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 * Copyright (c) 2012, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
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package java.util.stream;

import java.util.Arrays;
import java.util.IntSummaryStatistics;
import java.util.Objects;
import java.util.OptionalDouble;
import java.util.OptionalInt;
import java.util.PrimitiveIterator;
import java.util.Spliterator;
import java.util.Spliterators;
import java.util.function.BiConsumer;
import java.util.function.Function;
import java.util.function.IntBinaryOperator;
import java.util.function.IntConsumer;
import java.util.function.IntFunction;
import java.util.function.IntPredicate;
import java.util.function.IntSupplier;
import java.util.function.IntToDoubleFunction;
import java.util.function.IntToLongFunction;
import java.util.function.IntUnaryOperator;
import java.util.function.ObjIntConsumer;
import java.util.function.Supplier;

/**
 * A sequence of primitive int-valued elements supporting sequential and parallel
 * aggregate operations.  This is the {@code int} primitive specialization of
 * {@link Stream}.
 *
 * <p>The following example illustrates an aggregate operation using
 * {@link Stream} and {@link IntStream}, computing the sum of the weights of the
 * red widgets:
 *
 * <pre>{@code
 *     int sum = widgets.stream()
 *                      .filter(w -> w.getColor() == RED)
 *                      .mapToInt(w -> w.getWeight())
 *                      .sum();
 * }</pre>
 *
 * See the class documentation for {@link Stream} and the package documentation
 * for <a href="package-summary.html">java.util.stream</a> for additional
 * specification of streams, stream operations, stream pipelines, and
 * parallelism.
 *
 * @since 1.8
 * @see Stream
 * @see <a href="package-summary.html">java.util.stream</a>
 */
public interface IntStream extends BaseStream<Integer, IntStream> {

    /**
     * Returns a stream consisting of the elements of this stream that match
     * the given predicate.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                  <a href="package-summary.html#Statelessness">stateless</a>
     *                  predicate to apply to each element to determine if it
     *                  should be included
     * @return the new stream
     */
    IntStream filter(IntPredicate predicate);

    /**
     * Returns a stream consisting of the results of applying the given
     * function to the elements of this stream.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *               <a href="package-summary.html#Statelessness">stateless</a>
     *               function to apply to each element
     * @return the new stream
     */
    IntStream map(IntUnaryOperator mapper);

    /**
     * Returns an object-valued {@code Stream} consisting of the results of
     * applying the given function to the elements of this stream.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">
     *     intermediate operation</a>.
     *
     * @param <U> the element type of the new stream
     * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *               <a href="package-summary.html#Statelessness">stateless</a>
     *               function to apply to each element
     * @return the new stream
     */
    <U> Stream<U> mapToObj(IntFunction<? extends U> mapper);

    /**
     * Returns a {@code LongStream} consisting of the results of applying the
     * given function to the elements of this stream.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *               <a href="package-summary.html#Statelessness">stateless</a>
     *               function to apply to each element
     * @return the new stream
     */
    LongStream mapToLong(IntToLongFunction mapper);

    /**
     * Returns a {@code DoubleStream} consisting of the results of applying the
     * given function to the elements of this stream.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *               <a href="package-summary.html#Statelessness">stateless</a>
     *               function to apply to each element
     * @return the new stream
     */
    DoubleStream mapToDouble(IntToDoubleFunction mapper);

    /**
     * Returns a stream consisting of the results of replacing each element of
     * this stream with the contents of a mapped stream produced by applying
     * the provided mapping function to each element.  Each mapped stream is
     * {@link java.util.stream.BaseStream#close() closed} after its contents
     * have been placed into this stream.  (If a mapped stream is {@code null}
     * an empty stream is used, instead.)
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *               <a href="package-summary.html#Statelessness">stateless</a>
     *               function to apply to each element which produces an
     *               {@code IntStream} of new values
     * @return the new stream
     * @see Stream#flatMap(Function)
     */
    IntStream flatMap(IntFunction<? extends IntStream> mapper);

