1   /*
2    * Copyright (C) 2011 The Guava Authors
3    *
4    * Licensed under the Apache License, Version 2.0 (the "License");
5    * you may not use this file except in compliance with the License.
6    * You may obtain a copy of the License at
7    *
8    * http://www.apache.org/licenses/LICENSE-2.0
9    *
10   * Unless required by applicable law or agreed to in writing, software
11   * distributed under the License is distributed on an "AS IS" BASIS,
12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13   * See the License for the specific language governing permissions and
14   * limitations under the License.
15   */
16  
17  package com.google.common.math;
18  
19  import static java.math.BigInteger.ONE;
20  import static java.math.BigInteger.ZERO;
21  import static java.math.RoundingMode.CEILING;
22  import static java.math.RoundingMode.DOWN;
23  import static java.math.RoundingMode.FLOOR;
24  import static java.math.RoundingMode.HALF_DOWN;
25  import static java.math.RoundingMode.HALF_EVEN;
26  import static java.math.RoundingMode.HALF_UP;
27  import static java.math.RoundingMode.UP;
28  import static java.util.Arrays.asList;
29  
30  import com.google.common.annotations.GwtCompatible;
31  import com.google.common.base.Function;
32  import com.google.common.base.Predicate;
33  import com.google.common.collect.ImmutableList;
34  import com.google.common.collect.ImmutableSet;
35  import com.google.common.collect.Iterables;
36  import com.google.common.primitives.Doubles;
37  
38  import java.math.BigInteger;
39  import java.math.RoundingMode;
40  
41  /**
42   * Exhaustive input sets for every integral type.
43   *
44   * @author Louis Wasserman
45   */
46  @GwtCompatible
47  public class MathTesting {
48    static final ImmutableSet<RoundingMode> ALL_ROUNDING_MODES = ImmutableSet.copyOf(RoundingMode
49        .values());
50  
51    static final ImmutableList<RoundingMode> ALL_SAFE_ROUNDING_MODES = ImmutableList.of(DOWN, UP,
52        FLOOR, CEILING, HALF_EVEN, HALF_UP, HALF_DOWN);
53  
54    // Exponents to test for the pow() function.
55    static final ImmutableList<Integer> EXPONENTS = ImmutableList.of(0, 1, 2, 3, 4, 7, 10, 15,
56        20, 25, 40, 70);
57  
58    /* Helper function to make a Long value from an Integer. */
59    private static final Function<Integer, Long> TO_LONG = new Function<Integer, Long>() {
60      @Override
61      public Long apply(Integer n) {
62        return Long.valueOf(n);
63      }
64    };
65  
66    /* Helper function to make a BigInteger value from a Long. */
67    private static final Function<Long, BigInteger> TO_BIGINTEGER =
68        new Function<Long, BigInteger>() {
69          @Override
70          public BigInteger apply(Long n) {
71            return BigInteger.valueOf(n);
72          }
73        };
74  
75    private static final Function<Integer, Integer> NEGATE_INT = new Function<Integer, Integer>() {
76      @Override
77      public Integer apply(Integer x) {
78        return -x;
79      }
80    };
81  
82    private static final Function<Long, Long> NEGATE_LONG = new Function<Long, Long>() {
83      @Override
84      public Long apply(Long x) {
85        return -x;
86      }
87    };
88  
89    private static final Function<BigInteger, BigInteger> NEGATE_BIGINT =
90        new Function<BigInteger, BigInteger>() {
91          @Override
92          public BigInteger apply(BigInteger x) {
93            return x.negate();
94          }
95        };
96  
97    /*
98     * This list contains values that attempt to provoke overflow in integer operations. It contains
99     * positive values on or near 2^N for N near multiples of 8 (near byte boundaries).
100    */
101   static final ImmutableSet<Integer> POSITIVE_INTEGER_CANDIDATES;
102 
103   static final Iterable<Integer> NEGATIVE_INTEGER_CANDIDATES;
104 
105   static final Iterable<Integer> NONZERO_INTEGER_CANDIDATES;
106 
107   static final Iterable<Integer> ALL_INTEGER_CANDIDATES;
108 
109   static {
110     ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder();
111     // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
112     intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
113     // Add values up to 40. This covers cases like "square of a prime" and such.
114     for (int i = 1; i <= 40; i++) {
115       intValues.add(i);
116     }
117     // Now add values near 2^N for lots of values of N.
