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I am reading in some binary data that is in offset binary format. The signed integers in numpy are in twos compliment so the values are incorrect. To fix the data I need to flip the most significant bit. However, I am getting some unexpected results from the bitwise xor and not entirely sure what is going on.
Example:
data = np.array([1, 7, -1, -8], dtype='i1')
mask = 0b10000000
def print_bin(data, out):
for d, o in zip(data, out):
bin_data =np.binary_repr(d, d.dtype.itemsize*8)
bin_out = np.binary_repr(o, o.dtype.itemsize*8)
print(f'{bin_data} to {bin_out}')
print_bin(data, data ^ mask)
Output:
00000001 to 0000000010000001
00000111 to 0000000010000111
11111111 to 1111111101111111
11111000 to 1111111101111000
It seems numpy is maybe doing some kind of casting before the xor since the output is 16-bit integer. If I use the functional form np.bitwise_xor instead of ^ I get the same results. Interestingly if I do the xor with -mask the values come out correct. Or if I specify the dtype in the functional form.
print_bin(data, np.bitwise_xor(data, mask, dtype='i1'))
print_bin(data, data ^ -mask)
Output:
00000001 to 10000001
00000111 to 10000111
11111111 to 01111111
11111000 to 01111000
Can anyone explain exactly what is happening in the first case?
Your mask = 0b10000000 is an unsigned integer representation:
>>> mask
... 128
This would need 16 bits to represent as a signed integer, hence numpy casts all the ints to 16 bits to accommodate this operation. You are looking for the signed integer that has the binary representation '10000000'. This corresponds to the integer -128.
So mask = -128 should solve your problem! This is also why negating the mask works (-mask = -128 = '10000000' as a signed int.
Casting the mask to a int8 numpy integer will also do the trick:
>>> np.array(0b10000000, dtype='i1')
... array(-128, dtype=int8)
Say I have a number, 18573628, where each digit represents some kind of flag, and I want to check if the value of the fourth flag is set to 7 or not (which it is).
I do not want to use indexing. I want to in some way and with a flag mask, such as this:
00070000
I would normally use np.logical_and() or something like that, but that will consider any positive value to be True. How can I and while considering the value of a digit? For example, preforming the operation with
flags = 18573628
and
mask = 00070000
would yield 00010000
though trying a different mask, such as
mask = 00040000
would yield 00000000
What you can do is
if (x // 10**n % 10) == y:
...
to check if the n-th digit of x (counting from right) is equal to y
You have to use divide and modulo for a decimal mask:
flags = 18573628
mask = 10000
if (flags / mask) % 10 == 7:
do_something
You can convert the input number into an array of digit numbers and then simply indexing into that array with that specific index or indices would give us those digit(s). For doing that conversion, we can use np.fromstring, like so -
In [87]: nums = np.fromstring(str(18573628),dtype=np.uint8)-48
In [88]: nums
Out[88]: array([1, 8, 5, 7, 3, 6, 2, 8], dtype=uint8)
In [89]: nums[3] == 7
Out[89]: True
Say I have a number, 18573628, where each digit represents some kind of flag, and I want to check if the value of the fourth flag is set to 7
Firstly, bitwise operations like & are bit-wise, which is to say they operate on base-2 digits. They don't operate naturally on digits of any other base, although bases which are themselves powers of 2 work out ok.
To stick with bit-wise operations
You need to know how many values each flag can take, to figure out how many bits each flag needs to encode.
If you want to allow each flag the values zero to nine, you need four bits. However, in this scheme, your number won't behave like a normal integer (storing a base-10 digit in each 4-bit group is called Binary Coded Decimal).
The reason it won't behave like a normal integer is that flag values 1,2,3 will be stored as 1 * 16**2 + 2*16 + 3 instead of the 1 * 10**2 + 2*10 + 3 you'd normally expect. So you'd need to write some code to support this use. However, extracting flag n (counting from zero at the right) just becomes
def bcdFlagValue(bcd, flagnum):
if flagnum == 0:
return bcd & 0x0F;
return 0x0F & (bcd >> ((flagnum-1) * 4))
If you actually need a different range of values for each flag, you need to choose the correct number of bits, and adjust the shift and mask values appropriately.
In either case, you'll need a helper function if you want to print your flags as the base-10 number you showed.
To use normal base 10 numbers
You need to use division and modulo (as 6502 showed), because base-10 numbers don't fit evenly into base-2 bits, so simple bit operations don't work
Note
The BCD approach saves space at the cost of complexity, effort and some speed - from subsequent comments, it's probably simpler to just use the string of digit characters directly unless you really need to save 4 bits per digit.
if flags and mask are hexadecimal values, you can do:
flags = int("18573628", 16)
mask = int("00070000", 16)
result = flags & mask
print(hex(result))
=> '0x70000'
Without dealing with the particulars of your case (the SDSS data, which should be documented in the product specification), let's look at some options.
