OpenBitSet

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

using System;



namespace Lucene.Net.Util
{

    /// <summary>An "open" BitSet implementation that allows direct access to the array of words
    /// storing the bits.
    /// <p/>
    /// Unlike java.util.bitset, the fact that bits are packed into an array of longs
    /// is part of the interface.  This allows efficient implementation of other algorithms
    /// by someone other than the author.  It also allows one to efficiently implement
    /// alternate serialization or interchange formats.
    /// <p/>
    /// <code>OpenBitSet</code> is faster than <code>java.util.BitSet</code> in most operations
    /// and *much* faster at calculating cardinality of sets and results of set operations.
    /// It can also handle sets of larger cardinality (up to 64 * 2**32-1)
    /// <p/>
    /// The goals of <code>OpenBitSet</code> are the fastest implementation possible, and
    /// maximum code reuse.  Extra safety and encapsulation
    /// may always be built on top, but if that's built in, the cost can never be removed (and
    /// hence people re-implement their own version in order to get better performance).
    /// If you want a "safe", totally encapsulated (and slower and limited) BitSet
    /// class, use <code>java.util.BitSet</code>.
    /// <p/>
    /// <h3>Performance Results</h3>
    ///
    /// Test system: Pentium 4, Sun Java 1.5_06 -server -Xbatch -Xmx64M
    /// <br/>BitSet size = 1,000,000
    /// <br/>Results are java.util.BitSet time divided by OpenBitSet time.
    /// <table border="1">
    /// <tr>
    /// <th></th> <th>cardinality</th> <th>intersect_count</th> <th>union</th> <th>nextSetBit</th> <th>get</th> <th>iterator</th>
    /// </tr>
    /// <tr>
    /// <th>50% full</th> <td>3.36</td> <td>3.96</td> <td>1.44</td> <td>1.46</td> <td>1.99</td> <td>1.58</td>
    /// </tr>
    /// <tr>
    /// <th>1% full</th> <td>3.31</td> <td>3.90</td> <td>&#160;</td> <td>1.04</td> <td>&#160;</td> <td>0.99</td>
    /// </tr>
    /// </table>
    /// <br/>
    /// Test system: AMD Opteron, 64 bit linux, Sun Java 1.5_06 -server -Xbatch -Xmx64M
    /// <br/>BitSet size = 1,000,000
    /// <br/>Results are java.util.BitSet time divided by OpenBitSet time.
    /// <table border="1">
    /// <tr>
    /// <th></th> <th>cardinality</th> <th>intersect_count</th> <th>union</th> <th>nextSetBit</th> <th>get</th> <th>iterator</th>
    /// </tr>
    /// <tr>
    /// <th>50% full</th> <td>2.50</td> <td>3.50</td> <td>1.00</td> <td>1.03</td> <td>1.12</td> <td>1.25</td>
    /// </tr>
    /// <tr>
    /// <th>1% full</th> <td>2.51</td> <td>3.49</td> <td>&#160;</td> <td>1.00</td> <td>&#160;</td> <td>1.02</td>
    /// </tr>
    /// </table>
    /// </summary>
    /// <version>  $Id$
    /// </version>

    [Serializable]
    public class OpenBitSet : System.ICloneable
    {
        protected internal long[] bits;
        protected internal int wlen; // number of words (elements) used in the array

        /// <summary>Constructs an OpenBitSet large enough to hold numBits.
        ///
        /// </summary>
        /// <param name="numBits">
        /// </param>
        public OpenBitSet(long numBits)
        {
            bits = new long[Bits2words(numBits)];
            wlen = bits.Length;
        }

        public OpenBitSet()
            : this(64)
        {
        }

        /// <summary>Constructs an OpenBitSet from an existing long[].
        /// <br/>
        /// The first 64 bits are in long[0],
        /// with bit index 0 at the least significant bit, and bit index 63 at the most significant.
        /// Given a bit index,
        /// the word containing it is long[index/64], and it is at bit number index%64 within that word.
        /// <p/>
        /// numWords are the number of elements in the array that contain
        /// set bits (non-zero longs).
        /// numWords should be &lt;= bits.length, and
        /// any existing words in the array at position &gt;= numWords should be zero.
        ///
        /// </summary>
        public OpenBitSet(long[] bits, int numWords)
        {
            this.bits = bits;
            this.wlen = numWords;
        }

        /// <summary>This DocIdSet implementation is cacheable. </summary>
        public bool IsCacheable()
        {
            return true;
        }

        /// <summary>Returns the current capacity in bits (1 greater than the index of the last bit) </summary>
        public virtual long Capacity()
        {
            return bits.Length << 6;
        }

        /// <summary> Returns the current capacity of this set.  Included for
        /// compatibility.  This is *not* equal to {@link #cardinality}
        /// </summary>
        public virtual long Size()
        {
            return Capacity();
        }

        /// <summary>Returns true if there are no set bits </summary>
        public virtual bool IsEmpty()
        {
            return Cardinality() == 0;
        }

        /// <summary>Expert: returns the long[] storing the bits </summary>
        public virtual long[] GetBits()
        {
            return bits;
        }

        /// <summary>Expert: sets a new long[] to use as the bit storage </summary>
        public virtual void SetBits(long[] bits)
        {
            this.bits = bits;
        }

        /// <summary>Expert: gets the number of longs in the array that are in use </summary>
        public virtual int GetNumWords()
        {
            return wlen;
        }

        /// <summary>Expert: sets the number of longs in the array that are in use </summary>
        public virtual void SetNumWords(int nWords)
        {
            this.wlen = nWords;
        }



        /// <summary>Returns true or false for the specified bit index. </summary>
        public virtual bool Get(int index)
        {
            int i = index >> 6; // div 64
            // signed shift will keep a negative index and force an
            // array-index-out-of-bounds-exception, removing the need for an explicit check.
            if (i >= bits.Length)
                return false;

            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            return (bits[i] & bitmask) != 0;
        }


        /// <summary>Returns true or false for the specified bit index.
        /// The index should be less than the OpenBitSet size
        /// </summary>
        public virtual bool FastGet(int index)
        {
            int i = index >> 6; // div 64
            // signed shift will keep a negative index and force an
            // array-index-out-of-bounds-exception, removing the need for an explicit check.
            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            return (bits[i] & bitmask) != 0;
        }



        /// <summary>Returns true or false for the specified bit index</summary>
        public virtual bool Get(long index)
        {
            int i = (int)(index >> 6); // div 64
            if (i >= bits.Length)
                return false;
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            return (bits[i] & bitmask) != 0;
        }

        /// <summary>Returns true or false for the specified bit index.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual bool FastGet(long index)
        {
            int i = (int)(index >> 6); // div 64
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            return (bits[i] & bitmask) != 0;
        }

