1 /* 2 * Copyright (c) 2012, 2020, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 /** 27 * Classes to support functional-style operations on streams of elements, such 28 * as map-reduce transformations on collections. For example: 29 * 30 * <pre>{@code 31 * int sum = widgets.stream() 32 * .filter(b -> b.getColor() == RED) 33 * .mapToInt(b -> b.getWeight()) 34 * .sum(); 35 * }</pre> 36 * 37 * <p>Here we use {@code widgets}, a {@code Collection<Widget>}, 38 * as a source for a stream, and then perform a filter-map-reduce on the stream 39 * to obtain the sum of the weights of the red widgets. (Summation is an 40 * example of a <a href="package-summary.html#Reduction">reduction</a> 41 * operation.) 42 * 43 * <p>The key abstraction introduced in this package is <em>stream</em>. The 44 * classes {@link java.util.stream.Stream}, {@link java.util.stream.IntStream}, 45 * {@link java.util.stream.LongStream}, and {@link java.util.stream.DoubleStream} 46 * are streams over objects and the primitive {@code int}, {@code long} and 47 * {@code double} types. Streams differ from collections in several ways: 48 * 49 * <ul> 50 * <li>No storage. A stream is not a data structure that stores elements; 51 * instead, it conveys elements from a source such as a data structure, 52 * an array, a generator function, or an I/O channel, through a pipeline of 53 * computational operations.</li> 54 * <li>Functional in nature. An operation on a stream produces a result, 55 * but does not modify its source. For example, filtering a {@code Stream} 56 * obtained from a collection produces a new {@code Stream} without the 57 * filtered elements, rather than removing elements from the source 58 * collection.</li> 59 * <li>Laziness-seeking. Many stream operations, such as filtering, mapping, 60 * or duplicate removal, can be implemented lazily, exposing opportunities 61 * for optimization. For example, "find the first {@code String} with 62 * three consecutive vowels" need not examine all the input strings. 63 * Stream operations are divided into intermediate ({@code Stream}-producing) 64 * operations and terminal (value- or side-effect-producing) operations. 65 * Intermediate operations are always lazy.</li> 66 * <li>Possibly unbounded. While collections have a finite size, streams 67 * need not. Short-circuiting operations such as {@code limit(n)} or 68 * {@code findFirst()} can allow computations on infinite streams to 69 * complete in finite time.</li> 70 * <li>Consumable. The elements of a stream are only visited once during 71 * the life of a stream. Like an {@link java.util.Iterator}, a new stream 72 * must be generated to revisit the same elements of the source. 73 * </li> 74 * </ul> 75 * 76 * Streams can be obtained in a number of ways. Some examples include: 77 * <ul> 78 * <li>From a {@link java.util.Collection} via the {@code stream()} and 79 * {@code parallelStream()} methods;</li> 80 * <li>From an array via {@link java.util.Arrays#stream(Object[])};</li> 81 * <li>From static factory methods on the stream classes, such as 82 * {@link java.util.stream.Stream#of(Object[])}, 83 * {@link java.util.stream.IntStream#range(int, int)} 84 * or {@link java.util.stream.Stream#iterate(Object, UnaryOperator)};</li> 85 * <li>The lines of a file can be obtained from {@link java.io.BufferedReader#lines()};</li> 86 * <li>Streams of file paths can be obtained from methods in {@link java.nio.file.Files};</li> 87 * <li>Streams of random numbers can be obtained from {@link java.util.Random#ints()};</li> 88 * <li>Numerous other stream-bearing methods in the JDK, including 89 * {@link java.util.BitSet#stream()}, 90 * {@link java.util.regex.Pattern#splitAsStream(java.lang.CharSequence)}, 91 * and {@link java.util.jar.JarFile#stream()}.</li> 92 * </ul> 93 * 94 * <p>Additional stream sources can be provided by third-party libraries using 95 * <a href="package-summary.html#StreamSources">these techniques</a>. 96 * 97 * <h2><a id="StreamOps">Stream operations and pipelines</a></h2> 98 * 99 * <p>Stream operations are divided into <em>intermediate</em> and 100 * <em>terminal</em> operations, and are combined to form <em>stream 101 * pipelines</em>. A stream pipeline consists of a source (such as a 102 * {@code Collection}, an array, a generator function, or an I/O channel); 103 * followed by zero or more intermediate operations such as 104 * {@code Stream.filter} or {@code Stream.map}; and a terminal operation such 105 * as {@code Stream.forEach} or {@code Stream.reduce}. 106 * 107 * <p>Intermediate operations return a new stream. They are always 108 * <em>lazy</em>; executing an intermediate operation such as 109 * {@code filter()} does not actually perform any filtering, but instead 110 * creates a new stream that, when traversed, contains the elements of 111 * the initial stream that match the given predicate. Traversal 112 * of the pipeline source does not begin until the terminal operation of the 113 * pipeline is executed. 