BitVector.py

__version__ = '3.4.7'
__author__  = "Avinash Kak (kak@purdue.edu)"
__date__    = '2017-Janurary-26'
__url__     = 'https://engineering.purdue.edu/kak/dist/BitVector-3.4.7.html'
__copyright__ = "(C) 2017 Avinash Kak. Python Software Foundation."

__doc__ = '''

BitVector.py

Version: ''' + __version__ + '''
   

Date: ''' + __date__ + '''


@title
CHANGES IN THIS VERSION:

    Version 3.4.7 fixes a Python 3 specific bug in the write_to_file()
    method of the module.  While I was at it, I have also changed the name
    of the method write_bits_to_fileobject() to
    write_bits_to_stream_object() so that there is no confusion between
    write_to_file() and write_bits_to_fileobject().  For backward
    compatibility, write_bits_to_fileobject() will continue to work if you
    are writing a bitvector to a string stream object.

    Version 3.4.6 fixes what was hopefully the last remaining bug in using
    negative index values for slice assignments.

    See the "CHANGE HISTORY" section for a complete history of all the
    changes made in the different versions of this module.


@title
INTRODUCTION:
   
    The BitVector class is for a memory-efficient packed representation of
    bit arrays and for logical operations on such arrays. The operations
    supported on bit vectors are:

            __add__                for concatenation
            __and__                for bitwise logical AND
            __contains__
            __eq__, __ne__, __lt__, __le__, __gt__, __ge__
            __getitem__            for indexed and sliced access
            __int__                for returning integer value
            __invert__             for inverting the 1's and 0's
            __iter__               for iterating through 
            __len__                for len()
            __lshift__             for circular shifts to the left
            __or__                 for bitwise logical OR
            __rshift__             for circular shifts to the right
            __setitem__            for indexed and sliced setting
            __str__                for str()
            __xor__                for bitwise logical XOR
            close_file_object
            count_bits 
            count_bits_sparse      faster for sparse bit vectors     
            deep_copy
            divide_into_two
            gcd                    for greatest common divisor
            gen_random_bits
            get_bitvector_in_ascii
            get_bitvector_in_hex
            gf_divide_by_modulus   for modular divisions in GF(2^n)
            gf_MI                  for multiplicative inverse in GF(2^n)
            gf_multiply            for multiplications in GF(2)
            gf_multiply_modular    for multiplications in GF(2^n)
            hamming_distance
            int_val                for returning the integer value 
            is_power_of_2
            is_power_of_2_sparse   faster for sparse bit vectors
            jaccard_distance
            jaccard_similarity
            length                 
            min_canonical          for min int value canonical form
            multiplicative_inverse
            next_set_bit
            pad_from_left
            pad_from_right
            permute
            rank_of_bit_set_at_index
            read_bits_from_file
            reset
            reverse
            runs
            set_value
            shift_left             for non-circular left shift
            shift_right            for non-circular right shift
            test_for_primality
            unpermute
            write_bits_to_stream_object
            write_to_file

  
@title
CONSTRUCTING BIT VECTORS:

    You can construct a bit vector in the following different ways:

    @tagC0
    (C0)  You construct an EMPTY bit vector using the following syntax:

            bv  = BitVector(size = 0)

    @tagC1   
    (C1)  You can construct a bit vector directly from either a tuple or a
          list of bits, as in

            bv =  BitVector(bitlist = [1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1]) 

    @tagC2 
    (C2)  You can construct a bit vector from an integer by

            bv =  BitVector(intVal = 56789)

          The bits stored now will correspond to the binary representation
          of the integer.  The resulting bit vector is the shortest
          possible bit vector for the integer value supplied.  For example,
          when intVal is 0, the bit vector constructed will consist of just
          the bit 0.

    @tagC3
    (C3)  When initializing a bit vector with an intVal as shown above, you
          can also specify a size for the bit vector:

            bv = BitVector(intVal = 0, size = 8)

          will return the bit vector consisting of the bit pattern
          00000000.  The zero padding needed for meeting the size
          requirement is always on the left.  If the size supplied is
          smaller than what it takes to create the shortest possible bit
          vector for intVal, an exception is thrown.

    @tagC4
    (C4)  You can create a zero-initialized bit vector of a given size by

            bv  = BitVector(size = 62)

          This bit vector will hold exactly 62 bits, all initialized to
          the 0 bit value.

    @tagC5
    (C5)  You can construct a bit vector from a disk file by a two-step
          procedure. First you construct an instance of bit vector by
   
            bv  =  BitVector(filename = 'somefile')   

          This bit vector itself is incapable of holding the bits.  To now
          create bit vectors that actually hold the bits, you need to make
          the following sort of a call on the above variable bv:
 
            bv1 =  bv.read_bits_from_file(64)    

          bv1 will be a regular bit vector containing 64 bits from the disk
          file. If you want to re-read a file from the beginning for some
          reason, you must obviously first close the file object that was
          acquired with a call to the BitVector constructor with a filename
          argument.  This can be accomplished by

            bv.close_file_object()

    @tagC6
    (C6)  You can construct a bit vector from a string of 1's and 0's by
 
            bv  =  BitVector(bitstring = '110011110000')      

    @tagC7   
    (C7)  Yet another way to construct a bit vector is to read the bits
          directly from a file-like object, as in

            import io  
            x = "111100001111"
            fp_read = io.StringIO( x )
            bv = BitVector(fp = fp_read)
            print(bv)                              # 111100001111 

    @tagC8
    (C8)  You can also construct a bit vector directly from a text string
          as shown by the example:

            bv3 = BitVector(textstring = "hello")
            print(bv3)     # 0110100001100101011011000110110001101111
            mytext = bv3.get_bitvector_in_ascii()
            print mytext                           # hello

          The bit vector is constructed by using the one-byte ASCII
          encoding of the characters in the text string.

    @tagC9
    (C9)  You can also construct a bit vector directly from a string of hex
          digits as shown by the example:

            bv4 = BitVector(hexstring = "68656c6c6f")
            print(bv4)     # 0110100001100101011011000110110001101111
            myhexstring = bv4.get_bitvector_in_hex()
            print myhexstring                      # 68656c6c6

    @tagC10
    (C10) You can also construct a bit vector directly from a bytes type
          object you previously created in your script.  This can be useful
          when you are trying to recover the integer parameters stored in
          public and private keys.  A typical usage scenario:

            keydata = base64.b64decode(open(sys.argv[1]).read().split(None)[1])
            bv = BitVector.BitVector(rawbytes = keydata)
          
          where sys.argv[1] is meant to supply the name of a public key
          file (in this case an SSH RSA public key file).


@title   
OPERATIONS SUPPORTED BY THE BITVECTOR CLASS:

@title
DISPLAYING BIT VECTORS:

    @tag1
    (1) Since the BitVector class implements the __str__ method, a bit
        vector can be displayed on a terminal by

            print(bitvec)

        or, for only Python 2.x, by

            print bitvec 

        Basically, you can always obtain the string representation of a
        bit vector by

            str(bitvec)

        and integer value by

            int(bitvec)


@title
ACCESSING AND SETTING INDIVIDUAL BITS AND SLICES:

    @tag2   
    (2) Any single bit of a bit vector bv can be set to 1 or 0 by
 
            bv[M] = 1_or_0
            print( bv[M] )

        or, for just Python 2.x, by

            bv[M] = 1_or_0
            print bv[M]

        for accessing (and setting) the bit at the position that is indexed
        M.  You can retrieve the bit at position M by bv[M].  Note that the
        index 0 corresponds to the first bit at the left end of a bit
        pattern.  This is made possible by the implementation of the
        __getitem__ and __setitem__ methods.

    @tag3
    (3) A slice of a bit vector obtained by

            bv[i:j]

        is a bit vector constructed from the bits at index positions from i
        through j-1.  This is made possible by the implementation of the
        __getitem__ method.

    @tag4
    (4) You can also carry out slice assignment:

            bv1 = BitVector(size = 25)
            bv2 = BitVector(bitstring = '1010001')
            bv1[6:9]  = bv2[0:3]
            bv3 = BitVector(bitstring = '101')                 
            bv1[0:3]  = bv3

        The first slice assignment will set the 6th, 7th, and the 8th bits
        of the bit vector bv1 according to the first three bits of bv2.
        The second slice assignment will set the first three bits of bv1
        according to the three bits in bv3.  This is made possible by the
        slice setting code in the __setitem__ method.

    @tag5
    (5) You can iterate over a bit vector, as illustrated by

            for bit in bitvec:
                print(bit)

        This is made possible by the override definition for the special
        __iter__() method.

    @tag6
    (6) Negative subscripts for array-like indexing are supported.
        Therefore,

            bitvec[-i]

        is legal assuming that the index range is not violated.  A negative
        index carries the usual Python interpretation: The last element of
        a bit vector is indexed -1 and the first element -(n+1) if n is the
        total number of bits in the bit vector.  Negative subscripts are
        made possible by special-casing such access in the implementation
        of the __getitem__ method (actually it is the _getbit method).

    @tag7
    (7) You can reset a previously constructed bit vector to either the
        all-zeros state or the all-ones state by

            bv1 = BitVector(size = 25)
            ...
            ...
            bv1.reset(1)
            ...
            ...
            bv1.reset(0)

        The first call to reset() will set all the bits of bv1 to 1's and
        the second call all the bits to 0's.  What the method accomplishes
        can be thought of as in-place resetting of the bits.  The method
        does not return anything.


@title
LOGICAL OPERATIONS ON BIT VECTORS:

    @tag8   
    (8) Given two bit vectors bv1 and bv2, you can perform bitwise
        logical operations on them by

            result_bv  =  bv1 ^ bv2           # for bitwise XOR
            result_bv  =  bv1 & bv2           # for bitwise AND
            result_bv  =  bv1 | bv2           # for bitwise OR
            result_bv  =  ~bv1                # for bitwise negation

        These are made possible by implementing the __xor__, __and__,
        __or__, and __invert__ methods, respectively.


@title
COMPARING BIT VECTORS:

    @tag9
    (9) Given two bit vectors bv1 and bv2, you can carry out the following
        comparisons that return Boolean values:

            bv1 ==  bv2
            bv1 !=  bv2
            bv1 <   bv2
            bv1 <=  bv2
            bv1 >   bv2
            bv1 >=  bv2

        The equalities and inequalities are determined by the integer
        values associated with the bit vectors.  These operator
        overloadings are made possible by providing implementation code for
        __eq__, __ne__, __lt__, __le__, __gt__, and __ge__, respectively.

   
@title
OTHER SUPPORTED OPERATIONS:

   @tag10   
   (10) permute()
        unpermute()

        You can permute and unpermute bit vectors:

            bv_permuted   =  bv.permute(permutation_list)

            bv_unpermuted =  bv.unpermute(permutation_list)


        Both these methods return new bitvector objects.  Permuting a
        bitvector means that you select its bits in the sequence specified
        by the argument permutation_list. Calling unpermute() with the same
        argument permutation_list restores the sequence of bits to what it
        was in the original bitvector.

   @tag11 
   (11) circular shifts

        Left and right circular rotations can be carried out by
 
            bitvec  << N 

            bitvec  >> N

        for circular rotations to the left and to the right by N bit
        positions.  These operator overloadings are made possible by
        implementing the __lshift__ and __rshift__ methods, respectively.
        Note that both these operators return the bitvector on which they
        are invoked.  This allows for a chained invocation of these two
        operators.

   @tag12
   (12) shift_left()
        shift_right()

        If you want to shift in-place a bitvector non-circularly:

            bitvec = BitVector(bitstring = '10010000')
            bitvec.shift_left(3)              # 10000000
            bitvec.shift_right(3)             # 00010000
        
        As a bitvector is shifted non-circularly to the left or to the
        right, the exposed bit positions at the opposite end are filled
        with zeros. These two methods return the bitvector object on which
        they are invoked.  This is to allow for chained invocations of
        these methods.
        
   @tag13
   (13) divide_into_two()

        A bitvector containing an even number of bits can be divided into
        two equal parts by

            [left_half, right_half] = bitvec.divide_into_two()

        where left_half and right_half hold references to the two returned
        bitvectors.  The method throws an exception if called on a
        bitvector with an odd number of bits.

   @tag14
   (14) int_val()

        You can find the integer value of a bitvector object by

            bitvec.int_val()

        or by

            int(bitvec)

        As you expect, a call to int_val() returns an integer value.

   @tag15
   (15) string representation

        You can convert a bitvector into its string representation by

            str(bitvec)

   @tag16
   (16) concatenation

        Because __add__ is supplied, you can always join two bitvectors by

            bitvec3  =  bitvec1  +  bitvec2

        bitvec3 is a new bitvector object that contains all the bits of
        bitvec1 followed by all the bits of bitvec2.

   @tag17
   (17) length()

        You can find the length of a bitvector by

            len = bitvec.length()

   @tag18
   (18) deep_copy()

        You can make a deep copy of a bitvector by

            bitvec_copy =  bitvec.deep_copy()

        Subsequently, any alterations to either of the bitvector objects
        bitvec and bitvec_copy will not affect the other.

   @tag19
   (19) read_bits_from_file()

        As mentioned earlier, you can construct bitvectors directly from
        the bits in a disk file through the following calls.  As you can
        see, this requires two steps: First you make a call as illustrated
        by the first statement below.  The purpose of this call is to
        create a file object that is associated with the variable bv.
        Subsequent calls to read_bits_from_file(n) on this variable return
        a bitvector for each block of n bits thus read.  The
        read_bits_from_file() throws an exception if the argument n is not
        a multiple of 8.

            bv  =  BitVector(filename = 'somefile')   
            bv1 =  bv.read_bits_from_file(64)    
            bv2 =  bv.read_bits_from_file(64)    
            ...
            ...
            bv.close_file_object()

        When reading a file as shown above, you can test the attribute
        more_to_read of the bitvector object in order to find out if there
        is more to read in the file.  The while loop shown below reads all
        of a file in 64-bit blocks:

            bv = BitVector( filename = 'testinput4.txt' )
            print("Here are all the bits read from the file:")
            while (bv.more_to_read):
                bv_read = bv.read_bits_from_file( 64 )
                print(bv_read)
            bv.close_file_object()

        The size of the last bitvector constructed from a file corresponds
        to how many bytes remain unread in the file at that point.  It is
        your responsibility to zero-pad the last bitvector appropriately
        if, say, you are doing block encryption of the whole file.

   @tag20             
   (20) write_to_file()

        You can write a bit vector directly to a file by calling
        write_to_file(), as illustrated by the following example that reads
        one bitvector from a file and then writes it to another file:

            bv = BitVector(filename = 'input.txt')
            bv1 = bv.read_bits_from_file(64)        
            print(bv1)
            FILEOUT = open('output.bits', 'wb')
            bv1.write_to_file(FILEOUT)
            FILEOUT.close()
            bv = BitVector(filename = 'output.bits')
            bv2 = bv.read_bits_from_file(64)
            print(bv2)

        The method write_to_file() throws an exception if the size of the
        bitvector on which the method is invoked is not a multiple of 8.
        This method does not return anything.

        IMPORTANT FOR WINDOWS USERS: When writing an internally generated
                    bit vector out to a disk file, it is important to open
                    the file in the binary mode as shown.  Otherwise, the
                    bit pattern 00001010 ('\\n') in your bitstring will be
                    written out as 0000110100001010 ('\\r\\n'), which is
                    the linebreak on Windows machines.

   @tag21
   (21) write_bits_to_stream_object()

        You can also write a bitvector directly to a stream object, as
        illustrated by:

            fp_write = io.StringIO()
            bitvec.write_bits_to_stream_object(fp_write)
            print(fp_write.getvalue())   

        This method does not return anything. 

   @tag22
   (22) pad_from_left()
        pad_from_right()        

        You can pad a bitvector from the left or from the right with a
        designated number of zeros:

            bitvec.pad_from_left(n)

            bitvec.pad_from_right(n)

        These two methods return the bitvector object on which they are
        invoked. So you can think of these two calls as carrying out
        in-place extensions of the bitvector (although, under the hood, the
        extensions are carried out by giving new longer _vector attributes
        to the bitvector objects).

   @tag23
   (23) if x in y:

        You can test if a bit vector x is contained in another bit vector y
        by using the syntax 'if x in y'.  This is made possible by the
        override definition for the special __contains__ method.

   @tag24
   (24) set_value()

        You can call set_value() to change the bit pattern associated with
        a previously constructed bitvector object:

            bv = BitVector(intVal = 7, size =16)
            print(bv)                              # 0000000000000111
            bv.set_value(intVal = 45)
            print(bv)                              # 101101

        You can think of this method as carrying out an in-place resetting
        of the bit array in a bitvector. The method does not return
        anything.  The allowable modes for changing the internally stored
        bit pattern for a bitvector are the same as for the constructor.

   @tag25
   (25) count_bits()

        You can count the number of bits set in a BitVector instance by
  
            bv = BitVector(bitstring = '100111')
            print(bv.count_bits())                 # 4

        A call to count_bits() returns an integer value that is equal to
        the number of bits set in the bitvector.  