        /*
        // alternate implementation of get()
        public boolean get1(int index) {
        int i = index >> 6;                // div 64
        int bit = index & 0x3f;            // mod 64
        return ((bits[i]>>>bit) & 0x01) != 0;
        // this does a long shift and a bittest (on x86) vs
        // a long shift, and a long AND, (the test for zero is prob a no-op)
        // testing on a P4 indicates this is slower than (bits[i] & bitmask) != 0;
        }
        */


        /// <summary>returns 1 if the bit is set, 0 if not.
        /// The index should be less than the OpenBitSet size
        /// </summary>
        public virtual int GetBit(int index)
        {
            int i = index >> 6; // div 64
            int bit = index & 0x3f; // mod 64
            return ((int)((ulong)(bits[i]) >> bit)) & 0x01;
        }


        /*
        public boolean get2(int index) {
        int word = index >> 6;            // div 64
        int bit = index & 0x0000003f;     // mod 64
        return (bits[word] << bit) < 0;   // hmmm, this would work if bit order were reversed
        // we could right shift and check for parity bit, if it was available to us.
        }
        */

        /// <summary>sets a bit, expanding the set size if necessary </summary>
        public virtual void Set(long index)
        {
            int wordNum = ExpandingWordNum(index);
            int bit = (int)index & 0x3f;
            long bitmask = 1L << bit;
            bits[wordNum] |= bitmask;
        }


        /// <summary>Sets the bit at the specified index.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastSet(int index)
        {
            int wordNum = index >> 6; // div 64
            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] |= bitmask;
        }

        /// <summary>Sets the bit at the specified index.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastSet(long index)
        {
            int wordNum = (int)(index >> 6);
            int bit = (int)index & 0x3f;
            long bitmask = 1L << bit;
            bits[wordNum] |= bitmask;
        }

        /// <summary>Sets a range of bits, expanding the set size if necessary
        ///
        /// </summary>
        /// <param name="startIndex">lower index
        /// </param>
        /// <param name="endIndex">one-past the last bit to set
        /// </param>
        public virtual void Set(long startIndex, long endIndex)
        {
            if (endIndex <= startIndex)
                return;

            int startWord = (int)(startIndex >> 6);

            // since endIndex is one past the end, this is index of the last
            // word to be changed.
            int endWord = ExpandingWordNum(endIndex - 1);

            long startmask = -1L << (int)startIndex;
            long endmask = (long)(0xffffffffffffffffUL >> (int)-endIndex); // 64-(endIndex&0x3f) is the same as -endIndex due to wrap

            if (startWord == endWord)
            {
                bits[startWord] |= (startmask & endmask);
                return;
            }

            bits[startWord] |= startmask;
            for (int i = startWord + 1; i < endWord; i++)
                bits[i] = -1L;
            bits[endWord] |= endmask;
        }



        protected internal virtual int ExpandingWordNum(long index)
        {
            int wordNum = (int)(index >> 6);
            if (wordNum >= wlen)
            {
                EnsureCapacity(index + 1);
                wlen = wordNum + 1;
            }
            return wordNum;
        }


        /// <summary>clears a bit.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastClear(int index)
        {
            int wordNum = index >> 6;
            int bit = index & 0x03f;
            long bitmask = 1L << bit;
            bits[wordNum] &= ~bitmask;
            // hmmm, it takes one more instruction to clear than it does to set... any
            // way to work around this?  If there were only 63 bits per word, we could
            // use a right shift of 10111111...111 in binary to position the 0 in the
            // correct place (using sign extension).
            // Could also use Long.rotateRight() or rotateLeft() *if* they were converted
            // by the JVM into a native instruction.
            // bits[word] &= Long.rotateLeft(0xfffffffe,bit);
        }

        /// <summary>clears a bit.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastClear(long index)
        {
            int wordNum = (int)(index >> 6); // div 64
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] &= ~bitmask;
        }

        /// <summary>clears a bit, allowing access beyond the current set size without changing the size.</summary>
        public virtual void Clear(long index)
        {
            int wordNum = (int)(index >> 6); // div 64
            if (wordNum >= wlen)
                return;
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] &= ~bitmask;
        }

        /// <summary>Clears a range of bits.  Clearing past the end does not change the size of the set.
        ///
        /// </summary>
        /// <param name="startIndex">lower index
        /// </param>
        /// <param name="endIndex">one-past the last bit to clear
        /// </param>
        public virtual void Clear(int startIndex, int endIndex)
        {
            if (endIndex <= startIndex)
                return;

            int startWord = (startIndex >> 6);
            if (startWord >= wlen)
                return;

            // since endIndex is one past the end, this is index of the last
            // word to be changed.
            int endWord = ((endIndex - 1) >> 6);

            long startmask = -1L << startIndex;
            long endmask = (long)(0xffffffffffffffffUL >> -endIndex); // 64-(endIndex&0x3f) is the same as -endIndex due to wrap

            // invert masks since we are clearing
            startmask = ~startmask;
            endmask = ~endmask;

            if (startWord == endWord)
            {
                bits[startWord] &= (startmask | endmask);
                return;
            }

            bits[startWord] &= startmask;

            int middle = System.Math.Min(wlen, endWord);
            for (int i = startWord + 1; i < middle; i++)
                bits[i] = 0L;
            if (endWord < wlen)
            {
                bits[endWord] &= endmask;
            }
        }


        /// <summary>Clears a range of bits.  Clearing past the end does not change the size of the set.
        ///
        /// </summary>
        /// <param name="startIndex">lower index
        /// </param>
        /// <param name="endIndex">one-past the last bit to clear
        /// </param>
        public virtual void Clear(long startIndex, long endIndex)
        {
            if (endIndex <= startIndex)
                return;

            int startWord = (int)(startIndex >> 6);
            if (startWord >= wlen)
                return;

            // since endIndex is one past the end, this is index of the last
            // word to be changed.
            int endWord = (int)((endIndex - 1) >> 6);

            long startmask = -1L << (int)startIndex;
            long endmask = (long)(0xffffffffffffffffUL >> (int)-endIndex); // 64-(endIndex&0x3f) is the same as -endIndex due to wrap

            // invert masks since we are clearing
            startmask = ~startmask;
            endmask = ~endmask;

            if (startWord == endWord)
            {
                bits[startWord] &= (startmask | endmask);
                return;
            }

            bits[startWord] &= startmask;

            int middle = System.Math.Min(wlen, endWord);
            for (int i = startWord + 1; i < middle; i++)
                bits[i] = 0L;
            if (endWord < wlen)
            {
                bits[endWord] &= endmask;
            }
        }



        /// <summary>Sets a bit and returns the previous value.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual bool GetAndSet(int index)
        {
            int wordNum = index >> 6; // div 64
            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bool val = (bits[wordNum] & bitmask) != 0;
            bits[wordNum] |= bitmask;
            return val;
        }

        /// <summary>Sets a bit and returns the previous value.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual bool GetAndSet(long index)
        {
            int wordNum = (int)(index >> 6); // div 64
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bool val = (bits[wordNum] & bitmask) != 0;
            bits[wordNum] |= bitmask;
            return val;
        }

