🏣 Clean up for arxiv

book/ebook_src/bitwise_operations/bit_array.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Example of how to use a bit array in python as a "counter" dict'''
+
+def print_dupl_ba(l1):
+    '''
+    >>> l1 = [0, 1, 2, 3, 4, 2, 6, 7, 8, 9]
+    >>> print_dupl_ba(l1)
+    2
+    '''
+
+    bs = bytearray(10)
+    for i in range(len(l1)):
+        if i == l1[i]:
+            bs[i] = 1
+    for index, bit in enumerate(bs):
+        if bit == 0:
+            return l1[index]
+    return None
+
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+

book/ebook_src/bitwise_operations/bitwise.txt

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+				BIT-WISE
+			----------------------
+
+1. To find a number:
+11000101 is 2^0+2^2+2^6+2^7 = 197
+
+
+2. Left shifting:
+	0010 1011 << 4  ---> 1011 000
+
+
+3. Right shifting:
+	0010 1011 >> 4	---> 0000 0010
+	or it can be filled with the copy of the first bit, instead of 0:
+	1011 0010 >> 4  ---> 1111 1011
+
+
+4. XOR can cancels out:
+15 ^ 12 ^ 15 = 12
+
+
+5. 2^x:
+	left-shift 1 by x:
+	0000 0001 << x
+
+	so if x = 2, 2^2 = 4 -> 100
+
+	0000 0001 << 2  ---> 0000 0100
+
+
+6. Is power of 2?
+	just do x&(x-1).
+	if 0 --> yes!

book/ebook_src/bitwise_operations/clear_bits.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Clear a bit in a binary number.
+    Like the reverse of set bit:
+    1) first create a number filled of 1s,
+        with 0 at i (can create 0001000 and ~)
+    2) AND the number so it clears the ith bit
+'''
+
+
+
+def clear_bit(num, i):
+    mask = ~ (1 << i)   # -0b10001
+    return bin(num & mask)
+
+
+def clear_all_bits_from_i_to_0(num, i):
+    mask = ~ ( (1 << (i+1)) - 1)
+    return bin(num & mask)
+
+
+def clear_all_bits_from_most_sig_to_1(num, i):
+    mask =  ( 1 << i) -1
+    return bin(num & mask)
+
+
+if __name__ == '__main__':
+    num = int('10010000', 2)
+    print clear_bit(num, 4)   # '0b10000000'
+
+    num = int('10010011', 2)
+    print clear_all_bits_from_i_to_0(num, 2)  # '0b10010000'
+
+    num = int('1110011', 2)
+    print clear_all_bits_from_most_sig_to_1(num, 2)  #'0b11'

book/ebook_src/bitwise_operations/find_bit_len.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Find how many bits a int has:
+    1) Start with a mask of 1
+    2) Mask with AND
+    3) if result (if true): count += 1
+    (obs: to find the int of a bin do int('1001', 2)) and to show in bin
+    do bin(int))
+'''
+
+
+def find_bit_len(int_num):
+    lenght = 0
+    while int_num:
+        int_num >>= 1
+        lenght += 1
+    return lenght
+
+
+if __name__ == '__main__':
+    for i in range(17):
+        print(find_bit_len(i))
+        print i.bit_length()

book/ebook_src/bitwise_operations/find_how_many_1_binary.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Find how many 1s in the binary:
+    1) Start with a mask of 1
+    2) Mask with AND
+    3) if result (if true): count += 1
+    (obs: to find the int of a bin do int('1001',
+        2)) and to show in bin do bin(int))
+'''
+
+
+def find_how_many_1_in_a_binary(n):
+    '''
+    >>> find_how_many_1_in_a_binary(9)
+    2
+    '''
+
+    counter = 0
+    while n:
+        if n & 1:
+            counter += 1
+        n >>= 1
+    return counter
+
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+

book/ebook_src/bitwise_operations/get_bit.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Get a bit in a binary number:
+    1) Shifts 1 over by i bits
+    2) make an AND with the number
+    3) all the other than the bit at i are clean, now compare to 0
+    4) if the new value is not 0, bit i is 1
+'''
+
+
+def get_bit(num, i):
+    mask = 1 << i
+    return num & mask != 0
+
+
+if __name__ == '__main__':
+    num = int('0100100', 2)
+    get_bit(num, 0)   # 0
+    get_bit(num, 1)   # 0
+    get_bit(num, 2)   # 1
+    get_bit(num, 3)   # 0
+    get_bit(num, 4)   # 0
+    get_bit(num, 5)   # 1
+    get_bit(num, 6)   # 0
+

book/ebook_src/bitwise_operations/get_float_rep_bin.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' Given a real number between 0 and 1 (eg: 0.72), this method print the binary
+    representation. If the Number cannot be represented accurately in binary, with at
+    most 32 chars, print error:
+'''
+
+def get_float_rep(num):
+    '''
+    >>> get_float_rep(0.72)
+    ('Error 2', '.1011100001010001111010111000010')
+    >>> get_float_rep(0.1)
+    ('Error 2', '.0001100110011001100110011001100')
+    >>> get_float_rep(0.5)
+    '.1'
+    '''
+
+    if num >= 1 or num <= 0: return 'Error 1'
+    result = '.'
+    while num:
+        if len(result) >= 32: return 'Error 2', result
+        r = num*2
+        if r >= 1:
+            result += '1'
+            num = r - 1
+        else:
+            result += '0'
+            num = r
+    return result
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+