   @tag26
   (26) count_bits_sparse()

        For folks who use bit vectors with millions of bits in them but
        with only a few bits set, your bit counting will go much, much
        faster if you call count_bits_sparse() instead of count_bits():
        However, for dense bitvectors, I expect count_bits() to work
        faster.

            # a BitVector with 2 million bits:
            bv = BitVector(size = 2000000)
            bv[345234] = 1
            bv[233]=1
            bv[243]=1
            bv[18]=1
            bv[785] =1
            print(bv.count_bits_sparse())          # 5

        A call to count_bits_sparse() returns an integer whose value is the
        number of bits set in the bitvector.
          
   @tag27
   (27) jaccard_similarity()
        jaccard_distance()
        hamming_distance() 

        You can calculate the similarity and the distance between two
        bitvectors using the Jaccard similarity coefficient and the Jaccard
        distance.  Also, you can calculate the Hamming distance between two
        bitvectors:

            bv1 = BitVector(bitstring = '11111111')
            bv2 = BitVector(bitstring = '00101011')
            print bv1.jaccard_similarity(bv2)               # 0.675
            print(str(bv1.jaccard_distance(bv2)))           # 0.375
            print(str(bv1.hamming_distance(bv2)))           # 4

        For both jaccard_distance() and jaccard_similarity(), the value
        returned is a floating point number between 0 and 1.  The method
        hamming_distance() returns a number that is equal to the number of
        bit positions in which the two operand bitvectors disagree.

   @tag28
   (28) next_set_bit()

        Starting from a given bit position, you can find the position index
        of the next set bit by

            bv = BitVector(bitstring = '00000000000001')
            print(bv.next_set_bit(5))                       # 13

        In this example, we are asking next_set_bit() to return the index
        of the bit that is set after the bit position that is indexed 5. If
        no next set bit is found, the method returns -1.  A call to
        next_set_bit() always returns a number.

   @tag29
   (29) rank_of_bit_set_at_index()

        You can measure the "rank" of a bit that is set at a given
        position.  Rank is the number of bits that are set up to the
        position of the bit you are interested in.

            bv = BitVector(bitstring = '01010101011100')
            print(bv.rank_of_bit_set_at_index(10))          # 6

        The value 6 returned by this call to rank_of_bit_set_at_index() is
        the number of bits set up to the position indexed 10 (including
        that position). This method throws an exception if there is no bit
        set at the argument position. Otherwise, it returns the rank as a
        number.

   @tag30
   (30) is_power_of_2()
        is_power_of_2_sparse()

        You can test whether the integer value of a bit vector is a power
        of two.  The sparse version of this method will work much faster
        for very long bit vectors.  However, the regular version may work
        faster for dense bit vectors.

            bv = BitVector(bitstring = '10000000001110')
            print(bv.is_power_of_2())
            print(bv.is_power_of_2_sparse())

        Both these predicates return 1 for true and 0 for false.

   @tag31
   (31) reverse()

        Given a bit vector, you can construct a bit vector with all the
        bits reversed, in the sense that what was left to right before now
        becomes right to left.

            bv = BitVector(bitstring = '0001100000000000001')
            print(str(bv.reverse()))

        A call to reverse() returns a new bitvector object whose bits are
        in reverse order in relation to the bits in the bitvector on which
        the method is invoked.

   @tag32
   (32) gcd()

        You can find the greatest common divisor of two bit vectors:

            bv1 = BitVector(bitstring = '01100110')     # int val: 102
            bv2 = BitVector(bitstring = '011010')       # int val: 26 
            bv = bv1.gcd(bv2)
            print(int(bv))                              # 2

        The result returned by gcd() is a bitvector object.

   @tag33
   (33) multiplicative_inverse()

        This method calculates the multiplicative inverse using normal
        integer arithmetic.  [For such inverses in a Galois Field GF(2^n),
        use the method gf_MI().]

            bv_modulus = BitVector(intVal = 32)
            bv = BitVector(intVal = 17) 
            bv_result = bv.multiplicative_inverse( bv_modulus )
            if bv_result is not None:
                print(str(int(bv_result)))           # 17
            else: print "No multiplicative inverse in this case"
         
        What this example says is that the multiplicative inverse of 17
        modulo 32 is 17.  That is because 17 times 17 modulo 32 equals 1.
        When using this method, you must test the returned value for
        None. If the returned value is None, that means that the number
        corresponding to the bitvector on which the method is invoked does
        not possess a multiplicative-inverse with respect to the modulus.
        When the multiplicative inverse exists, the result returned by
        calling multiplicative_inverse() is a bitvector object.

   @tag34
   (34) gf_MI()

        To calculate the multiplicative inverse of a bit vector in the
        Galois Field GF(2^n) with respect to a modulus polynomial, call
        gf_MI() as follows:

            modulus = BitVector(bitstring = '100011011')
            n = 8
            a = BitVector(bitstring = '00110011')
            multi_inverse = a.gf_MI(modulus, n)
            print multi_inverse                        # 01101100

        A call to gf_MI() returns a bitvector object.

   @tag35
   (35) gf_multiply()

        If you just want to multiply two bit patterns in GF(2):

            a = BitVector(bitstring='0110001')
            b = BitVector(bitstring='0110')
            c = a.gf_multiply(b)
            print(c)                                   # 00010100110

        As you would expect, in general, the bitvector returned by this
        method is longer than the two operand bitvectors. A call to
        gf_multiply() returns a bitvector object.

   @tag36
   (36) gf_multiply_modular()

        If you want to carry out modular multiplications in the Galois
        Field GF(2^n):

            modulus = BitVector(bitstring='100011011') # AES modulus
            n = 8
            a = BitVector(bitstring='0110001')
            b = BitVector(bitstring='0110')
            c = a.gf_multiply_modular(b, modulus, n)
            print(c)                                   # 10100110

        The call to gf_multiply_modular() returns the product of the two
        bitvectors a and b modulo the bitvector modulus in GF(2^8). A call
        to gf_multiply_modular() returns is a bitvector object.

   @tag37
   (37) gf_divide_by_modulus()

        To divide a bitvector by a modulus bitvector in the Galois Field
        GF(2^n):

            mod = BitVector(bitstring='100011011')     # AES modulus
            n = 8
            a = BitVector(bitstring='11100010110001')
            quotient, remainder = a.gf_divide_by_modulus(mod, n)
            print(quotient)                            # 00000000111010
            print(remainder)                           # 10001111

        What this example illustrates is dividing the bitvector a by the
        modulus bitvector mod.  For a more general division of one
        bitvector a by another bitvector b, you would multiply a by the MI
        of b, where MI stands for "multiplicative inverse" as returned by
        the call to the method gf_MI().  A call to gf_divide_by_modulus()
        returns two bitvectors, one for the quotient and the other for the
        remainder.

   @tag38
   (38) runs()

        You can extract from a bitvector the runs of 1's and 0's in the
        vector as follows:

           bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
           print(str(bv.runs()))                      # ['111', '00', '1']

        The object returned by runs() is a list of strings, with each
        element of this list being a string of 1's and 0's.

   @tag39
   (39) gen_random_bits()

        You can generate a bitvector with random bits with the bits
        spanning a specified width.  For example, if you wanted a random
        bit vector to fully span 32 bits, you would say

            bv = BitVector(intVal = 0)
            bv = bv.gen_random_bits(32)  
            print(bv)                # 11011010001111011010011111000101

        As you would expect, gen_random_bits() returns a bitvector object.

   @tag40
   (40) test_for_primality()

        You can test whether a randomly generated bit vector is a prime
        number using the probabilistic Miller-Rabin test

            bv = BitVector(intVal = 0)
            bv = bv.gen_random_bits(32)  
            check = bv.test_for_primality()
            print(check)                 

        The test_for_primality() methods returns a floating point number
        close to 1 for prime numbers and 0 for composite numbers.  The
        actual value returned for a prime is the probability associated
        with the determination of its primality.

   @tag41
   (41) get_bitvector_in_ascii()

        You can call get_bitvector_in_ascii() to directly convert a bit
        vector into a text string (this is a useful thing to do only if the
        length of the vector is an integral multiple of 8 and every byte in
        your bitvector has a print representation):

            bv = BitVector(textstring = "hello")
            print(bv)        # 0110100001100101011011000110110001101111
            mytext = bv3.get_bitvector_in_ascii()
            print mytext                           # hello

        This method is useful when you encrypt text through its bitvector
        representation.  After decryption, you can recover the text using
        the call shown here.  A call to get_bitvector_in_ascii() returns a
        string.

   @tag42
   (42) get_bitvector_in_hex()

        You can directly convert a bit vector into a hex string (this is a
        useful thing to do only if the length of the vector is an integral
        multiple of 4):

            bv4 = BitVector(hexstring = "68656c6c6f")
            print(bv4)     # 0110100001100101011011000110110001101111
            myhexstring = bv4.get_bitvector_in_hex()
            print myhexstring                      # 68656c6c6

        This method throws an exception if the size of the bitvector is not
        a multiple of 4.  The method returns a string.

   @tag43 
   (43) close_file_object()

        When you construct bitvectors by block scanning a disk file, after
        you are done, you can call this method to close the file object
        that was created to read the file:

            bv  =  BitVector(filename = 'somefile')   
            bv1 =  bv.read_bits_from_file(64)    
            bv.close_file_object()

        The constructor call in the first statement creates a file object
        for reading the bits.  It is this file object that is closed when
        you call close_file_object().

   @tag44 
   (44) min_canonical()

        This methods returns the canonical form of a bitvector, which
        corresponds to a circularly rotated version of the bitvector with the
        largest number of leading zeros.

            bv     = BitVector(intVal = 5678, size = 14)
            min_bv = bv.min_canonical()
            print(bv)                          # 01011000101110
            print(min_bv)                      # 00010111001011
            print(int(min_bv))                 # 1483


@title
CHANGE HISTORY:

  Version 3.4.4

    This version fixes the behavior of the module for the edge case of an
    empty BitVector instance.  (An empty BitVector has no bits at all.)
    Previously, invoking the count_bits() and runs() methods on an empty
    BitVector instance produced results that were inconsistent with those
    from regular instances.

  Version 3.4.3

    This is a quick release that fixes the problem with the relative imports
    in the previous version. Python3 does not like relative imports.

  Version 3.4.2

    Unfortunately, the packaging of the previous version was not exporting
    the module metadata. That problem has been fixed in this version.

  Version 3.4.1

    This version fixes two module packaging errors in the previous version.
    One error related to the specification of the "packages" keyword in
    setup.py and the other error related to not updating the manifest with
    the HTML documentation file for the module.

  Version 3.4

    This version includes a bug fix and significant improvements to the
    documentation.  The new documentation is clearer about what is returned
    by each method and, when a method throws an exception, that fact is
    stated in the documentation associated with the method. The condition
    that triggers the exception is also stated. The bug fix was in the
    test_for_primality() method.  If invoked for testing the primality of
    1, it would get trapped in an infinite loop.  Additionally, when
    constructing a bitvector from a hex string, this version allows the hex
    characters to be in either case.  Previously, only lowercase hex
    characters were acceptable.  Finally, I have changed the names of a
    couple of methods to better reflect their function.  The old names
    would, however, continue to work for backward compatibility.

  Version 3.3.2:

    This version fixes a bug in the constructor code for creating a bit
    vector from a text string.  The bug was triggered by character escapes
    in such strings.

  Version 3.3.1:

    This is a minor upgrade to make the syntax of the API method
    declarations more uniform.  Previously, while most of the method names
    used underscores to connect multiple words, some used camelcasing.  Now
    all use underscores.  For backward compatibility, the old calls will
    continue to work.

  Version 3.3:

    This version includes: (1) One additional constructor mode that allows
    a bit vector to be constructed directly from the bytes type objects in
    the memory. (2) A bugfix in the slice function for the case when the
    upper and the lower bounds of the slice range are identical. (3) A
    bugfix for the next_set_bit() method.

  Version 3.2: 

    This version includes support for constructing bit vectors directly
    from text strings and hex strings.  This version also includes a safety
    check on the sizes of the two argument bit vectors when calculating
    Jaccard similarity between the two.

  Version 3.1.1: 

    This version includes: (1) a fix to the module test code to account for
    how string input is handled in the io.StringIO class in Python 2.7; (2)
    some improvements to the documentation.

  Version 3.1:

    This version includes: (1) Correction for a documentation error; (2)
    Fix for a bug in slice assignment when one or both of the slice limits
    were left unspecified; (3) The non-circular bit shift methods now
    return self so that they can be chained; (4) A method for testing a
    bitvector for its primality; and (5) A method that uses Python's
    'random.getrandbits()' to generate a bitvector that can serve as
    candidate for primes whose bitfield size is specified.

  Version 3.0:

    This is a Python 3.x compliant version of the latest incarnation of the
    BitVector module.  This version should work with both Python 2.x and
    Python 3.x.

  Version 2.2:

    Fixed a couple of bugs, the most important being in the bitvector
    initialization code for the cases when the user-specified value for
    size conflicts with the user-specified int value for the vector.
    Version 2.2 also includes a new method runs() that returns a list of
    strings of the consecutive runs of 1's and 0's in the bitvector.  The
    implementation of the circular shift operators has also been improved
    in Version 2.2. This version allows for a chained invocation of these
    operators.  Additionally, the circular shift operators now exhibit
    expected behavior if the user-specified shift value is negative.

  Version 2.1:

    Includes enhanced support for folks who use this class for computer
    security and cryptography work.  You can now call on the methods of the
    BitVector class to do Galois Field GF(2^n) arithmetic on bit arrays.
    This should save the users of this class the bother of having to write
    their own routines for finding multiplicative inverses in GF(2^n)
    finite fields.

  Version 2.0.1:

    Fixed numerous typos and other errors in the documentation page for the
    module.  The implementation code remains unchanged.

  Version 2.0:

    To address the needs of the folks who are using the BitVector class in
    data mining research, the new version of the class includes several
    additional methods.  Since the bitvectors used by these folks can be
    extremely long, possibly involving millions of bits, the new version of
    the class includes a much faster method for counting the total number
    of set bits when a bitvector is sparse.  [But note that this new bit
    counting method may perform poorly for dense bitvectors. So the old bit
    counting method has been retained.]  Also for data mining folks, the
    new version of the class is provided with similarity and distance
    calculation metrics such as the Jaccard similarity coefficient, the
    Jaccard distance, and the Hamming distance.  Again for the same folks,
    the class now also has a next_set_bit(from_index) method.  Other
    enhancements to the class include methods for folks who do research in
    cryptography.  Now you can directly calculate the greatest common
    divisor of two bitvectors, or find the multiplicative inverse of one
    bitvector modulo another bitvector.

  Version 1.5.1:

    Removed a bug from the implementation of the right circular shift
    operator.

  Version 1.5:

    This version should prove to be much more efficient for long
    bitvectors.  Efficiency in BitVector construction when only its size is
    specified was achieved by eliminating calls to _setbit().  The
    application of logical operators to two BitVectors of equal length was
    also made efficient by eliminating calls to the padding function.
    Another feature of this version is the count_bits() method that returns
    the total number of bits set in a BitVector instance.  Yet another
    feature of this version is the setValue() method that alters the bit
    pattern associated with a previously constructed BitVector.
   
  Version 1.4.1:

    The reset() method now returns 'self' to allow for cascaded invocation
    with the slicing operator.  Also removed the discrepancy between the
    value of the __copyright__ variable in the module and the value of
    license variable in setup.py.

  Version 1.4:

    This version includes the following two upgrades: 1) code for slice
    assignment; and 2) A reset function to reinitialize a previously
    constructed BitVector.  Additionally, the code was cleaned up with the
    help of pychecker.

  Version 1.3.2:

    Fixed a potentially misleading documentation issue for the Windows
    users of the BitVector class.  If you are writing an internally
    generated BitVector to a disk file, you must open the file in the
    binary mode.  If you don't, the bit patterns that correspond to line
    breaks will be misinterpreted.  On a Windows machine in the text mode,
    the bit pattern 000001010 ('\\n') will be written out to the disk as
    0000110100001010 ('\\r\\n').

  Version 1.3.1:

    Removed the inconsistency in the internal representation of bitvectors
    produced by logical bitwise operations vis-a-vis the bitvectors created
    by the constructor.  Previously, the logical bitwise operations
    resulted in bitvectors that had their bits packed into lists of ints,
    as opposed to arrays of unsigned shorts.

  Version 1.3:

    (a) One more constructor mode included: When initializing a new
    bitvector with an integer value, you can now also specify a size for
    the bitvector.  The constructor zero-pads the bitvector from the left
    with zeros. (b) The BitVector class now supports 'if x in y' syntax to
    test if the bit pattern 'x' is contained in the bit pattern 'y'.  (c)
    Improved syntax to conform to well-established Python idioms. (d) What
    used to be a comment before the beginning of each method definition is
    now a docstring.

