# coding=utf-8
__version__ = '3.5.0'
__author__ = "Avinash Kak (kak@purdue.edu)"
__date__ = '2021-May-30'
__url__ = 'https://engineering.purdue.edu/kak/dist/BitVector-3.5.0.html'
__copyright__ = "(C) 2021 Avinash Kak. Python Software Foundation."
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 is not None:
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. This is a faster implementation
# supplied by Elliot James Edmunds as a replacement for the previous version
# that you can find in Version 3.4.8.
# '''
# new_bv = BitVector( size=0 )
# if isinstance(self.vector, array.array):
# if sys.version_info[0] == 3:
# new_bv.vector.frombytes( self.vector.tobytes() )
# else:
# # The following does not work in Python 3.9
# new_bv.vector.fromstring( self.vector.tostring() )
# elif isinstance(self.vector, list) and sys.version_info[0] == 3:
# new_bv.vector = self.vector.copy()
# else:
# out_str = str(self) + str(other)
# return BitVector( bitstring = out_str )
# new_bv.size = self.size
# new_bv += other
# return new_bv
#
#
# def __iadd__(self, other):
# '''
# When extending an existing instance of a BitVector, __iadd__ should be faster
# than __add__ because we do not need to create a new BitVector. The call to
# __iadd__ simply modifies the current bitvector. __iadd__ is invoked when a
# user calls:
# bitvec1 += bitvec2
# Supplied by Elliot James Edmunds.
# '''
# if not isinstance(other, type(self)):
# raise TypeError("Can only join two BitVector objects, not {}".format(type(other)))
# # Calculate number of two-byte ints we will need to add and extend the vector
# two_byte_ints_to_add = (self.size + other.size + 15) // 16 - len(self.vector)
# self.vector.extend([0] * two_byte_ints_to_add)
# # Add the bits
# curr_bit = self.size % 16
# curr_two_byte_int = self.size // 16
# for bit in other:
# self.vector[curr_two_byte_int] = self.vector[curr_two_byte_int] | (bit << curr_bit)
# curr_bit += 1
# curr_two_byte_int += curr_bit // 16
# curr_bit %= 16
# # Increase the size
# self.size += other.size
# return self
#
def __add__(self, other):
'''
Restored from BitVector 3.4.5
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('0')
else:
fp.write('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):
for i in range(len(item)):
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))
def __eq__(self, other):
'''
Compare two bit vectors
'''
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))