114 * 115 * <p>Terminal operations, such as {@code Stream.forEach} or 116 * {@code IntStream.sum}, may traverse the stream to produce a result or a 117 * side-effect. After the terminal operation is performed, the stream pipeline 118 * is considered consumed, and can no longer be used; if you need to traverse 119 * the same data source again, you must return to the data source to get a new 120 * stream. In almost all cases, terminal operations are <em>eager</em>, 121 * completing their traversal of the data source and processing of the pipeline 122 * before returning. Only the terminal operations {@code iterator()} and 123 * {@code spliterator()} are not; these are provided as an "escape hatch" to enable 124 * arbitrary client-controlled pipeline traversals in the event that the 125 * existing operations are not sufficient to the task. 126 * 127 * <p> Processing streams lazily allows for significant efficiencies; in a 128 * pipeline such as the filter-map-sum example above, filtering, mapping, and 129 * summing can be fused into a single pass on the data, with minimal 130 * intermediate state. Laziness also allows avoiding examining all the data 131 * when it is not necessary; for operations such as "find the first string 132 * longer than 1000 characters", it is only necessary to examine just enough 133 * strings to find one that has the desired characteristics without examining 134 * all of the strings available from the source. (This behavior becomes even 135 * more important when the input stream is infinite and not merely large.) 136 * 137 * <p>Intermediate operations are further divided into <em>stateless</em> 138 * and <em>stateful</em> operations. Stateless operations, such as {@code filter} 139 * and {@code map}, retain no state from previously seen element when processing 140 * a new element -- each element can be processed 141 * independently of operations on other elements. Stateful operations, such as 142 * {@code distinct} and {@code sorted}, may incorporate state from previously 143 * seen elements when processing new elements. 144 * 145 * <p>Stateful operations may need to process the entire input 146 * before producing a result. For example, one cannot produce any results from 147 * sorting a stream until one has seen all elements of the stream. As a result, 148 * under parallel computation, some pipelines containing stateful intermediate 149 * operations may require multiple passes on the data or may need to buffer 150 * significant data. Pipelines containing exclusively stateless intermediate 151 * operations can be processed in a single pass, whether sequential or parallel, 152 * with minimal data buffering. 153 * 154 * <p>Further, some operations are deemed <em>short-circuiting</em> operations. 155 * An intermediate operation is short-circuiting if, when presented with 156 * infinite input, it may produce a finite stream as a result. A terminal 157 * operation is short-circuiting if, when presented with infinite input, it may 158 * terminate in finite time. Having a short-circuiting operation in the pipeline 159 * is a necessary, but not sufficient, condition for the processing of an infinite 160 * stream to terminate normally in finite time. 161 * 162 * <h3><a id="Parallelism">Parallelism</a></h3> 163 * 164 * <p>Processing elements with an explicit {@code for-}loop is inherently serial. 165 * Streams facilitate parallel execution by reframing the computation as a pipeline of 166 * aggregate operations, rather than as imperative operations on each individual 167 * element. All streams operations can execute either in serial or in parallel. 168 * The stream implementations in the JDK create serial streams unless parallelism is 169 * explicitly requested. For example, {@code Collection} has methods 170 * {@link java.util.Collection#stream} and {@link java.util.Collection#parallelStream}, 171 * which produce sequential and parallel streams respectively; other 172 * stream-bearing methods such as {@link java.util.stream.IntStream#range(int, int)} 173 * produce sequential streams but these streams can be efficiently parallelized by 174 * invoking their {@link java.util.stream.BaseStream#parallel()} method. 175 * To execute the prior "sum of weights of widgets" query in parallel, we would 176 * do: 177 * 178 * <pre>{@code 179 * int sumOfWeights = widgets.<b>parallelStream()</b> 180 * .filter(b -> b.getColor() == RED) 181 * .mapToInt(b -> b.getWeight()) 182 * .sum(); 183 * }</pre> 184 * 185 * <p>The only difference between the serial and parallel versions of this 186 * example is the creation of the initial stream, using "{@code parallelStream()}" 187 * instead of "{@code stream()}". The stream pipeline is executed sequentially or 188 * in parallel depending on the mode of the stream on which the terminal operation 189 * is invoked. The sequential or parallel mode of a stream can be determined with the 190 * {@link java.util.stream.BaseStream#isParallel()} method, and the 191 * stream's mode can be modified with the 192 * {@link java.util.stream.BaseStream#sequential()} and 193 * {@link java.util.stream.BaseStream#parallel()} operations. 194 * The most recent sequential or parallel mode setting applies to the 195 * execution of the entire stream pipeline. 