  Version 1.2:

    (a) One more constructor mode included: You can now construct a
    bitvector directly from a string of 1's and 0's.  (b) The class now
    constructs a shortest possible bit vector from an integer value.  So
    the bit vector for the integer value 0 is just one bit of value 0, and
    so on. (c) All the rich comparison operators are now overloaded. (d)
    The class now includes a new method 'intValue()' that returns the
    unsigned integer value of a bit vector.  This can also be done through
    '__int__'. (e) The package now includes a unittest based framework for
    testing out an installation.  This is in a separate directory called
    "TestBitVector".
   
  Version 1.1.1:

    The function that does block reads from a disk file now peeks ahead at
    the end of each block to see if there is anything remaining to be read
    in the file.  If nothing remains, the more_to_read attribute of the
    BitVector object is set to False.  This simplifies reading loops. This
    version also allows BitVectors of size 0 to be constructed


  Version 1.1:

    I have changed the API significantly to provide more ways for
    constructing a bit vector.  As a result, it is now necessary to supply
    a keyword argument to the constructor.
   

@title
INSTALLATION:

    The BitVector class was packaged using setuptools.  For installation,
    execute the following command-line in the source directory (this is the
    directory that contains the setup.py file after you have downloaded and
    uncompressed the tar archive):
 
        sudo python setup.py install

    and/or

        sudo python3 setup.py install

    On Linux distributions, this will install the module file at a location
    that looks like

        /usr/local/lib/python2.7/dist-packages/

    and for the case of Python3 like

        /usr/local/lib/python3.4/dist-packages/      

    If you do not have root access, you have the option of working directly
    off the directory in which you downloaded the software by simply
    placing the following statements at the top of your scripts that use
    the BitVector class

        import sys
        sys.path.append( "pathname_to_BitVector_directory" )

    To uninstall the module, simply delete the source directory, locate
    where BitVector was installed with "locate BitVector" and delete those
    files.  As mentioned above, the full pathname to the installed version
    is likely to look like /usr/local/lib/python2.7/dist-packages/BitVector*

    If you want to carry out a non-standard install of BitVector, look up
    the on-line information on Disutils by pointing your browser to

        http://docs.python.org/dist/dist.html


@title
HOW THE BIT VECTORS ARE STORED:
   
    The bits of a bit vector are stored in 16-bit unsigned ints
    following Josiah Carlson's recommendation to that effect on the
    Pyrex mailing list.  As you can see in the code for `__init__()',
    after resolving the argument with which the constructor is called,
    the very first thing the constructor does is to figure out how many
    of those 2-byte ints it needs for the bits (see how the value is
    assigned to the variable `two_byte_ints_needed' toward the end of
    `__init__()').  For example, if you wanted to store a 64-bit array,
    the variable 'two_byte_ints_needed' would be set to 4. (This does
    not mean that the size of a bit vector must be a multiple of 16.
    Any sized bit vectors can be constructed --- the constructor will
    choose the minimum number of two-byte ints needed.) Subsequently,
    the constructor acquires an array of zero-initialized 2-byte ints.
    The last thing that is done in the code for `__init__()' is to
    shift the bits into the array of two-byte ints.

    As mentioned above, note that it is not necessary for the size of a
    bit vector to be a multiple of 16 even though we are using C's
    unsigned short as as a basic unit for storing the bit arrays.  The
    class BitVector keeps track of the actual number of bits in the bit
    vector through the "size" instance variable.

    Note that, except for one case, the constructor must be called with
    a single keyword argument, which determines how the bit vector will
    be constructed.  The single exception to this rule is for the
    keyword argument `intVal' which can be used along with the `size'
    keyword argument.  When `intVal' is used without the `size' option,
    the bit vector constructed for the integer is the shortest possible
    bit vector.  On the other hand, when `size' is also specified, the
    bit vector is padded with zeroes from the left so that it has the
    specified size.  The code for `__init__()' begins by making sure
    your constructor call only uses the acceptable keywords.  The
    constraints on how many keywords can be used together in a
    constructor call are enforced when we process each keyword option
    separately in the rest of the code for `__init__()'.

    The first keyword option processed by `__init__()' is for
    `filename'.  When the constructor is called with the `filename'
    keyword, as in

           bv = BitVector(filename = 'myfilename')

    the call returns a bit vector on which you must subsequently invoke
    the `read_bits_from_file()' method to actually obtain a bit vector
    consisting of the bits that constitute the information stored in
    the file.

    The next keyword option considered in `__init__()' is for `fp',
    which is for constructing a bit vector by reading off the bits from
    a file-like object, as in

          x = "111100001111"
          fileobj = StringIO.StringIO( x )
          bv = BitVector( fp = fileobj )

    The keyword option `intVal' considered next is for converting an
    integer into a bit vector through a constructor call like

          bv = BitVector(intVal = 123456)

    The bits stored in the bit vector thus created correspond to the
    big-endian binary representation of the integer argument provided
    through `intVal' (meaning that the most significant bit will be at
    the leftmost position in the bit vector.)  THE BIT VECTOR
    CONSTRUCTED WITH THE ABOVE CALL IS THE SHORTEST POSSIBLE BIT VECTOR
    FOR THE INTEGER SUPPLIED.  As a case in point, when `intVal' is set
    to 0, the bit vector consists of a single bit is 0 also.  When
    constructing a bit vector with the `intVal' option, if you also
    want to impose a size condition on the bit vector, you can make a
    call like

          bv = BitVector(intVal = 46, size = 16)        

    which returns a bit vector of the indicated size by padding the
    shortest possible vector for the `intVal' option with zeros from
    the left.

    The next option processed by `__init_()' is for the `size' keyword
    when this keyword is used all by itself.  If you want a bit vector
    of just 0's of whatever size, you make a call like

          bv = BitVector(size = 61)

    This returns a bit vector that will hold exactly 61 bits, all
    initialized to the zero value.

    The next constructor keyword processed by `__init__()' is
    `bitstring'. This is to allow a bit vector to be constructed
    directly from a bit string as in

          bv = BitVector(bitstring = '00110011111')

    The keyword considered next is `bitlist' which allows a bit vector
    to be constructed from a list or a tuple of individual bits, as in
      
          bv = BitVector(bitlist = (1, 0, 1, 1, 0, 0, 1))

    The last two keyword options considered in `__init__()' are for
    keywords `textstring' and `hexstring'.  If you want to construct a
    bitvector directly from a text string, you call

          bv = BitVector(textstring = "hello")

    The bit vector created corresponds to the ASCII encodings of the
    individual characters in the text string.

    And if you want to do the same with a hex string, you call

          bv = BitVector(hexstring = "68656c6c6f")

    Now, as you would expect, the bits in the bit vector will
    correspond directly to the hex digits in your hex string.

   
@title
ACKNOWLEDGMENTS:

    The author is grateful to Oleg Broytmann for suggesting many
    improvements that were incorporated in Version 1.1 of this package.
    The author would like to thank Kurt Schwehr whose email resulted in
    the creation of Version 1.2.  Kurt also caught an error in my
    earlier version of 'setup.py' and suggested a unittest based
    approach to the testing of the package.  Kurt also supplied the
    Makefile that is included in this distribution.  The author would
    also like to thank all (Scott Daniels, Blair Houghton, and Steven
    D'Aprano) for their responses to my comp.lang.python query
    concerning how to make a Python input stream peekable.  This
    feature was included in Version 1.1.1.

    With regard to the changes incorporated in Version 1.3, thanks are
    owed to Kurt Schwehr and Gabriel Ricardo for bringing to my
    attention the bug related to the intVal method of initializing a
    bit vector when the value of intVal exceeded sys.maxint. This
    problem is fixed in Version 1.3.  Version 1.3 also includes many
    other improvements that make the syntax better conform to the
    standard idioms of Python.  These changes and the addition of the
    new constructor mode (that allows a bit vector of a given size to
    be constructed from an integer value) are also owing to Kurt's
    suggestions.

    With regard to the changes incorporated in Version 1.3.1, I would
    like to thank Michael Haggerty for noticing that the bitwise
    logical operators resulted in bit vectors that had their bits
    packed into lists of ints, as opposed to arrays of unsigned shorts.
    This inconsistency in representation has been removed in version
    1.3.1.  Michael has also suggested that since BitVector is mutable,
    I should be overloading __iand__(), __ior__(), etc., for in-place
    modifications of bit vectors.  Michael certainly makes a good
    point. But I am afraid that this change will break the code for the
    existing users of the BitVector class.

    I thank Mathieu Roy for bringing to my attention the problem with
    writing bitstrings out to a disk files on Windows machines.  This
    turned out to be a problem more with the documentation than with
    the BitVector class itself.  On a Windows machine, it is
    particularly important that a file you are writing a bitstring into
    be opened in binary mode since otherwise the bit pattern 00001010
    ('\\n') will be written out as 0000110100001010 ('\\r\\n').  This
    documentation fix resulted in Version 1.3.2.

    With regard to Version 1.4, the suggestions/bug reports made by
    John Kominek, Bob Morse, and Steve Ward contributed to this
    version.  I wish to thank all three. John wanted me to equip the
    class with a reset() method so that a previously constructed class
    could be reset to either all 0's or all 1's. Bob spotted loose
    local variables in the implementation --- presumably left over from
    a debugging phase of the code.  Bob recommended that I clean up the
    code with pychecker. That has been done.  Steve noticed that slice
    assignment was not working.  It should work now.

    Version 1.4.1 was prompted by John Kominek suggesting that if
    reset() returned self, then the slice operation could be combined
    with the reset operation.  Thanks John!  Another reason for 1.4.1
    was to remove the discrepancy between the value of the
    __copyright__ variable in the module and the value of license
    variable in setup.py.  This discrepancy was brought to my attention
    by David Eyk.  Thanks David!

    Version 1.5 has benefited greatly by the suggestions made by Ryan
    Cox.  By examining the BitVector execution with cProfile, Ryan
    observed that my implementation was making unnecessary method calls
    to _setbit() when just the size option is used for constructing a
    BitVector instance.  Since Python allocates cleaned up memory, it
    is unnecessary to set the individual bits of a vector if it is
    known in advance that they are all zero. Ryan made a similar
    observation for the logical operations applied to two BitVector
    instances of equal length.  He noticed that I was making
    unnecessary calls to _resize_pad_from_left() for the case of equal
    arguments to logical operations.  Ryan also recommended that I
    include a method that returns the total number of bits set in a
    BitVector instance.  The new method count_bits() does exactly
    that. Thanks Ryan for all your suggestions.  Version 1.5 also
    includes the method setValue() that allows the internally stored
    bit pattern associated with a previously constructed BitVector to
    be changed.  A need for this method was expressed by Aleix
    Conchillo.  Thanks Aleix.
    
    Version 1.5.1 is a quick release to fix a bug in the right circular
    shift operator.  This bug was discovered by Jasper Spaans.  Thanks
    very much Jasper.

    Version 2.0 was prompted mostly by the needs of the folks who play with
    very long bit vectors that may contain millions of bits.  Such bit
    vectors are encountered in data mining research and development.
    Towards that end, among the new methods in Version 2.0, the
    count_bits_sparse() was provided by Rhiannon Weaver.  She says when a
    bit vector contains over 2 million bits and, say, only five bits are
    set, her method is faster than the older count_bits() method by a
    factor of roughly 18.  Thanks Rhiannon. [The logic of the new
    implementation works best for very sparse bit vectors.  For very dense
    vectors, it may perform more slowly than the regular count_bits()
    method.  For that reason, I have retained the original method.]
    Rhiannon's implementation is based on what has been called the
    Kernighan way at the web site
    http://graphics.stanford.edu/~seander/bithacks.html.  Version 2.0 also
    includes a few additional functions posted at this web site for
    extracting information from bit fields.  Also included in this new
    version is the next_set_bit() method supplied by Jason Allum.  I
    believe this method is also useful for data mining folks.  Thanks
    Jason.  Additional methods in Version 2.0 include the similarity and
    the distance metrics for comparing two bit vectors, method for finding
    the greatest common divisor of two bit vectors, and a method that
    determines the multiplicative inverse of a bit vector vis-a-vis a
    modulus.  The last two methods should prove useful to folks in
    cryptography.

    With regard to Version 2.2, I would like to thank Ethan Price for
    bringing to my attention a bug in the BitVector initialization code
    for the case when both the int value and the size are user-
    specified and the two values happen to be inconsistent.  Ethan also
    discovered that the circular shift operators did not respond to
    negative values for the shift.  These and some other shortcomings
    discovered by Ethan have been fixed in Version 2.2.  Thanks Ethan!

    For two of the changes included in Version 3.1, I'd like to thank
    Libor Wagner and C. David Stahl.  Libor discovered a documentation
    error in the listing of the 'count_bits_sparse()' method and David
    discovered a bug in slice assignment when one or both of the slice
    limits are left unspecified.  These errors in Version 3.0 have been
    fixed in Version 3.1.

    Version 3.1.1 was triggered by two emails, one from John-Mark
    Gurney and the other from Nessim Kisserli, both related to the
    issue of compilation of the module.  John-Mark mentioned that since
    this module did not work with Python 2.4.3, the statement that the
    module was appropriate for all Python 2.x was not correct, and
    Nessim reported that he had run into a problem with the compilation
    of the test portion of the code with Python 2.7 where a string of
    1's and 0's is supplied to io.StringIO() for the construction of a
    memory file.  Both these issues have been resolved in 3.1.1.

    Version 3.2 was triggered by my own desire to include additional
    functionality in the module to make it more useful for experimenting
    with hash functions.  While I was at it, I also included in the module
    a couple of safety checks on the lengths of the two argument bit
    vectors when computing their Jaccard similarity.  I could see the need
    for these checks after receiving an email from Patrick Nisch about the
    error messages he was receiving during Jaccard similarity calculations.
    Thanks Patrick!

    Version 3.3 includes a correction by John Gleeson for a bug in the
    next_set_bit() method.  Thanks, John!

    Version 3.3.1 resulted from Thor Smith observing that my naming
    convention for the API methods was not uniform.  Whereas most used
    the underscore for joining multiple words, some were based on
    camelcasing. Thanks, Thor!

    Version 3.3.2 was in response to a bug discovery by Juan Corredor.
    The bug related to constructing bit vectors from text strings that
    include character escapes.  Thanks, Juan!

    Version 3.4.1 was triggered by an email from Kurt Schwehr who spotted
    an error in the setup.py of Version 3.4. Thanks, Kurt!

    Version 3.4.4 resulted from an email from Adam Foltzer who noticed that
    an empty BitVector instance did not behave like a regular instance.
    Previously, the module simply aborted if you called count_bits() on an
    empty BitVector instance and threw an exception if you called runs() on
    such an instance. The new version returns 0 for the former case and an
    empty list for the latter.  I should also mention that the new
    implementation of count_bits() was first suggested by Kurt Schwehr in
    an email a couple of months back.  My original implementation called on
    the reduce() method of the functools module to do the job.  Thanks to
    both Adam and Kurt!

    Version 3.4.5 was triggered by an email from William Pietri who
    discovered a bug in the code for making slice assignments.  While I was
    at it, thought I should also include in the module a new method that I
    have named min_canonical(). This method returns the "canonical" form of
    a bit pattern, which corresponds to a circularly shifted version of the
    pattern with the largest number of leading zeros.  Such canonical forms
    of bit patterns play an important role in image texture
    characterization algorithms.  If you are curious as to how, see my
    "Texture and Color Tutorial" at
    https://engineering.purdue.edu/kak/Tutorials/TextureAndColor.pdf
    

@title
ABOUT THE AUTHOR:

    The author, Avinash Kak, recently finished his 17-year long Objects
    Trilogy project with the publication of the book "Designing with
    Objects" by John-Wiley. If interested, check out his web page at Purdue
    to find out what the Objects Trilogy project was all about. You might
    like "Designing with Objects" especially if you enjoyed reading Harry
    Potter as a kid (or even as an adult, for that matter).


@title
SOME EXAMPLE CODE:

    #!/usr/bin/env python
    import BitVector

    # Construct a bit vector from a list or tuple of bits:
    bv = BitVector.BitVector( bitlist = (1, 0, 0, 1) )
    print(bv)                                # 1001

    # Construct a bit vector from an integer:
    bv = BitVector.BitVector( intVal = 5678 )
    print(bv)                                # 0001011000101110

    # Construct a bit vector of a given size from a given
    # integer:
    bv = BitVector( intVal = 45, size = 16 )
    print(bv)                                # 0000000000101101

    # Construct a zero-initialized bit vector of a given size:
    bv = BitVector.BitVector( size = 5 )
    print(bv)                                # 00000

    # Construct a bit vector from a bit string:
    bv = BitVector.BitVector( bitstring = '110001' )     
    print(bv[0], bv[1], bv[2], bv[3], bv[4], bv[5])       # 1 1 0 0 0 1
    print(bv[-1], bv[-2], bv[-3], bv[-4], bv[-5], bv[-6]) # 1 0 0 0 1 1

    # Construct a bit vector from a file like object:
    import io
    x = "111100001111"
    fp_read = io.StringIO( x )
    bv = BitVector( fp = fp_read )
    print(bv)                                             # 111100001111 

    # Experiments with bitwise logical operations:
    bv3 = bv1 | bv2                              
    bv3 = bv1 & bv2
    bv3 = bv1 ^ bv2
    bv6 = ~bv5

    # Find the length of a bit vector
    print( str(len( bitvec ) ) )

    # Find the integer value of a bit vector
    print( bitvec.intValue() )

    # Open a file for reading bit vectors from
    bv = BitVector.BitVector( filename = 'TestBitVector/testinput1.txt' )
    print( bv )                                 # nothing yet
    bv1 = bv.read_bits_from_file(64)    
    print( bv1 )                            # first 64 bits from the file

    # Divide a bit vector into two equal sub-vectors:
    [bv1, bv2] = bitvec.divide_into_two()

    # Permute and Un-Permute a bit vector:
    bv2 = bitvec.permute( permutation_list )
    bv2 = bitvec.unpermute( permutation_list )

    # Try circular shifts to the left and to the right
    bitvec << 7
    bitvec >> 7

    # Try 'if x in y' syntax for bit vectors:
    bv1 = BitVector( bitstring = '0011001100' )
    bv2 = BitVector( bitstring = '110011' )
    if bv2 in bv1:
        print( "%s is in %s" % (bv2, bv1) )
    else:
        print( "%s is not in %s" % (bv2, bv1) )

    .....
    .....