118     for (int exponent : asList(2, 3, 4, 9, 15, 16, 17, 24, 25, 30)) {
119       int x = 1 << exponent;
120       intValues.add(x, x + 1, x - 1);
121     }
122     intValues.add(9999).add(10000).add(10001).add(1000000); // near powers of 10
123     intValues.add(5792).add(5793); // sqrt(2^25) rounded up and down
124     POSITIVE_INTEGER_CANDIDATES = intValues.build();
125     NEGATIVE_INTEGER_CANDIDATES = ImmutableList.copyOf(Iterables.concat(
126         Iterables.transform(POSITIVE_INTEGER_CANDIDATES, NEGATE_INT),
127         ImmutableList.of(Integer.MIN_VALUE)));
128     NONZERO_INTEGER_CANDIDATES = ImmutableList.copyOf(
129         Iterables.concat(POSITIVE_INTEGER_CANDIDATES, NEGATIVE_INTEGER_CANDIDATES));
130     ALL_INTEGER_CANDIDATES = Iterables.concat(NONZERO_INTEGER_CANDIDATES, ImmutableList.of(0));
131   }
132 
133   /*
134    * This list contains values that attempt to provoke overflow in long operations. It contains
135    * positive values on or near 2^N for N near multiples of 8 (near byte boundaries). This list is
136    * a superset of POSITIVE_INTEGER_CANDIDATES.
137    */
138   static final ImmutableSet<Long> POSITIVE_LONG_CANDIDATES;
139 
140   static final Iterable<Long> NEGATIVE_LONG_CANDIDATES;
141 
142   static final Iterable<Long> NONZERO_LONG_CANDIDATES;
143 
144   static final Iterable<Long> ALL_LONG_CANDIDATES;
145 
146   static {
147     ImmutableSet.Builder<Long> longValues = ImmutableSet.builder();
148     // First of all add all the integer candidate values.
149     longValues.addAll(Iterables.transform(POSITIVE_INTEGER_CANDIDATES, TO_LONG));
150     // Add boundary values manually to avoid over/under flow (this covers 2^N for 31 and 63).
151     longValues.add(Integer.MAX_VALUE + 1L, Long.MAX_VALUE - 1L, Long.MAX_VALUE);
152 
153     // Now add values near 2^N for lots of values of N.
154     for (int exponent : asList(32, 33, 39, 40, 41, 47, 48, 49, 55, 56, 57)) {
155       long x = 1L << exponent;
156       longValues.add(x, x + 1, x - 1);
157     }
158     longValues.add(194368031998L).add(194368031999L); // sqrt(2^75) rounded up and down
159     POSITIVE_LONG_CANDIDATES = longValues.build();
160     NEGATIVE_LONG_CANDIDATES =
161         Iterables.concat(Iterables.transform(POSITIVE_LONG_CANDIDATES, NEGATE_LONG),
162             ImmutableList.of(Long.MIN_VALUE));
163     NONZERO_LONG_CANDIDATES = Iterables.concat(POSITIVE_LONG_CANDIDATES, NEGATIVE_LONG_CANDIDATES);
164     ALL_LONG_CANDIDATES = Iterables.concat(NONZERO_LONG_CANDIDATES, ImmutableList.of(0L));
165   }
166 
167   /*
168    * This list contains values that attempt to provoke overflow in big integer operations. It
169    * contains positive values on or near 2^N for N near multiples of 8 (near byte boundaries). This
170    * list is a superset of POSITIVE_LONG_CANDIDATES.
171    */
172   static final ImmutableSet<BigInteger> POSITIVE_BIGINTEGER_CANDIDATES;
173 
174   static final Iterable<BigInteger> NEGATIVE_BIGINTEGER_CANDIDATES;
175 
176   static final Iterable<BigInteger> NONZERO_BIGINTEGER_CANDIDATES;
177 
178   static final Iterable<BigInteger> ALL_BIGINTEGER_CANDIDATES;
179 
180   static {
181     ImmutableSet.Builder<BigInteger> bigValues = ImmutableSet.builder();
182     // First of all add all the long candidate values.
183     bigValues.addAll(Iterables.transform(POSITIVE_LONG_CANDIDATES, TO_BIGINTEGER));
184     // Add boundary values manually to avoid over/under flow.
185     bigValues.add(BigInteger.valueOf(Long.MAX_VALUE).add(ONE));
186     // Now add values near 2^N for lots of values of N.
