/* * 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 java.math.BigInteger.ONE; 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.UP; import static java.util.Arrays.asList; import com.google.common.annotations.GwtCompatible; import com.google.common.base.Function; import com.google.common.base.Predicate; import com.google.common.collect.ImmutableList; import com.google.common.collect.ImmutableSet; import com.google.common.collect.Iterables; import com.google.common.primitives.Doubles; import java.math.BigInteger; import java.math.RoundingMode; /** * Exhaustive input sets for every integral type. * * @author lowasser@google.com (Louis Wasserman) */ @GwtCompatible public class MathTesting { static final ImmutableSet<RoundingMode> ALL_ROUNDING_MODES = ImmutableSet.copyOf(RoundingMode .values()); static final ImmutableList<RoundingMode> ALL_SAFE_ROUNDING_MODES = ImmutableList.of(DOWN, UP, FLOOR, CEILING, HALF_EVEN, HALF_UP, HALF_DOWN); // Exponents to test for the pow() function. static final ImmutableList<Integer> EXPONENTS = ImmutableList.of(0, 1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 25, 30, 40, 70); /* Helper function to make a Long value from an Integer. */ private static final Function<Integer, Long> TO_LONG = new Function<Integer, Long>() { @Override public Long apply(Integer n) { return Long.valueOf(n); } }; /* Helper function to make a BigInteger value from a Long. */ private static final Function<Long, BigInteger> TO_BIGINTEGER = new Function<Long, BigInteger>() { @Override public BigInteger apply(Long n) { return BigInteger.valueOf(n); } }; private static final Function<Integer, Integer> NEGATE_INT = new Function<Integer, Integer>() { @Override public Integer apply(Integer x) { return -x; } }; private static final Function<Long, Long> NEGATE_LONG = new Function<Long, Long>() { @Override public Long apply(Long x) { return -x; } }; private static final Function<BigInteger, BigInteger> NEGATE_BIGINT = new Function<BigInteger, BigInteger>() { @Override public BigInteger apply(BigInteger x) { return x.negate(); } }; /* * This list contains values that attempt to provoke overflow in integer operations. It contains * positive values on or near 2^N for N near multiples of 8 (near byte boundaries). */ static final ImmutableSet<Integer> POSITIVE_INTEGER_CANDIDATES; static final Iterable<Integer> NEGATIVE_INTEGER_CANDIDATES; static final Iterable<Integer> NONZERO_INTEGER_CANDIDATES; static final Iterable<Integer> ALL_INTEGER_CANDIDATES; static { ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder(); // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31). intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE); // Add values up to 64. This covers cases like "square of a prime" and such. for (int i = 1; i <= 64; i++) { intValues.add(i); } // Now add values near 2^N for lots of values of N. for (int exponent : asList(2, 3, 4, 5, 6, 7, 8, 9, 15, 16, 17, 23, 24, 25)) { int x = 1 << exponent; intValues.add(x, x + 1, x - 1); } intValues.add(9999).add(10000).add(10001).add(1000000); // near powers of 10 intValues.add(5792).add(5793); // sqrt(2^25) rounded up and down POSITIVE_INTEGER_CANDIDATES = intValues.build(); NEGATIVE_INTEGER_CANDIDATES = Iterables.concat(Iterables.transform(POSITIVE_INTEGER_CANDIDATES, NEGATE_INT), ImmutableList.of(Integer.MIN_VALUE)); NONZERO_INTEGER_CANDIDATES = Iterables.concat(POSITIVE_INTEGER_CANDIDATES, NEGATIVE_INTEGER_CANDIDATES); ALL_INTEGER_CANDIDATES = Iterables.concat(NONZERO_INTEGER_CANDIDATES, ImmutableList.of(0)); } /* * This list contains values that attempt to provoke overflow in long operations. It contains * positive values on or near 2^N for N near multiples of 8 (near byte boundaries). This list is * a superset of POSITIVE_INTEGER_CANDIDATES. */ static final ImmutableSet<Long> POSITIVE_LONG_CANDIDATES; static final Iterable<Long> NEGATIVE_LONG_CANDIDATES; static final Iterable<Long> NONZERO_LONG_CANDIDATES; static final Iterable<Long> ALL_LONG_CANDIDATES; static { ImmutableSet.Builder<Long> longValues = ImmutableSet.builder(); // First of all add all the integer candidate values. longValues.addAll(Iterables.transform(POSITIVE_INTEGER_CANDIDATES, TO_LONG)); // Add boundary values manually to avoid over/under flow (this covers 2^N for 31 and 63). longValues.add(Integer.MAX_VALUE + 1L, Long.MAX_VALUE - 1L, Long.MAX_VALUE); // Now add values near 2^N for lots of values of N. for (int exponent : asList(32, 33, 39, 40, 41, 47, 48, 49, 55, 56, 57)) { long x = 1L << exponent; longValues.add(x, x + 1, x - 1); } longValues.add(194368031998L).add(194368031999L); // sqrt(2^75) rounded up and down POSITIVE_LONG_CANDIDATES = longValues.build(); NEGATIVE_LONG_CANDIDATES = Iterables.concat(Iterables.transform(POSITIVE_LONG_CANDIDATES, NEGATE_LONG), ImmutableList.of(Long.MIN_VALUE)); NONZERO_LONG_CANDIDATES = Iterables.concat(POSITIVE_LONG_CANDIDATES, NEGATIVE_LONG_CANDIDATES); ALL_LONG_CANDIDATES = Iterables.concat(NONZERO_LONG_CANDIDATES, ImmutableList.of(0L)); } /* * This list contains values that attempt to provoke overflow in big integer operations. It * contains positive values on or near 2^N for N near multiples of 8 (near byte boundaries). This * list is a superset of POSITIVE_LONG_CANDIDATES. */ static final ImmutableSet<BigInteger> POSITIVE_BIGINTEGER_CANDIDATES; static final Iterable<BigInteger> NEGATIVE_BIGINTEGER_CANDIDATES; static final Iterable<BigInteger> NONZERO_BIGINTEGER_CANDIDATES; static final Iterable<BigInteger> ALL_BIGINTEGER_CANDIDATES; static { ImmutableSet.Builder<BigInteger> bigValues = ImmutableSet.builder(); // First of all add all the long candidate values. bigValues.addAll(Iterables.transform(POSITIVE_LONG_CANDIDATES, TO_BIGINTEGER)); // Add boundary values manually to avoid over/under flow. bigValues.add(BigInteger.valueOf(Long.MAX_VALUE).add(ONE)); // Now add values near 2^N for lots of values of N. for (int exponent : asList(64, 65, 71, 72, 73, 79, 80, 81, 255, 256, 257, 511, 512, 513, Double.MAX_EXPONENT - 1, Double.MAX_EXPONENT, Double.MAX_EXPONENT + 1)) { BigInteger x = ONE.shiftLeft(exponent); bigValues.add(x, x.add(ONE), x.subtract(ONE)); } bigValues.add(new BigInteger("218838949120258359057546633")); // sqrt(2^175) rounded up and // down bigValues.add(new BigInteger("218838949120258359057546634")); POSITIVE_BIGINTEGER_CANDIDATES = bigValues.build(); NEGATIVE_BIGINTEGER_CANDIDATES = Iterables.transform(POSITIVE_BIGINTEGER_CANDIDATES, NEGATE_BIGINT); NONZERO_BIGINTEGER_CANDIDATES = Iterables.concat(POSITIVE_BIGINTEGER_CANDIDATES, NEGATIVE_BIGINTEGER_CANDIDATES); ALL_BIGINTEGER_CANDIDATES = Iterables.concat(NONZERO_BIGINTEGER_CANDIDATES, ImmutableList.of(ZERO)); } static final ImmutableSet<Double> INTEGRAL_DOUBLE_CANDIDATES; static final ImmutableSet<Double> FRACTIONAL_DOUBLE_CANDIDATES; static final Iterable<Double> FINITE_DOUBLE_CANDIDATES; static final Iterable<Double> POSITIVE_FINITE_DOUBLE_CANDIDATES; static final Iterable<Double> ALL_DOUBLE_CANDIDATES; static { ImmutableSet.Builder<Double> integralBuilder = ImmutableSet.builder(); ImmutableSet.Builder<Double> fractionalBuilder = ImmutableSet.builder(); integralBuilder.addAll(Doubles.asList(0.0, -0.0, Double.MAX_VALUE, -Double.MAX_VALUE)); // Add small multiples of MIN_VALUE and MIN_NORMAL for (int scale = 1; scale <= 4; scale++) { for (double d : Doubles.asList(Double.MIN_VALUE, Double.MIN_NORMAL)) { fractionalBuilder.add(d * scale).add(-d * scale); } } for (double d : Doubles.asList(0, 1, 2, 7, 51, 102, Math.scalb(1.0, 53), Integer.MIN_VALUE, Integer.MAX_VALUE, Long.MIN_VALUE, Long.MAX_VALUE)) { for (double delta : Doubles.asList(0.0, 1.0, 2.0)) { integralBuilder.addAll(Doubles.asList(d + delta, d - delta, -d - delta, -d + delta)); } for (double delta : Doubles.asList(0.01, 0.1, 0.25, 0.499, 0.5, 0.501, 0.7, 0.8)) { double x = d + delta; if (x != Math.round(x)) { fractionalBuilder.add(x); } } } INTEGRAL_DOUBLE_CANDIDATES = integralBuilder.build(); fractionalBuilder.add(1.414).add(1.415).add(Math.sqrt(2)); fractionalBuilder.add(5.656).add(5.657).add(4 * Math.sqrt(2)); for (double d : INTEGRAL_DOUBLE_CANDIDATES) { double x = 1 / d; if (x != Math.rint(x)) { fractionalBuilder.add(x); } } FRACTIONAL_DOUBLE_CANDIDATES = fractionalBuilder.build(); FINITE_DOUBLE_CANDIDATES = Iterables.concat(FRACTIONAL_DOUBLE_CANDIDATES, INTEGRAL_DOUBLE_CANDIDATES); POSITIVE_FINITE_DOUBLE_CANDIDATES = Iterables.filter(FINITE_DOUBLE_CANDIDATES, new Predicate<Double>() { @Override public boolean apply(Double input) { return input.doubleValue() > 0.0; } }); ALL_DOUBLE_CANDIDATES = Iterables.concat(FINITE_DOUBLE_CANDIDATES, asList(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.NaN)); } }