    (For a more complete working example, see the
     example code in the BitVectorDemo.py file in the
     Examples sub-directory.)

@endofdocs
'''


import array
import operator
import sys

_hexdict = { '0' : '0000', '1' : '0001', '2' : '0010', '3' : '0011',
             '4' : '0100', '5' : '0101', '6' : '0110', '7' : '0111',
             '8' : '1000', '9' : '1001', 'a' : '1010', 'b' : '1011',
             'c' : '1100', 'd' : '1101', 'e' : '1110', 'f' : '1111' }

def _readblock(blocksize, bitvector):                              
    ''' 
    If this function succeeds in reading all blocksize bits, it uses the
    tell-read-seek mechanism to peek ahead to see if there is anything more to be
    read in the file. If there is nothing further to be read, it sets the more_to_read
    attribute of the BitVector instance to False.  Obviously, this can only be done for
    seekable streams such as those connected with disk files.  According to Blair
    Houghton, a similar feature could presumably be implemented for socket streams by
    using recv() or recvfrom() if you set the flags argument to MSG_PEEK.
    '''
    global _hexdict                                                  
    bitstring = ''                                                   
    i = 0                                                            
    while ( i < blocksize / 8 ):                                     
        i += 1                                                       
        byte = bitvector.FILEIN.read(1)                              
        if byte == b'':                                              
            if len(bitstring) < blocksize:                           
                bitvector.more_to_read = False                      
            return bitstring                                        
        if sys.version_info[0] == 3:                                
            hexvalue = '%02x' % byte[0]                             
        else:                                                       
            hexvalue = hex( ord( byte ) )                           
            hexvalue = hexvalue[2:]                                 
            if len( hexvalue ) == 1:                                
                hexvalue = '0' + hexvalue                           
        bitstring += _hexdict[ hexvalue[0] ]                        
        bitstring += _hexdict[ hexvalue[1] ]                        
    file_pos = bitvector.FILEIN.tell()                              
    # peek at the next byte; moves file position only if a
    # byte is read
    next_byte = bitvector.FILEIN.read(1)                            
    if next_byte:                                                   
        # pretend we never read the byte                   
        bitvector.FILEIN.seek( file_pos )                           
    else:                                                           
        bitvector.more_to_read = False                              
    return bitstring                                                


#------------------------------  BitVector Class Definition   --------------------------------

class BitVector( object ):                                           

    def __init__( self, *args, **kwargs ):                           
        if args:                                                     
               raise ValueError(                                     
                      '''BitVector constructor can only be called with keyword arguments for the following keywords: '''
                      '''filename, fp, size, intVal, bitlist, bitstring, hexstring, textstring, and rawbytes)''')   
        allowed_keys = 'bitlist','bitstring','filename','fp','intVal', 'size','textstring','hexstring','rawbytes'
        keywords_used = kwargs.keys()                               
        for keyword in keywords_used:                               
            if keyword not in allowed_keys:                         
                raise ValueError("Wrong keyword used --- check spelling")
        filename=fp=intVal=size=bitlist=bitstring=textstring=hexstring=rawbytes=None  
        if 'filename' in kwargs   : filename=kwargs.pop('filename')  
        if 'fp' in kwargs         : fp = kwargs.pop('fp')            
        if 'size' in kwargs       : size = kwargs.pop('size')        
        if 'intVal' in kwargs     : intVal = kwargs.pop('intVal')    
        if 'bitlist' in kwargs    : bitlist = kwargs.pop('bitlist')  
        if 'bitstring' in kwargs  : bitstring = kwargs.pop('bitstring')  
        if 'hexstring' in kwargs  : hexstring = kwargs.pop('hexstring')      
        if 'textstring' in kwargs : textstring = kwargs.pop('textstring')      
        if 'rawbytes' in kwargs   : rawbytes = kwargs.pop('rawbytes')
        self.filename = None                                        
        self.size = 0                                               
        self.FILEIN = None                                          
        self.FILEOUT = None                                         
        if filename:                                                
            if fp or size or intVal or bitlist or bitstring or hexstring or textstring or rawbytes: 
                raise ValueError('''When filename is specified, you cannot give values '''
                                 '''to any other constructor args''')
            self.filename = filename                                
            self.FILEIN = open(filename, 'rb')                    
            self.more_to_read = True                                
            return                                                  
        elif fp:                                                    
            if filename or size or intVal or bitlist or bitstring or hexstring or textstring or rawbytes:
                raise ValueError('''When fileobject is specified, you cannot give '''
                                 '''values to any other constructor args''')
            bits = self.read_bits_from_fileobject(fp)             
            bitlist =  list(map(int, bits))                       
            self.size = len( bitlist )                              
        elif intVal or intVal == 0:                                 
            if filename or fp or bitlist or bitstring or hexstring or textstring or rawbytes:
                raise ValueError('''When intVal is specified, you can only give a '''
                                 '''value to the 'size' constructor arg''')
            if intVal == 0:                                         
                bitlist = [0]                                       
                if size is None:                                    
                    self.size = 1                                   
                elif size == 0:                                     
                    raise ValueError('''The value specified for size must be at least '''
                                     '''as large as for the smallest bit vector possible '''
                                     '''for intVal''')                   
                else:                                               
                    if size < len(bitlist):                         
                        raise ValueError('''The value specified for size must be at least '''
                                         '''as large as for the smallest bit vector '''
                                         '''possible for intVal''')
                    n = size - len(bitlist)                         
                    bitlist = [0]*n + bitlist                       
                    self.size = len(bitlist)                      
            else:                                                   
                hexVal = hex(intVal).lower().rstrip('l')          
                hexVal = hexVal[2:]                                 
                if len(hexVal) == 1:                              
                    hexVal = '0' + hexVal                           
                bitlist = ''.join(map(lambda x: _hexdict[x],hexVal))
                bitlist =  list(map( int, bitlist))                
                i = 0                                               
                while (i < len(bitlist)):                       
                    if bitlist[i] == 1: break                       
                    i += 1                                          
                del bitlist[0:i]                                    
                if size is None:                                    
                    self.size = len(bitlist)                      
                elif size == 0:                                     
                    if size < len(bitlist):                         
                        raise ValueError('''The value specified for size must be at least '''
                                         '''as large as for the smallest bit vector possible '''
                                         '''for intVal''')
                else:                                               
                    if size < len(bitlist):                         
                        raise ValueError('''The value specified for size must be at least '''
                                         '''as large as for the smallest bit vector possible '''
                                         '''for intVal''')
                    n = size - len(bitlist)                         
                    bitlist = [0]*n + bitlist                       
                    self.size = len( bitlist )                      
        elif size is not None and size >= 0:                        
            if filename or fp or intVal or bitlist or bitstring or hexstring or textstring or rawbytes:
                raise ValueError('''When size is specified (without an intVal), you cannot '''
                                 '''give values to any other constructor args''')
            self.size = size                                        
            two_byte_ints_needed = (size + 15) // 16                
            self.vector = array.array('H', [0]*two_byte_ints_needed)
            return                                                  
        elif bitstring or bitstring == '':                          
            if filename or fp or size or intVal or bitlist or hexstring or textstring or rawbytes:
                raise ValueError('''When a bitstring is specified, you cannot give '''
                                 '''values to any other constructor args''')
            bitlist =  list(map(int, list(bitstring)))            
            self.size = len(bitlist)                              
        elif bitlist:                                               
            if filename or fp or size or intVal or bitstring or hexstring or textstring or rawbytes:
                raise ValueError('''When bits are specified, you cannot give values '''
                                 '''to any other constructor args''')
            self.size = len(bitlist)                              
        elif textstring or textstring == '':
            if filename or fp or size or intVal or bitlist or bitstring or hexstring or rawbytes:
                raise ValueError('''When bits are specified through textstring, you '''
                                 '''cannot give values to any other constructor args''')
            hexlist = ''.join(map(lambda x: x[2:], map(lambda x: hex(x) if len(hex(x)[2:])==2 
                                 else hex(x)[:2] + '0' + hex(x)[2:], map(ord, list(textstring)))))
            bitlist = list(map(int,list(''.join(map(lambda x: _hexdict[x], list(hexlist))))))
            self.size = len(bitlist)                        
        elif hexstring or hexstring == '':
            if filename or fp or size or intVal or bitlist or bitstring or textstring or rawbytes:
                raise ValueError('''When bits are specified through hexstring, you '''
                                 '''cannot give values to any other constructor args''')
            bitlist = list(map(int,list(''.join(map(lambda x: _hexdict[x], list(hexstring.lower()))))))
            self.size = len(bitlist)                              
        elif rawbytes:
            if filename or fp or size or intVal or bitlist or bitstring or textstring or hexstring:
                raise ValueError('''When bits are specified through rawbytes, you '''
                                 '''cannot give values to any other constructor args''')
            import binascii
            hexlist = binascii.hexlify(rawbytes)
            if sys.version_info[0] == 3:
                bitlist = list(map(int,list(''.join(map(lambda x: _hexdict[x], list(map(chr,list(hexlist))))))))
            else:
                bitlist = list(map(int,list(''.join(map(lambda x: _hexdict[x], list(hexlist))))))
            self.size = len(bitlist)  
        else:                                                       
            raise ValueError("wrong arg(s) for constructor")        
        two_byte_ints_needed = (len(bitlist) + 15) // 16            
        self.vector = array.array( 'H', [0]*two_byte_ints_needed )  
        list( map( self._setbit, range(len(bitlist)), bitlist) )    

    def _setbit(self, posn, val):                                
        'Set the bit at the designated position to the value shown'
        if val not in (0, 1):                                      
            raise ValueError( "incorrect value for a bit" )        
        if isinstance( posn, (tuple) ):                            
            posn = posn[0]                                         
        if  posn >= self.size or posn < -self.size:                
            raise ValueError( "index range error" )                
        if posn < 0: posn = self.size + posn                       
        block_index = posn // 16                                   
        shift = posn & 15                                          
        cv = self.vector[block_index]                              
        if ( cv >> shift ) & 1 != val:                             
            self.vector[block_index] = cv ^ (1 << shift)           

    def _getbit(self, pos):                                      
        'Get the bit from the designated position'
        if not isinstance( pos, slice ):                           
            if  pos >= self.size or pos < -self.size:              
                raise ValueError( "index range error" )            
            if pos < 0: pos = self.size + pos                      
            return ( self.vector[pos//16] >> (pos&15) ) & 1        
        else:                                                      
            slicebits = []
            i,j = pos.start,pos.stop
            if i is None and j is None:                     
                return self.deep_copy()                              
            if i is None:
                if j >= 0:
                    if j > len(self):
                        raise ValueError('illegal slice index values')         
                    for x in range(j):                                         
                        slicebits.append( self[x] )                              
                    return BitVector( bitlist = slicebits )                      
                else:
                    if abs(j) > len(self):
                        raise ValueError('illegal slice index values')         
                    for x in range(len(self) - abs(j)):
                        slicebits.append( self[x] )                              
                    return BitVector( bitlist = slicebits )                      
            if j is None:
                if i >= 0:
                    if i > len(self):
                        raise ValueError('illegal slice index values')         
                    for x in range(i,len(self)):
                        slicebits.append( self[x] )                              
                    return BitVector( bitlist = slicebits )                      
                else:
                    if abs(i) > len(self):
                        raise ValueError('illegal slice index values')         
                    for x in range(len(self) - abs(i), len(self)):
                        slicebits.append( self[x] )                              
                    return BitVector( bitlist = slicebits ) 
            if (i >= 0 and j >= 0) and i > j:
                raise ValueError('illegal slice index values')         
            if (i < 0 and j >= 0) and (len(self) - abs(i)) > j:
                raise ValueError('illegal slice index values')         
            if (i >= 0 and j < 0):
                if len(self) - abs(j) < i:
                    raise ValueError('illegal slice index values')         
                else:
                    for x in range(i, len(self) - abs(j)):
                        slicebits.append( self[x] )                              
                    return BitVector( bitlist = slicebits ) 
            if self.size == 0:                                           
                return BitVector( bitstring = '' )                       
            if i == j:                                        
                return BitVector( bitstring = '' )                       
            for x in range(i,j):                                         
                slicebits.append( self[x] )                              
            return BitVector( bitlist = slicebits )                      
    
    def __xor__(self, other):                                      
        '''
        Take a bitwise 'XOR' of the bit vector on which the method is invoked with
        the argument bit vector.  Return the result as a new bit vector.  If the two
        bit vectors are not of the same size, pad the shorter one with zeros from the
        left.
        '''
        if self.size < other.size:                                  
            bv1 = self._resize_pad_from_left(other.size - self.size)
            bv2 = other                                             
        elif self.size > other.size:                                
            bv1 = self                                              
            bv2 = other._resize_pad_from_left(self.size - other.size)
        else:                                                        
            bv1 = self                                               
            bv2 = other                                             
        res = BitVector( size = bv1.size )                          
        lpb = map(operator.__xor__, bv1.vector, bv2.vector)         
        res.vector = array.array( 'H', lpb )                        
        return res                                                  

    def __and__(self, other):                                       
        '''
        Take a bitwise 'AND' of the bit vector on which the method is invoked with
        the argument bit vector.  Return the result as a new bit vector.  If the two
        bit vectors are not of the same size, pad the shorter one with zeros from the
        left.
        '''      
        if self.size < other.size:                                  
            bv1 = self._resize_pad_from_left(other.size - self.size)
            bv2 = other                                             
        elif self.size > other.size:                                
            bv1 = self                                              
            bv2 = other._resize_pad_from_left(self.size - other.size)
        else:                                                        
            bv1 = self                                               
            bv2 = other                                             
        res = BitVector( size = bv1.size )                          
        lpb = map(operator.__and__, bv1.vector, bv2.vector)         
        res.vector = array.array( 'H', lpb )                        
        return res                                                  

    def __or__(self, other):                                        
        '''
        Take a bitwise 'OR' of the bit vector on which the method is invoked with the
        argument bit vector.  Return the result as a new bit vector.  If the two bit
        vectors are not of the same size, pad the shorter one with zero's from the
        left.
        '''
        if self.size < other.size:                                  
            bv1 = self._resize_pad_from_left(other.size - self.size)
            bv2 = other                                             
        elif self.size > other.size:                                
            bv1 = self                                              
            bv2 = other._resize_pad_from_left(self.size - other.size)
        else:                                                       
            bv1 = self                                              
            bv2 = other                                             
        res = BitVector( size = bv1.size )                          
        lpb = map(operator.__or__, bv1.vector, bv2.vector)          
        res.vector = array.array( 'H', lpb )                        
        return res                                                  

    def __invert__(self):                                           
        '''
        Invert the bits in the bit vector on which the method is invoked
        and return the result as a new bit vector.
        '''
        res = BitVector( size = self.size )                         
        lpb = list(map( operator.__inv__, self.vector ))            
        res.vector = array.array( 'H' )                             
        for i in range(len(lpb)):                                   
            res.vector.append( lpb[i] & 0x0000FFFF )                
        return res                                                  

    def __add__(self, other):                                       
        '''
        Because __add__ is supplied, you can always join two bitvectors by

            bitvec3  =  bitvec1  +  bitvec2

        bitvec3 is a new bitvector object that contains all the bits of
        bitvec1 followed by all the bits of bitvec2.
        '''
        i = 0                                                       
        outlist = []                                                
        while i < self.size:                                    
            outlist.append(self[i])                               
            i += 1                                                  
        i = 0                                                       
        while i < other.size:                                   
            outlist.append( other[i] )                              
            i += 1                                                  
        return BitVector( bitlist = outlist )                       

    def _getsize(self):                                             
        'Return the number of bits in a bit vector.'
        return self.size                                            

    def read_bits_from_file(self, blocksize):                       
        '''
        You can construct bitvectors directly from the bits in a disk file
        through the calls shown below.  As you can see, this requires two
        steps: First you make a call as illustrated by the first statement
        below.  The purpose of this call is to create a file object that is
        associated with the variable bv.  Subsequent calls to
        read_bits_from_file(n) on this variable return a bitvector for each
        block of n bits thus read.  The read_bits_from_file() throws an
        exception if the argument n is not a multiple of 8.

            bv  =  BitVector(filename = 'somefile')   
            bv1 =  bv.read_bits_from_file(64)    
            bv2 =  bv.read_bits_from_file(64)    
            ...
            ...
            bv.close_file_object()

        When reading a file as shown above, you can test the attribute
        more_to_read of the bitvector object in order to find out if there
        is more to read in the file.  The while loop shown below reads all
        of a file in 64-bit blocks:

            bv = BitVector( filename = 'testinput4.txt' )
            print("Here are all the bits read from the file:")
            while (bv.more_to_read):
                bv_read = bv.read_bits_from_file( 64 )
                print(bv_read)
            bv.close_file_object()

        The size of the last bitvector constructed from a file corresponds
        to how many bytes remain unread in the file at that point.  It is
        your responsibility to zero-pad the last bitvector appropriately
        if, say, you are doing block encryption of the whole file.
        '''
        error_str = '''You need to first construct a BitVector
        object with a filename as  argument'''                      
        if not self.filename:                                       
            raise SyntaxError( error_str )                          
        if blocksize % 8 != 0:                                      
            raise ValueError( "block size must be a multiple of 8" )
        bitstr = _readblock( blocksize, self )                      
        if len( bitstr ) == 0:                                      
            return BitVector( size = 0 )                            
        else:                                                       
            return BitVector( bitstring = bitstr )                  

    def read_bits_from_fileobject( self, fp ):                      
        '''
        This function is meant to read a bit string from a file like
        object.
        '''
        bitlist = []                                                
        while 1:                                                    
            bit = fp.read()                                         
            if bit == '': return bitlist                            
            bitlist += bit                                          

    def write_bits_to_stream_object( self, fp ):                       
        '''
        You can write a bitvector directly to a stream object, as
        illustrated by:

            fp_write = io.StringIO()
            bitvec.write_bits_to_stream_object(fp_write)
            print(fp_write.getvalue())   

        This method does not return anything. 

