/*
* 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_BIGINTEGER_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.NEGATIVE_BIGINTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.NEGATIVE_INTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.NONZERO_BIGINTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.POSITIVE_BIGINTEGER_CANDIDATES;
import static java.math.BigInteger.ONE;
import static java.math.BigInteger.TEN;
import static java.math.BigInteger.ZERO;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.DOWN;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.HALF_DOWN;
import static java.math.RoundingMode.HALF_EVEN;
import static java.math.RoundingMode.HALF_UP;
import static java.math.RoundingMode.UNNECESSARY;
import static java.math.RoundingMode.UP;
import static java.util.Arrays.asList;
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 BigIntegerMath.
*
* @author Louis Wasserman
*/
@GwtCompatible(emulated = true)
public class BigIntegerMathTest extends TestCase {
@GwtIncompatible("TODO")
public void testConstantSqrt2PrecomputedBits() {
assertEquals(BigIntegerMath.sqrt(
BigInteger.ZERO.setBit(2 * BigIntegerMath.SQRT2_PRECOMPUTE_THRESHOLD + 1), FLOOR),
BigIntegerMath.SQRT2_PRECOMPUTED_BITS);
}
public void testIsPowerOfTwo() {
for (BigInteger x : ALL_BIGINTEGER_CANDIDATES) {
// Checks for a single bit set.
boolean expected = x.signum() > 0 & x.and(x.subtract(ONE)).equals(ZERO);
assertEquals(expected, BigIntegerMath.isPowerOfTwo(x));
}
}
public void testLog2ZeroAlwaysThrows() {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.log2(ZERO, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
public void testLog2NegativeAlwaysThrows() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.log2(x.negate(), mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
public void testLog2Floor() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(FLOOR, DOWN)) {
int result = BigIntegerMath.log2(x, mode);
assertTrue(ZERO.setBit(result).compareTo(x) <= 0);
assertTrue(ZERO.setBit(result + 1).compareTo(x) > 0);
}
}
}
public void testLog2Ceiling() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(CEILING, UP)) {
int result = BigIntegerMath.log2(x, mode);
assertTrue(ZERO.setBit(result).compareTo(x) >= 0);
assertTrue(result == 0 || ZERO.setBit(result - 1).compareTo(x) < 0);
}
}
}
// Relies on the correctness of isPowerOfTwo(BigInteger).
public void testLog2Exact() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
// We only expect an exception if x was not a power of 2.
boolean isPowerOf2 = BigIntegerMath.isPowerOfTwo(x);
try {
assertEquals(x, ZERO.setBit(BigIntegerMath.log2(x, UNNECESSARY)));
assertTrue(isPowerOf2);
} catch (ArithmeticException e) {
assertFalse(isPowerOf2);
}
}
}
public void testLog2HalfUp() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int result = BigIntegerMath.log2(x, HALF_UP);
BigInteger x2 = x.pow(2);
// x^2 < 2^(2 * result + 1), or else we would have rounded up
assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) > 0);
// x^2 >= 2^(2 * result - 1), or else we would have rounded down
assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
}
}
public void testLog2HalfDown() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int result = BigIntegerMath.log2(x, HALF_DOWN);
BigInteger x2 = x.pow(2);
// x^2 <= 2^(2 * result + 1), or else we would have rounded up
assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) >= 0);
// x^2 > 2^(2 * result - 1), or else we would have rounded down
assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) < 0);
}
}
// Relies on the correctness of log2(BigInteger, {HALF_UP,HALF_DOWN}).
public void testLog2HalfEven() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int halfEven = BigIntegerMath.log2(x, HALF_EVEN);
// Now figure out what rounding mode we should behave like (it depends if FLOOR was
// odd/even).
boolean floorWasEven = (BigIntegerMath.log2(x, FLOOR) & 1) == 0;
assertEquals(BigIntegerMath.log2(x, floorWasEven ? HALF_DOWN : HALF_UP), halfEven);
}
}
@GwtIncompatible("TODO")
public void testLog10ZeroAlwaysThrows() {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.log10(ZERO, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("TODO")
public void testLog10NegativeAlwaysThrows() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.log10(x.negate(), mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
@GwtIncompatible("TODO")
public void testLog10Floor() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(FLOOR, DOWN)) {
int result = BigIntegerMath.log10(x, mode);
assertTrue(TEN.pow(result).compareTo(x) <= 0);
assertTrue(TEN.pow(result + 1).compareTo(x) > 0);
}
}
}
@GwtIncompatible("TODO")
public void testLog10Ceiling() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(CEILING, UP)) {
int result = BigIntegerMath.log10(x, mode);
assertTrue(TEN.pow(result).compareTo(x) >= 0);
assertTrue(result == 0 || TEN.pow(result - 1).compareTo(x) < 0);
}
}
}
// Relies on the correctness of log10(BigInteger, FLOOR).