    /**
     * Returns a stream consisting of the distinct elements of this stream.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">stateful
     * intermediate operation</a>.
     *
     * @return the new stream
     */
    IntStream distinct();

    /**
     * Returns a stream consisting of the elements of this stream in sorted
     * order.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">stateful
     * intermediate operation</a>.
     *
     * @return the new stream
     */
    IntStream sorted();

    /**
     * Returns a stream consisting of the elements of this stream, additionally
     * performing the provided action on each element as elements are consumed
     * from the resulting stream.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * <p>For parallel stream pipelines, the action may be called at
     * whatever time and in whatever thread the element is made available by the
     * upstream operation.  If the action modifies shared state,
     * it is responsible for providing the required synchronization.
     *
     * @apiNote This method exists mainly to support debugging, where you want
     * to see the elements as they flow past a certain point in a pipeline:
     * <pre>{@code
     *     IntStream.of(1, 2, 3, 4)
     *         .filter(e -> e > 2)
     *         .peek(e -> System.out.println("Filtered value: " + e))
     *         .map(e -> e * e)
     *         .peek(e -> System.out.println("Mapped value: " + e))
     *         .sum();
     * }</pre>
     *
     * @param action a <a href="package-summary.html#NonInterference">
     *               non-interfering</a> action to perform on the elements as
     *               they are consumed from the stream
     * @return the new stream
     */
    IntStream peek(IntConsumer action);

    /**
     * Returns a stream consisting of the elements of this stream, truncated
     * to be no longer than {@code maxSize} in length.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * stateful intermediate operation</a>.
     *
     * @apiNote
     * While {@code limit()} is generally a cheap operation on sequential
     * stream pipelines, it can be quite expensive on ordered parallel pipelines,
     * especially for large values of {@code maxSize}, since {@code limit(n)}
     * is constrained to return not just any <em>n</em> elements, but the
     * <em>first n</em> elements in the encounter order.  Using an unordered
     * stream source (such as {@link #generate(IntSupplier)}) or removing the
     * ordering constraint with {@link #unordered()} may result in significant
     * speedups of {@code limit()} in parallel pipelines, if the semantics of
     * your situation permit.  If consistency with encounter order is required,
     * and you are experiencing poor performance or memory utilization with
     * {@code limit()} in parallel pipelines, switching to sequential execution
     * with {@link #sequential()} may improve performance.
     *
     * @param maxSize the number of elements the stream should be limited to
     * @return the new stream
     * @throws IllegalArgumentException if {@code maxSize} is negative
     */
    IntStream limit(long maxSize);

    /**
     * Returns a stream consisting of the remaining elements of this stream
     * after discarding the first {@code n} elements of the stream.
     * If this stream contains fewer than {@code n} elements then an
     * empty stream will be returned.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">stateful
     * intermediate operation</a>.
     *
     * @apiNote
     * While {@code skip()} is generally a cheap operation on sequential
     * stream pipelines, it can be quite expensive on ordered parallel pipelines,
     * especially for large values of {@code n}, since {@code skip(n)}
     * is constrained to skip not just any <em>n</em> elements, but the
     * <em>first n</em> elements in the encounter order.  Using an unordered
     * stream source (such as {@link #generate(IntSupplier)}) or removing the
     * ordering constraint with {@link #unordered()} may result in significant
     * speedups of {@code skip()} in parallel pipelines, if the semantics of
     * your situation permit.  If consistency with encounter order is required,
     * and you are experiencing poor performance or memory utilization with
     * {@code skip()} in parallel pipelines, switching to sequential execution
     * with {@link #sequential()} may improve performance.
     *
     * @param n the number of leading elements to skip
     * @return the new stream
     * @throws IllegalArgumentException if {@code n} is negative
     */
    IntStream skip(long n);

