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The bit array data structure is implemented in Java as the BitSet class. Unfortunately, this fails to scale without compression. JavaEWAH is a word-aligned compressed variant of the Java bitset class. It uses a 64-bit run-length encoding (RLE) compression scheme. The goal of word-aligned compression is not to achieve the best compression, but rather to improve query processing time. Hence, we try to save CPU cycles, maybe at the expense of storage. However, the EWAH scheme we implemented is always more efficient storage-wise than an uncompressed bitmap (implemented in Java as the BitSet class). Unlike some alternatives, javaewah does not rely on a patented scheme.

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package com.googlecode.javaewah32;

/*
 * Copyright 2009-2016, Daniel Lemire, Cliff Moon, David McIntosh, Robert Becho, Google Inc., Veronika Zenz, Owen Kaser, Gregory Ssi-Yan-Kai, Rory Graves
 * Licensed under the Apache License, Version 2.0.
 */

import com.googlecode.javaewah.IntIterator;

import static com.googlecode.javaewah32.EWAHCompressedBitmap32.WORD_IN_BITS;

/**
 * The ReverseIntIterator32 is the 32 bit implementation of the IntIterator
 * interface, which efficiently returns the stream of integers represented by a
 * ReverseEWAHIterator32 in reverse order.
 *
 * @author Gregory Ssi-Yan-Kai
 */
final class ReverseIntIterator32 implements IntIterator {

    private final ReverseEWAHIterator32 ewahIter;
    private final int sizeInBits;
    private final Buffer32 buffer;
    private int position;
    private boolean runningBit;
    private int runningLength;
    private int word;
    private int wordPosition;
    private int wordLength;
    private int literalPosition;
    private boolean hasNext;

    ReverseIntIterator32(ReverseEWAHIterator32 ewahIter, int sizeInBits) {
        this.ewahIter = ewahIter;
        this.sizeInBits = sizeInBits;
        this.buffer = ewahIter.buffer();
        this.runningLength = sizeInBits - 1;
        this.hasNext = this.moveToPreviousRLW();
    }

    @Override
    public boolean hasNext() {
        return this.hasNext;
    }

    @Override
    public int next() {
        final int answer;
        if (literalHasNext()) {
            final int t = this.word & -this.word;
            answer = this.literalPosition - Integer.bitCount(t - 1);
            this.word ^= t;
        } else {
            answer = this.position--;
        }
        this.hasNext = this.moveToPreviousRLW();
        return answer;
    }

    private boolean moveToPreviousRLW() {
        while (!literalHasNext() && !runningHasNext()) {
            if (!this.ewahIter.hasPrevious()) {
                return false;
            }
            setRLW(this.ewahIter.previous());
        }
        return true;
    }

    private void setRLW(RunningLengthWord32 rlw) {
        this.wordLength = rlw.getNumberOfLiteralWords();
        this.wordPosition = this.ewahIter.position();
        this.position = this.runningLength;
        this.runningLength -= WORD_IN_BITS * (rlw.getRunningLength() + this.wordLength);
        if (this.position == this.sizeInBits - 1) {
            final int usedBitsInLast = this.sizeInBits % WORD_IN_BITS;
            if(usedBitsInLast > 0) {
                this.runningLength += WORD_IN_BITS - usedBitsInLast;
                if (this.wordLength > 0) {
                    this.word = Integer.reverse(this.buffer.getWord(this.wordPosition + this.wordLength--));
                    this.word = (this.word >>> (WORD_IN_BITS - usedBitsInLast));
                    this.literalPosition = this.position;
                    this.position -= usedBitsInLast;
                }
            }
        }
        this.runningBit = rlw.getRunningBit();
    }

    private boolean runningHasNext() {
        return this.runningBit && this.runningLength < this.position;
    }

    private boolean literalHasNext() {
        while (this.word == 0 && this.wordLength > 0) {
            this.word = Integer.reverse(this.buffer.getWord(this.wordPosition + this.wordLength--));
            this.literalPosition = this.position;
            this.position -= WORD_IN_BITS;
        }
        return this.word != 0;
    }

}