book/ebook_src/bitwise_operations/insert_small_bin_into_big_bin.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+
+''' Given two 32-bit numbers, N and M, and two bit positions, i and j, this
+    method insert M into N such that M starts at bit j and ends at bit i:
+    1) clear the bits j thru i in N'
+    2) shift M so that it lines up with bits j thru i
+    3) merge M and N
+'''
+
+def insert_small_bin_into_big_bin(M, N, i, j):
+    '''
+    >>> N = 0b10000000000
+    >>> M = 0b10011
+    >>> j = 6
+    >>> i = 2
+    >>> insert_small_bin_into_big_bin(M, N, i, j)
+    '0b10001001100'
+    '''
+
+    allOnes = ~0
+    left = allOnes << (j+1) # 1110000
+    right = ( (1 << i) - 1) # 0000111
+    mask = left | right     # 1110111
+    N_cleared = N & mask
+    M_shifted = M << i
+
+    return bin( N_cleared | M_shifted)
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+

book/ebook_src/bitwise_operations/next_with_same_num_1s.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+
+''' Give a positive int, print the next smallest and next largest ints with
+    same number of 1 bits.
+    The brute force is:
+    1) find number of 1 bits
+    2) loop above and down until find same, checking for each
+'''
+
+
+
+def print_prev_same_1s(num):
+    n1s = find_num_1s(num)
+    # find prev
+    i = num-1
+    while True:
+        n1s_here = find_num_1s(i)
+        if n1s_here == n1s:
+            return bin(i)
+        i -= 1
+        if i < 0:
+            return None
+
+def print_next_same_1s(num):
+    n1s = find_num_1s(num)
+    # find next
+    i = num+1
+    while True:
+        n1s_here = find_num_1s(i)
+        if n1s_here == n1s:
+            return bin(i)
+        i += 1
+        if i < 0:
+            return None
+
+
+
+def find_num_1s(num):
+    counter = 0
+    while num:
+        if num & 1:
+            counter += 1
+        num >>= 1
+    return counter
+
+
+
+
+
+if __name__ == '__main__':
+    num = 0b1001
+    n = '0b1010'
+    p = '0b110'
+    print_prev_same_1s(num) == p
+    print_next_same_1s(num) == n
+

book/ebook_src/bitwise_operations/num_bits_to_convert_2_nums.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+
+''' This method returns the number of bits that are necessary to change to convert two
+    numbers A and B:
+    1) XOR
+    2) count 1s
+'''
+
+def count_bits_swap2(a, b):
+    count = 0
+    m = a^b
+    while m:
+        count +=1
+        m = m & (m-1)
+    return count
+
+
+
+def count_bits_swap(a, b):
+    m = a^b
+    return count_1s(m)
+
+
+def count_1s(m):
+    count = 0
+    while m:
+        if m& 1 :
+            count +=1
+        m >>= 1
+    return count
+
+
+if __name__ == '__main__':
+    a = int('10010000', 2)
+    b = int('01011010', 2)
+    print count_bits_swap(a, b)  #4
+    print count_bits_swap2(a, b)  #4

book/ebook_src/bitwise_operations/set_bit.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+
+
+''' Set a bit in a binary number:
+    1) Shifts 1 over by i bits
+    2) make an OR with the number, only the value at bit i will change and all the others bit
+    of the mask are zero so will not affect the num
+'''
+
+
+def set_bit(num, i):
+    mask = 1 << i
+    return bin( num | mask )
+
+
+if __name__ == '__main__':
+    num = int('0100100', 2)
+    print set_bit(num, 0)   #'0b100101'
+    print set_bit(num, 1)   #'0b100110'
+    print set_bit(num, 2)   # nothing change '0b100100'
+    print set_bit(num, 3)   #'0b101100'
+    print set_bit(num, 4) #'0b110100'
+    print set_bit(num, 5)     # nothing change '0b100100'

book/ebook_src/bitwise_operations/swap_in_place.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+'''
+    swapping values in place without extra memory
+'''
+
+
+def swap_bit(a, b):
+    '''
+    >>> swap_bit(14, 73)
+    (73, 14)
+    '''
+    a = a^b
+    b = a^b
+    a = a^b
+    return a, b
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

book/ebook_src/bitwise_operations/swap_odd_even.py

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+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+
+''' Swap odd and even bits in a smart way in a binary:
+    1) first for odds, take n and move the odd:
+        (a) Mask all odd bits with 10101010 (0xAA)
+        (b) shift by right by 1
+    2) do the same to ints with 01010101
+    3) merge
+'''
+
+
+
+def swap_odd_even(num):
+    '''
+    >>> num = 0b11011101
+    >>> result = '0b1101110'
+    >>> swap_odd_even(num) == result
+    True
+    '''
+
+    mask_odd = 0xAA # 0b10101010
+    mask_even = 0x55 # 0b1010101
+    odd = num & mask_odd
+    odd >>= 1
+    even = num & mask_even
+    even >>= 1
+    return bin(odd | even)
+
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+

book/ebook_src/bitwise_operations/update_bit.py

@@ -0,0 +1,22 @@
+#!/usr/bin/env python
+
+__author__ = "bt3"
+
+''' This method merges set bit and clean bit:
+    1) first clear the bit at i using a mask such as 1110111
+    2) then shift the intended value v by i bits
+    3) this will create a number with bit i to v and all other to 0
+    4) finally update the ith bit with or
+'''
+
+
+
+def  update_bit(num, i, v):
+    mask = ~ (1 << i)
+    return bin( (num & mask) | (v << i) )
+
+
+if __name__ == '__main__':
+    num = int('10010000', 2)
+    print update_bit(num, 2, 1)   # '0b10010100'
+