    /**
     * Performs an action for each element of this stream.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * <p>For parallel stream pipelines, this operation does <em>not</em>
     * guarantee to respect the encounter order of the stream, as doing so
     * would sacrifice the benefit of parallelism.  For any given element, the
     * action may be performed at whatever time and in whatever thread the
     * library chooses.  If the action accesses shared state, it is
     * responsible for providing the required synchronization.
     *
     * @param action a <a href="package-summary.html#NonInterference">
     *               non-interfering</a> action to perform on the elements
     */
    void forEach(IntConsumer action);

    /**
     * Performs an action for each element of this stream, guaranteeing that
     * each element is processed in encounter order for streams that have a
     * defined encounter order.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @param action a <a href="package-summary.html#NonInterference">
     *               non-interfering</a> action to perform on the elements
     * @see #forEach(IntConsumer)
     */
    void forEachOrdered(IntConsumer action);

    /**
     * Returns an array containing the elements of this stream.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @return an array containing the elements of this stream
     */
    int[] toArray();

    /**
     * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
     * elements of this stream, using the provided identity value and an
     * <a href="package-summary.html#Associativity">associative</a>
     * accumulation function, and returns the reduced value.  This is equivalent
     * to:
     * <pre>{@code
     *     int result = identity;
     *     for (int element : this stream)
     *         result = accumulator.applyAsInt(result, element)
     *     return result;
     * }</pre>
     *
     * but is not constrained to execute sequentially.
     *
     * <p>The {@code identity} value must be an identity for the accumulator
     * function. This means that for all {@code x},
     * {@code accumulator.apply(identity, x)} is equal to {@code x}.
     * The {@code accumulator} function must be an
     * <a href="package-summary.html#Associativity">associative</a> function.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @apiNote Sum, min, max, and average are all special cases of reduction.
     * Summing a stream of numbers can be expressed as:
     *
     * <pre>{@code
     *     int sum = integers.reduce(0, (a, b) -> a+b);
     * }</pre>
     *
     * or more compactly:
     *
     * <pre>{@code
     *     int sum = integers.reduce(0, Integer::sum);
     * }</pre>
     *
     * <p>While this may seem a more roundabout way to perform an aggregation
     * compared to simply mutating a running total in a loop, reduction
     * operations parallelize more gracefully, without needing additional
     * synchronization and with greatly reduced risk of data races.
     *
     * @param identity the identity value for the accumulating function
     * @param op an <a href="package-summary.html#Associativity">associative</a>,
     *           <a href="package-summary.html#NonInterference">non-interfering</a>,
     *           <a href="package-summary.html#Statelessness">stateless</a>
     *           function for combining two values
     * @return the result of the reduction
     * @see #sum()
     * @see #min()
     * @see #max()
     * @see #average()
     */
    int reduce(int identity, IntBinaryOperator op);

    /**
     * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
     * elements of this stream, using an
     * <a href="package-summary.html#Associativity">associative</a> accumulation
     * function, and returns an {@code OptionalInt} describing the reduced value,
     * if any. This is equivalent to:
     * <pre>{@code
     *     boolean foundAny = false;
     *     int result = null;
     *     for (int element : this stream) {
     *         if (!foundAny) {
     *             foundAny = true;
     *             result = element;
     *         }
     *         else
     *             result = accumulator.applyAsInt(result, element);
     *     }
     *     return foundAny ? OptionalInt.of(result) : OptionalInt.empty();
     * }</pre>
     *
     * but is not constrained to execute sequentially.
     *
     * <p>The {@code accumulator} function must be an
     * <a href="package-summary.html#Associativity">associative</a> function.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @param op an <a href="package-summary.html#Associativity">associative</a>,
     *           <a href="package-summary.html#NonInterference">non-interfering</a>,
     *           <a href="package-summary.html#Statelessness">stateless</a>
     *           function for combining two values
     * @return the result of the reduction
     * @see #reduce(int, IntBinaryOperator)
     */
    OptionalInt reduce(IntBinaryOperator op);