First, you need to to know if it is to be read in big-endian or little-endian order (is the first bit to the right or to the left). Then you need to know the size of each flag. For a series of yes-no parameters, it could simply be 1 bit (0 or 1). For up to four options, it could be two bits (00, 01, 10, 11), etc. It is also possible that some combinations are reserved for future expansion, don't currently have meaning, and should not be expected to occur in the data. I've also seen instances where the flag size varies, so first n bits mean refer to parameter x, next n bits refer to parameter y, etc.
There is a good explanation of the concept as part of Landsat-8 satellite imagery:
http://landsat.usgs.gov/qualityband.php
To read the values, you convert the base 10 integer to binary, and traverse it in the specified chunks, converting back to int to obtain the parameter values according to your product specification.
In order to test building an Xor operation with more basic building blocks (using Nand, Or, and And in my case) I need to be able to do a Not operation. The built-in not only seems to do this with single bits. If I do:
x = 0b1100
x = not x
I should get 0b0011 but instead I just get 0b0. What am I doing wrong? Or is Python just missing this basic functionality?
I know that Python has a built-in Xor function but I've been using Python to test things for an HDL project/course where I need to build an Xor gate. I wanted to test this in Python but I can't without an equivalent to a Not gate.
The problem with using ~ in Python, is that it works with signed integers. This is also the only way that really makes sense unless you limit yourself to a particular number of bits. It will work ok with bitwise math, but it can make it hard to interpret the intermediate results.
For 4 bit logic, you should just subtract from 0b1111
0b1111 - 0b1100 # == 0b0011
For 8 bit logic, subtract from 0b11111111 etc.
The general form is
def bit_not(n, numbits=8):
return (1 << numbits) - 1 - n
Another way to achieve this, is to assign a mask like this (should be all 1's):
mask = 0b1111
Then xor it with your number like this:
number = 0b1100
mask = 0b1111
print(bin(number ^ mask))
You can refer the xor truth table to know why it works.
Python bitwise ~ operator invert all bits of integer but we can't see native result because all integers in Python has signed representation.
Indirectly we can examine that:
>>> a = 65
>>> a ^ ~a
-1
Or the same:
>>> a + ~a
-1
Ther result -1 means all bits are set. But the minus sign ahead don't allow us to directly examine this fact:
>>> bin(-1)
'-0b1'
The solution is simple: we must use unsigned integers.
First way is to import numpy or ctypes modules wich both support unsigned integers. But numpy more simplest using than ctypes (at least for me):
import numpy as np
a = np.uint8(0b1100)
y = ~x
Check result:
>>> bin(x)
'0b1100'
>>> bin(y)
'0b11110011'
And finally check:
>>> x + y
255
Unsigned integer '255' for 8-bits integers (bytes) mean the same as '-1' becouse has all bits set to 1. Make sure:
>>> np.uint8(-1)
255
And another simplest solution, not quite right, but if you want to include additional modules, you can invert all bits with XOR operation, where second argument has all bits are set to 1:
a = 0b1100
b = a ^ 0xFF
This operation will also drop most significant bit of signed integer and we can see result like this:
>>> print('{:>08b}'.format(a))
00001100
>>> print('{:>08b}'.format(b))
11110011
Finally solution contains one more operation and therefore is not optimal:
>>> b = ~a & 0xFF
>>> print('{:>08b}'.format(b))
11110011
Try this, it's called the bitwise complement operator:
~0b1100
The answers here collectively have great nuggets in each one, but all do not scale well with depending on edge cases.
Rather than fix upon an 8-bit mask or requiring the programmer to change how many bits are in the mask, simply create a mask based on input via bit_length():
def bit_not(num):
return num ^ ((1 << num.bit_length()) - 1)
string of binary can be used to preserve the left 0s, since we know that:
bin(0b000101) # '0b101'
bin(0b101) # '0b101'
This function will return string format of the NOT of input number
def not_bitwise(n):
'''
n: input string of binary number (positive or negative)
return: binary number (string format)
'''
head, tail = n.split('b')
not_bin = head+'b'+tail.replace('0','a').replace('1','0').replace('a','1')
return not_bin
Example:
In[266]: not_bitwise('0b0001101')
Out[266]: '0b1110010'
In[267]: int(not_bitwise('0b0001101'), 2)
Out[267]: 114
In[268]: not_bitwise('-0b1010101')
Out[268]: '-0b0101010'
In[269]: int(not_bitwise('-0b1010101'), 2)
Out[269]: -42
The general form given by John La Rooy, can be simplified in this way (python == 2.7 and >=3.1):
def bit_not(n):
return (1 << n.bit_length()) - 1 - n
What's the usage of the tilde operator in Python?