        /// <summary>flips a bit.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastFlip(int index)
        {
            int wordNum = index >> 6; // div 64
            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] ^= bitmask;
        }

        /// <summary>flips a bit.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual void FastFlip(long index)
        {
            int wordNum = (int)(index >> 6); // div 64
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] ^= bitmask;
        }

        /// <summary>flips a bit, expanding the set size if necessary </summary>
        public virtual void Flip(long index)
        {
            int wordNum = ExpandingWordNum(index);
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] ^= bitmask;
        }

        /// <summary>flips a bit and returns the resulting bit value.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual bool FlipAndGet(int index)
        {
            int wordNum = index >> 6; // div 64
            int bit = index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] ^= bitmask;
            return (bits[wordNum] & bitmask) != 0;
        }

        /// <summary>flips a bit and returns the resulting bit value.
        /// The index should be less than the OpenBitSet size.
        /// </summary>
        public virtual bool FlipAndGet(long index)
        {
            int wordNum = (int)(index >> 6); // div 64
            int bit = (int)index & 0x3f; // mod 64
            long bitmask = 1L << bit;
            bits[wordNum] ^= bitmask;
            return (bits[wordNum] & bitmask) != 0;
        }

        /// <summary>Flips a range of bits, expanding the set size if necessary
        ///
        /// </summary>
        /// <param name="startIndex">lower index
        /// </param>
        /// <param name="endIndex">one-past the last bit to flip
        /// </param>
        public virtual void Flip(long startIndex, long endIndex)
        {
            if (endIndex <= startIndex)
                return;
            int startWord = (int)(startIndex >> 6);

            // since endIndex is one past the end, this is index of the last
            // word to be changed.
            int endWord = ExpandingWordNum(endIndex - 1);

            /*** Grrr, java shifting wraps around so -1L>>>64 == -1
            * for that reason, make sure not to use endmask if the bits to flip will
            * be zero in the last word (redefine endWord to be the last changed...)
            long startmask = -1L << (startIndex & 0x3f);     // example: 11111...111000
            long endmask = -1L >>> (64-(endIndex & 0x3f));   // example: 00111...111111
            ***/

            long startmask = -1L << (int)startIndex;
            long endmask = (long)(0xffffffffffffffffUL >> (int)-endIndex); // 64-(endIndex&0x3f) is the same as -endIndex due to wrap

            if (startWord == endWord)
            {
                bits[startWord] ^= (startmask & endmask);
                return;
            }

            bits[startWord] ^= startmask;

            for (int i = startWord + 1; i < endWord; i++)
            {
                bits[i] = ~bits[i];
            }

            bits[endWord] ^= endmask;
        }


        /*
        public static int pop(long v0, long v1, long v2, long v3) {
        // derived from pop_array by setting last four elems to 0.
        // exchanges one pop() call for 10 elementary operations
        // saving about 7 instructions... is there a better way?
        long twosA=v0 & v1;
        long ones=v0^v1;

        long u2=ones^v2;
        long twosB =(ones&v2)|(u2&v3);
        ones=u2^v3;

        long fours=(twosA&twosB);
        long twos=twosA^twosB;

        return (pop(fours)<<2)
        + (pop(twos)<<1)
        + pop(ones);

        }
        */


        /// <returns> the number of set bits
        /// </returns>
        public virtual long Cardinality()
        {
            return BitUtil.Pop_array(bits, 0, wlen);
        }

        /// <summary>Returns the popcount or cardinality of the intersection of the two sets.
        /// Neither set is modified.
        /// </summary>
        public static long IntersectionCount(OpenBitSet a, OpenBitSet b)
        {
            return BitUtil.Pop_intersect(a.bits, b.bits, 0, System.Math.Min(a.wlen, b.wlen));
        }

        /// <summary>Returns the popcount or cardinality of the union of the two sets.
        /// Neither set is modified.
        /// </summary>
        public static long UnionCount(OpenBitSet a, OpenBitSet b)
        {
            long tot = BitUtil.Pop_union(a.bits, b.bits, 0, System.Math.Min(a.wlen, b.wlen));
            if (a.wlen < b.wlen)
            {
                tot += BitUtil.Pop_array(b.bits, a.wlen, b.wlen - a.wlen);
            }
            else if (a.wlen > b.wlen)
            {
                tot += BitUtil.Pop_array(a.bits, b.wlen, a.wlen - b.wlen);
            }
            return tot;
        }

        /// <summary>Returns the popcount or cardinality of "a and not b"
        /// or "intersection(a, not(b))".
        /// Neither set is modified.
        /// </summary>
        public static long AndNotCount(OpenBitSet a, OpenBitSet b)
        {
            long tot = BitUtil.Pop_andnot(a.bits, b.bits, 0, System.Math.Min(a.wlen, b.wlen));
            if (a.wlen > b.wlen)
            {
                tot += BitUtil.Pop_array(a.bits, b.wlen, a.wlen - b.wlen);
            }
            return tot;
        }

        /// <summary>Returns the popcount or cardinality of the exclusive-or of the two sets.
        /// Neither set is modified.
        /// </summary>
        public static long XorCount(OpenBitSet a, OpenBitSet b)
        {
            long tot = BitUtil.Pop_xor(a.bits, b.bits, 0, System.Math.Min(a.wlen, b.wlen));
            if (a.wlen < b.wlen)
            {
                tot += BitUtil.Pop_array(b.bits, a.wlen, b.wlen - a.wlen);
            }
            else if (a.wlen > b.wlen)
            {
                tot += BitUtil.Pop_array(a.bits, b.wlen, a.wlen - b.wlen);
            }
            return tot;
        }


        /// <summary>Returns the index of the first set bit starting at the index specified.
        /// -1 is returned if there are no more set bits.
        /// </summary>
        public virtual int NextSetBit(int index)
        {
            int i = index >> 6;
            if (i >= wlen)
                return -1;
            int subIndex = index & 0x3f; // index within the word
            long word = bits[i] >> subIndex; // skip all the bits to the right of index

            if (word != 0)
            {
                return (i << 6) + subIndex + BitUtil.Ntz(word);
            }

            while (++i < wlen)
            {
                word = bits[i];
                if (word != 0)
                    return (i << 6) + BitUtil.Ntz(word);
            }

            return -1;
        }

        /// <summary>Returns the index of the first set bit starting at the index specified.
        /// -1 is returned if there are no more set bits.
        /// </summary>
        public virtual long NextSetBit(long index)
        {
            int i = (int)(index >> 6);
            if (i >= wlen)
                return -1;
            int subIndex = (int)index & 0x3f; // index within the word
            long word = (long)((ulong)bits[i] >> subIndex); // skip all the bits to the right of index

            if (word != 0)
            {
                return (((long)i) << 6) + (subIndex + BitUtil.Ntz(word));
            }

            while (++i < wlen)
            {
                word = bits[i];
                if (word != 0)
                    return (((long)i) << 6) + BitUtil.Ntz(word);
            }

            return -1;
        }




        public virtual System.Object Clone()
        {
            try
            {
                OpenBitSet obs = new OpenBitSet((long[])bits.Clone(), wlen);
                //obs.bits = new long[obs.bits.Length];
                //obs.bits.CopyTo(obs.bits, 0); // hopefully an array clone is as fast(er) than arraycopy
                return obs;
            }
            catch (System.Exception e)
            {
                throw new System.SystemException(e.Message, e);
            }
        }