        This function is meant to write a bitvector directly to a file like
        object.  Note that whereas 'write_to_file' method creates a memory
        footprint that corresponds exactly to the bitvector, the
        'write_bits_to_stream_object' actually writes out the 1's and 0's as
        individual items to the file object.  That makes this method
        convenient for creating a string representation of a bitvector,
        especially if you use the StringIO class, as shown in the test
        code.
        '''
        for bit_index in range(self.size):                          
            if sys.version_info[0] == 3:                            
                if self[bit_index] == 0:                            
                    fp.write( str('0') )                            
                else:                                               
                    fp.write( str('1') )                            
            else:                                                   
                if self[bit_index] == 0:                            
                    fp.write( unicode('0') )                        
                else:                                               
                    fp.write( unicode('1') )                        

    write_bits_to_fileobject = write_bits_to_stream_object

    def divide_into_two(self):                                      
        '''
        A bitvector containing an even number of bits can be divided into
        two equal parts by

            [left_half, right_half] = bitvec.divide_into_two()

        where left_half and right_half hold references to the two returned
        bitvectors.  The method throws an exception when called on a
        bitvector with an odd number of bits.
        '''
        if self.size % 2 != 0:                                     
            raise ValueError( "must have even num bits" )          
        i = 0                                                      
        outlist1 = []                                              
        while ( i < self.size /2 ):                                
            outlist1.append( self[i] )                             
            i += 1                                                 
        outlist2 = []                                              
        while ( i < self.size ):                                   
            outlist2.append( self[i] )                             
            i += 1                                                 
        return [ BitVector( bitlist = outlist1 ),
                 BitVector( bitlist = outlist2 ) ]                 

    def permute(self, permute_list):                               
        '''
        This method returns a new bitvector object.  Permuting a bitvector means
        that you select its bits in the sequence specified by the argument
        permute_list.
        '''
        if max(permute_list) > self.size -1:                       
            raise ValueError( "Bad permutation index" )            
        outlist = []                                               
        i = 0                                                      
        while ( i < len( permute_list ) ):                         
            outlist.append( self[ permute_list[i] ] )              
            i += 1                                                 
        return BitVector( bitlist = outlist )                      

    def unpermute(self, permute_list):                              
        '''
        This method returns a new bitvector object. As indicated earlier
        for the permute() method, permuting a bitvector means that you
        select its bits in the sequence specified by the argument
        permute_list. Calling unpermute() with the same argument
        permute_list restores the sequence of bits to what it was in
        the original bitvector.
        '''
        if max(permute_list) > self.size -1:                        
            raise ValueError( "Bad permutation index" )             
        if self.size != len( permute_list ):                        
            raise ValueError( "Bad size for permute list" )         
        out_bv = BitVector( size = self.size )                      
        i = 0                                                       
        while i < len(permute_list):                            
            out_bv[ permute_list[i] ] = self[i]                     
            i += 1                                                  
        return out_bv                                               

    def write_to_file(self, file_out):                              
        '''
        You can write a bit vector directly to a file by calling
        write_to_file(), as illustrated by the following example that reads
        one bitvector from a file and then writes it to another file:

            bv = BitVector(filename = 'input.txt')
            bv1 = bv.read_bits_from_file(64)        
            print(bv1)
            FILEOUT = open('output.bits', 'wb')
            bv1.write_to_file(FILEOUT)
            FILEOUT.close()
            bv = BitVector(filename = 'output.bits')
            bv2 = bv.read_bits_from_file(64)
            print(bv2)

        Since all file I/O is byte oriented, the method write_to_file()
        throws an exception if the size of the bitvector on which the
        method is invoked is not a multiple of 8.  This method does not
        return anything.

        IMPORTANT FOR WINDOWS USERS: When writing an internally generated
                    bit vector out to a disk file, it is important to open
                    the file in the binary mode as shown.  Otherwise, the
                    bit pattern 00001010 ('\\n') in your bitstring will be
                    written out as 0000110100001010 ('\\r\\n'), which is
                    the linebreak on Windows machines.
        '''
        err_str = '''Only a bit vector whose length is a multiple of 8 can
            be written to a file.  Use the padding functions to satisfy
            this constraint.'''                                     
        if not self.FILEOUT:                                        
            self.FILEOUT = file_out                                 
        if self.size % 8:                                           
            raise ValueError( err_str )                             
        for byte in range( int(self.size/8) ):                      
            value = 0                                               
            for bit in range(8):                                    
                value += (self._getbit( byte*8+(7 - bit) ) << bit ) 
            if sys.version_info[0] == 3:                            
                file_out.write( bytes([value]) )        
            else:                                                   
                file_out.write( chr(value) )                        

    def close_file_object(self):                                    
        '''
        When you construct bitvectors by block scanning a disk file, after
        you are done, you can call this method to close the file object
        that was created to read the file:

            bv  =  BitVector(filename = 'somefile')   
            bv1 =  bv.read_bits_from_file(64)    
            bv.close_file_object()

        The constructor call in the first statement creates a file object
        for reading the bits.  It is this file object that is closed when
        you call close_file_object().
        '''
        if not self.FILEIN:                                         
            raise SyntaxError( "No associated open file" )          
        self.FILEIN.close()                                         

    def int_val(self):                                             
        'Return the integer value of a bitvector'
        intVal = 0                                                  
        for i in range(self.size):                                  
            intVal += self[i] * (2 ** (self.size - i - 1))          
        return intVal                                               

    intValue = int_val

    def get_bitvector_in_ascii(self):
        '''
        You can call get_bitvector_in_ascii() to directly convert a bit
        vector into a text string (this is a useful thing to do only if the
        length of the vector is an integral multiple of 8 and every byte in
        your bitvector has a print representation):

            bv = BitVector(textstring = "hello")
            print(bv)        # 0110100001100101011011000110110001101111
            mytext = bv3.get_bitvector_in_ascii()
            print mytext                           # hello

        This method is useful when you encrypt text through its bitvector
        representation.  After decryption, you can recover the text using
        the call shown here.  A call to get_bitvector_in_ascii() returns a
        string.
        '''
        if self.size % 8:                                           
            raise ValueError('''\nThe bitvector for get_bitvector_in_ascii() 
                                  must be an integral multiple of 8 bits''')
        return ''.join(map(chr, map(int,[self[i:i+8] for i in range(0,self.size,8)])))

    # For backward compatibility:
    get_text_from_bitvector = get_bitvector_in_ascii
    getTextFromBitVector = get_bitvector_in_ascii

    def get_bitvector_in_hex(self):
        '''
        You can directly convert a bit vector into a hex string (this is a
        useful thing to do only if the length of the vector is an integral
        multiple of 4):

            bv4 = BitVector(hexstring = "68656c6c6f")
            print(bv4)     # 0110100001100101011011000110110001101111
            myhexstring = bv4.get_bitvector_in_hex()
            print myhexstring                      # 68656c6c6

        This method throws an exception if the size of the bitvector is not
        a multiple of 4.  The method returns a string that is formed by
        scanning the bits from the left and replacing each sequence of 4
        bits by its corresponding hex digit.
        '''
        if self.size % 4:                                           
            raise ValueError('''\nThe bitvector for get_bitvector_in_hex() '''
                             '''must be an integral multiple of 4 bits''')
        return ''.join(map(lambda x: x.replace('0x',''), \
                       map(hex,map(int,[self[i:i+4] for i in range(0,self.size,4)]))))

    # For backward compatibility:
    get_hex_string_from_bitvector = get_bitvector_in_hex
    getHexStringFromBitVector = get_bitvector_in_hex

    def __lshift__( self, n ):                                     
        '''
        Left circular rotation of a BitVector through N positions can be
        carried out by
 
            bitvec  << N 

        This operator overloading is made possible by implementing the
        __lshift__ method defined here.  Note that this operator returns
        the bitvector on which it is invoked.  This allows for a chained
        invocation of the operator

        '''
        if self.size == 0:                                         
            raise ValueError('''Circular shift of an empty vector
                                makes no sense''')                 
        if n < 0:                                                  
            return self >> abs(n)                                  
        for i in range(n):                                         
            self.circular_rotate_left_by_one()                     
        return self                                                

    def __rshift__( self, n ):                                     
        '''
        Right circular rotation of a BitVector through N positions can be
        carried out by

            bitvec  >> N

        This operator overloading is made possible by implementing the
        __rshift__ method defined here.  Note that this operator returns
        the bitvector on which it is invoked.  This allows for a chained
        invocation of the operator.
        '''
        if self.size == 0:                                         
            raise ValueError('''Circular shift of an empty vector makes no sense''')                 
        if n < 0:                                                  
            return self << abs(n)                                  
        for i in range(n):                                         
            self.circular_rotate_right_by_one()                    
        return self                                                

    def circular_rotate_left_by_one(self):                         
        'For a one-bit in-place left circular shift'
        size = len(self.vector)                                    
        bitstring_leftmost_bit = self.vector[0] & 1                
        left_most_bits = list(map(operator.__and__, self.vector, [1]*size)) 
        left_most_bits.append(left_most_bits[0])                   
        del(left_most_bits[0])                                     
        self.vector = list(map(operator.__rshift__, self.vector, [1]*size)) 
        self.vector = list(map( operator.__or__, self.vector, \
                              list( map(operator.__lshift__, left_most_bits, [15]*size) )))   
                                                                   
        self._setbit(self.size -1, bitstring_leftmost_bit)         

    def circular_rotate_right_by_one(self):                        
        'For a one-bit in-place right circular shift'
        size = len(self.vector)                                    
        bitstring_rightmost_bit = self[self.size - 1]              
        right_most_bits = list(map( operator.__and__,
                               self.vector, [0x8000]*size ))       
        self.vector = list(map( operator.__and__, self.vector, [~0x8000]*size ))
        right_most_bits.insert(0, bitstring_rightmost_bit)         
        right_most_bits.pop()                                      
        self.vector = list(map(operator.__lshift__, self.vector, [1]*size))
        self.vector = list(map( operator.__or__, self.vector, \
                                list(map(operator.__rshift__, right_most_bits, [15]*size))))  
                                                                   
        self._setbit(0, bitstring_rightmost_bit)                   

    def circular_rot_left(self):                                   
        '''
        This is merely another implementation of the method
        circular_rotate_left_by_one() shown above.  This one does NOT use map
        functions.  This method carries out a one-bit left circular shift of a bit
        vector.
        '''
        max_index = (self.size -1)  // 16                       
        left_most_bit = self.vector[0] & 1                      
        self.vector[0] = self.vector[0] >> 1                    
        for i in range(1, max_index + 1):                       
            left_bit = self.vector[i] & 1                       
            self.vector[i] = self.vector[i] >> 1                
            self.vector[i-1] |= left_bit << 15                  
        self._setbit(self.size -1, left_most_bit)               

    def circular_rot_right(self):                               
        '''
        This is merely another implementation of the method
        circular_rotate_right_by_one() shown above.  This one does NOT use map
        functions.  This method does a one-bit right circular shift of a bit vector.
        '''
        max_index = (self.size -1)  // 16                       
        right_most_bit = self[self.size - 1]                    
        self.vector[max_index] &= ~0x8000                       
        self.vector[max_index] = self.vector[max_index] << 1    
        for i in range(max_index-1, -1, -1):                    
            right_bit = self.vector[i] & 0x8000                 
            self.vector[i] &= ~0x8000                           
            self.vector[i] = self.vector[i] << 1                
            self.vector[i+1] |= right_bit >> 15                 
        self._setbit(0, right_most_bit)                         

    def shift_left_by_one(self):                                
        '''
        For a one-bit in-place left non-circular shift.  Note that bitvector size
        does not change.  The leftmost bit that moves past the first element of the
        bitvector is discarded and rightmost bit of the returned vector is set to
        zero.
        '''
        size = len(self.vector)                                 
        left_most_bits = list(map(operator.__and__, self.vector, [1]*size))  
        left_most_bits.append(left_most_bits[0])                    
        del(left_most_bits[0])                                      
        self.vector = list(map(operator.__rshift__, self.vector, [1]*size)) 
        self.vector = list(map( operator.__or__, self.vector, \
                               list(map(operator.__lshift__, left_most_bits, [15]*size))))
        self._setbit(self.size -1, 0)                                

    def shift_right_by_one(self):                                    
        '''
        For a one-bit in-place right non-circular shift.  Note that bitvector size
        does not change.  The rightmost bit that moves past the last element of the
        bitvector is discarded and leftmost bit of the returned vector is set to
        zero.
        '''
        size = len(self.vector)                                      
        right_most_bits = list(map( operator.__and__, self.vector, [0x8000]*size ))         
        self.vector = list(map( operator.__and__, self.vector, [~0x8000]*size )) 
        right_most_bits.insert(0, 0)                                 
        right_most_bits.pop()                                        
        self.vector = list(map(operator.__lshift__, self.vector, [1]*size))    
        self.vector = list(map( operator.__or__, self.vector, \
                                   list(map(operator.__rshift__,right_most_bits, [15]*size))))
        self._setbit(0, 0)                                           

    def shift_left( self, n ):                                       
        '''
        Call this method if you want to shift in-place a bitvector to the left
        non-circularly.  As a bitvector is shifted non-circularly to the
        left, the exposed bit positions at the right end are filled with
        zeros. This method returns the bitvector object on which it is
        invoked.  This is to allow for chained invocations of the method.
        '''
        for i in range(n):                                           
            self.shift_left_by_one()                                 
        return self                                                  

    def shift_right( self, n ):                                      
        '''
        Call this method if you want to shift in-place a bitvector to the right
        non-circularly.  As a bitvector is shifted non-circularly to the
        right, the exposed bit positions at the left end are filled with
        zeros. This method returns the bitvector object on which it is
        invoked.  This is to allow for chained invocations of the method.
        '''
        for i in range(n):                                           
            self.shift_right_by_one()                                
        return self                                                  