196 * 197 * <p>Except for operations identified as explicitly nondeterministic, such 198 * as {@code findAny()}, whether a stream executes sequentially or in parallel 199 * should not change the result of the computation. 200 * 201 * <p>Most stream operations accept parameters that describe user-specified 202 * behavior, which are often lambda expressions. To preserve correct behavior, 203 * these <em>behavioral parameters</em> must be <em>non-interfering</em>, and in 204 * most cases must be <em>stateless</em>. Such parameters are always instances 205 * of a <a href="../function/package-summary.html">functional interface</a> such 206 * as {@link java.util.function.Function}, and are often lambda expressions or 207 * method references. 208 * 209 * <h3><a id="NonInterference">Non-interference</a></h3> 210 * 211 * Streams enable you to execute possibly-parallel aggregate operations over a 212 * variety of data sources, including even non-thread-safe collections such as 213 * {@code ArrayList}. This is possible only if we can prevent 214 * <em>interference</em> with the data source during the execution of a stream 215 * pipeline. Except for the escape-hatch operations {@code iterator()} and 216 * {@code spliterator()}, execution begins when the terminal operation is 217 * invoked, and ends when the terminal operation completes. For most data 218 * sources, preventing interference means ensuring that the data source is 219 * <em>not modified at all</em> during the execution of the stream pipeline. 220 * The notable exception to this are streams whose sources are concurrent 221 * collections, which are specifically designed to handle concurrent modification. 222 * Concurrent stream sources are those whose {@code Spliterator} reports the 223 * {@code CONCURRENT} characteristic. 224 * 225 * <p>Accordingly, behavioral parameters in stream pipelines whose source might 226 * not be concurrent should never modify the stream's data source. 227 * A behavioral parameter is said to <em>interfere</em> with a non-concurrent 228 * data source if it modifies, or causes to be 229 * modified, the stream's data source. The need for non-interference applies 230 * to all pipelines, not just parallel ones. Unless the stream source is 231 * concurrent, modifying a stream's data source during execution of a stream 232 * pipeline can cause exceptions, incorrect answers, or nonconformant behavior. 233 * 234 * For well-behaved stream sources, the source can be modified before the 235 * terminal operation commences and those modifications will be reflected in 236 * the covered elements. For example, consider the following code: 237 * 238 * <pre>{@code 239 * List<String> l = new ArrayList(Arrays.asList("one", "two")); 240 * Stream<String> sl = l.stream(); 241 * l.add("three"); 242 * String s = sl.collect(joining(" ")); 243 * }</pre> 244 * 245 * First a list is created consisting of two strings: "one"; and "two". Then a 246 * stream is created from that list. Next the list is modified by adding a third 247 * string: "three". Finally the elements of the stream are collected and joined 248 * together. Since the list was modified before the terminal {@code collect} 249 * operation commenced the result will be a string of "one two three". All the 250 * streams returned from JDK collections, and most other JDK classes, 251 * are well-behaved in this manner; for streams generated by other libraries, see 252 * <a href="package-summary.html#StreamSources">Low-level stream 253 * construction</a> for requirements for building well-behaved streams. 254 * 255 * <h3><a id="Statelessness">Stateless behaviors</a></h3> 256 * 257 * Stream pipeline results may be nondeterministic or incorrect if the behavioral 258 * parameters to the stream operations are <em>stateful</em>. A stateful lambda 259 * (or other object implementing the appropriate functional interface) is one 260 * whose result depends on any state which might change during the execution 261 * of the stream pipeline. An example of a stateful lambda is the parameter 262 * to {@code map()} in: 263 * 264 * <pre>{@code 265 * Set<Integer> seen = Collections.synchronizedSet(new HashSet<>()); 266 * stream.parallel().map(e -> { if (seen.add(e)) return 0; else return e; })... 267 * }</pre> 268 * 269 * Here, if the mapping operation is performed in parallel, the results for the 270 * same input could vary from run to run, due to thread scheduling differences, 271 * whereas, with a stateless lambda expression the results would always be the 272 * same. 273 * 274 * <p>Note also that attempting to access mutable state from behavioral parameters 275 * presents you with a bad choice with respect to safety and performance; if 276 * you do not synchronize access to that state, you have a data race and 277 * therefore your code is broken, but if you do synchronize access to that 278 * state, you risk having contention undermine the parallelism you are seeking 279 * to benefit from. The best approach is to avoid stateful behavioral 280 * parameters to stream operations entirely; there is usually a way to 281 * restructure the stream pipeline to avoid statefulness. 