    /**
     * Performs a <a href="package-summary.html#MutableReduction">mutable
     * reduction</a> operation on the elements of this stream.  A mutable
     * reduction is one in which the reduced value is a mutable result container,
     * such as an {@code ArrayList}, and elements are incorporated by updating
     * the state of the result rather than by replacing the result.  This
     * produces a result equivalent to:
     * <pre>{@code
     *     R result = supplier.get();
     *     for (int element : this stream)
     *         accumulator.accept(result, element);
     *     return result;
     * }</pre>
     *
     * <p>Like {@link #reduce(int, IntBinaryOperator)}, {@code collect} operations
     * can be parallelized without requiring additional synchronization.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @param <R> type of the result
     * @param supplier a function that creates a new result container. For a
     *                 parallel execution, this function may be called
     *                 multiple times and must return a fresh value each time.
     * @param accumulator an <a href="package-summary.html#Associativity">associative</a>,
     *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                    <a href="package-summary.html#Statelessness">stateless</a>
     *                    function for incorporating an additional element into a result
     * @param combiner an <a href="package-summary.html#Associativity">associative</a>,
     *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                    <a href="package-summary.html#Statelessness">stateless</a>
     *                    function for combining two values, which must be
     *                    compatible with the accumulator function
     * @return the result of the reduction
     * @see Stream#collect(Supplier, BiConsumer, BiConsumer)
     */
    <R> R collect(Supplier<R> supplier,
                  ObjIntConsumer<R> accumulator,
                  BiConsumer<R, R> combiner);

    /**
     * Returns the sum of elements in this stream.  This is a special case
     * of a <a href="package-summary.html#Reduction">reduction</a>
     * and is equivalent to:
     * <pre>{@code
     *     return reduce(0, Integer::sum);
     * }</pre>
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @return the sum of elements in this stream
     */
    int sum();

    /**
     * Returns an {@code OptionalInt} describing the minimum element of this
     * stream, or an empty optional if this stream is empty.  This is a special
     * case of a <a href="package-summary.html#Reduction">reduction</a>
     * and is equivalent to:
     * <pre>{@code
     *     return reduce(Integer::min);
     * }</pre>
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
     *
     * @return an {@code OptionalInt} containing the minimum element of this
     * stream, or an empty {@code OptionalInt} if the stream is empty
     */
    OptionalInt min();

    /**
     * Returns an {@code OptionalInt} describing the maximum element of this
     * stream, or an empty optional if this stream is empty.  This is a special
     * case of a <a href="package-summary.html#Reduction">reduction</a>
     * and is equivalent to:
     * <pre>{@code
     *     return reduce(Integer::max);
     * }</pre>
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @return an {@code OptionalInt} containing the maximum element of this
     * stream, or an empty {@code OptionalInt} if the stream is empty
     */
    OptionalInt max();

    /**
     * Returns the count of elements in this stream.  This is a special case of
     * a <a href="package-summary.html#Reduction">reduction</a> and is
     * equivalent to:
     * <pre>{@code
     *     return mapToLong(e -> 1L).sum();
     * }</pre>
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
     *
     * @return the count of elements in this stream
     */
    long count();

    /**
     * Returns an {@code OptionalDouble} describing the arithmetic mean of elements of
     * this stream, or an empty optional if this stream is empty.  This is a
     * special case of a
     * <a href="package-summary.html#Reduction">reduction</a>.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @return an {@code OptionalDouble} containing the average element of this
     * stream, or an empty optional if the stream is empty
     */
    OptionalDouble average();

    /**
     * Returns an {@code IntSummaryStatistics} describing various
     * summary data about the elements of this stream.  This is a special
     * case of a <a href="package-summary.html#Reduction">reduction</a>.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">terminal
     * operation</a>.
     *
     * @return an {@code IntSummaryStatistics} describing various summary data
     * about the elements of this stream
     */
    IntSummaryStatistics summaryStatistics();