    # Allow array like subscripting for getting and setting:
    __getitem__ = _getbit                                            

    def __setitem__(self, pos, item):                                
        '''
        This is needed for both slice assignments and for index assignments.  It
        checks the types of pos and item to see if the call is for slice assignment.
        For slice assignment, pos must be of type 'slice' and item of type BitVector.
        For index assignment, the argument types are checked in the _setbit() method.
        '''      
        # The following section is for slice assignment:
        if isinstance(pos, slice):                                 
            if (not isinstance( item, BitVector )):                  
                raise TypeError("For slice assignment, the right hand side must be a BitVector")    
            if (pos.start is None and pos.stop is None):                     
                return item.deep_copy()                              
            if pos.start is None:                                      
                if pos.stop >= 0:
                    if pos.stop != len(item):                         
                        raise ValueError('incompatible lengths for slice assignment 1')   
                    for i in range(pos.stop):                           
                        self[i] = item[i]                             
                else:
                    if len(self) - abs(pos.stop) != len(item):                                         
                        raise ValueError('incompatible lengths for slice assignment 2')   
                    for i in range(len(self) + pos.stop):                                
                        self[i] = item[i]                             
                return
            if pos.stop is None:                                      
                if pos.start >= 0:
                    if ((len(self) - pos.start) != len(item)):          
                        raise ValueError('incompatible lengths for slice assignment 3')   
                    for i in range(len(item)-1):                        
                        self[pos.start + i] = item[i]                 
                else:
                    if abs(pos.start) != len(item): 
                        raise ValueError('incompatible lengths for slice assignment 4')   
                    for i in range(len(item)):
                        self[len(self) + pos.start + i] = item[i]                 
                return
            if pos.start >=0 and pos.stop < 0:
                if ( (len(self) + pos.stop - pos.start) != len(item) ):                          
                    raise ValueError('incompatible lengths for slice assignment 5')   
                for i in range( pos.start, len(self) + pos.stop ):              
                    self[i] = item[ i - pos.start ]                 
                return
            if pos.start < 0 and pos.stop >= 0:
                if ( (len(self) - pos.stop + pos.start) != len(item) ):                          
                    raise ValueError('incompatible lengths for slice assignment 6')   
                for i in range( len(self) + pos.start, pos.stop ):              
                    self[i] = item[ i - pos.start ]                 
                return
            if ( (pos.stop - pos.start) != len(item) ):         
                raise ValueError('incompatible lengths for slice assignment 7')   
            for i in range( pos.start, pos.stop ):              
                self[i] = item[ i - pos.start ]                 
            return                                              
        # For index assignment use _setbit()
        self._setbit(pos, item)                                   

    # Allow len() to work:
    __len__ = _getsize                                               
    # Allow int() to work:
    __int__ = int_val

    def __iter__(self):                                            
        '''
        To allow iterations over a bit vector by supporting the 'for bit in
        bit_vector' syntax:
        '''
        return BitVectorIterator(self)                             

    def __str__(self):                                             
        'To create a print representation'
        if self.size == 0:                                           
            return ''                                                
        return ''.join(map(str, self))                           

    # Compare two bit vectors:
    def __eq__(self, other):                                         
        if self.size != other.size:                                  
            return False                                             
        i = 0                                                        
        while ( i < self.size ):                                     
            if (self[i] != other[i]): return False                   
            i += 1                                                   
        return True                                                  
    def __ne__(self, other):                                         
        return not self == other                                    
    def __lt__(self, other):                                        
        return self.intValue() < other.intValue()                   
    def __le__(self, other):                                        
        return self.intValue() <= other.intValue()                  
    def __gt__(self, other):                                        
        return self.intValue() > other.intValue()                   
    def __ge__(self, other):                                        
        return self.intValue() >= other.intValue()                  

    def deep_copy( self ):                                     
        '''
        You can make a deep copy of a bitvector by

            bitvec_copy =  bitvec.deep_copy()

        Subsequently, any alterations to either of the bitvector objects
        bitvec and bitvec_copy will not affect the other.
        '''
        copy = str( self )                                           
        return BitVector( bitstring = copy )                         

    # For backward compatibility:
    _make_deep_copy = deep_copy

    def _resize_pad_from_left( self, n ):                            
        '''
        Resize a bit vector by padding with n 0's from the left. Return the result as
        a new bit vector.
        '''
        new_str = '0'*n + str( self )                                
        return BitVector( bitstring = new_str )                      

    def _resize_pad_from_right( self, n ):                           
        '''
        Resize a bit vector by padding with n 0's from the right. Return the result
        as a new bit vector.
        '''
        new_str = str( self ) + '0'*n                                
        return BitVector( bitstring = new_str )                      

    def pad_from_left( self, n ):                                   
        '''
        You can pad a bitvector at its the left end with a designated number of
        zeros with this method. This method returns the bitvector object on
        which it is invoked. So you can think of this method as carrying
        out an in-place extension of a bitvector (although, under the hood,
        the extension is carried out by giving a new longer _vector
        attribute to the bitvector object).
        '''
        new_str = '0'*n + str( self )                               
        bitlist =  list(map( int, list(new_str) ))                  
        self.size = len( bitlist )                                  
        two_byte_ints_needed = (len(bitlist) + 15) // 16            
        self.vector = array.array( 'H', [0]*two_byte_ints_needed )  
        list(map( self._setbit, enumerate(bitlist), bitlist))       

    def pad_from_right( self, n ):                                  
        '''
        You can pad a bitvector at its right end with a designated number of
        zeros with this method. This method returns the bitvector object on
        which it is invoked. So you can think of this method as carrying
        out an in-place extension of a bitvector (although, under the hood,
        the extension is carried out by giving a new longer _vector
        attribute to the bitvector object).
        '''
        new_str = str( self ) + '0'*n                               
        bitlist =  list(map( int, list(new_str) ))                  
        self.size = len( bitlist )                                  
        two_byte_ints_needed = (len(bitlist) + 15) // 16            
        self.vector = array.array( 'H', [0]*two_byte_ints_needed )  
        list(map( self._setbit, enumerate(bitlist), bitlist))       

    def __contains__( self, otherBitVec ):                           
        '''
        This supports 'if x in y' and 'if x not in y' syntax for bit vectors.
        '''
        if self.size == 0:                                           
              raise ValueError("First arg bitvec has no bits")       
        elif self.size < otherBitVec.size:                           
              raise ValueError("First arg bitvec too short")         
        max_index = self.size - otherBitVec.size + 1                 
        for i in range(max_index):                                   
              if self[i:i+otherBitVec.size] == otherBitVec:          
                    return True                                      
        return False                                                

    def reset( self, val ):                                         
        '''
        Resets a previously created BitVector to either all zeros or all ones
        depending on the argument val.  Returns self to allow for syntax like
               bv = bv1[3:6].reset(1)
        or
               bv = bv1[:].reset(1)
        '''
        if val not in (0,1):                                         
            raise ValueError( "Incorrect reset argument" )           
        bitlist = [val for i in range( self.size )]                  
        list(map( self._setbit, enumerate(bitlist), bitlist ))       
        return self                                                  

    def count_bits( self ):                                          
        '''
        You can count the number of bits set in a BitVector instance by
  
            bv = BitVector(bitstring = '100111')
            print(bv.count_bits())                 # 4

        A call to count_bits() returns an integer value that is equal to
        the number of bits set in the bitvector.  
        '''
        return sum(self)

    def set_value(self, *args, **kwargs):                            
        '''
        You can call set_value() to change the bit pattern associated with
        a previously constructed bitvector object:

            bv = BitVector(intVal = 7, size =16)
            print(bv)                              # 0000000000000111
            bv.set_value(intVal = 45)
            print(bv)                              # 101101

        You can think of this method as carrying out an in-place resetting
        of the bit array in a bitvector. The method does not return
        anything.  The allowable modes for changing the internally stored
        bit array for a bitvector are the same as for the constructor.
        '''
        self.__init__( *args, **kwargs )                             

    # For backward compatibility:    
    setValue = set_value

    def count_bits_sparse(self):                                   
        '''
        For folks who use bit vectors with millions of bits in them but
        with only a few bits set, your bit counting will go much, much
        faster if you call count_bits_sparse() instead of count_bits():
        However, for dense bitvectors, I expect count_bits() to work
        faster.

            # a BitVector with 2 million bits:
            bv = BitVector(size = 2000000)
            bv[345234] = 1
            bv[233]=1
            bv[243]=1
            bv[18]=1
            bv[785] =1
            print(bv.count_bits_sparse())          # 5

        A call to count_bits_sparse() returns an integer whose value is the
        number of bits set in the bitvector.  Rhiannon, who contributed
        this method, estimates that if a bit vector with over 2 millions
        bits has only five bits set, this will return the answer in 1/18 of
        the time taken by the count_bits() method. Rhianon's implementation
        is based on an algorithm generally known as the Brian Kernighan's
        way, although its antecedents predate its mention by Kernighan and
        Ritchie.
        '''
        num = 0                                                      
        for intval in self.vector:                                   
            if intval == 0: continue                                 
            c = 0; iv = intval                                       
            while iv > 0:                                            
                iv = iv & (iv -1)                                    
                c = c + 1                                            
            num = num + c                                            
        return num                                                  

    def jaccard_similarity(self, other):                          
        '''
        You can calculate the similarity between two bitvectors using the
        Jaccard similarity coefficient.

            bv1 = BitVector(bitstring = '11111111')
            bv2 = BitVector(bitstring = '00101011')
            print bv1.jaccard_similarity(bv2)               # 0.675

        The value returned is a floating point number between 0 and 1.
        '''
        assert self.intValue() > 0 or other.intValue() > 0, 'Jaccard called on two zero vectors --- NOT ALLOWED'   
        assert self.size == other.size, 'bitvectors for comparing with Jaccard must be of equal length'  
        intersect = self & other                                     
        union = self | other                                         
        return ( intersect.count_bits_sparse() / float( union.count_bits_sparse() ) )             

    def jaccard_distance( self, other ):                             
        '''
        You can calculate the distance between two bitvectors using the
        Jaccard distance coefficient.

            bv1 = BitVector(bitstring = '11111111')
            bv2 = BitVector(bitstring = '00101011')
            print(str(bv1.jaccard_distance(bv2)))           # 0.375

        The value returned is a floating point number between 0 and 1.  
        '''
        assert self.size == other.size, 'vectors of unequal length'  
        return 1 - self.jaccard_similarity( other )                  

    def hamming_distance( self, other ):                            
        '''
        You can compare two bitvectors with the Hamming distance:

            bv1 = BitVector(bitstring = '11111111')
            bv2 = BitVector(bitstring = '00101011')
            print(str(bv1.hamming_distance(bv2)))           # 4

        This method returns a number that is equal to the number of bit
        positions in which the two operand bitvectors disagree.
        '''
        assert self.size == other.size, 'vectors of unequal length' 
        diff = self ^ other                                         
        return diff.count_bits_sparse()                             

    def next_set_bit(self, from_index=0):                           
        '''
        Starting from a given bit position, you can find the position index
        of the next set bit by

            bv = BitVector(bitstring = '00000000000001')
            print(bv.next_set_bit(5))                       # 13

        In this example, we are asking next_set_bit() to return the index
        of the bit that is set after the bit position that is indexed 5. If
        no next set bit is found, the method returns -1.  A call to
        next_set_bit() always returns a number.  This method was
        contributed originally by Jason Allum and updated subsequently by
        John Gleeson.
        '''
        assert from_index >= 0, 'from_index must be nonnegative'
        i = from_index
        v = self.vector
        l = len(v)
        o = i >> 4
        s = i & 0x0F
        i = o << 4
        while o < l:
            h = v[o]
            if h:
                i += s
                m = 1 << s
                while m != (1 << 0x10):
                    if h & m: return i
                    m <<= 1
                    i += 1
            else:
                i += 0x10
            s = 0
            o += 1
        return -1

    def rank_of_bit_set_at_index(self, position):                 
        '''
        You can measure the "rank" of a bit that is set at a given
        position.  Rank is the number of bits that are set up to the
        position of the bit you are interested in.

            bv = BitVector(bitstring = '01010101011100')
            print(bv.rank_of_bit_set_at_index(10))          # 6

        The value 6 returned by this call to rank_of_bit_set_at_index() is
        the number of bits set up to the position indexed 10 (including
        that position). This method throws an exception if there is no bit
        set at the argument position. Otherwise, it returns the rank as a
        number.
        '''
        assert self[position] == 1, 'the arg bit not set'
        bv = self[0:position+1]                                     
        return bv.count_bits()                                      

    def is_power_of_2( self ):                                         
        '''
        You can test whether the integer value of a bit vector is a power of
        two.  (The sparse version of this method works much faster for very
        long bit vectors.)  However, the regular version defined here may
        work faster for dense bit vectors.

            bv = BitVector(bitstring = '10000000001110')
            print(bv.is_power_of_2())

        This predicate returns 1 for true and 0 for false.
        '''
        if self.intValue() == 0: return False                       
        bv = self & BitVector( intVal = self.intValue() - 1 )       
        if bv.intValue() == 0: return True                          
        return False                                                

    # For backward compatibility:
    isPowerOf2 = is_power_of_2

    def is_power_of_2_sparse(self):                                  
        '''
        You can test whether the integer value of a bit vector is a power of
        two.  This sparse version works much faster for very long bit
        vectors.  (However, the regular version defined above may work
        faster for dense bit vectors.)

            bv = BitVector(bitstring = '10000000001110')
            print(bv.is_power_of_2_sparse())

        This predicate returns 1 for true and 0 for false.
        '''
        if self.count_bits_sparse() == 1: return True               
        return False                                                

    # For backward compatibility:
    isPowerOf2_sparse = is_power_of_2_sparse

    def reverse(self):                                            
        '''
        Given a bit vector, you can construct a bit vector with all the
        bits reversed, in the sense that what was left to right before now
        becomes right to left.

            bv = BitVector(bitstring = '0001100000000000001')
            print(str(bv.reverse()))

        A call to reverse() returns a new bitvector object whose bits are
        in reverse order in relation to the bits in the bitvector on which
        the method is invoked.
        '''
        reverseList = []                                            
        i = 1                                                       
        while ( i < self.size + 1 ):                                
            reverseList.append( self[ -i ] )                        
            i += 1                                                  
        return BitVector( bitlist = reverseList )                   

    def gcd(self, other):                                         
        '''
        Using Euclid's Algorithm, returns the greatest common divisor of
        the integer value of the bitvector on which the method is invoked
        and the integer value of the argument bitvector:

            bv1 = BitVector(bitstring = '01100110')     # int val: 102
            bv2 = BitVector(bitstring = '011010')       # int val: 26 
            bv = bv1.gcd(bv2)
            print(int(bv))                              # 2

        The result returned by gcd() is a bitvector object.
        '''
        a = self.intValue(); b = other.intValue()                   
        if a < b: a,b = b,a                                         
        while b != 0:                                               
            a, b = b, a % b                                         
        return BitVector( intVal = a )                              

    def multiplicative_inverse(self, modulus):                    
        '''
        Using the Extended Euclid's Algorithm, this method calculates the
        multiplicative inverse using normal integer arithmetic.  [For such
        inverses in a Galois Field GF(2^n), use the method gf_MI().]

            bv_modulus = BitVector(intVal = 32)
            bv = BitVector(intVal = 17) 
            bv_result = bv.multiplicative_inverse( bv_modulus )
            if bv_result is not None:
                print(str(int(bv_result)))           # 17
            else: print "No multiplicative inverse in this case"
         
        What this example says is that the multiplicative inverse of 17
        modulo 32 is 17.  That is because 17 times 17 modulo 32 equals 1.
        When using this method, you must test the returned value for
        None. If the returned value is None, that means that the number
        corresponding to the bitvector on which the method is invoked does
        not possess a multiplicative-inverse with respect to the modulus.
        When the multiplicative inverse exists, the result returned by
        calling multiplicative_inverse() is a bitvector object.
        '''
        MOD = mod = modulus.intValue(); num = self.intValue()       
        x, x_old = 0, 1                                             
        y, y_old = 1, 0                                             
        while mod:                                                  
            quotient = num // mod                                   
            num, mod = mod, num % mod                               
            x, x_old = x_old - x * quotient, x                      
            y, y_old = y_old - y * quotient, y                      
        if num != 1:                                                
            return None                                             
        else:                                                       
            MI = (x_old + MOD) % MOD                                
            return BitVector( intVal = MI )                         

    def length(self):                                               
        return self.size                                            

    def gf_multiply(self, b):                                       
        '''
        If you want to multiply two bit patterns in GF(2):

            a = BitVector(bitstring='0110001')
            b = BitVector(bitstring='0110')
            c = a.gf_multiply(b)
            print(c)                                   # 00010100110

        As you would expect, in general, the bitvector returned by this
        method is longer than the two operand bitvectors. A call to
        gf_multiply() returns a bitvector object.
        '''
        a = self.deep_copy()                                        
        b_copy = b.deep_copy()                                      
        a_highest_power = a.length() - a.next_set_bit(0) - 1        
        b_highest_power = b.length() - b_copy.next_set_bit(0) - 1   
        result = BitVector( size = a.length()+b_copy.length() )     
        a.pad_from_left( result.length() - a.length() )             
        b_copy.pad_from_left( result.length() - b_copy.length() )   
        for i,bit in enumerate(b_copy):                             
            if bit == 1:                                            
                power = b_copy.length() - i - 1                     
                a_copy = a.deep_copy()                              
                a_copy.shift_left( power )                          
                result ^=  a_copy                                   
        return result                                               

    def gf_divide_by_modulus(self, mod, n):                                    
        '''
        To divide a bitvector by a modulus bitvector in the Galois Field
        GF(2^n):

            mod = BitVector(bitstring='100011011')     # AES modulus
            n = 8
            a = BitVector(bitstring='11100010110001')
            quotient, remainder = a.gf_divide_by_modulus(mod, n)
            print(quotient)                            # 00000000111010
            print(remainder)                           # 10001111

