/* * 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.testing.NullPointerTester; import junit.framework.TestCase; import java.math.BigDecimal; import java.math.BigInteger; import java.math.RoundingMode; /** * Tests for LongMath. * * @author Louis Wasserman */ public class LongMathTest extends TestCase { public void testConstantMaxPowerOfSqrt2Unsigned() { assertEquals(BigIntegerMath.sqrt(BigInteger.ZERO.setBit(2 * Long.SIZE - 1), FLOOR).longValue(), LongMath.MAX_POWER_OF_SQRT2_UNSIGNED); } public void testConstantsPowersOf10() { for (int i = 0; i < LongMath.POWERS_OF_10.length; i++) { assertEquals(LongMath.checkedPow(10, i), LongMath.POWERS_OF_10[i]); } try { LongMath.checkedPow(10, LongMath.POWERS_OF_10.length); fail("Expected ArithmeticException"); } catch (ArithmeticException expected) {} } public void testConstantsHalfPowersOf10() { for (int i = 0; i < LongMath.HALF_POWERS_OF_10.length; i++) { assertEquals(BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * i + 1), FLOOR), BigInteger.valueOf(LongMath.HALF_POWERS_OF_10[i])); } BigInteger nextBigger = BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * LongMath.HALF_POWERS_OF_10.length + 1), FLOOR); assertTrue(nextBigger.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0); } public void testConstantsSqrtMaxLong() { assertEquals(LongMath.sqrt(Long.MAX_VALUE, FLOOR), LongMath.FLOOR_SQRT_MAX_LONG); } 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) {} } public void testConstantsBiggestBinomials() { for (int k = 0; k < LongMath.BIGGEST_BINOMIALS.length; k++) { assertTrue(fitsInLong(BigIntegerMath.binomial(LongMath.BIGGEST_BINOMIALS[k], k))); assertTrue(LongMath.BIGGEST_BINOMIALS[k] == Integer.MAX_VALUE || !fitsInLong(BigIntegerMath.binomial(LongMath.BIGGEST_BINOMIALS[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.BIGGEST_BINOMIALS.length; assertFalse(fitsInLong(BigIntegerMath.binomial(2 * k, k))); // 2 * k is the smallest value for which we don't replace k with (n-k). } public void testConstantsBiggestSimpleBinomials() { for (int k = 0; k < LongMath.BIGGEST_SIMPLE_BINOMIALS.length; k++) { assertTrue(LongMath.BIGGEST_SIMPLE_BINOMIALS[k] <= LongMath.BIGGEST_BINOMIALS[k]); simpleBinomial(LongMath.BIGGEST_SIMPLE_BINOMIALS[k], k); // mustn't throw if (LongMath.BIGGEST_SIMPLE_BINOMIALS[k] < Integer.MAX_VALUE) { // unless all n are fair game with this k try { simpleBinomial(LongMath.BIGGEST_SIMPLE_BINOMIALS[k] + 1, k); fail("Expected ArithmeticException"); } catch (ArithmeticException expected) {} } } try { int k = LongMath.BIGGEST_SIMPLE_BINOMIALS.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) {} } // Throws an ArithmeticException if "the simple implementation" of binomial coefficients overflows 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; } public void testIsPowerOfTwo() { for (long x : ALL_LONG_CANDIDATES) { // Checks for a single bit set. boolean expected = x > 0 & (x & (x - 1)) == 0L; 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); } } } public void testLog10ZeroAlwaysThrows() { for (RoundingMode mode : ALL_ROUNDING_MODES) { try { LongMath.log10(0L, mode); fail("Expected IllegalArgumentException"); } catch (IllegalArgumentException expected) {} } } 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. 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). 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); } } } public void testLog10TrivialOnPowerOf10() { long x = 1000000000000L; for (RoundingMode mode : ALL_ROUNDING_MODES) { assertEquals(12, LongMath.log10(x, mode)); } } 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. 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). */ public void testSqrtExactMatchesFloorOrThrows() { for (long x : POSITIVE_LONG_CANDIDATES) { long logFloor = LongMath.sqrt(x, FLOOR); // We only expect an exception if x was not a perfect square. boolean isPerfectSquare = (logFloor * logFloor == x); try { assertEquals(logFloor, LongMath.sqrt(x, UNNECESSARY)); assertTrue(isPerfectSquare); } catch (ArithmeticException e) { assertFalse(isPerfectSquare); } } } public void testPow() { for (long i : ALL_LONG_CANDIDATES) { for (int exp : EXPONENTS) { assertEquals(LongMath.pow(i, exp), valueOf(i) .pow(exp) .longValue()); } } } 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)); } } } } 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); } } } } public void testZeroDivIsAlwaysZero() { for (long q : NONZERO_LONG_CANDIDATES) { for (RoundingMode mode : ALL_ROUNDING_MODES) { assertEquals(0L, LongMath.divide(0L, q, mode)); } } } 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) {} } } } 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)); } } } 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) {} } } } public void testIntModZeroModulusFails() { for (long x : ALL_LONG_CANDIDATES) { try { LongMath.mod(x, 0); fail("Expected AE"); } catch (ArithmeticException expected) {} } } 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)); } } } 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 testGCD() { for (long a : POSITIVE_LONG_CANDIDATES) { for (long b : POSITIVE_LONG_CANDIDATES) { assertEquals(valueOf(a).gcd(valueOf(b)), valueOf(LongMath.gcd(a, b))); } } } 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)); } 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) {} } } 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) {} } } 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); } } } } 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); } } } } 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); } } } } 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. 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)); } } 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)); } } } 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) {} } } private boolean fitsInLong(BigInteger big) { return big.bitLength() <= 63; } public void testNullPointers() throws Exception { NullPointerTester tester = new NullPointerTester(); tester.setDefault(RoundingMode.class, FLOOR); tester.setDefault(int.class, 1); tester.setDefault(long.class, 1L); tester.testAllPublicStaticMethods(LongMath.class); } }