One thing I can think about is do something in both sides of a string or list, such as check if a string is palindromic or not:
def is_palindromic(s):
return all(s[i] == s[~i] for i in range(len(s) / 2))
Any other good usage?
It is a unary operator (taking a single argument) that is borrowed from C, where all data types are just different ways of interpreting bytes. It is the "invert" or "complement" operation, in which all the bits of the input data are reversed.
In Python, for integers, the bits of the twos-complement representation of the integer are reversed (as in b <- b XOR 1 for each individual bit), and the result interpreted again as a twos-complement integer. So for integers, ~x is equivalent to (-x) - 1.
The reified form of the ~ operator is provided as operator.invert. To support this operator in your own class, give it an __invert__(self) method.
>>> import operator
>>> class Foo:
... def __invert__(self):
... print 'invert'
...
>>> x = Foo()
>>> operator.invert(x)
invert
>>> ~x
invert
Any class in which it is meaningful to have a "complement" or "inverse" of an instance that is also an instance of the same class is a possible candidate for the invert operator. However, operator overloading can lead to confusion if misused, so be sure that it really makes sense to do so before supplying an __invert__ method to your class. (Note that byte-strings [ex: '\xff'] do not support this operator, even though it is meaningful to invert all the bits of a byte-string.)
~ is the bitwise complement operator in python which essentially calculates -x - 1
So a table would look like
i ~i
-----
0 -1
1 -2
2 -3
3 -4
4 -5
5 -6
So for i = 0 it would compare s[0] with s[len(s) - 1], for i = 1, s[1] with s[len(s) - 2].
As for your other question, this can be useful for a range of bitwise hacks.
One should note that in the case of array indexing, array[~i] amounts to reversed_array[i]. It can be seen as indexing starting from the end of the array:
[0, 1, 2, 3, 4, 5, 6, 7, 8]
^ ^
i ~i
Besides being a bitwise complement operator, ~ can also help revert a boolean value, though it is not the conventional bool type here, rather you should use numpy.bool_.
This is explained in,
import numpy as np
assert ~np.True_ == np.False_
Reversing logical value can be useful sometimes, e.g., below ~ operator is used to cleanse your dataset and return you a column without NaN.
from numpy import NaN
import pandas as pd
matrix = pd.DataFrame([1,2,3,4,NaN], columns=['Number'], dtype='float64')
# Remove NaN in column 'Number'
matrix['Number'][~matrix['Number'].isnull()]
The only time I've ever used this in practice is with numpy/pandas. For example, with the .isin() dataframe method.
In the docs they show this basic example
>>> df.isin([0, 2])
num_legs num_wings
falcon True True
dog False True
But what if instead you wanted all the rows not in [0, 2]?
>>> ~df.isin([0, 2])
num_legs num_wings
falcon False False
dog True False
I was solving this leetcode problem and I came across this beautiful solution by a user named Zitao Wang.
The problem goes like this for each element in the given array find the product of all the remaining numbers without making use of divison and in O(n) time
The standard solution is:
Pass 1: For all elements compute product of all the elements to the left of it
Pass 2: For all elements compute product of all the elements to the right of it
and then multiplying them for the final answer
His solution uses only one for loop by making use of. He computes the left product and right product on the fly using ~
def productExceptSelf(self, nums):
res = [1]*len(nums)
lprod = 1
rprod = 1
for i in range(len(nums)):
res[i] *= lprod
lprod *= nums[i]
res[~i] *= rprod
rprod *= nums[~i]
return res
Explaining why -x -1 is correct in general (for integers)
Sometimes (example), people are surprised by the mathematical behaviour of the ~ operator. They might reason, for example, that rather than evaluating to -19, the result of ~18 should be 13 (since bin(18) gives '0b10010', inverting the bits would give '0b01101' which represents 13 - right?). Or perhaps they might expect 237 (treating the input as signed 8-bit quantity), or some other positive value corresponding to larger integer sizes (such as the machine word size).
Note, here, that the signed interpretation of the bits 11101101 (which, treated as unsigned, give 237) is... -19. The same will happen for larger numbers of bits. In fact, as long as we use at least 6 bits, and treating the result as signed, we get the same answer: -19.
The mathematical rule - negate, and then subtract one - holds for all inputs, as long as we use enough bits, and treat the result as signed.
