# coding=utf-8
__version__ = '3.4.8'
__author__ = "Avinash Kak (kak@purdue.edu)"
__date__ = '2018-March-21'
__url__ = 'https://engineering.purdue.edu/kak/dist/BitVector-3.4.8.html'
__copyright__ = "(C) 2018 Avinash Kak. Python Software Foundation."
__doc__ = '''
BitVector.py
Version: ''' + __version__ + '''
Author: Avinash Kak (kak@purdue.edu)
Date: ''' + __date__ + '''
@title
CHANGES IN THIS VERSION:
Version 3.4.8 fixes a bug in the slice assignment logic in the
implementation of __setitem__(). This version also makes the module
ready for Version 3.5.3 of Python3 that requires that when you write to
a string stream object, you do so with literals of type bytes.
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.
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 3.4.6
Version 3.4.6 fixes what was hopefully the last remaining bug in using
negative index values for slice assignments.
Version 3.4.5
Version 3.4.5 fixes an important bug in the code meant for slice
assignment. This bug made itself evident when using negative
start/stop values for slice assignment. Additionally, this version
includes a new method named min_canonical() that returns a circularly
rotated form of a BitVector with the maximum number of leading zeros.
Such canonical forms of bit patterns are used in the "Local Binary
Pattern" algorithm for characterizing image textures.
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 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
The two bug fixes made in Version 3.4.8 were triggered by emails from
Aurélien Buhrig and Bob Janssen. Aurélien found an error in one of my
statements in the implementation of __setitem__(). And Bob reported
that my implementation of the method write_bits_to_stream_object() was
not working with Version 3.5.3 of Python. Version 3.4.8 of BitVector
incorporates the fix provided by Aurélien and contains special-case
logic for writing to stream objects in Version 3.5.3 of Python3.
@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_old( 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') )
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:
if sys.version_info[1] == 5 and sys.version_info[2] <= 2:
fp.write( str('0') )
else:
fp.write( b'0' )
else:
if sys.version_info[1] == 5 and sys.version_info[2] <= 2:
fp.write( str('1') )
else:
fp.write( b'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))
# 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))
