001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.statistics.descriptive;
018
019import java.math.BigInteger;
020
021/**
022 * Returns the sum of the squares of the available values. Uses the following definition:
023 *
024 * <p>\[ \sum_{i=1}^n x_i^2 \]
025 *
026 * <p>where \( n \) is the number of samples.
027 *
028 * <ul>
029 *   <li>The result is zero if no values are observed.
030 * </ul>
031 *
032 * <p>The implementation uses an exact integer sum to compute the sum of squared values.
033 * The exact sum is returned using {@link #getAsBigInteger()}. Methods that return {@code int} or
034 * {@code long} primitives will raise an exception if the result overflows.
035 *
036 * <p>Note that the implementation does not use {@code BigInteger} arithmetic; for
037 * performance the sum is computed using primitives to create an unsigned 128-bit integer.
038 * Support is provided for at least 2<sup>63</sup> observations.
039 *
040 * <p>This class is designed to work with (though does not require)
041 * {@linkplain java.util.stream streams}.
042 *
043 * <p><strong>This implementation is not thread safe.</strong>
044 * If multiple threads access an instance of this class concurrently,
045 * and at least one of the threads invokes the {@link java.util.function.IntConsumer#accept(int) accept} or
046 * {@link StatisticAccumulator#combine(StatisticResult) combine} method, it must be synchronized externally.
047 *
048 * <p>However, it is safe to use {@link java.util.function.IntConsumer#accept(int) accept}
049 * and {@link StatisticAccumulator#combine(StatisticResult) combine}
050 * as {@code accumulator} and {@code combiner} functions of
051 * {@link java.util.stream.Collector Collector} on a parallel stream,
052 * because the parallel implementation of {@link java.util.stream.Stream#collect Stream.collect()}
053 * provides the necessary partitioning, isolation, and merging of results for
054 * safe and efficient parallel execution.
055 *
056 * @since 1.1
057 */
058public final class IntSumOfSquares implements IntStatistic, StatisticAccumulator<IntSumOfSquares> {
059    /** Small array sample size.
060     * Used to avoid computing with UInt96 then converting to UInt128. */
061    private static final int SMALL_SAMPLE = 10;
062
063    /** Sum of the squared values. */
064    private final UInt128 sumSq;
065
066    /**
067     * Create an instance.
068     */
069    private IntSumOfSquares() {
070        this(UInt128.create());
071    }
072
073    /**
074     * Create an instance.
075     *
076     * @param sumSq Sum of the squared values.
077     */
078    private IntSumOfSquares(UInt128 sumSq) {
079        this.sumSq = sumSq;
080    }
081
082    /**
083     * Creates an instance.
084     *
085     * <p>The initial result is zero.
086     *
087     * @return {@code IntSumOfSquares} instance.
088     */
089    public static IntSumOfSquares create() {
090        return new IntSumOfSquares();
091    }
092
093    /**
094     * Returns an instance populated using the input {@code values}.
095     *
096     * @param values Values.
097     * @return {@code IntSumOfSquares} instance.
098     */
099    public static IntSumOfSquares of(int... values) {
100        // Small arrays can be processed using the object
101        if (values.length < SMALL_SAMPLE) {
102            final IntSumOfSquares stat = new IntSumOfSquares();
103            for (final int x : values) {
104                stat.accept(x);
105            }
106            return stat;
107        }
108
109        // Arrays can be processed using specialised counts knowing the maximum limit
110        // for an array is 2^31 values.
111        final UInt96 ss = UInt96.create();
112        // Process pairs as we know two maximum value int^2 will not overflow
113        // an unsigned long.
114        final int end = values.length & ~0x1;
115        for (int i = 0; i < end; i += 2) {
116            final long x = values[i];
117            final long y = values[i + 1];
118            ss.addPositive(x * x + y * y);
119        }
120        if (end < values.length) {
121            final long x = values[end];
122            ss.addPositive(x * x);
123        }
124
125        // Convert
126        return new IntSumOfSquares(UInt128.of(ss));
127    }
128
129    /**
130     * Gets the sum of squares.
131     *
132     * <p>This is package private for use in {@link IntStatistics}.
133     *
134     * @return the sum of squares
135     */
136    UInt128 getSumOfSquares() {
137        return sumSq;
138    }
139
140    /**
141     * Updates the state of the statistic to reflect the addition of {@code value}.
142     *
143     * @param value Value.
144     */
145    @Override
146    public void accept(int value) {
147        sumSq.addPositive((long) value * value);
148    }
149
150    /**
151     * Gets the sum of squares of all input values.
152     *
153     * <p>When no values have been added, the result is zero.
154     *
155     * <p>Warning: This will raise an {@link ArithmeticException}
156     * if the result is not within the range {@code [0, 2^31)}.
157     *
158     * @return sum of all values.
159     * @throws ArithmeticException if the {@code result} overflows an {@code int}
160     * @see #getAsBigInteger()
161     */
162    @Override
163    public int getAsInt() {
164        return sumSq.toIntExact();
165    }
166
167    /**
168     * Gets the sum of squares of all input values.
169     *
170     * <p>When no values have been added, the result is zero.
171     *
172     * <p>Warning: This will raise an {@link ArithmeticException}
173     * if the result is not within the range {@code [0, 2^63)}.
174     *
175     * @return sum of all values.
176     * @throws ArithmeticException if the {@code result} overflows a {@code long}
177     * @see #getAsBigInteger()
178     */
179    @Override
180    public long getAsLong() {
181        return sumSq.toLongExact();
182    }
183
184    /**
185     * Gets the sum of squares of all input values.
186     *
187     * <p>When no values have been added, the result is zero.
188     *
189     * <p>Note that this conversion can lose information about the precision of the
190     * {@code BigInteger} value.
191     *
192     * @return sum of squares of all values.
193     * @see #getAsBigInteger()
194     */
195    @Override
196    public double getAsDouble() {
197        return sumSq.toDouble();
198    }
199
200    /**
201     * Gets the sum of squares of all input values.
202     *
203     * <p>When no values have been added, the result is zero.
204     *
205     * @return sum of squares of all values.
206     */
207    @Override
208    public BigInteger getAsBigInteger() {
209        return sumSq.toBigInteger();
210    }
211
212    @Override
213    public IntSumOfSquares combine(IntSumOfSquares other) {
214        sumSq.add(other.sumSq);
215        return this;
216    }
217}