And, this being Python, conceptually numbers use an arbitrary number of bits. The implementation will allocate more space automatically, according to what is necessary to represent the number. (For example, if the value would "fit" in one machine word, then only one is used; the data type abstracts the process of sign-extending the number out to infinity.) It also does not have any separate unsigned-integer type; integers simply are signed in Python. (After all, since we aren't in control of the amount of memory used anyway, what's the point in denying access to negative values?)
This breaks intuition for a lot of people coming from a C environment, in which it's arguably best practice to use only unsigned types for bit manipulation and then apply 2s-complement interpretation later (and only if appropriate; if a value is being treated as a group of "flags", then a signed interpretation is unlikely to make sense). Python's implementation of ~, however, is consistent with its other design choices.
How to force unsigned behaviour
If we wanted to get 13, 237 or anything else like that from inverting the bits of 18, we would need some external mechanism to specify how many bits to invert. (Again, 18 conceptually has arbitrarily many leading 0s in its binary representation in an arbitrary number of bits; inverting them would result in something with leading 1s; and interpreting that in 2s complement would give a negative result.)
The simplest approach is to simply mask off those arbitrarily-many bits. To get 13 from inverting 18, we want 5 bits, so we mask with 0b11111, i.e., 31. More generally (and giving the same interface for the original behaviour):
def invert(value, bits=None):
result = ~value
return result if bits is None else (result & ((1 << bits) - 1))
Another way, per Andrew Jenkins' answer at the linked example question, is to XOR directly with the mask. Interestingly enough, we can use XOR to handle the default, arbitrary-precision case. We simply use an arbitrary-sized mask, i.e. an integer that conceptually has an arbitrary number of 1 bits in its binary representation - i.e., -1. Thus:
def invert(value, bits=None):
return value ^ (-1 if bits is None else ((1 << bits) - 1))
However, using XOR like this will give strange results for a negative value - because all those arbitrarily-many set bits "before" (in more-significant positions) the XOR mask weren't cleared:
>>> invert(-19, 5) # notice the result is equal to 18 - 32
-14
it's called Binary One’s Complement (~)
It returns the one’s complement of a number’s binary. It flips the bits. Binary for 2 is 00000010. Its one’s complement is 11111101.
This is binary for -3. So, this results in -3. Similarly, ~1 results in -2.
~-3
Output : 2
Again, one’s complement of -3 is 2.
This is minor usage is tilde...
def split_train_test_by_id(data, test_ratio, id_column):
ids = data[id_column]
in_test_set = ids.apply(lambda id_: test_set_check(id_, test_ratio))
return data.loc[~in_test_set], data.loc[in_test_set]
the code above is from "Hands On Machine Learning"
you use tilde (~ sign) as alternative to - sign index marker
just like you use minus - is for integer index
ex)
array = [1,2,3,4,5,6]
print(array[-1])
is the samething as
print(array[~1])
I use python 2.6
>>> hex(-199703103)
'-0xbe73a3f'
>>> hex(199703103)
'0xbe73a3f'
Positive and negative value are the same?
When I use calc, the value is FFFFFFFFF418C5C1.
Python's integers can grow arbitrarily large. In order to compute the raw two's-complement the way you want it, you would need to specify the desired bit width. Your example shows -199703103 in 64-bit two's complement, but it just as well could have been 32-bit or 128-bit, resulting in a different number of 0xf's at the start.
hex() doesn't do that. I suggest the following as an alternative:
def tohex(val, nbits):
return hex((val + (1 << nbits)) % (1 << nbits))
print tohex(-199703103, 64)
print tohex(199703103, 64)
This prints out:
0xfffffffff418c5c1L
0xbe73a3fL
Because Python integers are arbitrarily large, you have to mask the values to limit conversion to the number of bits you want for your 2s complement representation.
>>> hex(-199703103 & (2**32-1)) # 32-bit
'0xf418c5c1L'
>>> hex(-199703103 & (2**64-1)) # 64-bit
'0xfffffffff418c5c1L'
Python displays the simple case of hex(-199703103) as a negative hex value (-0xbe73a3f) because the 2s complement representation would have an infinite number of Fs in front of it for an arbitrary precision number. The mask value (2**32-1 == 0xFFFFFFFF) limits this:
FFF...FFFFFFFFFFFFFFFFFFFFFFFFF418c5c1
& FFFFFFFF
--------------------------------------
F418c5c1
Adding to Marks answer, if you want a different output format, use
'{:X}'.format(-199703103 & (2**32-1))
For those who want leading zeros for positive numbers, try this:
val = 42
nbits = 16
'{:04X}'.format(val & ((1 << nbits)-1))
Thanks #tm1, for the inspiration!