        /// <summary>this = this AND other </summary>
        public virtual void Intersect(OpenBitSet other)
        {
            int newLen = System.Math.Min(this.wlen, other.wlen);
            long[] thisArr = this.bits;
            long[] otherArr = other.bits;
            // testing against zero can be more efficient
            int pos = newLen;
            while (--pos >= 0)
            {
                thisArr[pos] &= otherArr[pos];
            }
            if (this.wlen > newLen)
            {
                // fill zeros from the new shorter length to the old length
                for (int i = newLen; i < this.wlen; i++)
                    bits[i] = 0L;
            }
            this.wlen = newLen;
        }

        /// <summary>this = this OR other </summary>
        public virtual void Union(OpenBitSet other)
        {
            int newLen = System.Math.Max(wlen, other.wlen);
            EnsureCapacityWords(newLen);

            long[] thisArr = this.bits;
            long[] otherArr = other.bits;
            int pos = System.Math.Min(wlen, other.wlen);
            while (--pos >= 0)
            {
                thisArr[pos] |= otherArr[pos];
            }
            if (this.wlen < newLen)
            {
                Array.Copy(otherArr, this.wlen, thisArr, this.wlen, newLen - this.wlen);
            }
            this.wlen = newLen;
        }


        /// <summary>Remove all elements set in other. this = this AND_NOT other </summary>
        public virtual void Remove(OpenBitSet other)
        {
            int idx = System.Math.Min(wlen, other.wlen);
            long[] thisArr = this.bits;
            long[] otherArr = other.bits;
            while (--idx >= 0)
            {
                thisArr[idx] &= ~otherArr[idx];
            }
        }

        /// <summary>this = this XOR other </summary>
        public virtual void Xor(OpenBitSet other)
        {
            int newLen = System.Math.Max(wlen, other.wlen);
            EnsureCapacityWords(newLen);

            long[] thisArr = this.bits;
            long[] otherArr = other.bits;
            int pos = System.Math.Min(wlen, other.wlen);
            while (--pos >= 0)
            {
                thisArr[pos] ^= otherArr[pos];
            }
            if (this.wlen < newLen)
            {
                Array.Copy(otherArr, this.wlen, thisArr, this.wlen, newLen - this.wlen);
            }
            this.wlen = newLen;
        }


        // some BitSet compatability methods

        //** see {@link intersect} */
        public virtual void And(OpenBitSet other)
        {
            Intersect(other);
        }

        //** see {@link union} */
        public virtual void Or(OpenBitSet other)
        {
            Union(other);
        }

        //** see {@link andNot} */
        public virtual void AndNot(OpenBitSet other)
        {
            Remove(other);
        }

        /// <summary>returns true if the sets have any elements in common </summary>
        public virtual bool Intersects(OpenBitSet other)
        {
            int pos = System.Math.Min(this.wlen, other.wlen);
            long[] thisArr = this.bits;
            long[] otherArr = other.bits;
            while (--pos >= 0)
            {
                if ((thisArr[pos] & otherArr[pos]) != 0)
                    return true;
            }
            return false;
        }



        /// <summary>Expand the long[] with the size given as a number of words (64 bit longs).
        /// getNumWords() is unchanged by this call.
        /// </summary>
        public virtual void EnsureCapacityWords(int numWords)
        {
            if (bits.Length < numWords)
            {
                bits = ArrayUtil.Grow(bits, numWords);
            }
        }

        /// <summary>Ensure that the long[] is big enough to hold numBits, expanding it if necessary.
        /// getNumWords() is unchanged by this call.
        /// </summary>
        public virtual void EnsureCapacity(long numBits)
        {
            EnsureCapacityWords(Bits2words(numBits));
        }

        /// <summary>Lowers numWords, the number of words in use,
        /// by checking for trailing zero words.
        /// </summary>
        public virtual void TrimTrailingZeros()
        {
            int idx = wlen - 1;
            while (idx >= 0 && bits[idx] == 0)
                idx--;
            wlen = idx + 1;
        }

        /// <summary>returns the number of 64 bit words it would take to hold numBits </summary>
        public static int Bits2words(long numBits)
        {
            return (int)((((numBits - 1) >> 6)) + 1);
        }


        /// <summary>returns true if both sets have the same bits set </summary>
        public override bool Equals(System.Object o)
        {
            if (this == o)
                return true;
            if (!(o is OpenBitSet))
                return false;
            OpenBitSet a;
            OpenBitSet b = (OpenBitSet)o;
            // make a the larger set.
            if (b.wlen > this.wlen)
            {
                a = b; b = this;
            }
            else
            {
                a = this;
            }

            // check for any set bits out of the range of b
            for (int i = a.wlen - 1; i >= b.wlen; i--)
            {
                if (a.bits[i] != 0)
                    return false;
            }

            for (int i = b.wlen - 1; i >= 0; i--)
            {
                if (a.bits[i] != b.bits[i])
                    return false;
            }

            return true;
        }

        public override int GetHashCode()
        {
            // Start with a zero hash and use a mix that results in zero if the input is zero.
            // This effectively truncates trailing zeros without an explicit check.
            long h = 0;
            for (int i = bits.Length; --i >= 0; )
            {
                h ^= bits[i];
                h = (h << 1) | (Support.URShift(h, 63)); // rotate left
            }
            // fold leftmost bits into right and add a constant to prevent
            // empty sets from returning 0, which is too common.
            return (int)(((h >> 32) ^ h) + 0x98761234);
        }


    }

    // from org.apache.solr.util rev 555343

    /// <summary>A variety of high efficiencly bit twiddling routines.
    ///
    /// </summary>
    /// <version>  $Id$
    /// </version>
    public class BitUtil
    {

        /// <summary>Returns the number of bits set in the long </summary>
        public static int Pop(long x)
        {
            /* Hacker's Delight 32 bit pop function:
            * http://www.hackersdelight.org/HDcode/newCode/pop_arrayHS.cc
            *
            int pop(unsigned x) {
            x = x - ((x >> 1) & 0x55555555);
            x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
            x = (x + (x >> 4)) & 0x0F0F0F0F;
            x = x + (x >> 8);
            x = x + (x >> 16);
            return x & 0x0000003F;
            }
            ***/

            // 64 bit java version of the C function from above
            x = x - ((Support.URShift(x, 1)) & 0x5555555555555555L);
            x = (x & 0x3333333333333333L) + ((Support.URShift(x, 2)) & 0x3333333333333333L);
            x = (x + (Support.URShift(x, 4))) & 0x0F0F0F0F0F0F0F0FL;
            x = x + (Support.URShift(x, 8));
            x = x + (Support.URShift(x, 16));
            x = x + (Support.URShift(x, 32));
            return ((int)x) & 0x7F;
        }

