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Adding multibit-manipulation algorithm implemented with bitwise operations #11418
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c7d9135
Create multibit_manipulation.py
billbreit bb46e1a
Fix errrors in multibit_manipulation
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,254 @@ | ||
| """Bit integer manipulation, both single bit and multi-bit list-like | ||
| slicing functions ( get, set, insert, remove ) implemented with | ||
| builtin bitwise operations. | ||
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| See: | ||
| https://high-python-ext-3-algorithms.readthedocs.io/ko/latest/chapter5.html#insert-bit | ||
| https://en.wikipedia.org/wiki/Bit_manipulation#Bit_manipulation_operations | ||
| https://github.com/billbreit/BitWiseApps | ||
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| All parameters must be must be int >= 0, referred to as a 'bit integer'. | ||
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| bint:int | ||
| The bit integer to be accessed or returned as modified. | ||
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| index:int | ||
| The offset into the bit position from right, | ||
| 0b010111 -> list [1,1,1,0,1,0]. big-endian -> little-endian | ||
| For inserts, index is the position to the right of index, | ||
| index 0 -> right of rightmost bit. | ||
| For gets, sets and removes, it is the position of the bit itself. | ||
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| value:int | ||
| Either [0,1] for single bit, or int value for multibit, | ||
| bit_length(value) <= bitlen. | ||
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| bitlen:int | ||
| The effective mask length, spec. leading zeros | ||
| ( bitlen 4 value 1 -> 0001 ) | ||
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| The bitwise expressions may look convoluted, but basically, there are | ||
| just three parts: left-hand side, value, right-hand side. | ||
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| For example, say you want to insert two ones in the middle of 0b101101, | ||
| that is -> 0b10111101. Index is 3 ( 0 ,1, 2, 3 from the right ) and the | ||
| value is 3 (0b11) with a bit length of 2. | ||
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||
| - Shift >> index right to produce 0b101 | ||
| - Shift left << bit length to produce 0b10100. | ||
| - OR in the ones producing 0b10111. | ||
| - Left shift << index producing 0b10111000. | ||
| - Using a bit mask (1 << index)-1 -> 0b111, AND with the original bint, | ||
| ( 0b101101 & 0b111 ) -> 0b101. | ||
| - OR that into the working 0b10111000, that is, ( 0b10111000 | 0b101 ) | ||
| -> 0b10111101. | ||
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||
| To remove the center two bits of 0b101101 -> 0b1001, the process is mostly | ||
| the same. Index is 2 for the remove operation on the right-center bit | ||
| rather than 3 for inserting, because we are referring to the bit itself | ||
| rather the position to the right of the bit index. | ||
|
|
||
| - The initial right shift is index (2 ) + bit_length(2), taking out the two | ||
| middle bits and producing 0b10. | ||
| - The left shift of index produces 0b1000. | ||
| - The original bint is ANDed with bitmask 0b11 producing 0b01 which is | ||
| ORed with 0b1000 yielding the target 0b1001. | ||
|
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||
| Bit manipulation operations can be tricky to debug. In the insert example | ||
| above, the result of inserting 0b11 in the center ( index=3 ) or to the | ||
| right ( index=2 ) produces the same correct result despite the unintended | ||
| misspecification. Why is it working sometimes and not others ? Frequently, | ||
| it's the result of inserting at the wrong index, for the hundredth time ! | ||
|
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| Various bit insert/remove solutions exist using bin() string functions | ||
| and slicing, but this bitwise implementation is significantly faster | ||
| (about 3x) on Python for big ints (2^100). | ||
|
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||
| See https://github.com/billbreit/BitWiseApps/blob/main/dev/time_ops.py | ||
|
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| """ | ||
|
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| bit_length = int.bit_length | ||
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| def bit_get(bint: int, index: int) -> int: | ||
| """Get value of bit at index in bint. | ||
|
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||
| >>> bit_get(15, 0) | ||
| 1 | ||
| >>> bit_get(15, 4) | ||
| 0 | ||
| >>> bit_get(0, 4) | ||
| 0 | ||
| >>> bit_get(-1, 2) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: All input values must be positive integers. | ||
| >>> bit_get(0, -1) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: All input values must be positive integers. | ||
| """ | ||
|
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| return multibit_get(bint, index, 1) | ||
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| def bit_set(bint: int, index: int, value: int = 1) -> int: | ||
| """Set bit at index to value 1 or 0, like set() or unset(). | ||
|
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||
| >>> bit_set(15, 0, 0) | ||
| 14 | ||
| >>> bit_set(15, 4, 1) | ||
| 31 | ||
| >>> bit_set(31, 6, 0) | ||
| 31 | ||
| >>> bit_set(31, 6, 3) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Input value must be 1 or 0. | ||
| """ | ||
|
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||
| if value not in [0, 1]: | ||
