigIntegerMath.factorial(n);
long expectedLong = fitsInLong(expectedBig) ? expectedBig.longValue() : Long.MAX_VALUE;
assertEquals(expectedLong, LongMath.factorial(n));
}
}
@GwtIncompatible("TODO")
public void testFactorialNegative() {
for (int n : NEGATIVE_INTEGER_CANDIDATES) {
try {
LongMath.factorial(n);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
// Depends on the correctness of BigIntegerMath.binomial.
public void testBinomial() {
for (int n = 0; n <= 70; n++) {
for (int k = 0; k <= n; k++) {
BigInteger expectedBig = BigIntegerMath.binomial(n, k);
long expectedLong = fitsInLong(expectedBig) ? expectedBig.longValue() : Long.MAX_VALUE;
assertEquals(expectedLong, LongMath.binomial(n, k));
}
}
}
@GwtIncompatible("Slow")
public void testBinomial_exhaustiveNotOverflowing() {
// Tests all of the inputs to LongMath.binomial that won't cause it to overflow, that weren't
// tested in the previous method, for k >= 3.
for (int k = 3; k < LongMath.biggestBinomials.length; k++) {
for (int n = 70; n <= LongMath.biggestBinomials[k]; n++) {
assertEquals(BigIntegerMath.binomial(n, k).longValue(), LongMath.binomial(n, k));
}
}
}
public void testBinomialOutside() {
for (int n = 0; n <= 50; n++) {
try {
LongMath.binomial(n, -1);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
try {
LongMath.binomial(n, n + 1);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
public void testBinomialNegative() {
for (int n : NEGATIVE_INTEGER_CANDIDATES) {
try {
LongMath.binomial(n, 0);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("far too slow")
public void testSqrtOfPerfectSquareAsDoubleIsPerfect() {
// This takes just over a minute on my machine.
for (long n = 0; n <= LongMath.FLOOR_SQRT_MAX_LONG; n++) {
long actual = (long) Math.sqrt(n * n);
assertTrue(actual == n);
}
}
public void testSqrtOfLongIsAtMostFloorSqrtMaxLong() {
long sqrtMaxLong = (long) Math.sqrt(Long.MAX_VALUE);
assertTrue(sqrtMaxLong <= LongMath.FLOOR_SQRT_MAX_LONG);
}
@GwtIncompatible("java.math.BigInteger")
public void testMean() {
// Odd-sized ranges have an obvious mean
assertMean(2, 1, 3);
assertMean(-2, -3, -1);
assertMean(0, -1, 1);
assertMean(1, -1, 3);
assertMean((1L << 62) - 1, -1, Long.MAX_VALUE);
// Even-sized ranges should prefer the lower mean
assertMean(2, 1, 4);
assertMean(-3, -4, -1);
assertMean(0, -1, 2);
assertMean(0, Long.MIN_VALUE + 2, Long.MAX_VALUE);
assertMean(0, 0, 1);
assertMean(-1, -1, 0);
assertMean(-1, Long.MIN_VALUE, Long.MAX_VALUE);
// x == y == mean
assertMean(1, 1, 1);
assertMean(0, 0, 0);
assertMean(-1, -1, -1);
assertMean(Long.MIN_VALUE, Long.MIN_VALUE, Long.MIN_VALUE);
assertMean(Long.MAX_VALUE, Long.MAX_VALUE, Long.MAX_VALUE);
// Exhaustive checks
for (long x : ALL_LONG_CANDIDATES) {
for (long y : ALL_LONG_CANDIDATES) {
assertMean(x, y);
}
}
}
/**
* Helper method that asserts the arithmetic mean of x and y is equal
* to the expectedMean.
*/
private static void assertMean(long expectedMean, long x, long y) {
assertEquals("The expectedMean should be the same as computeMeanSafely",
expectedMean, computeMeanSafely(x, y));
assertMean(x, y);
}
/**
* Helper method that asserts the arithmetic mean of x and y is equal
*to the result of computeMeanSafely.
*/
private static void assertMean(long x, long y) {
long expectedMean = computeMeanSafely(x, y);
assertEquals(expectedMean, LongMath.mean(x, y));
assertEquals("The mean of x and y should equal the mean of y and x",
expectedMean, LongMath.mean(y, x));
}
/**
* Computes the mean in a way that is obvious and resilient to
* overflow by using BigInteger arithmetic.
*/
private static long computeMeanSafely(long x, long y) {
BigInteger bigX = BigInteger.valueOf(x);
BigInteger bigY = BigInteger.valueOf(y);
BigDecimal bigMean = new BigDecimal(bigX.add(bigY))
.divide(BigDecimal.valueOf(2), BigDecimal.ROUND_FLOOR);
// parseInt blows up on overflow as opposed to intValue() which does not.
return Long.parseLong(bigMean.toString());
}
private static boolean fitsInLong(BigInteger big) {
return big.bitLength() <= 63;
}
@GwtIncompatible("NullPointerTester")
public void testNullPointers() {
NullPointerTester tester = new NullPointerTester();
tester.setDefault(int.class, 1);
tester.setDefault(long.class, 1L);
tester.testAllPublicStaticMethods(LongMath.class);
}
}