282 * 283 * <h3><a id="SideEffects">Side-effects</a></h3> 284 * 285 * Side-effects in behavioral parameters to stream operations are, in general, 286 * discouraged, as they can often lead to unwitting violations of the 287 * statelessness requirement, as well as other thread-safety hazards. 288 * 289 * <p>If the behavioral parameters do have side-effects, unless explicitly 290 * stated, there are no guarantees as to: 291 * <ul> 292 * <li>the <a href="../concurrent/package-summary.html#MemoryVisibility"> 293 * <i>visibility</i></a> of those side-effects to other threads;</li> 294 * <li>that different operations on the "same" element within the same stream 295 * pipeline are executed in the same thread; and</li> 296 * <li>that behavioral parameters are always invoked, since a stream 297 * implementation is free to elide operations (or entire stages) from a 298 * stream pipeline if it can prove that it would not affect the result of the 299 * computation. 300 * </li> 301 * </ul> 302 * <p>The ordering of side-effects may be surprising. Even when a pipeline is 303 * constrained to produce a <em>result</em> that is consistent with the 304 * encounter order of the stream source (for example, 305 * {@code IntStream.range(0,5).parallel().map(x -> x*2).toArray()} 306 * must produce {@code [0, 2, 4, 6, 8]}), no guarantees are made as to the order 307 * in which the mapper function is applied to individual elements, or in what 308 * thread any behavioral parameter is executed for a given element. 309 * 310 * <p>The eliding of side-effects may also be surprising. With the exception of 311 * terminal operations {@link java.util.stream.Stream#forEach forEach} and 312 * {@link java.util.stream.Stream#forEachOrdered forEachOrdered}, side-effects 313 * of behavioral parameters may not always be executed when the stream 314 * implementation can optimize away the execution of behavioral parameters 315 * without affecting the result of the computation. (For a specific example 316 * see the API note documented on the {@link java.util.stream.Stream#count count} 317 * operation.) 318 * 319 * <p>Many computations where one might be tempted to use side effects can be more 320 * safely and efficiently expressed without side-effects, such as using 321 * <a href="package-summary.html#Reduction">reduction</a> instead of mutable 322 * accumulators. However, side-effects such as using {@code println()} for debugging 323 * purposes are usually harmless. A small number of stream operations, such as 324 * {@code forEach()} and {@code peek()}, can operate only via side-effects; 325 * these should be used with care. 326 * 327 * <p>As an example of how to transform a stream pipeline that inappropriately 328 * uses side-effects to one that does not, the following code searches a stream 329 * of strings for those matching a given regular expression, and puts the 330 * matches in a list. 331 * 332 * <pre>{@code 333 * ArrayList<String> results = new ArrayList<>(); 334 * stream.filter(s -> pattern.matcher(s).matches()) 335 * .forEach(s -> results.add(s)); // Unnecessary use of side-effects! 336 * }</pre> 337 * 338 * This code unnecessarily uses side-effects. If executed in parallel, the 339 * non-thread-safety of {@code ArrayList} would cause incorrect results, and 340 * adding needed synchronization would cause contention, undermining the 341 * benefit of parallelism. Furthermore, using side-effects here is completely 342 * unnecessary; the {@code forEach()} can simply be replaced with a reduction 343 * operation that is safer, more efficient, and more amenable to 344 * parallelization: 345 * 346 * <pre>{@code 347 * List<String>results = 348 * stream.filter(s -> pattern.matcher(s).matches()) 349 * .collect(Collectors.toList()); // No side-effects! 350 * }</pre> 351 * 352 * <h3><a id="Ordering">Ordering</a></h3> 353 * 354 * <p>Streams may or may not have a defined <em>encounter order</em>. Whether 355 * or not a stream has an encounter order depends on the source and the 356 * intermediate operations. Certain stream sources (such as {@code List} or 357 * arrays) are intrinsically ordered, whereas others (such as {@code HashSet}) 358 * are not. Some intermediate operations, such as {@code sorted()}, may impose 359 * an encounter order on an otherwise unordered stream, and others may render an 360 * ordered stream unordered, such as {@link java.util.stream.BaseStream#unordered()}. 361 * Further, some terminal operations may ignore encounter order, such as 362 * {@code forEach()}. 363 * 364 * <p>If a stream is ordered, most operations are constrained to operate on the 365 * elements in their encounter order; if the source of a stream is a {@code List} 366 * containing {@code [1, 2, 3]}, then the result of executing {@code map(x -> x*2)} 367 * must be {@code [2, 4, 6]}. However, if the source has no defined encounter 368 * order, then any permutation of the values {@code [2, 4, 6]} would be a valid 369 * result. 