@GwtIncompatible("TODO")
public void testLog10Exact() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int logFloor = BigIntegerMath.log10(x, FLOOR);
boolean expectSuccess = TEN.pow(logFloor).equals(x);
try {
assertEquals(logFloor, BigIntegerMath.log10(x, UNNECESSARY));
assertTrue(expectSuccess);
} catch (ArithmeticException e) {
assertFalse(expectSuccess);
}
}
}
@GwtIncompatible("TODO")
public void testLog10HalfUp() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int result = BigIntegerMath.log10(x, HALF_UP);
BigInteger x2 = x.pow(2);
// x^2 < 10^(2 * result + 1), or else we would have rounded up
assertTrue(TEN.pow(2 * result + 1).compareTo(x2) > 0);
// x^2 >= 10^(2 * result - 1), or else we would have rounded down
assertTrue(result == 0 || TEN.pow(2 * result - 1).compareTo(x2) <= 0);
}
}
@GwtIncompatible("TODO")
public void testLog10HalfDown() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int result = BigIntegerMath.log10(x, HALF_DOWN);
BigInteger x2 = x.pow(2);
// x^2 <= 10^(2 * result + 1), or else we would have rounded up
assertTrue(TEN.pow(2 * result + 1).compareTo(x2) >= 0);
// x^2 > 10^(2 * result - 1), or else we would have rounded down
assertTrue(result == 0 || TEN.pow(2 * result - 1).compareTo(x2) < 0);
}
}
// Relies on the correctness of log10(BigInteger, {HALF_UP,HALF_DOWN}).
@GwtIncompatible("TODO")
public void testLog10HalfEven() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
int halfEven = BigIntegerMath.log10(x, HALF_EVEN);
// Now figure out what rounding mode we should behave like (it depends if FLOOR was
// odd/even).
boolean floorWasEven = (BigIntegerMath.log10(x, FLOOR) & 1) == 0;
assertEquals(BigIntegerMath.log10(x, floorWasEven ? HALF_DOWN : HALF_UP), halfEven);
}
}
@GwtIncompatible("TODO")
public void testLog10TrivialOnPowerOf10() {
BigInteger x = BigInteger.TEN.pow(100);
for (RoundingMode mode : ALL_ROUNDING_MODES) {
assertEquals(100, BigIntegerMath.log10(x, mode));
}
}
@GwtIncompatible("TODO")
public void testSqrtZeroAlwaysZero() {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
assertEquals(ZERO, BigIntegerMath.sqrt(ZERO, mode));
}
}
@GwtIncompatible("TODO")
public void testSqrtNegativeAlwaysThrows() {
for (BigInteger x : NEGATIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.sqrt(x, mode);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
}
@GwtIncompatible("TODO")
public void testSqrtFloor() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(FLOOR, DOWN)) {
BigInteger result = BigIntegerMath.sqrt(x, mode);
assertTrue(result.compareTo(ZERO) > 0);
assertTrue(result.pow(2).compareTo(x) <= 0);
assertTrue(result.add(ONE).pow(2).compareTo(x) > 0);
}
}
}
@GwtIncompatible("TODO")
public void testSqrtCeiling() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : asList(CEILING, UP)) {
BigInteger result = BigIntegerMath.sqrt(x, mode);
assertTrue(result.compareTo(ZERO) > 0);
assertTrue(result.pow(2).compareTo(x) >= 0);
assertTrue(result.signum() == 0 || result.subtract(ONE).pow(2).compareTo(x) < 0);
}
}
}
// Relies on the correctness of sqrt(BigInteger, FLOOR).
@GwtIncompatible("TODO")
public void testSqrtExact() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
BigInteger floor = BigIntegerMath.sqrt(x, FLOOR);
// We only expect an exception if x was not a perfect square.
boolean isPerfectSquare = floor.pow(2).equals(x);
try {
assertEquals(floor, BigIntegerMath.sqrt(x, UNNECESSARY));
assertTrue(isPerfectSquare);
} catch (ArithmeticException e) {
assertFalse(isPerfectSquare);
}
}
}
@GwtIncompatible("TODO")
public void testSqrtHalfUp() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
BigInteger result = BigIntegerMath.sqrt(x, HALF_UP);
BigInteger plusHalfSquared = result.pow(2).add(result).shiftLeft(2).add(ONE);
BigInteger x4 = x.shiftLeft(2);
// sqrt(x) < result + 0.5, so 4 * x < (result + 0.5)^2 * 4
// (result + 0.5)^2 * 4 = (result^2 + result)*4 + 1
assertTrue(x4.compareTo(plusHalfSquared) < 0);
BigInteger minusHalfSquared = result.pow(2).subtract(result).shiftLeft(2).add(ONE);
// sqrt(x) > result - 0.5, so 4 * x > (result - 0.5)^2 * 4
// (result - 0.5)^2 * 4 = (result^2 - result)*4 + 1
assertTrue(result.equals(ZERO) || x4.compareTo(minusHalfSquared) >= 0);
}
}
@GwtIncompatible("TODO")
public void testSqrtHalfDown() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
BigInteger result = BigIntegerMath.sqrt(x, HALF_DOWN);
BigInteger plusHalfSquared = result.pow(2).add(result).shiftLeft(2).add(ONE);
BigInteger x4 = x.shiftLeft(2);
// sqrt(x) <= result + 0.5, so 4 * x <= (result + 0.5)^2 * 4
// (result + 0.5)^2 * 4 = (result^2 + result)*4 + 1
assertTrue(x4.compareTo(plusHalfSquared) <= 0);
BigInteger minusHalfSquared = result.pow(2).subtract(result).shiftLeft(2).add(ONE);
// sqrt(x) > result - 0.5, so 4 * x > (result - 0.5)^2 * 4
// (result - 0.5)^2 * 4 = (result^2 - result)*4 + 1
assertTrue(result.equals(ZERO) || x4.compareTo(minusHalfSquared) > 0);
}
}
// Relies on the correctness of sqrt(BigInteger, {HALF_UP,HALF_DOWN}).
