BitVector (version 3.1.1, 2012-June-9) |
BitVector.py
Version: 3.1.1
Author: Avinash Kak (kak@purdue.edu)
Date: 2012-June-9
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CHANGE LOG:
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.
INSTALLATION:
The BitVector class was packaged using Distutils. 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):
python setup.py install
You have to have root privileges for this to work. On Linux
distributions, this will install the module file at a location that
looks like
/usr/lib/python2.6/site-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/lib/python2.6/site-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
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 access
__getslice__ for slice 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 slice setting
__str__for str()
__xor__for bitwise logical XOR
count_bits
count_bits_sparse faster for sparse bit vectors
deep_copy
divide_into_two
gcdfor greatest common divisor
gen_rand_bits_for_prime
gf_divide for divisions in GF(2^n)
gf_MI for multiplicative inverse in GF(2^n)
gf_multiplyfor multiplications in GF(2)
gf_multiply_modularfor multiplications in GF(2^n)
hamming_distance
intValue for returning the integer value
isPowerOf2
isPowerOf2_sparse faster for sparse bit vectors
jaccard_distance
jaccard_similarity
length
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
shift_left for non-circular left shift
shift_rightfor non-circular right shift
slice assignment
setValue
test_for_primality
unpermute
write_to_file
write_bits_to_fileobject
CONSTRUCTING BIT VECTORS:
You can construct a bit vector in seven different ways.
(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] )
(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.
(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.
(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.
(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()
(C6) You can construct a bit vector from a string of 1's and 0's by
bv = BitVector( bitstring = '110011110000' )
(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
OPERATIONS SUPPORTED BY THE BITVECTOR CLASS:
DISPLAYING BIT VECTORS:
(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 )
ACCESSING AND SETTING INDIVIDUAL BITS AND SLICES:
(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.
(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 __getslice__ method.
(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.
(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.
(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).
(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.
LOGICAL OPERATIONS ON BIT VECTORS:
(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.
COMPARING BIT VECTORS:
(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.
OTHER SUPPORTED OPERATIONS:
(10) You can permute and unpermute bit vectors:
bv_permuted = bv.permute( permutation_list )
bv_unpermuted = bv.unpermute( permutation_list )
(11) 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.
(12) If you want to shift a bitvector non-circularly:
bitvec = BitVector( bitstring = '10010000' )
bitvec.shift_left(3) # 10000000
bitvec.shift_right(3) # 00010000
Obviously, for a sufficient large left or right non-circular
shift, you will end up with a bitvector that is all zeros.
(13) A bit vector 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 bit vectors.
(14) You can find the integer value of a bit array by
bitvec.intValue()
or by
int( bitvec )
(15) You can convert a bit vector into its string representation by
str( bitvec )
(16) Because __add__ is supplied, you can always join two bit vectors
by
bitvec3 = bitvec1 + bitvec2
bitvec3 is a new bit vector that contains all the bits of
bitvec1 followed by all the bits of bitvec2.
(17) You can find the length of a bitvector by
len = bitvec.length()
(18) You can make a deep copy of a bitvector by
bitvec_copy = bitvec.deep_copy()
(19) You can write a bit vector directly to a file, as illustrated
by the following example that reads one bit vector 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 )
IMPORTANT: The size of a bit vector must be a multiple of of 8
for this write function to work. If this
condition is not met, the function will throw an
exception.
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.
(20) You can also write a bit vector directly to a stream object, as
illustrated by
fp_write = io.StringIO()
bitvec.write_bits_to_fileobject( fp_write )
print( fp_write.getvalue() )
(21) You can pad a bit vector from the left or from the right with a
designated number of zeros
bitvec.pad_from_left( n )
bitvec.pad_from_right( n )
In the first case, the new bit vector will be the same as the
old bit vector except for the additional n zeros on the left.
The same thing happens in the second case except that now the
additional n zeros will be on the right.
(22) 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.
(23) You can change the bit pattern associated with a previously
constructed BitVector instance:
bv = BitVector( intVal = 7, size =16 )
print( bv ) # 0000000000000111
bv.setValue( intVal = 45 )
print( bv ) # 101101
(24) You can count the number of bits set in a BitVector instance by
bv = BitVector( bitstring = '100111' )
print( bv.count_bits() ) # 4
(25) 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():
# 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
(26) You can calculate the similarity and the distance between two
bit vectors using the Jaccard similarity coefficient and the
Jaccard distance. Also, you can calculate the Hamming distance
between two bit vectors:
bv1 = BitVector( bitstring = '11111111' )
bv2 = BitVector( bitstring = '00101011' )
print bv1.jaccard_similarity( bv2 )
print( str( bv1.jaccard_distance( bv2 ) ) )
print( str( bv1.hamming_distance( bv2 ) ) )
(27) Starting from a given bit position, you can find the position
index of the next set bit:
bv = BitVector( bitstring = '00000000000001' )
print( bv.next_set_bit( 5 ) ) # 13
since the position index of the SET bit after the bit
whose position index 5 is 13.
