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     * <p>When the input is an empty array, the result is zero.
097     *
098     * @param values Values.
099     * @return {@code IntSumOfSquares} instance.
100     */
101    public static IntSumOfSquares of(int... values) {
102        return createFromRange(values, 0, values.length);
103    }
104
105    /**
106     * Returns an instance populated using the specified range of {@code values}.
107     *
108     * <p>When the range is empty, the result is zero.
109     *
110     * @param values Values.
111     * @param from Inclusive start of the range.
112     * @param to Exclusive end of the range.
113     * @return {@code IntSumOfSquares} instance.
114     * @throws IndexOutOfBoundsException if the sub-range is out of bounds
115     * @since 1.2
116     */
117    public static IntSumOfSquares ofRange(int[] values, int from, int to) {
118        Statistics.checkFromToIndex(from, to, values.length);
119        return createFromRange(values, from, to);
120    }
121
122    /**
123     * Create an instance using the specified range of {@code values}.
124     *
125     * <p>Warning: No range checks are performed.
126     *
127     * @param values Values.
128     * @param from Inclusive start of the range.
129     * @param to Exclusive end of the range.
130     * @return {@code IntSumOfSquares} instance.
131     */
132    static IntSumOfSquares createFromRange(int[] values, int from, int to) {
133        // Small arrays can be processed using the object
134        final int length = to - from;
135        if (length < SMALL_SAMPLE) {
136            final IntSumOfSquares stat = new IntSumOfSquares();
137            for (int i = from; i < to; i++) {
138                stat.accept(values[i]);
139            }
140            return stat;
141        }
142
143        // Arrays can be processed using specialised counts knowing the maximum limit
144        // for an array is 2^31 values.
145        final UInt96 ss = UInt96.create();
146        // Process pairs as we know two maximum value int^2 will not overflow
147        // an unsigned long.
148        final int end = from + (length & ~0x1);
149        for (int i = from; i < end; i += 2) {
150            final long x = values[i];
151            final long y = values[i + 1];
152            ss.addPositive(x * x + y * y);
153        }
154        if (end < to) {
155            final long x = values[end];
156            ss.addPositive(x * x);
157        }
158
159        // Convert
160        return new IntSumOfSquares(UInt128.of(ss));
161    }
162
163    /**
164     * Gets the sum of squares.
165     *
166     * <p>This is package private for use in {@link IntStatistics}.
167     *
168     * @return the sum of squares
169     */
170    UInt128 getSumOfSquares() {
171        return sumSq;
172    }
173
174    /**
175     * Updates the state of the statistic to reflect the addition of {@code value}.
176     *
177     * @param value Value.
178     */
179    @Override
180    public void accept(int value) {
181        sumSq.addPositive((long) value * value);
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>Warning: This will raise an {@link ArithmeticException}
190     * if the result is not within the range {@code [0, 2^31)}.
191     *
192     * @return sum of all values.
193     * @throws ArithmeticException if the {@code result} overflows an {@code int}
194     * @see #getAsBigInteger()
195     */
196    @Override
197    public int getAsInt() {
198        return sumSq.toIntExact();
199    }
200
201    /**
202     * Gets the sum of squares of all input values.
203     *
204     * <p>When no values have been added, the result is zero.
205     *
206     * <p>Warning: This will raise an {@link ArithmeticException}
207     * if the result is not within the range {@code [0, 2^63)}.
208     *
209     * @return sum of all values.
210     * @throws ArithmeticException if the {@code result} overflows a {@code long}
211     * @see #getAsBigInteger()
212     */
213    @Override
214    public long getAsLong() {
215        return sumSq.toLongExact();
216    }
217
218    /**
219     * Gets the sum of squares of all input values.
220     *
221     * <p>When no values have been added, the result is zero.
222     *
223     * <p>Note that this conversion can lose information about the precision of the
224     * {@code BigInteger} value.
225     *
226     * @return sum of squares of all values.
227     * @see #getAsBigInteger()
228     */
229    @Override
230    public double getAsDouble() {
231        return sumSq.toDouble();
232    }
233
234    /**
235     * Gets the sum of squares of all input values.
236     *
237     * <p>When no values have been added, the result is zero.
238     *
239     * @return sum of squares of all values.
240     */
241    @Override
242    public BigInteger getAsBigInteger() {
243        return sumSq.toBigInteger();
244    }
245
246    @Override
247    public IntSumOfSquares combine(IntSumOfSquares other) {
248        sumSq.add(other.sumSq);
249        return this;
250    }
251}