@GwtIncompatible("TODO")
public void testSqrtHalfEven() {
for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
BigInteger halfEven = BigIntegerMath.sqrt(x, HALF_EVEN);
// Now figure out what rounding mode we should behave like (it depends if FLOOR was
// odd/even).
boolean floorWasOdd = BigIntegerMath.sqrt(x, FLOOR).testBit(0);
assertEquals(BigIntegerMath.sqrt(x, floorWasOdd ? HALF_UP : HALF_DOWN), halfEven);
}
}
@GwtIncompatible("TODO")
public void testDivNonZero() {
for (BigInteger p : NONZERO_BIGINTEGER_CANDIDATES) {
for (BigInteger q : NONZERO_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
BigInteger expected =
new BigDecimal(p).divide(new BigDecimal(q), 0, mode).toBigIntegerExact();
assertEquals(expected, BigIntegerMath.divide(p, q, mode));
}
}
}
}
@GwtIncompatible("TODO")
public void testDivNonZeroExact() {
for (BigInteger p : NONZERO_BIGINTEGER_CANDIDATES) {
for (BigInteger q : NONZERO_BIGINTEGER_CANDIDATES) {
boolean dividesEvenly = p.remainder(q).equals(ZERO);
try {
assertEquals(p, BigIntegerMath.divide(p, q, UNNECESSARY).multiply(q));
assertTrue(dividesEvenly);
} catch (ArithmeticException e) {
assertFalse(dividesEvenly);
}
}
}
}
@GwtIncompatible("TODO")
public void testZeroDivIsAlwaysZero() {
for (BigInteger q : NONZERO_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
assertEquals(ZERO, BigIntegerMath.divide(ZERO, q, mode));
}
}
}
@GwtIncompatible("TODO")
public void testDivByZeroAlwaysFails() {
for (BigInteger p : ALL_BIGINTEGER_CANDIDATES) {
for (RoundingMode mode : ALL_ROUNDING_MODES) {
try {
BigIntegerMath.divide(p, ZERO, mode);
fail("Expected ArithmeticException");
} catch (ArithmeticException expected) {}
}
}
}
public void testFactorial() {
BigInteger expected = BigInteger.ONE;
for (int i = 1; i <= 300; i++) {
expected = expected.multiply(BigInteger.valueOf(i));
assertEquals(expected, BigIntegerMath.factorial(i));
}
}
public void testFactorial0() {
assertEquals(BigInteger.ONE, BigIntegerMath.factorial(0));
}
public void testFactorialNegative() {
for (int n : NEGATIVE_INTEGER_CANDIDATES) {
try {
BigIntegerMath.factorial(n);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
public void testBinomialSmall() {
runBinomialTest(0, 30);
}
@GwtIncompatible("too slow")
public void testBinomialLarge() {
runBinomialTest(31, 100);
}
// Depends on the correctness of BigIntegerMath.factorial
private static void runBinomialTest(int firstN, int lastN) {
for (int n = firstN; n <= lastN; n++) {
for (int k = 0; k <= n; k++) {
BigInteger expected = BigIntegerMath
.factorial(n)
.divide(BigIntegerMath.factorial(k))
.divide(BigIntegerMath.factorial(n - k));
assertEquals(expected, BigIntegerMath.binomial(n, k));
}
}
}
public void testBinomialOutside() {
for (int n = 0; n <= 50; n++) {
try {
BigIntegerMath.binomial(n, -1);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
try {
BigIntegerMath.binomial(n, n + 1);
fail("Expected IllegalArgumentException");
} catch (IllegalArgumentException expected) {}
}
}
@GwtIncompatible("NullPointerTester")
public void testNullPointers() {
NullPointerTester tester = new NullPointerTester();
tester.setDefault(BigInteger.class, ONE);
tester.setDefault(RoundingMode.class, FLOOR);
tester.setDefault(int.class, 1);
tester.setDefault(long.class, 1L);
tester.testAllPublicStaticMethods(BigIntegerMath.class);
}
}