(28) 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
(29) 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 small bit vectors.
bv = BitVector( bitstring = '10000000001110' )
print( bv.isPowerOf2() )
print( bv.isPowerOf2_sparse() )
(30) 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() ) )
(31) 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
(32) You can find the multiplicative inverse of a bit vector
vis-a-vis a given modulus:
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"
This multiplicative inverse is calculated using normal integer
arithmetic. For multiplicative inverses in GF(2^n), use the
gf_MI() method described below.
(33) To find the multiplicative inverse of a bit vector in
GF(2^n) with respect to a modulus polynomial, you can do
the following:
modulus = BitVector( bitstring = '100011011' )
n = 8
a = BitVector( bitstring = '00110011' )
multi_inverse = a.gf_MI( modulus, n )
print multi_inverse# 01101100
(34) 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
(35) On the other hand, if you want to carry out modular
multiplications 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( c )# 10100110
(36) To divide by a modulus bitvector in GF(2^n):
mod = BitVector( bitstring='100011011' ) # AES modulus
n = 8
bitvec = BitVector( bitstring='11100010110001' )
quotient, remainder = bitvec.gf_divide(mod, n)
print( quotient ) # 00000000111010
print( remainder ) # 10001111
(37) You can extract from a bit vector the runs of 1's and 0's
in the vector
bv = BitVector( bitlist = (1,1, 1, 0, 0, 1) )
print( str(bv.runs()) )# ['111', '00', '1']
(38) You can generate a bit vector with random bits that span in
full the specified width. For example, if you wanted the
random bit vector to fully span 32 bits, you would say
bv = BitVector( intVal = 0 )
bv = bv.gen_rand_bits_for_prime(32)
print(bv)# 11011010001111011010011111000101
(39) 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_rand_bits_for_prime(32)
check = bv.test_for_primality()
print(check)
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. After resolving the argument with which the
constructor is called (which happens in lines (A11) through (A89)
of the file BitVector.py), the very first thing that the
constructor does is to figure out in line (A90) as to how many of
those 2-byte ints it needs for the bits. For example, if you
wanted to store a 64-bit array, the variable 'two_byte_ints_needed'
in line (A90) 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.) Line (A91) creates an array of
2-byte ints and initializes it with the required number of zeros.
Line (A92) then shifts the bits into the array of two-byte ints.
As mentioned above, note that it is not necessary for the size of
the 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 attribute.
With regard to the code in lines (A11) through (A89) of the file
BitVector.py, 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 with 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.
Lines (A21) through (A27) are for the following sort of a call
bv = BitVector( filename = 'myfilename' )
This 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.
Lines (A28) through (A33) are for the case when you want to
construct a bit vector by reading the bits off a file-like object,
as in
x = "111100001111"
fileobj = StringIO.StringIO( x )
bv = BitVector( fp = fileobj )
Lines (A34) through (A71) are for the case when you want to
construct a bit vector from an integer, as in
bv = BitVector( intVal = 123456 )
The bits stored in the bit vector will correspond to the binary
representation of the integer argument provided. The bit vector
constructed with the above call will be the shortest possible bit
vector for the integer supplied. As a case in point, when the
intVal is 0, the bit vector will consist of a single bit which will
be 0 also. The code in lines (A34) through (A71) can also handle
the following sort of a call
bv = BitVector( intVal = 46, size = 16 )
which returns a bit vector of a specific size by padding the
shortest possible bit vector the the intVal with zeros from the
left.
Lines (A72) through (A78) are for constructing a bit vector with
just the size information, as in
bv = BitVector( size = 61 )
This returns a bit vector that will hold exactly 61 bits, all
initialized to the zero value.
Lines (A79) through (A83) are for constructing a bit vector from a
bitstring, as in
bv = BitVector( bitstring = '00110011111' )
Finally, lines (A84) through (A87) are for constructing a bit
vector from a list or a tuple of the individual bits:
bv = BitVector( bitlist = (1, 0, 1, 1, 0, 0, 1) )
The bit vector constructed is initialized with the supplied bits.
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. I
believe 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 only,
say, 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.
ABOUT THE AUTHOR:
Avi Kak is the author of "Programming with Objects: A Comparative
Presentation of Object-Oriented Programming with C++ and Java",
published by John-Wiley in 2003. This book presents a new approach
to the combined learning of two large object-oriented languages,
C++ and Java. It is being used as a text in a number of
educational programs around the world. This book has also been
translated into Chinese. Avi Kak is also the author of "Scripting
with Objects: A Comparative Presentation of Object-Oriented
Scripting with Perl and Python," published in 2008 by John-Wiley.
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.)
Modules | ||||||
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Classes | ||||||||||||||
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Data | ||
__author__ = 'Avinash Kak (kak@purdue.edu)' __copyright__ = '(C) 2012 Avinash Kak. Python Software Foundation.' __date__ = '2012-June-9' __url__ = 'https://engineering.purdue.edu/kak/dist/BitVector-3.1.1.html' __version__ = '3.1.1' |
Author | ||
Avinash Kak (kak@purdue.edu) |