187     for (int exponent : asList(64, 65, 71, 72, 73, 79, 80, 81, 255, 256, 257, 511, 512, 513,
188         Double.MAX_EXPONENT - 1, Double.MAX_EXPONENT, Double.MAX_EXPONENT + 1)) {
189       BigInteger x = ONE.shiftLeft(exponent);
190       bigValues.add(x, x.add(ONE), x.subtract(ONE));
191     }
192     bigValues.add(new BigInteger("218838949120258359057546633")); // sqrt(2^175) rounded up and
193                                                                   // down
194     bigValues.add(new BigInteger("218838949120258359057546634"));
195     POSITIVE_BIGINTEGER_CANDIDATES = bigValues.build();
196     NEGATIVE_BIGINTEGER_CANDIDATES =
197         Iterables.transform(POSITIVE_BIGINTEGER_CANDIDATES, NEGATE_BIGINT);
198     NONZERO_BIGINTEGER_CANDIDATES =
199         Iterables.concat(POSITIVE_BIGINTEGER_CANDIDATES, NEGATIVE_BIGINTEGER_CANDIDATES);
200     ALL_BIGINTEGER_CANDIDATES =
201         Iterables.concat(NONZERO_BIGINTEGER_CANDIDATES, ImmutableList.of(ZERO));
202   }
203 
204   static final ImmutableSet<Double> INTEGRAL_DOUBLE_CANDIDATES;
205   static final ImmutableSet<Double> FRACTIONAL_DOUBLE_CANDIDATES;
206   static final Iterable<Double> INFINITIES = Doubles.asList(
207       Double.POSITIVE_INFINITY,
208       Double.NEGATIVE_INFINITY);
209   static final Iterable<Double> FINITE_DOUBLE_CANDIDATES;
210   static final Iterable<Double> POSITIVE_FINITE_DOUBLE_CANDIDATES;
211   static final Iterable<Double> ALL_DOUBLE_CANDIDATES;
212   static final Iterable<Double> DOUBLE_CANDIDATES_EXCEPT_NAN;
213   static {
214     ImmutableSet.Builder<Double> integralBuilder = ImmutableSet.builder();
215     ImmutableSet.Builder<Double> fractionalBuilder = ImmutableSet.builder();
216     integralBuilder.addAll(Doubles.asList(0.0, -0.0, Double.MAX_VALUE, -Double.MAX_VALUE));
217     // Add small multiples of MIN_VALUE and MIN_NORMAL
218     for (int scale = 1; scale <= 4; scale++) {
219       for (double d : Doubles.asList(Double.MIN_VALUE, Double.MIN_NORMAL)) {
220         fractionalBuilder.add(d * scale).add(-d * scale);
221       }
222     }
223     for (double d : Doubles.asList(0, 1, 2, 7, 51, 102, Math.scalb(1.0, 53), Integer.MIN_VALUE,
224         Integer.MAX_VALUE, Long.MIN_VALUE, Long.MAX_VALUE)) {
225       for (double delta : Doubles.asList(0.0, 1.0, 2.0)) {
226         integralBuilder.addAll(Doubles.asList(d + delta, d - delta, -d - delta, -d + delta));
227       }
228       for (double delta : Doubles.asList(0.01, 0.1, 0.25, 0.499, 0.5, 0.501, 0.7, 0.8)) {
229         double x = d + delta;
230         if (x != Math.round(x)) {
231           fractionalBuilder.add(x);
232         }
233       }
234     }
235     INTEGRAL_DOUBLE_CANDIDATES = integralBuilder.build();
236     fractionalBuilder.add(1.414).add(1.415).add(Math.sqrt(2));
237     fractionalBuilder.add(5.656).add(5.657).add(4 * Math.sqrt(2));
238     for (double d : INTEGRAL_DOUBLE_CANDIDATES) {
239       double x = 1 / d;
240       if (x != Math.rint(x)) {
241         fractionalBuilder.add(x);
242       }
243     }
244     FRACTIONAL_DOUBLE_CANDIDATES = fractionalBuilder.build();
245     FINITE_DOUBLE_CANDIDATES =
246         Iterables.concat(FRACTIONAL_DOUBLE_CANDIDATES, INTEGRAL_DOUBLE_CANDIDATES);
247     POSITIVE_FINITE_DOUBLE_CANDIDATES =
248         Iterables.filter(FINITE_DOUBLE_CANDIDATES, new Predicate<Double>() {
249           @Override
250           public boolean apply(Double input) {
251             return input.doubleValue() > 0.0;
252           }
253         });
254     DOUBLE_CANDIDATES_EXCEPT_NAN = Iterables.concat(FINITE_DOUBLE_CANDIDATES, INFINITIES);
255     ALL_DOUBLE_CANDIDATES =
256         Iterables.concat(DOUBLE_CANDIDATES_EXCEPT_NAN, asList(Double.NaN));
257   }
258 }