/*
* 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 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, 30)) {
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> INFINITIES = Doubles.asList(
Double.POSITIVE_INFINITY,
Double.NEGATIVE_INFINITY);
static final Iterable<Double> FINITE_DOUBLE_CANDIDATES;
static final Iterable<Double> POSITIVE_FINITE_DOUBLE_CANDIDATES;
static final Iterable<Double> ALL_DOUBLE_CANDIDATES;
static final Iterable<Double> DOUBLE_CANDIDATES_EXCEPT_NAN;
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;
}
});
DOUBLE_CANDIDATES_EXCEPT_NAN = Iterables.concat(FINITE_DOUBLE_CANDIDATES, INFINITIES);
ALL_DOUBLE_CANDIDATES =
Iterables.concat(DOUBLE_CANDIDATES_EXCEPT_NAN, asList(Double.NaN));
}
}