        /// <summary> Returns the number of set bits in an array of longs. </summary>
        public static long Pop_array(long[] A, int wordOffset, int numWords)
        {
            /*
            * Robert Harley and David Seal's bit counting algorithm, as documented
            * in the revisions of Hacker's Delight
            * http://www.hackersdelight.org/revisions.pdf
            * http://www.hackersdelight.org/HDcode/newCode/pop_arrayHS.cc
            *
            * This function was adapted to Java, and extended to use 64 bit words.
            * if only we had access to wider registers like SSE from java...
            *
            * This function can be transformed to compute the popcount of other functions
            * on bitsets via something like this:
            * sed 's/A\[\([^]]*\)\]/\(A[\1] \& B[\1]\)/g'
            *
            */
            int n = wordOffset + numWords;
            long tot = 0, tot8 = 0;
            long ones = 0, twos = 0, fours = 0;

            int i;
            for (i = wordOffset; i <= n - 8; i += 8)
            {
                /***  C macro from Hacker's Delight
                #define CSA(h,l, a,b,c) \
                {unsigned u = a ^ b; unsigned v = c; \
                h = (a & b) | (u & v); l = u ^ v;}
                ***/

                long twosA, twosB, foursA, foursB, eights;

                // CSA(twosA, ones, ones, A[i], A[i+1])
                {
                    long b = A[i], c = A[i + 1];
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, A[i+2], A[i+3])
                {
                    long b = A[i + 2], c = A[i + 3];
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursA, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                //CSA(twosA, ones, ones, A[i+4], A[i+5])
                {
                    long b = A[i + 4], c = A[i + 5];
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, A[i+6], A[i+7])
                {
                    long b = A[i + 6], c = A[i + 7];
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursB, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursB = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }

                //CSA(eights, fours, fours, foursA, foursB)
                {
                    long u = fours ^ foursA;
                    eights = (fours & foursA) | (u & foursB);
                    fours = u ^ foursB;
                }
                tot8 += Pop(eights);
            }

            // handle trailing words in a binary-search manner...
            // derived from the loop above by setting specific elements to 0.
            // the original method in Hackers Delight used a simple for loop:
            //   for (i = i; i < n; i++)      // Add in the last elements
            //  tot = tot + pop(A[i]);

            if (i <= n - 4)
            {
                long twosA, twosB, foursA, eights;
                {
                    long b = A[i], c = A[i + 1];
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long b = A[i + 2], c = A[i + 3];
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 4;
            }

            if (i <= n - 2)
            {
                long b = A[i], c = A[i + 1];
                long u = ones ^ b;
                long twosA = (ones & b) | (u & c);
                ones = u ^ c;

                long foursA = twos & twosA;
                twos = twos ^ twosA;

                long eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 2;
            }

            if (i < n)
            {
                tot += Pop(A[i]);
            }

            tot += (Pop(fours) << 2) + (Pop(twos) << 1) + Pop(ones) + (tot8 << 3);

            return tot;
        }

        /// <summary>Returns the popcount or cardinality of the two sets after an intersection.
        /// Neither array is modified.
        /// </summary>
        public static long Pop_intersect(long[] A, long[] B, int wordOffset, int numWords)
        {
            // generated from pop_array via sed 's/A\[\([^]]*\)\]/\(A[\1] \& B[\1]\)/g'
            int n = wordOffset + numWords;
            long tot = 0, tot8 = 0;
            long ones = 0, twos = 0, fours = 0;

            int i;
            for (i = wordOffset; i <= n - 8; i += 8)
            {
                long twosA, twosB, foursA, foursB, eights;

                // CSA(twosA, ones, ones, (A[i] & B[i]), (A[i+1] & B[i+1]))
                {
                    long b = (A[i] & B[i]), c = (A[i + 1] & B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+2] & B[i+2]), (A[i+3] & B[i+3]))
                {
                    long b = (A[i + 2] & B[i + 2]), c = (A[i + 3] & B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursA, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                //CSA(twosA, ones, ones, (A[i+4] & B[i+4]), (A[i+5] & B[i+5]))
                {
                    long b = (A[i + 4] & B[i + 4]), c = (A[i + 5] & B[i + 5]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+6] & B[i+6]), (A[i+7] & B[i+7]))
                {
                    long b = (A[i + 6] & B[i + 6]), c = (A[i + 7] & B[i + 7]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursB, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursB = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }

                //CSA(eights, fours, fours, foursA, foursB)
                {
                    long u = fours ^ foursA;
                    eights = (fours & foursA) | (u & foursB);
                    fours = u ^ foursB;
                }
                tot8 += Pop(eights);
            }


            if (i <= n - 4)
            {
                long twosA, twosB, foursA, eights;
                {
                    long b = (A[i] & B[i]), c = (A[i + 1] & B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long b = (A[i + 2] & B[i + 2]), c = (A[i + 3] & B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 4;
            }

            if (i <= n - 2)
            {
                long b = (A[i] & B[i]), c = (A[i + 1] & B[i + 1]);
                long u = ones ^ b;
                long twosA = (ones & b) | (u & c);
                ones = u ^ c;

                long foursA = twos & twosA;
                twos = twos ^ twosA;

                long eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 2;
            }

            if (i < n)
            {
                tot += Pop((A[i] & B[i]));
            }

            tot += (Pop(fours) << 2) + (Pop(twos) << 1) + Pop(ones) + (tot8 << 3);

            return tot;
        }

        /// <summary>Returns the popcount or cardinality of the union of two sets.
        /// Neither array is modified.
        /// </summary>
        public static long Pop_union(long[] A, long[] B, int wordOffset, int numWords)
        {
            // generated from pop_array via sed 's/A\[\([^]]*\)\]/\(A[\1] \| B[\1]\)/g'
            int n = wordOffset + numWords;
            long tot = 0, tot8 = 0;
            long ones = 0, twos = 0, fours = 0;

            int i;
            for (i = wordOffset; i <= n - 8; i += 8)
            {
                /***  C macro from Hacker's Delight
                #define CSA(h,l, a,b,c) \
                {unsigned u = a ^ b; unsigned v = c; \
                h = (a & b) | (u & v); l = u ^ v;}
                ***/

                long twosA, twosB, foursA, foursB, eights;

                // CSA(twosA, ones, ones, (A[i] | B[i]), (A[i+1] | B[i+1]))
                {
                    long b = (A[i] | B[i]), c = (A[i + 1] | B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+2] | B[i+2]), (A[i+3] | B[i+3]))
                {
                    long b = (A[i + 2] | B[i + 2]), c = (A[i + 3] | B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursA, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                //CSA(twosA, ones, ones, (A[i+4] | B[i+4]), (A[i+5] | B[i+5]))
                {
                    long b = (A[i + 4] | B[i + 4]), c = (A[i + 5] | B[i + 5]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+6] | B[i+6]), (A[i+7] | B[i+7]))
                {
                    long b = (A[i + 6] | B[i + 6]), c = (A[i + 7] | B[i + 7]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursB, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursB = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }

                //CSA(eights, fours, fours, foursA, foursB)
                {
                    long u = fours ^ foursA;
                    eights = (fours & foursA) | (u & foursB);
                    fours = u ^ foursB;
                }
                tot8 += Pop(eights);
            }


            if (i <= n - 4)
            {
                long twosA, twosB, foursA, eights;
                {
                    long b = (A[i] | B[i]), c = (A[i + 1] | B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long b = (A[i + 2] | B[i + 2]), c = (A[i + 3] | B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 4;
            }

            if (i <= n - 2)
            {
                long b = (A[i] | B[i]), c = (A[i + 1] | B[i + 1]);
                long u = ones ^ b;
                long twosA = (ones & b) | (u & c);
                ones = u ^ c;

                long foursA = twos & twosA;
                twos = twos ^ twosA;

                long eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 2;
            }

            if (i < n)
            {
                tot += Pop((A[i] | B[i]));
            }

            tot += (Pop(fours) << 2) + (Pop(twos) << 1) + Pop(ones) + (tot8 << 3);

            return tot;
        }

        /// <summary>Returns the popcount or cardinality of A &amp; ~B
        /// Neither array is modified.
        /// </summary>
        public static long Pop_andnot(long[] A, long[] B, int wordOffset, int numWords)
        {
            // generated from pop_array via sed 's/A\[\([^]]*\)\]/\(A[\1] \& ~B[\1]\)/g'
            int n = wordOffset + numWords;
            long tot = 0, tot8 = 0;
            long ones = 0, twos = 0, fours = 0;

            int i;
            for (i = wordOffset; i <= n - 8; i += 8)
            {
                /***  C macro from Hacker's Delight
                #define CSA(h,l, a,b,c) \
                {unsigned u = a ^ b; unsigned v = c; \
                h = (a & b) | (u & v); l = u ^ v;}
                ***/

                long twosA, twosB, foursA, foursB, eights;

                // CSA(twosA, ones, ones, (A[i] & ~B[i]), (A[i+1] & ~B[i+1]))
                {
                    long b = (A[i] & ~B[i]), c = (A[i + 1] & ~B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+2] & ~B[i+2]), (A[i+3] & ~B[i+3]))
                {
                    long b = (A[i + 2] & ~B[i + 2]), c = (A[i + 3] & ~B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursA, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                //CSA(twosA, ones, ones, (A[i+4] & ~B[i+4]), (A[i+5] & ~B[i+5]))
                {
                    long b = (A[i + 4] & ~B[i + 4]), c = (A[i + 5] & ~B[i + 5]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+6] & ~B[i+6]), (A[i+7] & ~B[i+7]))
                {
                    long b = (A[i + 6] & ~B[i + 6]), c = (A[i + 7] & ~B[i + 7]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursB, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursB = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }

                //CSA(eights, fours, fours, foursA, foursB)
                {
                    long u = fours ^ foursA;
                    eights = (fours & foursA) | (u & foursB);
                    fours = u ^ foursB;
                }
                tot8 += Pop(eights);
            }


            if (i <= n - 4)
            {
                long twosA, twosB, foursA, eights;
                {
                    long b = (A[i] & ~B[i]), c = (A[i + 1] & ~B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long b = (A[i + 2] & ~B[i + 2]), c = (A[i + 3] & ~B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 4;
            }

            if (i <= n - 2)
            {
                long b = (A[i] & ~B[i]), c = (A[i + 1] & ~B[i + 1]);
                long u = ones ^ b;
                long twosA = (ones & b) | (u & c);
                ones = u ^ c;

                long foursA = twos & twosA;
                twos = twos ^ twosA;

                long eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 2;
            }

            if (i < n)
            {
                tot += Pop((A[i] & ~B[i]));
            }

            tot += (Pop(fours) << 2) + (Pop(twos) << 1) + Pop(ones) + (tot8 << 3);

            return tot;
        }

        public static long Pop_xor(long[] A, long[] B, int wordOffset, int numWords)
        {
            int n = wordOffset + numWords;
            long tot = 0, tot8 = 0;
            long ones = 0, twos = 0, fours = 0;

            int i;
            for (i = wordOffset; i <= n - 8; i += 8)
            {
                /***  C macro from Hacker's Delight
                #define CSA(h,l, a,b,c) \
                {unsigned u = a ^ b; unsigned v = c; \
                h = (a & b) | (u & v); l = u ^ v;}
                ***/

                long twosA, twosB, foursA, foursB, eights;

                // CSA(twosA, ones, ones, (A[i] ^ B[i]), (A[i+1] ^ B[i+1]))
                {
                    long b = (A[i] ^ B[i]), c = (A[i + 1] ^ B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+2] ^ B[i+2]), (A[i+3] ^ B[i+3]))
                {
                    long b = (A[i + 2] ^ B[i + 2]), c = (A[i + 3] ^ B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursA, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                //CSA(twosA, ones, ones, (A[i+4] ^ B[i+4]), (A[i+5] ^ B[i+5]))
                {
                    long b = (A[i + 4] ^ B[i + 4]), c = (A[i + 5] ^ B[i + 5]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                // CSA(twosB, ones, ones, (A[i+6] ^ B[i+6]), (A[i+7] ^ B[i+7]))
                {
                    long b = (A[i + 6] ^ B[i + 6]), c = (A[i + 7] ^ B[i + 7]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                //CSA(foursB, twos, twos, twosA, twosB)
                {
                    long u = twos ^ twosA;
                    foursB = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }

                //CSA(eights, fours, fours, foursA, foursB)
                {
                    long u = fours ^ foursA;
                    eights = (fours & foursA) | (u & foursB);
                    fours = u ^ foursB;
                }
                tot8 += Pop(eights);
            }


            if (i <= n - 4)
            {
                long twosA, twosB, foursA, eights;
                {
                    long b = (A[i] ^ B[i]), c = (A[i + 1] ^ B[i + 1]);
                    long u = ones ^ b;
                    twosA = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long b = (A[i + 2] ^ B[i + 2]), c = (A[i + 3] ^ B[i + 3]);
                    long u = ones ^ b;
                    twosB = (ones & b) | (u & c);
                    ones = u ^ c;
                }
                {
                    long u = twos ^ twosA;
                    foursA = (twos & twosA) | (u & twosB);
                    twos = u ^ twosB;
                }
                eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 4;
            }

            if (i <= n - 2)
            {
                long b = (A[i] ^ B[i]), c = (A[i + 1] ^ B[i + 1]);
                long u = ones ^ b;
                long twosA = (ones & b) | (u & c);
                ones = u ^ c;

                long foursA = twos & twosA;
                twos = twos ^ twosA;

                long eights = fours & foursA;
                fours = fours ^ foursA;

                tot8 += Pop(eights);
                i += 2;
            }

            if (i < n)
            {
                tot += Pop((A[i] ^ B[i]));
            }

            tot += (Pop(fours) << 2) + (Pop(twos) << 1) + Pop(ones) + (tot8 << 3);

            return tot;
        }

        /* python code to generate ntzTable
        def ntz(val):
        if val==0: return 8
        i=0
        while (val&0x01)==0:
        i = i+1
        val >>= 1
        return i
        print ','.join([ str(ntz(i)) for i in range(256) ])
        ***/
        /// <summary>table of number of trailing zeros in a byte </summary>
        public static readonly sbyte[] ntzTable = new sbyte[] { 8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 };


