BitVector-3.4.1.html

Python: module BitVector BitVector (version 3.4.1, 2015-May-4) BitVector.py Version: 3.4.1 Author: Avinash Kak (kak@purdue.edu) Date: 2015-May-4 Download Version 3.4.1: gztar bztar View version 3.4.1 code in browser Switch to Version 3.4.2 CHANGE LOG: 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. 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): 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/local/lib/python2.7/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 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 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 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 slice assignment test_for_primality unpermute write_to_file write_bits_to_fileobject CONSTRUCTING BIT VECTORS: You can construct a bit vector in the following different ways: (C0) You construct an EMPTY bit vector using the following syntax: bv = BitVector(size = 0) (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 (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. (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 (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). 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. What the method accomplishes can be thought of as in-place resetting of the bits. The method does not return anything. 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) 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. (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. (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. (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. (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. (15) string representation You can convert a bitvector into its string representation by str(bitvec) (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. (17) length() You can find the length of a bitvector by len = bitvec.length() (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. (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. (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. (21) write_bits_to_fileobject() You can also write a bitvector directly to a stream object, as illustrated by: fp_write = io.StringIO() bitvec.write_bits_to_fileobject(fp_write) print(fp_write.getvalue()) This method does not return anything. (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). (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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. (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(). 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. 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. Version 3.2 was triggered by my own desire to include additional functionality in the module to make it more useful for experimenting with hashing functions. While I was at it, I also included in it a couple of safety checks on the lengths of the two arguments 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! 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.) Imported Modules array operator sys Classes BitVectorIterator __builtin__.object BitVector class BitVector(__builtin__.object) Methods defined here: __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. __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. __contains__(self, otherBitVec) This supports 'if x in y' and 'if x not in y' syntax for bit vectors. __eq__(self, other) # Compare two bit vectors: __ge__(self, other) __getitem__ = _getbit(self, pos) __getslice__(self, i, j) Fetch slices with [i:j], [:], etc. __gt__(self, other) __init__(self, *args, **kwargs) __int__ = int_val(self) __invert__(self) Invert the bits in the bit vector on which the method is invoked and return the result as a new bit vector. __iter__(self) To allow iterations over a bit vector by supporting the 'for bit in bit_vector' syntax: __le__(self, other) __len__ = _getsize(self) __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 __lt__(self, other) __ne__(self, other) __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. __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. __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. __str__(self) To create a print representation __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. 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. 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. circular_rotate_left_by_one(self) For a one-bit in-place left circular shift circular_rotate_right_by_one(self) For a one-bit in-place right circular shift 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(). 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. 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. 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. 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. 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. gen_rand_bits_for_prime = gen_random_bits(self, width) 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. getHexStringFromBitVector = get_bitvector_in_hex(self) getTextFromBitVector = get_bitvector_in_ascii(self) 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. 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. get_hex_string_from_bitvector = get_bitvector_in_hex(self) get_text_from_bitvector = get_bitvector_in_ascii(self) 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. gf_divide = gf_divide_by_modulus(self, mod, n) 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. 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. 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. 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. intValue = int_val(self) int_val(self) Return the integer value of a bitvector isPowerOf2 = is_power_of_2(self) isPowerOf2_sparse = is_power_of_2_sparse(self) 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. 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. 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. 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. length(self) 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. 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. 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). 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). 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. 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. 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. read_bits_from_fileobject(self, fp) This function is meant to read a bit string from a file like object. 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) 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. 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. setValue = set_value(self, *args, **kwargs) 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. 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. 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. 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. 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. 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. 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. write_bits_to_fileobject(self, fp) You can write a bitvector directly to a stream object, as illustrated by: fp_write = io.StringIO() bitvec.write_bits_to_fileobject(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_fileobject' 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. 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) Sicne 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. Data descriptors defined here: __dict__ dictionary for instance variables (if defined) __weakref__ list of weak references to the object (if defined) class BitVectorIterator Methods defined here: __init__(self, bitvec) __iter__(self) __next__ = next(self) next(self) Data __author__ = 'Avinash Kak (kak@purdue.edu)' __copyright__ = '(C) 2015 Avinash Kak. Python Software Foundation.' __date__ = '2015-May-4' __url__ = 'https://engineering.purdue.edu/kak/dist/BitVector-3.4.1.html' __version__ = '3.4.1' Author Avinash Kak (kak@purdue.edu)

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		__author__ = 'Avinash Kak (kak@purdue.edu)' __copyright__ = '(C) 2015 Avinash Kak. Python Software Foundation.' __date__ = '2015-May-4' __url__ = 'https://engineering.purdue.edu/kak/dist/BitVector-3.4.1.html' __version__ = '3.4.1'