    /**
     * Returns whether any elements of this stream match the provided
     * predicate.  May not evaluate the predicate on all elements if not
     * necessary for determining the result.  If the stream is empty then
     * {@code false} is returned and the predicate is not evaluated.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * terminal operation</a>.
     *
     * @apiNote
     * This method evaluates the <em>existential quantification</em> of the
     * predicate over the elements of the stream (for some x P(x)).
     *
     * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                  <a href="package-summary.html#Statelessness">stateless</a>
     *                  predicate to apply to elements of this stream
     * @return {@code true} if any elements of the stream match the provided
     * predicate, otherwise {@code false}
     */
    boolean anyMatch(IntPredicate predicate);

    /**
     * Returns whether all elements of this stream match the provided predicate.
     * May not evaluate the predicate on all elements if not necessary for
     * determining the result.  If the stream is empty then {@code true} is
     * returned and the predicate is not evaluated.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * terminal operation</a>.
     *
     * @apiNote
     * This method evaluates the <em>universal quantification</em> of the
     * predicate over the elements of the stream (for all x P(x)).  If the
     * stream is empty, the quantification is said to be <em>vacuously
     * satisfied</em> and is always {@code true} (regardless of P(x)).
     *
     * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                  <a href="package-summary.html#Statelessness">stateless</a>
     *                  predicate to apply to elements of this stream
     * @return {@code true} if either all elements of the stream match the
     * provided predicate or the stream is empty, otherwise {@code false}
     */
    boolean allMatch(IntPredicate predicate);

    /**
     * Returns whether no elements of this stream match the provided predicate.
     * May not evaluate the predicate on all elements if not necessary for
     * determining the result.  If the stream is empty then {@code true} is
     * returned and the predicate is not evaluated.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * terminal operation</a>.
     *
     * @apiNote
     * This method evaluates the <em>universal quantification</em> of the
     * negated predicate over the elements of the stream (for all x ~P(x)).  If
     * the stream is empty, the quantification is said to be vacuously satisfied
     * and is always {@code true}, regardless of P(x).
     *
     * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
     *                  <a href="package-summary.html#Statelessness">stateless</a>
     *                  predicate to apply to elements of this stream
     * @return {@code true} if either no elements of the stream match the
     * provided predicate or the stream is empty, otherwise {@code false}
     */
    boolean noneMatch(IntPredicate predicate);

    /**
     * Returns an {@link OptionalInt} describing the first element of this
     * stream, or an empty {@code OptionalInt} if the stream is empty.  If the
     * stream has no encounter order, then any element may be returned.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * terminal operation</a>.
     *
     * @return an {@code OptionalInt} describing the first element of this stream,
     * or an empty {@code OptionalInt} if the stream is empty
     */
    OptionalInt findFirst();

    /**
     * Returns an {@link OptionalInt} describing some element of the stream, or
     * an empty {@code OptionalInt} if the stream is empty.
     *
     * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
     * terminal operation</a>.
     *
     * <p>The behavior of this operation is explicitly nondeterministic; it is
     * free to select any element in the stream.  This is to allow for maximal
     * performance in parallel operations; the cost is that multiple invocations
     * on the same source may not return the same result.  (If a stable result
     * is desired, use {@link #findFirst()} instead.)
     *
     * @return an {@code OptionalInt} describing some element of this stream, or
     * an empty {@code OptionalInt} if the stream is empty
     * @see #findFirst()
     */
    OptionalInt findAny();

    /**
     * Returns a {@code LongStream} consisting of the elements of this stream,
     * converted to {@code long}.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @return a {@code LongStream} consisting of the elements of this stream,
     * converted to {@code long}
     */
    LongStream asLongStream();