370 * 371 * <p>For sequential streams, the presence or absence of an encounter order does 372 * not affect performance, only determinism. If a stream is ordered, repeated 373 * execution of identical stream pipelines on an identical source will produce 374 * an identical result; if it is not ordered, repeated execution might produce 375 * different results. 376 * 377 * <p>For parallel streams, relaxing the ordering constraint can sometimes enable 378 * more efficient execution. Certain aggregate operations, 379 * such as filtering duplicates ({@code distinct()}) or grouped reductions 380 * ({@code Collectors.groupingBy()}) can be implemented more efficiently if ordering of elements 381 * is not relevant. Similarly, operations that are intrinsically tied to encounter order, 382 * such as {@code limit()}, may require 383 * buffering to ensure proper ordering, undermining the benefit of parallelism. 384 * In cases where the stream has an encounter order, but the user does not 385 * particularly <em>care</em> about that encounter order, explicitly de-ordering 386 * the stream with {@link java.util.stream.BaseStream#unordered() unordered()} may 387 * improve parallel performance for some stateful or terminal operations. 388 * However, most stream pipelines, such as the "sum of weight of blocks" example 389 * above, still parallelize efficiently even under ordering constraints. 390 * 391 * <h2><a id="Reduction">Reduction operations</a></h2> 392 * 393 * A <em>reduction</em> operation (also called a <em>fold</em>) takes a sequence 394 * of input elements and combines them into a single summary result by repeated 395 * application of a combining operation, such as finding the sum or maximum of 396 * a set of numbers, or accumulating elements into a list. The streams classes have 397 * multiple forms of general reduction operations, called 398 * {@link java.util.stream.Stream#reduce(java.util.function.BinaryOperator) reduce()} 399 * and {@link java.util.stream.Stream#collect(java.util.stream.Collector) collect()}, 400 * as well as multiple specialized reduction forms such as 401 * {@link java.util.stream.IntStream#sum() sum()}, {@link java.util.stream.IntStream#max() max()}, 402 * or {@link java.util.stream.IntStream#count() count()}. 403 * 404 * <p>Of course, such operations can be readily implemented as simple sequential 405 * loops, as in: 406 * <pre>{@code 407 * int sum = 0; 408 * for (int x : numbers) { 409 * sum += x; 410 * } 411 * }</pre> 412 * However, there are good reasons to prefer a reduce operation 413 * over a mutative accumulation such as the above. Not only is a reduction 414 * "more abstract" -- it operates on the stream as a whole rather than individual 415 * elements -- but a properly constructed reduce operation is inherently 416 * parallelizable, so long as the function(s) used to process the elements 417 * are <a href="package-summary.html#Associativity">associative</a> and 418 * <a href="package-summary.html#Statelessness">stateless</a>. 419 * For example, given a stream of numbers for which we want to find the sum, we 420 * can write: 421 * <pre>{@code 422 * int sum = numbers.stream().reduce(0, (x,y) -> x+y); 423 * }</pre> 424 * or: 425 * <pre>{@code 426 * int sum = numbers.stream().reduce(0, Integer::sum); 427 * }</pre> 428 * 429 * <p>These reduction operations can run safely in parallel with almost no 430 * modification: 431 * <pre>{@code 432 * int sum = numbers.parallelStream().reduce(0, Integer::sum); 433 * }</pre> 434 * 435 * <p>Reduction parallellizes well because the implementation 436 * can operate on subsets of the data in parallel, and then combine the 437 * intermediate results to get the final correct answer. (Even if the language 438 * had a "parallel for-each" construct, the mutative accumulation approach would 439 * still required the developer to provide 440 * thread-safe updates to the shared accumulating variable {@code sum}, and 441 * the required synchronization would then likely eliminate any performance gain from 442 * parallelism.) Using {@code reduce()} instead removes all of the 443 * burden of parallelizing the reduction operation, and the library can provide 444 * an efficient parallel implementation with no additional synchronization 445 * required. 446 * 447 * <p>The "widgets" examples shown earlier shows how reduction combines with 448 * other operations to replace for loops with bulk operations. If {@code widgets} 449 * is a collection of {@code Widget} objects, which have a {@code getWeight} method, 450 * we can find the heaviest widget with: 451 * <pre>{@code 452 * OptionalInt heaviest = widgets.parallelStream() 453 * .mapToInt(Widget::getWeight) 454 * .max(); 455 * }</pre> 456 * 457 * <p>In its more general form, a {@code reduce} operation on elements of type 458 * {@code <T>} yielding a result of type {@code <U>} requires three parameters: 459 * <pre>{@code 460 * <U> U reduce(U identity, 461 * BiFunction<U, ? super T, U> accumulator, 462 * BinaryOperator<U> combiner); 463 * }</pre> 464 * Here, the <em>identity</em> element is both an initial seed value for the reduction 465 * and a default result if there are no input elements. The <em>accumulator</em> 466 * function takes a partial result and the next element, and produces a new 467 * partial result. The <em>combiner</em> function combines two partial results 468 * to produce a new partial result. (The combiner is necessary in parallel 469 * reductions, where the input is partitioned, a partial accumulation computed 470 * for each partition, and then the partial results are combined to produce a 471 * final result.) 