        What this example illustrates is dividing the bitvector a by the
        modulus bitvector mod.  For a more general division of one
        bitvector a by another bitvector b, you would multiply a by the MI
        of b, where MI stands for "multiplicative inverse" as returned by
        the call to the method gf_MI().  A call to gf_divide_by_modulus()
        returns two bitvectors, one for the quotient and the other for the
        remainder.
        '''
        num = self                                                  
        if mod.length() > n+1:                                      
            raise ValueError("Modulus bit pattern too long")        
        quotient = BitVector( intVal = 0, size = num.length() )     
        remainder = num.deep_copy()                                 
        i = 0                                                       
        while 1:                                                    
            i = i+1                                                 
            if (i==num.length()): break                            
            mod_highest_power = mod.length()-mod.next_set_bit(0)-1 
            if remainder.next_set_bit(0) == -1:                    
                remainder_highest_power = 0                        
            else:                                                  
                remainder_highest_power = remainder.length() - remainder.next_set_bit(0) - 1  
            if (remainder_highest_power < mod_highest_power) or int(remainder)==0:                            
                break                                              
            else:                                                  
                exponent_shift = remainder_highest_power - mod_highest_power    
                quotient[quotient.length()-exponent_shift-1] = 1   
                quotient_mod_product = mod.deep_copy();            
                quotient_mod_product.pad_from_left(remainder.length() - mod.length())
                quotient_mod_product.shift_left(exponent_shift)    
                remainder = remainder ^ quotient_mod_product       
        if remainder.length() > n:                                 
            remainder = remainder[remainder.length()-n:]           
        return quotient, remainder                                 

    # For backward compatibility:
    gf_divide = gf_divide_by_modulus

    def gf_multiply_modular(self, b, mod, n):                      
        '''
        If you want to carry out modular multiplications in the Galois
        Field GF(2^n):

            modulus = BitVector(bitstring='100011011') # AES modulus
            n = 8
            a = BitVector(bitstring='0110001')
            b = BitVector(bitstring='0110')
            c = a.gf_multiply_modular(b, modulus, n)
            print(c)                                   # 10100110

        The call to gf_multiply_modular() returns the product of the two
        bitvectors a and b modulo the bitvector modulus in GF(2^8). A call
        to gf_multiply_modular() returns is a bitvector object.
        '''
        a = self                                                   
        a_copy = a.deep_copy()                                     
        b_copy = b.deep_copy()                                     
        product = a_copy.gf_multiply(b_copy)                       
        quotient, remainder = product.gf_divide_by_modulus(mod, n)            
        return remainder                                           

    def gf_MI(self, mod, n):                                       
        '''
        To calculate the multiplicative inverse of a bit vector in the
        Galois Field GF(2^n) with respect to a modulus polynomial, call
        gf_MI() as follows:

            modulus = BitVector(bitstring = '100011011')
            n = 8
            a = BitVector(bitstring = '00110011')
            multi_inverse = a.gf_MI(modulus, n)
            print multi_inverse                        # 01101100

        A call to gf_MI() returns a bitvector object.
        '''
        num = self                                                 
        NUM = num.deep_copy(); MOD = mod.deep_copy()               
        x = BitVector( size=mod.length() )                         
        x_old = BitVector( intVal=1, size=mod.length() )           
        y = BitVector( intVal=1, size=mod.length() )               
        y_old = BitVector( size=mod.length() )                     
        while int(mod):                                            
            quotient, remainder = num.gf_divide_by_modulus(mod, n)            
            num, mod = mod, remainder                              
            x, x_old = x_old ^ quotient.gf_multiply(x), x          
            y, y_old = y_old ^ quotient.gf_multiply(y), y          
        if int(num) != 1:                                          
            return "NO MI. However, the GCD of ", str(NUM), " and ", \
                                 str(MOD), " is ", str(num)        
        else:                                                      
            z = x_old ^ MOD                                        
            quotient, remainder = z.gf_divide_by_modulus(MOD, n)              
            return remainder                                       

    def runs(self):                                                
        '''
        You can extract from a bitvector the runs of 1's and 0's in the
        vector as follows:

           bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
           print(str(bv.runs()))                      # ['111', '00', '1']

        The object returned by runs() is a list of strings, with each
        element of this list being a string of 1's and 0's.
        '''
        allruns = []                                               
        if self.size == 0:                                         
            return allruns
        run = ''                                                   
        previous_bit = self[0]                                     
        if previous_bit == 0:                                      
            run = '0'                                              
        else:                                                      
            run = '1'                                              
        for bit in list(self)[1:]:                                 
            if bit == 0 and previous_bit == 0:                     
                run += '0'                                         
            elif bit == 1 and previous_bit == 0:                   
                allruns.append( run )                              
                run = '1'                                          
            elif bit == 0 and previous_bit == 1:                   
                allruns.append( run )                              
                run = '0'                                          
            else:                                                  
                run += '1'                                         
            previous_bit = bit                                     
        allruns.append( run )                                      
        return allruns                                             

    def test_for_primality(self):                                  
        '''
        You can test whether a randomly generated bit vector is a prime
        number using the probabilistic Miller-Rabin test

            bv = BitVector(intVal = 0)
            bv = bv.gen_random_bits(32)  
            check = bv.test_for_primality()
            print(check)                 

        The test_for_primality() methods returns a floating point number
        close to 1 for prime numbers and 0 for composite numbers.  The
        actual value returned for a prime is the probability associated
        with the determination of its primality.
        '''
        p = int(self)                                              
        if p == 1: return 0
        probes = [2,3,5,7,11,13,17]                                
        for a in probes:                                           
            if a == p: return 1                                    
        if any([p % a == 0 for a in probes]): return 0             
        k, q = 0, p-1                                              
        while not q&1:                                             
            q >>= 1                                                
            k += 1                                                 
        for a in probes:                                           
            a_raised_to_q = pow(a, q, p)                           
            if a_raised_to_q == 1 or a_raised_to_q == p-1: continue
            a_raised_to_jq = a_raised_to_q                         
            primeflag = 0                                          
            for j in range(k-1):                                   
                a_raised_to_jq = pow(a_raised_to_jq, 2, p)         
                if a_raised_to_jq == p-1:                          
                    primeflag = 1                                  
                    break                                          
            if not primeflag: return 0                             
        probability_of_prime = 1 - 1.0/(4 ** len(probes))          
        return probability_of_prime                                

    def gen_random_bits(self, width):                      
        '''
        You can generate a bitvector with random bits with the bits
        spanning a specified width.  For example, if you wanted a random
        bit vector to fully span 32 bits, you would say

            bv = BitVector(intVal = 0)
            bv = bv.gen_random_bits(32)  
            print(bv)                # 11011010001111011010011111000101

        As you would expect, gen_random_bits() returns a bitvector object.

        The bulk of the work here is done by calling random.getrandbits(
        width) which returns an integer whose binary code representation
        will NOT BE LARGER than the argument 'width'.  When random numbers
        are generated as candidates for primes, you often want to make sure
        that the random number thus created spans the full width specified
        by 'width' and that the number is odd.  This we do by setting the
        two most significant bits and the least significant bit.
        '''
        import random                                              
        candidate = random.getrandbits( width )                    
        candidate |= 1                                             
        candidate |= (1 << width-1)                                
        candidate |= (2 << width-3)                                
        return BitVector( intVal = candidate )                     

    # For backward compatibility: 
    gen_rand_bits_for_prime = gen_random_bits

    def min_canonical(self):  
        '''
        This method returns the "canonical" form of a BitVector instance that is obtained by
        circularly rotating the bit pattern through all possible shifts and returning the
        pattern with the maximum number of leading zeros.  This is also the minimum int value
        version of a bit pattern.  This method is useful in the "Local Binary Pattern"
        algorithm for characterizing image textures.  If you are curious as to how, see my
        tutorial on "Measuring Texture and Color in Images."
        '''
        intvals_for_circular_shifts  =  [int(self << 1) for _ in range(len(self))] 
        return BitVector( intVal = min(intvals_for_circular_shifts), size = len(self))


#--------------------------------  BitVectorIterator Class -----------------------------------

class BitVectorIterator:                                           
    def __init__( self, bitvec ):                                  
        self.items = []                                            
        for i in range( bitvec.size ):                             
            self.items.append( bitvec._getbit(i) )                 
        self.index = -1                                            
    def __iter__( self ):                                          
        return self                                                
    def next( self ):                                              
        self.index += 1                                            
        if self.index < len( self.items ):                         
            return self.items[ self.index ]                        
        else:                                                      
            raise StopIteration                                    
    __next__ = next                                                

#-----------------------------------  End of Class Definition -------------------------------

#----------------------------------     Test Code Follows    --------------------------------

if __name__ == '__main__':

    # Construct an EMPTY bit vector (a bit vector of size 0):
    print("\nConstructing an EMPTY bit vector (a bit vector of size 0):")
    bv1 = BitVector( size = 0 )
    print(bv1)                                   # no output

    # Construct a bit vector of size 2:
    print("\nConstructing a bit vector of size 2:")
    bv2 = BitVector( size = 2 )
    print(bv2)                                   # 00

    # Joining two bit vectors:
    print("\nConcatenating two previously constructed bit vectors:")
    result = bv1 + bv2
    print(result)                                # 00

    # Construct a bit vector with a tuple of bits:
    print("\nConstructing a bit vector from a tuple of bits:")
    bv = BitVector(bitlist=(1, 0, 0, 1))
    print(bv)                                    # 1001

    # Construct a bit vector with a list of bits:    
    print("\nConstruct a bit vector from a list of bits:")
    bv = BitVector(bitlist=[1, 1, 0, 1])
    print(bv)                                    # 1101

    # Construct a bit vector from an integer
    bv = BitVector(intVal=5678)
    print("\nBit vector constructed from integer 5678:")
    print(bv)                                    # 1011000101110
    print("\nBit vector constructed from integer 0:")
    bv = BitVector(intVal=0)
    print(bv)                                    # 0
    print("\nBit vector constructed from integer 2:")
    bv = BitVector(intVal=2)
    print(bv)                                    # 10
    print("\nBit vector constructed from integer 3:")
    bv = BitVector(intVal=3)
    print(bv)                                    # 11
    print("\nBit vector constructed from integer 123456:")
    bv = BitVector(intVal=123456)
    print(bv)                                    # 11110001001000000
    print("\nInt value of the previous bit vector as computed by int_val():")
    print(bv.int_val())                         # 123456
    print("\nInt value of the previous bit vector as computed by int():")
    print(int(bv))                               # 123456

    # Construct a bit vector from a very large integer:
    x = 12345678901234567890123456789012345678901234567890123456789012345678901234567890
    bv = BitVector(intVal=x)
    print("\nHere is a bit vector constructed from a very large integer:")
    print(bv)
    print("The integer value of the above bit vector is:%d" % int(bv))

    # Construct a bit vector directly from a file-like object:
    import io
    x = "111100001111"
    x = ""
    if sys.version_info[0] == 3:    
        x = "111100001111"
    else:                           
        x = unicode("111100001111")
    fp_read = io.StringIO(x)
    bv = BitVector( fp = fp_read )
    print("\nBit vector constructed directed from a file like object:")
    print(bv)                                    # 111100001111 

    # Construct a bit vector directly from a bit string:
    bv = BitVector( bitstring = '00110011' )
    print("\nBit Vector constructed directly from a bit string:")
    print(bv)                                    # 00110011

    bv = BitVector(bitstring = '')
    print("\nBit Vector constructed directly from an empty bit string:")
    print(bv)                                    # nothing
    print("\nInteger value of the previous bit vector:")
    print(bv.int_val())                         # 0

    print("\nConstructing a bit vector from the textstring 'hello':")
    bv3 = BitVector(textstring = "hello")
    print(bv3)
    mytext = bv3.get_bitvector_in_ascii()
    print("Text recovered from the previous bitvector: ")
    print(mytext)                                         # hello
    print("\nConstructing a bit vector from the textstring 'hello\\njello':")
    bv3 = BitVector(textstring = "hello\njello")
    print(bv3)
    mytext = bv3.get_bitvector_in_ascii()
    print("Text recovered from the previous bitvector:")
    print(mytext)                                         # hello
                                                          # jello

    print("\nConstructing a bit vector from the hexstring '68656c6c6f':")
    bv4 = BitVector(hexstring = "68656c6c6f")
    print(bv4)
    myhexstring = bv4.get_bitvector_in_hex()
    print("Hex string recovered from the previous bitvector: ")
    print(myhexstring)                                    # 68656c6c6f

    print("\nDemonstrating the raw bytes mode of constructing a bit vector (useful for reading public and private keys):")
    mypubkey = 'ssh-rsa AAAAB3NzaC1yc2EAAAABIwAAAQEA5amriY96HQS8Y/nKc8zu3zOylvpOn3vzMmWwrtyDy+aBvns4UC1RXoaD9rDKqNNMCBAQwWDsYwCAFsrBzbxRQONHePX8lRWgM87MseWGlu6WPzWGiJMclTAO9CTknplG9wlNzLQBj3dP1M895iLF6jvJ7GR+V3CRU6UUbMmRvgPcsfv6ec9RRPm/B8ftUuQICL0jt4tKdPG45PBJUylHs71FuE9FJNp01hrj1EMFObNTcsy9zuis0YPyzArTYSOUsGglleExAQYi7iLh17pAa+y6fZrGLsptgqryuftN9Q4NqPuTiFjlqRowCDU7sSxKDgU7bzhshyVx3+pzXO4D2Q== kak@pixie'
    import base64
    if sys.version_info[0] == 3:    
        import binascii
        keydata = base64.b64decode(bytes(mypubkey.split(None)[1], 'utf-8'))
    else:
        keydata = base64.b64decode(mypubkey.split(None)[1])
    bv = BitVector( rawbytes = keydata )
    print(bv)

    # Test array-like indexing for a bit vector:
    bv = BitVector( bitstring = '110001' )
    print("\nPrints out bits individually from bitstring 110001:")
    print(bv[0], bv[1], bv[2], bv[3], bv[4], bv[5])       # 1 1 0 0 0 1
    print("\nSame as above but using negative array indexing:")
    print(bv[-1], bv[-2], bv[-3], bv[-4], bv[-5], bv[-6]) # 1 0 0 0 1 1

    # Test setting bit values with positive and negative
    # accessors:
    bv = BitVector( bitstring = '1111' )
    print("\nBitstring for 1111:")
    print(bv)                                    # 1111

    print("\nReset individual bits of above vector:")
    bv[0]=0;bv[1]=0;bv[2]=0;bv[3]=0        
    print(bv)                                    # 0000
    print("\nDo the same as above with negative indices:")
    bv[-1]=1;bv[-2]=1;bv[-4]=1
    print(bv)                                    # 1011

    print("\nCheck equality and inequality ops:")
    bv1 = BitVector( bitstring = '00110011' )
    bv2 = BitVector( bitlist = [0,0,1,1,0,0,1,1] )
    print(bv1 == bv2)                           # True
    print(bv1 != bv2)                           # False
    print(bv1 < bv2)                            # False
    print(bv1 <= bv2)                           # True
    bv3 = BitVector( intVal = 5678 )
    print(bv3.int_val())                        # 5678
    print(bv3)                                  # 1011000101110
    print(bv1 == bv3)                           # False
    print(bv3 > bv1)                            # True
    print(bv3 >= bv1)                           # True

    # Write a bit vector to a file like object
    fp_write = io.StringIO()
    bv.write_bits_to_fileobject( fp_write )
    print("\nGet bit vector written out to a file-like object:")
    print(fp_write.getvalue())                  # 1011 

    print("\nExperiments with bitwise logical operations:")
    bv3 = bv1 | bv2                              
    print(bv3)                                  # 00110011
    bv3 = bv1 & bv2
    print(bv3)                                  # 00110011
    bv3 = bv1 + bv2
    print(bv3)                                  # 0011001100110011
    bv4 = BitVector( size = 3 )
    print(bv4)                                  # 000
    bv5 = bv3 + bv4
    print(bv5)                                  # 0011001100110011000
    bv6 = ~bv5
    print(bv6)                                  # 1100110011001100111
    bv7 = bv5 & bv6
    print(bv7)                                  # 0000000000000000000
    bv7 = bv5 | bv6
    print(bv7)                                  # 1111111111111111111

    print("\nTry logical operations on bit vectors of different sizes:")
    print(BitVector( intVal = 6 ) ^ BitVector( intVal = 13 ))   # 1011
    print(BitVector( intVal = 6 ) & BitVector( intVal = 13 ))   # 0100
    print(BitVector( intVal = 6 ) | BitVector( intVal = 13 ))   # 1111

    print(BitVector( intVal = 1 ) ^ BitVector( intVal = 13 ))   # 1100
    print(BitVector( intVal = 1 ) & BitVector( intVal = 13 ))   # 0001
    print(BitVector( intVal = 1 ) | BitVector( intVal = 13 ))   # 1101

    print("\nExperiments with setbit() and len():")
    bv7[7] = 0
    print(bv7)                                   # 1111111011111111111
    print(len( bv7 ))                            # 19
    bv8 = (bv5 & bv6) ^ bv7
    print(bv8)                                   # 1111111011111111111

    print("\nConstruct a bit vector from what is in the file testinput1.txt:")
    bv = BitVector( filename = 'TestBitVector/testinput1.txt' )
    #print bv                                    # nothing to show
    bv1 = bv.read_bits_from_file(64)    
    print("\nPrint out the first 64 bits read from the file:")
    print(bv1)
         # 0100000100100000011010000111010101101110011001110111001001111001
    print("\nRead the next 64 bits from the same file:")
    bv2 = bv.read_bits_from_file(64)    
    print(bv2)
         # 0010000001100010011100100110111101110111011011100010000001100110
    print("\nTake xor of the previous two bit vectors:")
    bv3 = bv1 ^ bv2
    print(bv3)
         # 0110000101000010000110100001101000011001000010010101001000011111

    print("\nExperiment with dividing an even-sized vector into two:")
    [bv4, bv5] = bv3.divide_into_two()
    print(bv4)                            # 01100001010000100001101000011010
    print(bv5)                            # 00011001000010010101001000011111