    /**
     * Returns a {@code DoubleStream} consisting of the elements of this stream,
     * converted to {@code double}.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @return a {@code DoubleStream} consisting of the elements of this stream,
     * converted to {@code double}
     */
    DoubleStream asDoubleStream();

    /**
     * Returns a {@code Stream} consisting of the elements of this stream,
     * each boxed to an {@code Integer}.
     *
     * <p>This is an <a href="package-summary.html#StreamOps">intermediate
     * operation</a>.
     *
     * @return a {@code Stream} consistent of the elements of this stream,
     * each boxed to an {@code Integer}
     */
    Stream<Integer> boxed();

    @Override
    IntStream sequential();

    @Override
    IntStream parallel();

    @Override
    PrimitiveIterator.OfInt iterator();

    @Override
    Spliterator.OfInt spliterator();

    // Static factories

    /**
     * Returns a builder for an {@code IntStream}.
     *
     * @return a stream builder
     */
    public static Builder builder() {
        return new Streams.IntStreamBuilderImpl();
    }

    /**
     * Returns an empty sequential {@code IntStream}.
     *
     * @return an empty sequential stream
     */
    public static IntStream empty() {
        return StreamSupport.intStream(Spliterators.emptyIntSpliterator(), false);
    }

    /**
     * Returns a sequential {@code IntStream} containing a single element.
     *
     * @param t the single element
     * @return a singleton sequential stream
     */
    public static IntStream of(int t) {
        return StreamSupport.intStream(new Streams.IntStreamBuilderImpl(t), false);
    }

    /**
     * Returns a sequential ordered stream whose elements are the specified values.
     *
     * @param values the elements of the new stream
     * @return the new stream
     */
    public static IntStream of(int... values) {
        return Arrays.stream(values);
    }

    /**
     * Returns an infinite sequential ordered {@code IntStream} produced by iterative
     * application of a function {@code f} to an initial element {@code seed},
     * producing a {@code Stream} consisting of {@code seed}, {@code f(seed)},
     * {@code f(f(seed))}, etc.
     *
     * <p>The first element (position {@code 0}) in the {@code IntStream} will be
     * the provided {@code seed}.  For {@code n > 0}, the element at position
     * {@code n}, will be the result of applying the function {@code f} to the
     * element at position {@code n - 1}.
     *
     * @param seed the initial element
     * @param f a function to be applied to the previous element to produce
     *          a new element
     * @return A new sequential {@code IntStream}
     */
    public static IntStream iterate(final int seed, final IntUnaryOperator f) {
        Objects.requireNonNull(f);
        final PrimitiveIterator.OfInt iterator = new PrimitiveIterator.OfInt() {
            int t = seed;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public int nextInt() {
                int v = t;
                t = f.applyAsInt(t);
                return v;
            }
        };
        return StreamSupport.intStream(Spliterators.spliteratorUnknownSize(
                iterator,
                Spliterator.ORDERED | Spliterator.IMMUTABLE | Spliterator.NONNULL), false);
    }

    /**
     * Returns an infinite sequential unordered stream where each element is
     * generated by the provided {@code IntSupplier}.  This is suitable for
     * generating constant streams, streams of random elements, etc.
     *
     * @param s the {@code IntSupplier} for generated elements
     * @return a new infinite sequential unordered {@code IntStream}
     */
    public static IntStream generate(IntSupplier s) {
        Objects.requireNonNull(s);
        return StreamSupport.intStream(
                new StreamSpliterators.InfiniteSupplyingSpliterator.OfInt(Long.MAX_VALUE, s), false);
    }