472 * 473 * <p>More formally, the {@code identity} value must be an <em>identity</em> for 474 * the combiner function. This means that for all {@code u}, 475 * {@code combiner.apply(identity, u)} is equal to {@code u}. Additionally, the 476 * {@code combiner} function must be <a href="package-summary.html#Associativity">associative</a> and 477 * must be compatible with the {@code accumulator} function: for all {@code u} 478 * and {@code t}, {@code combiner.apply(u, accumulator.apply(identity, t))} must 479 * be {@code equals()} to {@code accumulator.apply(u, t)}. 480 * 481 * <p>The three-argument form is a generalization of the two-argument form, 482 * incorporating a mapping step into the accumulation step. We could 483 * re-cast the simple sum-of-weights example using the more general form as 484 * follows: 485 * <pre>{@code 486 * int sumOfWeights = widgets.stream() 487 * .reduce(0, 488 * (sum, b) -> sum + b.getWeight(), 489 * Integer::sum); 490 * }</pre> 491 * though the explicit map-reduce form is more readable and therefore should 492 * usually be preferred. The generalized form is provided for cases where 493 * significant work can be optimized away by combining mapping and reducing 494 * into a single function. 495 * 496 * <h3><a id="MutableReduction">Mutable reduction</a></h3> 497 * 498 * A <em>mutable reduction operation</em> accumulates input elements into a 499 * mutable result container, such as a {@code Collection} or {@code StringBuilder}, 500 * as it processes the elements in the stream. 501 * 502 * <p>If we wanted to take a stream of strings and concatenate them into a 503 * single long string, we <em>could</em> achieve this with ordinary reduction: 504 * <pre>{@code 505 * String concatenated = strings.reduce("", String::concat) 506 * }</pre> 507 * 508 * <p>We would get the desired result, and it would even work in parallel. However, 509 * we might not be happy about the performance! Such an implementation would do 510 * a great deal of string copying, and the run time would be <em>O(n^2)</em> in 511 * the number of characters. A more performant approach would be to accumulate 512 * the results into a {@link java.lang.StringBuilder}, which is a mutable 513 * container for accumulating strings. We can use the same technique to 514 * parallelize mutable reduction as we do with ordinary reduction. 515 * 516 * <p>The mutable reduction operation is called 517 * {@link java.util.stream.Stream#collect(Collector) collect()}, 518 * as it collects together the desired results into a result container such 519 * as a {@code Collection}. 520 * A {@code collect} operation requires three functions: 521 * a supplier function to construct new instances of the result container, an 522 * accumulator function to incorporate an input element into a result 523 * container, and a combining function to merge the contents of one result 524 * container into another. The form of this is very similar to the general 525 * form of ordinary reduction: 526 * <pre>{@code 527 * <R> R collect(Supplier<R> supplier, 528 * BiConsumer<R, ? super T> accumulator, 529 * BiConsumer<R, R> combiner); 530 * }</pre> 531 * <p>As with {@code reduce()}, a benefit of expressing {@code collect} in this 532 * abstract way is that it is directly amenable to parallelization: we can 533 * accumulate partial results in parallel and then combine them, so long as the 534 * accumulation and combining functions satisfy the appropriate requirements. 535 * For example, to collect the String representations of the elements in a 536 * stream into an {@code ArrayList}, we could write the obvious sequential 537 * for-each form: 538 * <pre>{@code 539 * ArrayList<String> strings = new ArrayList<>(); 540 * for (T element : stream) { 541 * strings.add(element.toString()); 542 * } 543 * }</pre> 544 * Or we could use a parallelizable collect form: 545 * <pre>{@code 546 * ArrayList<String> strings = stream.collect(() -> new ArrayList<>(), 547 * (c, e) -> c.add(e.toString()), 548 * (c1, c2) -> c1.addAll(c2)); 549 * }</pre> 550 * or, pulling the mapping operation out of the accumulator function, we could 551 * express it more succinctly as: 552 * <pre>{@code 553 * List<String> strings = stream.map(Object::toString) 554 * .collect(ArrayList::new, ArrayList::add, ArrayList::addAll); 555 * }</pre> 556 * Here, our supplier is just the {@link java.util.ArrayList#ArrayList() 557 * ArrayList constructor}, the accumulator adds the stringified element to an 558 * {@code ArrayList}, and the combiner simply uses {@link java.util.ArrayList#addAll addAll} 559 * to copy the strings from one container into the other. 