        /// <summary>Returns number of trailing zeros in a 64 bit long value. </summary>
        public static int Ntz(long val)
        {
            // A full binary search to determine the low byte was slower than
            // a linear search for nextSetBit().  This is most likely because
            // the implementation of nextSetBit() shifts bits to the right, increasing
            // the probability that the first non-zero byte is in the rhs.
            //
            // This implementation does a single binary search at the top level only
            // so that all other bit shifting can be done on ints instead of longs to
            // remain friendly to 32 bit architectures.  In addition, the case of a
            // non-zero first byte is checked for first because it is the most common
            // in dense bit arrays.

            int lower = (int)val;
            int lowByte = lower & 0xff;
            if (lowByte != 0)
                return ntzTable[lowByte];

            if (lower != 0)
            {
                lowByte = (Support.URShift(lower, 8)) & 0xff;
                if (lowByte != 0)
                    return ntzTable[lowByte] + 8;
                lowByte = (Support.URShift(lower, 16)) & 0xff;
                if (lowByte != 0)
                    return ntzTable[lowByte] + 16;
                // no need to mask off low byte for the last byte in the 32 bit word
                // no need to check for zero on the last byte either.
                return ntzTable[Support.URShift(lower, 24)] + 24;
            }
            else
            {
                // grab upper 32 bits
                int upper = (int)(val >> 32);
                lowByte = upper & 0xff;
                if (lowByte != 0)
                    return ntzTable[lowByte] + 32;
                lowByte = (Support.URShift(upper, 8)) & 0xff;
                if (lowByte != 0)
                    return ntzTable[lowByte] + 40;
                lowByte = (Support.URShift(upper, 16)) & 0xff;
                if (lowByte != 0)
                    return ntzTable[lowByte] + 48;
                // no need to mask off low byte for the last byte in the 32 bit word
                // no need to check for zero on the last byte either.
                return ntzTable[Support.URShift(upper, 24)] + 56;
            }
        }

        /// <summary>Returns number of trailing zeros in a 32 bit int value. </summary>
        public static int Ntz(int val)
        {
            // This implementation does a single binary search at the top level only.
            // In addition, the case of a non-zero first byte is checked for first
            // because it is the most common in dense bit arrays.

            int lowByte = val & 0xff;
            if (lowByte != 0)
                return ntzTable[lowByte];
            lowByte = (Support.URShift(val, 8)) & 0xff;
            if (lowByte != 0)
                return ntzTable[lowByte] + 8;
            lowByte = (Support.URShift(val, 16)) & 0xff;
            if (lowByte != 0)
                return ntzTable[lowByte] + 16;
            // no need to mask off low byte for the last byte.
            // no need to check for zero on the last byte either.
            return ntzTable[Support.URShift(val, 24)] + 24;
        }

        /// <summary>returns 0 based index of first set bit
        /// (only works for x!=0)
        /// <br/> This is an alternate implementation of ntz()
        /// </summary>
        public static int Ntz2(long x)
        {
            int n = 0;
            int y = (int)x;
            if (y == 0)
            {
                n += 32; y = (int)(Support.URShift(x, 32));
            } // the only 64 bit shift necessary
            if ((y & 0x0000FFFF) == 0)
            {
                n += 16; y = Support.URShift(y, 16);
            }
            if ((y & 0x000000FF) == 0)
            {
                n += 8; y = Support.URShift(y, 8);
            }
            return (ntzTable[y & 0xff]) + n;
        }

        /// <summary>returns 0 based index of first set bit
        /// <br/> This is an alternate implementation of ntz()
        /// </summary>
        public static int Ntz3(long x)
        {
            // another implementation taken from Hackers Delight, extended to 64 bits
            // and converted to Java.
            // Many 32 bit ntz algorithms are at http://www.hackersdelight.org/HDcode/ntz.cc
            int n = 1;

            // do the first step as a long, all others as ints.
            int y = (int)x;
            if (y == 0)
            {
                n += 32; y = (int)(Support.URShift(x, 32));
            }
            if ((y & 0x0000FFFF) == 0)
            {
                n += 16; y = Support.URShift(y, 16);
            }
            if ((y & 0x000000FF) == 0)
            {
                n += 8; y = Support.URShift(y, 8);
            }
            if ((y & 0x0000000F) == 0)
            {
                n += 4; y = Support.URShift(y, 4);
            }
            if ((y & 0x00000003) == 0)
            {
                n += 2; y = Support.URShift(y, 2);
            }
            return n - (y & 1);
        }


        /// <summary>returns true if v is a power of two or zero</summary>
        public static bool IsPowerOfTwo(int v)
        {
            return ((v & (v - 1)) == 0);
        }

        /// <summary>returns true if v is a power of two or zero</summary>
        public static bool IsPowerOfTwo(long v)
        {
            return ((v & (v - 1)) == 0);
        }

        /// <summary>returns the next highest power of two, or the current value if it's already a power of two or zero</summary>
        public static int NextHighestPowerOfTwo(int v)
        {
            v--;
            v |= v >> 1;
            v |= v >> 2;
            v |= v >> 4;
            v |= v >> 8;
            v |= v >> 16;
            v++;
            return v;
        }

        /// <summary>returns the next highest power of two, or the current value if it's already a power of two or zero</summary>
        public static long NextHighestPowerOfTwo(long v)
        {
            v--;
            v |= v >> 1;
            v |= v >> 2;
            v |= v >> 4;
            v |= v >> 8;
            v |= v >> 16;
            v |= v >> 32;
            v++;
            return v;
        }
    }

    /// <summary> Methods for manipulating arrays.</summary>
    public sealed class ArrayUtil
    {
        /*
        Begin Apache Harmony code

        Revision taken on Friday, June 12. https://svn.apache.org/repos/asf/harmony/enhanced/classlib/archive/java6/modules/luni/src/main/java/java/lang/Integer.java

        */

        /// <summary> Parses the string argument as if it was an int value and returns the
        /// result. Throws NumberFormatException if the string does not represent an
        /// int quantity.
        ///
        /// </summary>
        /// <param name="chars">a string representation of an int quantity.
        /// </param>
        /// <returns> int the value represented by the argument
        /// </returns>
        /// <throws>  NumberFormatException if the argument could not be parsed as an int quantity. </throws>
        public static int ParseInt(char[] chars)
        {
            return ParseInt(chars, 0, chars.Length, 10);
        }