| raise ValueError("Input value must be 1 or 0.") | ||
|
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| return multibit_set(bint, index, 1, value) | ||
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||
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| def bit_insert(bint: int, index: int, value: int = 1) -> int: | ||
| """Insert bit value before index. | ||
|
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||
| >>> bit_insert(15, 0, 0) | ||
| 30 | ||
| >>> bit_insert(15, 0, 1) | ||
| 31 | ||
| >>> bit_insert(15, 4, 1) | ||
| 31 | ||
| >>> bit_insert(31, 6, 0) | ||
| 31 | ||
| """ | ||
|
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||
| if value not in [0, 1]: | ||
| raise ValueError("Input value must be 1 or 0.") | ||
|
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||
| return multibit_insert(bint, index, 1, value) | ||
|
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||
|
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||
| def bit_remove(bint: int, index: int) -> int: | ||
| """Remove the bit at index from bint. | ||
|
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||
| >>> bit_remove(15, 0) | ||
| 7 | ||
| >>> bit_remove(15, 1) | ||
| 7 | ||
| >>> bit_remove(31, 4) | ||
| 15 | ||
| >>> bit_remove(31, 6) | ||
| 31 | ||
| """ | ||
|
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| return multibit_remove(bint, index, 1) | ||
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| def multibit_get(bint: int, index: int, bit_len: int) -> int: | ||
| """Get bit_len number of bits starting from index. | ||
| 819 = 1100110011. | ||
|
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||
| >>> multibit_get(0, 1, 1) | ||
| 0 | ||
| >>> multibit_get(15, 0, 3) | ||
| 7 | ||
| >>> multibit_get(819, 2, 4) | ||
| 12 | ||
| >>> multibit_get(819, 4, 6) | ||
| 51 | ||
| """ | ||
|
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||
| if bint < 0 or index < 0 or bit_len < 0: | ||
| raise ValueError("All input values must be positive integers.") | ||
|
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| return (bint >> index) & ((1 << bit_len) - 1) | ||
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||
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| def multibit_set(bint: int, index: int, bit_len: int, value: int) -> int: | ||
| """Overlay bint at index with value for bit_len bits. | ||
|
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||
| >>> multibit_set(0, 1, 1, 0) | ||
| 0 | ||
| >>> multibit_set(15, 0, 2, 0) | ||
| 12 | ||
| >>> multibit_set(22, 0, 1, 1) | ||
| 23 | ||
| >>> multibit_set(22, 2, 1, 0) | ||
| 18 | ||
| >>> multibit_set(22, 2, 1, 3) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Bit length of value can not be greater than specified bit length. | ||
| """ | ||
|
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||
| if bint < 0 or index < 0 or bit_len < 0 or value < 0: | ||
| raise ValueError("All input values must be positive integers.") | ||
| if bit_length(value) > bit_len: | ||
| raise ValueError( | ||
| "Bit length of value can not be greater than specified bit length." | ||
| ) | ||
|
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||
| return ((((bint >> (index + bit_len)) << bit_len) | value) << index) | ( | ||
| bint & (1 << index) - 1 | ||
| ) | ||
|
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||
|
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||
| def multibit_insert(bint: int, index: int, bit_len: int, value: int) -> int: | ||
| """Insert value before index-th slot | ||
|
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||
| >>> multibit_insert(0, 1, 1, 1) | ||
| 2 | ||
| >>> multibit_insert(15, 1, 2, 0) | ||
| 57 | ||
| >>> multibit_insert(22, 0, 1, 1) | ||
| 45 | ||
| >>> multibit_insert(22, 2, 1, 0) | ||
| 42 | ||
| >>> multibit_insert(22, 2, 0, 0) | ||
| 22 | ||
| >>> multibit_insert(22, 2, 1, 3) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Bit length of value can not be greater than specified bit length. | ||
| """ | ||
|
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||
| if bint < 0 or index < 0 or bit_len < 0 or value < 0: | ||
| raise ValueError("All input values must be positive integers.") | ||
| if bit_length(value) > bit_len: | ||
| raise ValueError( | ||
| "Bit length of value can not be greater than specified bit length." | ||
| ) | ||
|
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||
| return ((((bint >> index) << bit_len) | value) << index) | bint & ((1 << index) - 1) | ||
|
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| def multibit_remove(bint: int, index: int, bit_len: int) -> int: | ||
| """Remove bits in bint from index to index+bit_len. | ||
|
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||
| >>> multibit_remove(3, 1, 1) | ||
| 1 | ||
| >>> multibit_remove(15, 1, 2) | ||
| 3 | ||
| >>> multibit_remove(22, 0, 1) | ||
| 11 | ||
| >>> multibit_remove(22, 2, 2) | ||
| 6 | ||
| >>> multibit_remove(22, 2, 6) | ||
| 2 | ||
| """ | ||
|
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| if bint < 0 or index < 0 or bit_len < 0: | ||
| raise ValueError("All input values must be positive integers.") | ||
|
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| return ((bint >> index + bit_len) << index) | bint & ((1 << index) - 1) | ||
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|
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| if __name__ == "__main__": | ||
| import doctest | ||
|
|
||
| doctest.testmod() | ||
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An error occurred while parsing the file:
bit_manipulation/multibit_manipulation.py