    # Permute a bit vector:
    print("\nWe will use this bit vector for experiments with permute()")
    bv1 = BitVector( bitlist = [1, 0, 0, 1, 1, 0, 1] )
    print(bv1)                                    # 1001101

    bv2 = bv1.permute( [6, 2, 0, 1] )
    print("\nPermuted and contracted form of the previous bit vector:")
    print(bv2)                                    # 1010

    print("\nExperiment with writing an internally generated bit vector out to a disk file:")
    bv1 = BitVector( bitstring = '00001010' ) 
    FILEOUT = open( 'TestBitVector/test.txt', 'wb' )
    bv1.write_to_file( FILEOUT )
    FILEOUT.close()
    bv2 = BitVector( filename = 'TestBitVector/test.txt' )
    bv3 = bv2.read_bits_from_file( 32 )
    print("\nDisplay bit vectors written out to file and read back from the file and their respective lengths:")
    print( str(bv1) + " " + str(bv3))
    print(str(len(bv1)) + " " + str(len(bv3)))

    print("\nExperiments with reading a file from the beginning to end:")
    bv = BitVector( filename = 'TestBitVector/testinput4.txt' )
    print("\nHere are all the bits read from the file:")
    while (bv.more_to_read):
        bv_read = bv.read_bits_from_file( 64 )
        print(bv_read)
    print("\n")

    print("\nExperiment with closing a file object and start extracting bit vectors from the file from the beginning again:")
    bv.close_file_object()
    bv = BitVector( filename = 'TestBitVector/testinput4.txt' )
    bv1 = bv.read_bits_from_file(64)        
    print("\nHere are all the first 64 bits read from the file again after the file object was closed and opened again:")
    print(bv1)
    FILEOUT = open( 'TestBitVector/testinput5.txt', 'wb' )
    bv1.write_to_file( FILEOUT )
    FILEOUT.close()

    print("\nExperiment in 64-bit permutation and unpermutation of the previous 64-bit bitvector:")
    print("The permutation array was generated separately by the Fisher-Yates shuffle algorithm:")
    bv2 = bv1.permute( [22, 47, 33, 36, 18, 6, 32, 29, 54, 62, 4,
                        9, 42, 39, 45, 59, 8, 50, 35, 20, 25, 49,
                        15, 61, 55, 60, 0, 14, 38, 40, 23, 17, 41,
                        10, 57, 12, 30, 3, 52, 11, 26, 43, 21, 13,
                        58, 37, 48, 28, 1, 63, 2, 31, 53, 56, 44, 24,
                        51, 19, 7, 5, 34, 27, 16, 46] )
    print("Permuted bit vector:")
    print(bv2)

    bv3 = bv2.unpermute( [22, 47, 33, 36, 18, 6, 32, 29, 54, 62, 4,
                          9, 42, 39, 45, 59, 8, 50, 35, 20, 25, 49,
                          15, 61, 55, 60, 0, 14, 38, 40, 23, 17, 41,
                          10, 57, 12, 30, 3, 52, 11, 26, 43, 21, 13,
                          58, 37, 48, 28, 1, 63, 2, 31, 53, 56, 44, 24,
                          51, 19, 7, 5, 34, 27, 16, 46] )    
    print("Unpurmute the bit vector:")
    print(bv3)

    print("\nTry circular shifts to the left and to the right for the following bit vector:")
    print(bv3)   # 0100000100100000011010000111010101101110011001110111001001111001
    print("\nCircular shift to the left by 7 positions:")
    bv3 << 7
    print(bv3)   # 1001000000110100001110101011011100110011101110010011110010100000

    print("\nCircular shift to the right by 7 positions:")
    bv3 >> 7
    print(bv3)   # 0100000100100000011010000111010101101110011001110111001001111001

    print("Test len() on the above bit vector:")
    print(len( bv3 ))                      # 64

    print("\nTest forming a [5:22] slice of the above bit vector:")
    bv4 = bv3[5:22]
    print(bv4)                             # 00100100000011010

    print("\nTest the iterator:")
    for bit in bv4:
        print(bit)                         # 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0

    print("\nDemonstrate padding a bit vector from left:")
    bv = BitVector(bitstring = '101010')
    bv.pad_from_left(4)
    print(bv)                              # 0000101010

    print("\nDemonstrate padding a bit vector from right:")
    bv.pad_from_right(4)
    print(bv)                              # 00001010100000

    print("\nTest the syntax 'if bit_vector_1 in bit_vector_2' syntax:")
    try:
        bv1 = BitVector(bitstring = '0011001100')
        bv2 = BitVector(bitstring = '110011')
        if bv2 in bv1:
            print("%s is in %s" % (bv2, bv1))
        else:
            print("%s is not in %s" % (bv2, bv1))
    except ValueError as arg:
        print("Error Message: " + str(arg))

    print("\nTest the size modifier when a bit vector is initialized with the intVal method:")
    bv = BitVector(intVal = 45, size = 16)
    print(bv)                             # 0000000000101101
    bv = BitVector(intVal = 0, size = 8)    
    print(bv)                             # 00000000
    bv = BitVector(intVal = 1, size = 8)    
    print(bv)                             # 00000001

    print("\nTesting slice assignment:")
    bv1 = BitVector( size = 25 )
    print("bv1= " + str(bv1))             # 0000000000000000000000000
    bv2 = BitVector( bitstring = '1010001' )
    print("bv2= " + str(bv2))             # 1010001
    bv1[6:9]  = bv2[0:3]
    print("bv1= " + str(bv1))             # 0000001010000000000000000
    bv1[:5] = bv1[5:10]
    print("bv1= " + str(bv1))             # 0101001010000000000000000
    bv1[20:] = bv1[5:10]
    print("bv1= " + str(bv1))             # 0101001010000000000001010
    bv1[:] = bv1[:]
    print("bv1= " + str(bv1))             # 0101001010000000000001010
    bv3 = bv1[:]
    print("bv3= " + str(bv3))             # 0101001010000000000001010

    print("\nTesting reset function:")
    bv1.reset(1)             
    print("bv1= " + str(bv1))             # 1111111111111111111111111
    print(bv1[3:9].reset(0))              # 000000
    print(bv1[:].reset(0))                # 0000000000000000000000000

    print("\nTesting count_bit():")
    bv = BitVector(intVal = 45, size = 16)
    y = bv.count_bits()
    print(y)                              # 4
    bv = BitVector(bitstring = '100111')
    print(bv.count_bits())                # 4
    bv = BitVector(bitstring = '00111000')
    print(bv.count_bits())                # 3
    bv = BitVector(bitstring = '001')
    print(bv.count_bits())                # 1
    bv = BitVector(bitstring = '00000000000000')
    print(bv.count_bits())                # 0

    print("\nTest set_value idea:")
    bv = BitVector(intVal = 7, size =16)
    print(bv)                             # 0000000000000111
    bv.set_value(intVal = 45)
    print(bv)                             # 101101

    print("\nTesting count_bits_sparse():")
    bv = BitVector(size = 2000000)
    bv[345234] = 1
    bv[233]=1
    bv[243]=1
    bv[18]=1
    bv[785] =1
    print("The number of bits set: " + str(bv.count_bits_sparse()))    # 5

    print("\nTesting Jaccard similarity and distance and Hamming distance:")
    bv1 = BitVector(bitstring = '11111111')
    bv2 = BitVector(bitstring = '00101011')
    print("Jaccard similarity: " + str(bv1.jaccard_similarity(bv2))) # 0.5
    print("Jaccard distance: " + str(bv1.jaccard_distance(bv2)))     # 0.5
    print("Hamming distance: " + str(bv1.hamming_distance(bv2)))     # 4

    print("\nTesting next_set_bit():")
    bv = BitVector(bitstring = '00000000000001')
    print(bv.next_set_bit(5))                                    # 13
    bv = BitVector(bitstring = '000000000000001')
    print(bv.next_set_bit(5))                                    # 14
    bv = BitVector(bitstring = '0000000000000001')
    print(bv.next_set_bit(5))                                    # 15
    bv = BitVector(bitstring = '00000000000000001')
    print(bv.next_set_bit(5))                                    # 16

    print("\nTesting rank_of_bit_set_at_index():")
    bv = BitVector(bitstring = '01010101011100')
    print(bv.rank_of_bit_set_at_index( 10 ))                     # 6

    print("\nTesting is_power_of_2():")
    bv = BitVector(bitstring = '10000000001110')
    print("int value: " + str(int(bv)))                          # 826
    print(bv.is_power_of_2())                                    # False
    print("\nTesting is_power_of_2_sparse():")              
    print(bv.is_power_of_2_sparse())                             # False

    print("\nTesting reverse():")
    bv = BitVector(bitstring = '0001100000000000001')
    print("original bv: " + str(bv))             # 0001100000000000001
    print("reversed bv: " + str(bv.reverse()))   # 1000000000000011000

    print("\nTesting Greatest Common Divisor (gcd):")
    bv1 = BitVector(bitstring = '01100110')
    print("first arg bv: " + str(bv1) + " of int value: " + str(int(bv1))) #102
    bv2 = BitVector(bitstring = '011010') 
    print("second arg bv: " + str(bv2) + " of int value: " + str(int(bv2)))# 26
    bv = bv1.gcd(bv2)
    print("gcd bitvec is: " + str(bv) + " of int value: " + str(int(bv)))  # 2

    print("\nTesting multiplicative_inverse:")
    bv_modulus = BitVector(intVal = 32)
    print("modulus is bitvec: " + str(bv_modulus) + " of int value: " + str(int(bv_modulus)))
    bv = BitVector(intVal = 17) 
    print("bv: " + str(bv) + " of int value: " + str(int(bv)))
    result = bv.multiplicative_inverse(bv_modulus)
    if result is not None:
        print("MI bitvec is: " + str(result) + " of int value: " + str(int(result)))
    else: print("No multiplicative inverse in this case")
                                                      # 17
    print("\nTest multiplication in GF(2):")
    a = BitVector(bitstring='0110001')
    b = BitVector(bitstring='0110')
    c = a.gf_multiply(b)
    print("Product of a=" + str(a) + " b=" + str(b) + " is " + str(c))
                                                      # 00010100110

    print("\nTest division in GF(2^n):")
    mod = BitVector(bitstring='100011011')            # AES modulus
    n = 8
    a = BitVector(bitstring='11100010110001')
    quotient, remainder = a.gf_divide_by_modulus(mod, n)
    print("Dividing a=" + str(a) + " by mod=" + str(mod) + " in GF(2^8) returns the quotient " 
                                       + str(quotient) + " and the remainder " + str(remainder))
                                                     # 10001111 

    print("\nTest modular multiplication in GF(2^n):")
    modulus = BitVector(bitstring='100011011')       # AES modulus
    n = 8
    a = BitVector(bitstring='0110001')
    b = BitVector(bitstring='0110')
    c = a.gf_multiply_modular(b, modulus, n)
    print("Modular product of a=" + str(a) + " b=" + str(b) + " in GF(2^8) is " + str(c))
                                                     # 10100110

    print("\nTest multiplicative inverses in GF(2^3) with " + "modulus polynomial = x^3 + x + 1:")
    print("Find multiplicative inverse of a single bit array")
    modulus = BitVector(bitstring='100011011')       # AES modulus
    n = 8
    a = BitVector(bitstring='00110011')
    mi = a.gf_MI(modulus,n)
    print("Multiplicative inverse of " + str(a) + " in GF(2^8) is " + str(mi))

    print("\nIn the following three rows shown, the first row shows the " +\
          "\nbinary code words, the second the multiplicative inverses," +\
          "\nand the third the product of a binary word with its" +\
          "\nmultiplicative inverse:\n")
    mod = BitVector(bitstring = '1011')
    n = 3
    bitarrays = [BitVector(intVal=x, size=n) for x in range(1,2**3)]
    mi_list = [x.gf_MI(mod,n) for x in bitarrays]
    mi_str_list = [str(x.gf_MI(mod,n)) for x in bitarrays]
    print("bit arrays in GF(2^3): " + str([str(x) for x in bitarrays]))
    print("multiplicati_inverses: " +  str(mi_str_list))

    products = [ str(bitarrays[i].gf_multiply_modular(mi_list[i], mod, n)) \
                        for i in range(len(bitarrays)) ]
    print("bit_array * multi_inv: " + str(products))

    # UNCOMMENT THE FOLLOWING LINES FOR
    # DISPLAYING ALL OF THE MULTIPLICATIVE 
    # INVERSES IN GF(2^8) WITH THE AES MODULUS:

#    print("\nMultiplicative inverses in GF(2^8) with "  + \
#                      "modulus polynomial x^8 + x^4 + x^3 + x + 1:")
#    print("\n(This may take a few seconds)\n")
#    mod = BitVector(bitstring = '100011011')
#    n = 8
#    bitarrays = [BitVector(intVal=x, size=n) for x in range(1,2**8)]
#    mi_list = [x.gf_MI(mod,n) for x in bitarrays]
#    mi_str_list = [str(x.gf_MI(mod,n)) for x in bitarrays]
#    print("\nMultiplicative Inverses:\n\n" + str(mi_str_list))
#    products = [ str(bitarrays[i].gf_multiply_modular(mi_list[i], mod, n)) \
#                        for i in range(len(bitarrays)) ]
#    print("\nShown below is the product of each binary code word " +\
#                     "in GF(2^3) and its multiplicative inverse:\n\n")
#    print(products)

    print("\nExperimenting with runs():")
    bv = BitVector(bitlist = (1, 0, 0, 1))
    print("For bit vector: " + str(bv))
    print("       the runs are: " + str(bv.runs()))
    bv = BitVector(bitlist = (1, 0))
    print("For bit vector: " + str(bv))
    print("       the runs are: " + str(bv.runs()))
    bv = BitVector(bitlist = (0, 1))
    print("For bit vector: " + str(bv))
    print("       the runs are: " + str(bv.runs()))
    bv = BitVector(bitlist = (0, 0, 0, 1))
    print("For bit vector: " + str(bv))
    print("       the runs are: " + str(bv.runs()))
    bv = BitVector(bitlist = (0, 1, 1, 0))
    print("For bit vector: " + str(bv))
    print("       the runs are: " + str(bv.runs()))

    print("\nExperiments with chained invocations of circular shifts:")
    bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
    print(bv)
    bv >> 1
    print(bv)
    bv >> 1 >> 1
    print(bv)
    bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
    print(bv)
    bv << 1
    print(bv)
    bv << 1 << 1
    print(bv)

    print("\nExperiments with chained invocations of NON-circular shifts:")
    bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
    print(bv)
    bv.shift_right(1)
    print(bv)
    bv.shift_right(1).shift_right(1)
    print(bv)
    bv = BitVector(bitlist = (1,1, 1, 0, 0, 1))
    print(bv)
    bv.shift_left(1)
    print(bv)
    bv.shift_left(1).shift_left(1)
    print(bv)

    # UNCOMMENT THE FOLLOWING LINES TO TEST THE
    # PRIMALITY TESTING METHOD. IT SHOULD SHOW
    # THAT ALL OF THE FOLLOWING NUMBERS ARE PRIME:
#    print("\nExperiments with primality testing. If a number is not prime, its primality " +
#          "test output must be zero.  Otherwise, it should a number very close to 1.0.")
#    primes = [179, 233, 283, 353, 419, 467, 547, 607, 661, 739, 811, 877, \
#              947, 1019, 1087, 1153, 1229, 1297, 1381, 1453, 1523, 1597, \
#              1663, 1741, 1823, 1901, 7001, 7109, 7211, 7307, 7417, 7507, \
#              7573, 7649, 7727, 7841]
#    for p in primes:
#        bv = BitVector(intVal = p)
#        check = bv.test_for_primality()
#        print("The primality test for " + str(p) + ": " + str(check))

    print("\nGenerate 32-bit wide candidate for primality testing:")
    bv = BitVector(intVal = 0)
    bv = bv.gen_random_bits(32)
    print(bv)
    check = bv.test_for_primality()
    print("The primality test for " + str(int(bv)) + ": " + str(check))