560 * 561 * <p>The three aspects of {@code collect} -- supplier, accumulator, and 562 * combiner -- are tightly coupled. We can use the abstraction of a 563 * {@link java.util.stream.Collector} to capture all three aspects. The 564 * above example for collecting strings into a {@code List} can be rewritten 565 * using a standard {@code Collector} as: 566 * <pre>{@code 567 * List<String> strings = stream.map(Object::toString) 568 * .collect(Collectors.toList()); 569 * }</pre> 570 * 571 * <p>Packaging mutable reductions into a Collector has another advantage: 572 * composability. The class {@link java.util.stream.Collectors} contains a 573 * number of predefined factories for collectors, including combinators 574 * that transform one collector into another. For example, suppose we have a 575 * collector that computes the sum of the salaries of a stream of 576 * employees, as follows: 577 * 578 * <pre>{@code 579 * Collector<Employee, ?, Integer> summingSalaries 580 * = Collectors.summingInt(Employee::getSalary); 581 * }</pre> 582 * 583 * (The {@code ?} for the second type parameter merely indicates that we don't 584 * care about the intermediate representation used by this collector.) 585 * If we wanted to create a collector to tabulate the sum of salaries by 586 * department, we could reuse {@code summingSalaries} using 587 * {@link java.util.stream.Collectors#groupingBy(java.util.function.Function, java.util.stream.Collector) groupingBy}: 588 * 589 * <pre>{@code 590 * Map<Department, Integer> salariesByDept 591 * = employees.stream().collect(Collectors.groupingBy(Employee::getDepartment, 592 * summingSalaries)); 593 * }</pre> 594 * 595 * <p>As with the regular reduction operation, {@code collect()} operations can 596 * only be parallelized if appropriate conditions are met. For any partially 597 * accumulated result, combining it with an empty result container must 598 * produce an equivalent result. That is, for a partially accumulated result 599 * {@code p} that is the result of any series of accumulator and combiner 600 * invocations, {@code p} must be equivalent to 601 * {@code combiner.apply(p, supplier.get())}. 602 * 603 * <p>Further, however the computation is split, it must produce an equivalent 604 * result. For any input elements {@code t1} and {@code t2}, the results 605 * {@code r1} and {@code r2} in the computation below must be equivalent: 606 * <pre>{@code 607 * A a1 = supplier.get(); 608 * accumulator.accept(a1, t1); 609 * accumulator.accept(a1, t2); 610 * R r1 = finisher.apply(a1); // result without splitting 611 * 612 * A a2 = supplier.get(); 613 * accumulator.accept(a2, t1); 614 * A a3 = supplier.get(); 615 * accumulator.accept(a3, t2); 616 * R r2 = finisher.apply(combiner.apply(a2, a3)); // result with splitting 617 * }</pre> 618 * 619 * <p>Here, equivalence generally means according to {@link java.lang.Object#equals(Object)}. 620 * but in some cases equivalence may be relaxed to account for differences in 621 * order. 622 * 623 * <h3><a id="ConcurrentReduction">Reduction, concurrency, and ordering</a></h3> 624 * 625 * With some complex reduction operations, for example a {@code collect()} that 626 * produces a {@code Map}, such as: 627 * <pre>{@code 628 * Map<Buyer, List<Transaction>> salesByBuyer 629 * = txns.parallelStream() 630 * .collect(Collectors.groupingBy(Transaction::getBuyer)); 631 * }</pre> 632 * it may actually be counterproductive to perform the operation in parallel. 633 * This is because the combining step (merging one {@code Map} into another by 634 * key) can be expensive for some {@code Map} implementations. 635 * 636 * <p>Suppose, however, that the result container used in this reduction 637 * was a concurrently modifiable collection -- such as a 638 * {@link java.util.concurrent.ConcurrentHashMap}. In that case, the parallel 639 * invocations of the accumulator could actually deposit their results 640 * concurrently into the same shared result container, eliminating the need for 641 * the combiner to merge distinct result containers. This potentially provides 642 * a boost to the parallel execution performance. We call this a 643 * <em>concurrent</em> reduction. 644 * 645 * <p>A {@link java.util.stream.Collector} that supports concurrent reduction is 646 * marked with the {@link java.util.stream.Collector.Characteristics#CONCURRENT} 647 * characteristic. However, a concurrent collection also has a downside. If 648 * multiple threads are depositing results concurrently into a shared container, 649 * the order in which results are deposited is non-deterministic. Consequently, 650 * a concurrent reduction is only possible if ordering is not important for the 651 * stream being processed. The {@link java.util.stream.Stream#collect(Collector)} 652 * implementation will only perform a concurrent reduction if 653 * <ul> 654 * <li>The stream is parallel;</li> 655 * <li>The collector has the 656 * {@link java.util.stream.Collector.Characteristics#CONCURRENT} characteristic, 657 * and;</li> 658 * <li>Either the stream is unordered, or the collector has the 659 * {@link java.util.stream.Collector.Characteristics#UNORDERED} characteristic. 