Bitwise Operators and other things (need help)

[err1100]

Hello all -

I've been coding in Python for a couple of months now, and I recently ran across the following piece of code (where x is a set or list):

f = lambda x: [[y for j, y in enumerate(x) if (i >> j) & 1] for i in range(2**len(x))]

I was hoping someone could explain to me the following components:

1. 'y for j': after doing some reading, I think I understand the basic principles of * for *, but I still don't think I get exactly what Python is doing.

2. '(i >> j) & 1': I read something somewhere about shifting with '>>', but quite frankly, I'm still completely clueless. Also, I'm very new to bitwise operators and could use some explanation.

Thanks,
err1100

[jcao219]

It may be easier to understand when you take comprehensions out.

def myfunc(x):
	ret = []
	for i in range(2**len(x)):
		res = []
		for j, y in enumerate(x):
			if (i >> j) & 1:
				res.append(y)
		ret.append(res)
			
	return ret

[err1100]

Thanks jcao; that definitely clears things up a bit.
I guess my real problem, then, is understanding line 6 of your code. As I said, I'm really not clear on the functionality of '>>' or '&'.

Thanks again,
err1100

[jcao219]

Oh okay, so in Python the '>>' is an arithmetic RIGHT-SHIFT and the '&' is logical AND.

So AND is like this:
0 AND 0 = 0
0 AND 1 = 0
1 AND 1 = 1

So let's say you have two numbers: 42, 27

>>> bin(42)
    '0b101010'
>>> bin(27)
    '0b011011'

To AND them, you align them:
101010
011011
AND
001010

So that gives you 1010, you do int('1010',2) and you get your result:
10.

You can check, 42 & 27 .

[jcao219]

Now, right shift:

Let's say you have binary
101100
Then right shift by 1 (44 >> 1)
would be move all the digits right, so it becomes 0101100 (empty space is filled with 0)

right shift by 2 would make it 001011.

[err1100]

Ah. Thank you. The code makes a lot more sense now.
Sorry for not clarifying this before, but I have one more question:
This code was brought up in the context of returning all possible sub multi-sets of a list x, so what does the bitwise comparison have to do with that?

Thanks so much for all of your prompt responses,
err1100

[jcao219]

I'm not sure, perhaps it's some algorithm?