        /// <summary> Parses a char array into an int.</summary>
        /// <param name="chars">the character array
        /// </param>
        /// <param name="offset">The offset into the array
        /// </param>
        /// <param name="len">The length
        /// </param>
        /// <returns> the int
        /// </returns>
        /// <throws>  NumberFormatException if it can't parse </throws>
        public static int ParseInt(char[] chars, int offset, int len)
        {
            return ParseInt(chars, offset, len, 10);
        }

        /// <summary> Parses the string argument as if it was an int value and returns the
        /// result. Throws NumberFormatException if the string does not represent an
        /// int quantity. The second argument specifies the radix to use when parsing
        /// the value.
        ///
        /// </summary>
        /// <param name="chars">a string representation of an int quantity.
        /// </param>
        /// <param name="radix">the base to use for conversion.
        /// </param>
        /// <returns> int the value represented by the argument
        /// </returns>
        /// <throws>  NumberFormatException if the argument could not be parsed as an int quantity. </throws>
        public static int ParseInt(char[] chars, int offset, int len, int radix)
        {
            if (chars == null || radix < 2 || radix > 36)
            {
                throw new System.FormatException();
            }
            int i = 0;
            if (len == 0)
            {
                throw new System.FormatException("chars length is 0");
            }
            bool negative = chars[offset + i] == '-';
            if (negative && ++i == len)
            {
                throw new System.FormatException("can't convert to an int");
            }
            if (negative == true)
            {
                offset++;
                len--;
            }
            return Parse(chars, offset, len, radix, negative);
        }


        private static int Parse(char[] chars, int offset, int len, int radix, bool negative)
        {
            int max = System.Int32.MinValue / radix;
            int result = 0;
            for (int i = 0; i < len; i++)
            {
                int digit = (int)System.Char.GetNumericValue(chars[i + offset]);
                if (digit == -1)
                {
                    throw new System.FormatException("Unable to parse");
                }
                if (max > result)
                {
                    throw new System.FormatException("Unable to parse");
                }
                int next = result * radix - digit;
                if (next > result)
                {
                    throw new System.FormatException("Unable to parse");
                }
                result = next;
            }
            /*while (offset < len) {

            }*/
            if (!negative)
            {
                result = -result;
                if (result < 0)
                {
                    throw new System.FormatException("Unable to parse");
                }
            }
            return result;
        }


        /*

        END APACHE HARMONY CODE
        */


        public static int GetNextSize(int targetSize)
        {
            /* This over-allocates proportional to the list size, making room
            * for additional growth.  The over-allocation is mild, but is
            * enough to give linear-time amortized behavior over a long
            * sequence of appends() in the presence of a poorly-performing
            * system realloc().
            * The growth pattern is:  0, 4, 8, 16, 25, 35, 46, 58, 72, 88, ...
            */
            return (targetSize >> 3) + (targetSize < 9 ? 3 : 6) + targetSize;
        }

        public static int GetShrinkSize(int currentSize, int targetSize)
        {
            int newSize = GetNextSize(targetSize);
            // Only reallocate if we are "substantially" smaller.
            // This saves us from "running hot" (constantly making a
            // bit bigger then a bit smaller, over and over):
            if (newSize < currentSize / 2)
                return newSize;
            else
                return currentSize;
        }

        public static int[] Grow(int[] array, int minSize)
        {
            if (array.Length < minSize)
            {
                int[] newArray = new int[GetNextSize(minSize)];
                Array.Copy(array, 0, newArray, 0, array.Length);
                return newArray;
            }
            else
                return array;
        }

        public static int[] Grow(int[] array)
        {
            return Grow(array, 1 + array.Length);
        }

        public static int[] Shrink(int[] array, int targetSize)
        {
            int newSize = GetShrinkSize(array.Length, targetSize);
            if (newSize != array.Length)
            {
                int[] newArray = new int[newSize];
                Array.Copy(array, 0, newArray, 0, newSize);
                return newArray;
            }
            else
                return array;
        }

        public static long[] Grow(long[] array, int minSize)
        {
            if (array.Length < minSize)
            {
                long[] newArray = new long[GetNextSize(minSize)];
                Array.Copy(array, 0, newArray, 0, array.Length);
                return newArray;
            }
            else
                return array;
        }

        public static long[] Grow(long[] array)
        {
            return Grow(array, 1 + array.Length);
        }

        public static long[] Shrink(long[] array, int targetSize)
        {
            int newSize = GetShrinkSize(array.Length, targetSize);
            if (newSize != array.Length)
            {
                long[] newArray = new long[newSize];
                Array.Copy(array, 0, newArray, 0, newSize);
                return newArray;
            }
            else
                return array;
        }

        public static byte[] Grow(byte[] array, int minSize)
        {
            if (array.Length < minSize)
            {
                byte[] newArray = new byte[GetNextSize(minSize)];
                Array.Copy(array, 0, newArray, 0, array.Length);
                return newArray;
            }
            else
                return array;
        }

        public static byte[] Grow(byte[] array)
        {
            return Grow(array, 1 + array.Length);
        }

        public static byte[] Shrink(byte[] array, int targetSize)
        {
            int newSize = GetShrinkSize(array.Length, targetSize);
            if (newSize != array.Length)
            {
                byte[] newArray = new byte[newSize];
                Array.Copy(array, 0, newArray, 0, newSize);
                return newArray;
            }
            else
                return array;
        }

        /// <summary> Returns hash of chars in range start (inclusive) to
        /// end (inclusive)
        /// </summary>
        public static int HashCode(char[] array, int start, int end)
        {
            int code = 0;
            for (int i = end - 1; i >= start; i--)
                code = code * 31 + array[i];
            return code;
        }

        /// <summary> Returns hash of chars in range start (inclusive) to
        /// end (inclusive)
        /// </summary>
        public static int HashCode(byte[] array, int start, int end)
        {
            int code = 0;
            for (int i = end - 1; i >= start; i--)
                code = code * 31 + array[i];
            return code;
        }
    }

    public class Support
    {
        /// <summary>
        /// Performs an unsigned bitwise right shift with the specified number
        /// </summary>
        /// <param name="number">Number to operate on</param>
        /// <param name="bits">Ammount of bits to shift</param>
        /// <returns>The resulting number from the shift operation</returns>
        public static int URShift(int number, int bits)
        {
            return (int)(((uint)number) >> bits);
        }

        /// <summary>
        /// Performs an unsigned bitwise right shift with the specified number
        /// </summary>
        /// <param name="number">Number to operate on</param>
        /// <param name="bits">Ammount of bits to shift</param>
        /// <returns>The resulting number from the shift operation</returns>
        public static long URShift(long number, int bits)
        {
            return (long)(((ulong)number) >> bits);
        }
    }
}