660 * </ul> 661 * You can ensure the stream is unordered by using the 662 * {@link java.util.stream.BaseStream#unordered()} method. For example: 663 * <pre>{@code 664 * Map<Buyer, List<Transaction>> salesByBuyer 665 * = txns.parallelStream() 666 * .unordered() 667 * .collect(groupingByConcurrent(Transaction::getBuyer)); 668 * }</pre> 669 * (where {@link java.util.stream.Collectors#groupingByConcurrent} is the 670 * concurrent equivalent of {@code groupingBy}). 671 * 672 * <p>Note that if it is important that the elements for a given key appear in 673 * the order they appear in the source, then we cannot use a concurrent 674 * reduction, as ordering is one of the casualties of concurrent insertion. 675 * We would then be constrained to implement either a sequential reduction or 676 * a merge-based parallel reduction. 677 * 678 * <h3><a id="Associativity">Associativity</a></h3> 679 * 680 * An operator or function {@code op} is <em>associative</em> if the following 681 * holds: 682 * <pre>{@code 683 * (a op b) op c == a op (b op c) 684 * }</pre> 685 * The importance of this to parallel evaluation can be seen if we expand this 686 * to four terms: 687 * <pre>{@code 688 * a op b op c op d == (a op b) op (c op d) 689 * }</pre> 690 * So we can evaluate {@code (a op b)} in parallel with {@code (c op d)}, and 691 * then invoke {@code op} on the results. 692 * 693 * <p>Examples of associative operations include numeric addition, min, and 694 * max, and string concatenation. 695 * 696 * <h2><a id="StreamSources">Low-level stream construction</a></h2> 697 * 698 * So far, all the stream examples have used methods like 699 * {@link java.util.Collection#stream()} or {@link java.util.Arrays#stream(Object[])} 700 * to obtain a stream. How are those stream-bearing methods implemented? 701 * 702 * <p>The class {@link java.util.stream.StreamSupport} has a number of 703 * low-level methods for creating a stream, all using some form of a 704 * {@link java.util.Spliterator}. A spliterator is the parallel analogue of an 705 * {@link java.util.Iterator}; it describes a (possibly infinite) collection of 706 * elements, with support for sequentially advancing, bulk traversal, and 707 * splitting off some portion of the input into another spliterator which can 708 * be processed in parallel. At the lowest level, all streams are driven by a 709 * spliterator. 710 * 711 * <p>There are a number of implementation choices in implementing a 712 * spliterator, nearly all of which are tradeoffs between simplicity of 713 * implementation and runtime performance of streams using that spliterator. 714 * The simplest, but least performant, way to create a spliterator is to 715 * create one from an iterator using 716 * {@link java.util.Spliterators#spliteratorUnknownSize(java.util.Iterator, int)}. 717 * While such a spliterator will work, it will likely offer poor parallel 718 * performance, since we have lost sizing information (how big is the 719 * underlying data set), as well as being constrained to a simplistic 720 * splitting algorithm. 721 * 722 * <p>A higher-quality spliterator will provide balanced and known-size 723 * splits, accurate sizing information, and a number of other 724 * {@link java.util.Spliterator#characteristics() characteristics} of the 725 * spliterator or data that can be used by implementations to optimize 726 * execution. 727 * 728 * <p>Spliterators for mutable data sources have an additional challenge; 729 * timing of binding to the data, since the data could change between the time 730 * the spliterator is created and the time the stream pipeline is executed. 731 * Ideally, a spliterator for a stream would report a characteristic of 732 733 * {@code IMMUTABLE} or {@code CONCURRENT}; if not it should be 734 * <a href="../Spliterator.html#binding"><em>late-binding</em></a>. If a source 735 * cannot directly supply a recommended spliterator, it may indirectly supply 736 * a spliterator using a {@code Supplier}, and construct a stream via the 737 * {@code Supplier}-accepting versions of 738 * {@link java.util.stream.StreamSupport#stream(Supplier, int, boolean) stream()}. 739 * The spliterator is obtained from the supplier only after the terminal 740 * operation of the stream pipeline commences. 741 * 742 * <p>These requirements significantly reduce the scope of potential 743 * interference between mutations of the stream source and execution of stream 744 * pipelines. Streams based on spliterators with the desired characteristics, 745 * or those using the Supplier-based factory forms, are immune to 746 * modifications of the data source prior to commencement of the terminal 747 * operation (provided the behavioral parameters to the stream operations meet 748 * the required criteria for non-interference and statelessness). See 749 * <a href="package-summary.html#NonInterference">Non-Interference</a> 750 * for more details. 751 * 752 * @since 1.8 753 */ 754 package java.util.stream; 755 756 import java.util.function.BinaryOperator; 757 import java.util.function.UnaryOperator; 758