    /**
     * Returns a sequential ordered {@code IntStream} from {@code startInclusive}
     * (inclusive) to {@code endExclusive} (exclusive) by an incremental step of
     * {@code 1}.
     *
     * @apiNote
     * <p>An equivalent sequence of increasing values can be produced
     * sequentially using a {@code for} loop as follows:
     * <pre>{@code
     *     for (int i = startInclusive; i < endExclusive ; i++) { ... }
     * }</pre>
     *
     * @param startInclusive the (inclusive) initial value
     * @param endExclusive the exclusive upper bound
     * @return a sequential {@code IntStream} for the range of {@code int}
     *         elements
     */
    public static IntStream range(int startInclusive, int endExclusive) {
        if (startInclusive >= endExclusive) {
            return empty();
        } else {
            return StreamSupport.intStream(
                    new Streams.RangeIntSpliterator(startInclusive, endExclusive, false), false);
        }
    }

    /**
     * Returns a sequential ordered {@code IntStream} from {@code startInclusive}
     * (inclusive) to {@code endInclusive} (inclusive) by an incremental step of
     * {@code 1}.
     *
     * @apiNote
     * <p>An equivalent sequence of increasing values can be produced
     * sequentially using a {@code for} loop as follows:
     * <pre>{@code
     *     for (int i = startInclusive; i <= endInclusive ; i++) { ... }
     * }</pre>
     *
     * @param startInclusive the (inclusive) initial value
     * @param endInclusive the inclusive upper bound
     * @return a sequential {@code IntStream} for the range of {@code int}
     *         elements
     */
    public static IntStream rangeClosed(int startInclusive, int endInclusive) {
        if (startInclusive > endInclusive) {
            return empty();
        } else {
            return StreamSupport.intStream(
                    new Streams.RangeIntSpliterator(startInclusive, endInclusive, true), false);
        }
    }

    /**
     * Creates a lazily concatenated stream whose elements are all the
     * elements of the first stream followed by all the elements of the
     * second stream.  The resulting stream is ordered if both
     * of the input streams are ordered, and parallel if either of the input
     * streams is parallel.  When the resulting stream is closed, the close
     * handlers for both input streams are invoked.
     *
     * @implNote
     * Use caution when constructing streams from repeated concatenation.
     * Accessing an element of a deeply concatenated stream can result in deep
     * call chains, or even {@code StackOverflowException}.
     *
     * @param a the first stream
     * @param b the second stream
     * @return the concatenation of the two input streams
     */
    public static IntStream concat(IntStream a, IntStream b) {
        Objects.requireNonNull(a);
        Objects.requireNonNull(b);

        Spliterator.OfInt split = new Streams.ConcatSpliterator.OfInt(
                a.spliterator(), b.spliterator());
        IntStream stream = StreamSupport.intStream(split, a.isParallel() || b.isParallel());
        return stream.onClose(Streams.composedClose(a, b));
    }

    /**
     * A mutable builder for an {@code IntStream}.
     *
     * <p>A stream builder has a lifecycle, which starts in a building
     * phase, during which elements can be added, and then transitions to a built
     * phase, after which elements may not be added.  The built phase
     * begins when the {@link #build()} method is called, which creates an
     * ordered stream whose elements are the elements that were added to the
     * stream builder, in the order they were added.
     *
     * @see IntStream#builder()
     * @since 1.8
     */
    public interface Builder extends IntConsumer {

        /**
         * Adds an element to the stream being built.
         *
         * @throws IllegalStateException if the builder has already transitioned
         * to the built state
         */
        @Override
        void accept(int t);

        /**
         * Adds an element to the stream being built.
         *
         * @implSpec
         * The default implementation behaves as if:
         * <pre>{@code
         *     accept(t)
         *     return this;
         * }</pre>
         *
         * @param t the element to add
         * @return {@code this} builder
         * @throws IllegalStateException if the builder has already transitioned
         * to the built state
         */
        default Builder add(int t) {
            accept(t);
            return this;
        }

        /**
         * Builds the stream, transitioning this builder to the built state.
         * An {@code IllegalStateException} is thrown if there are further
         * attempts to operate on the builder after it has entered the built
         * state.
         *
         * @return the built stream
         * @throws IllegalStateException if the builder has already transitioned to
         * the built state
         */
        IntStream build();
    }
}
