user288609 user288609 - 1 year ago 59
Python Question

regarding understanding a python function using logical operators

I once read the following python function,

def f1(i, num_digits):
return np.array([i >> d & 1 for d in range(num_digits)])

I am not very clear on how does the part of
i >> d & 1
work. Running
will return

Answer Source

This function creates a list containing the last bit of i after it got shifted index times to the right.

Sounds cryptic? It is.

Here is what happens:

The list comprehension creates a list of size num_digits-1, using the values of the range expression (which are 0 to num_digits-1) to calculate the value of the item that is supposed to be at that index of the list. To calculate the value of the list item, the integer i is taken and the bits of it are shifted to the right by d places, where d is the current value of the range we are iterating over to construct our list. The >> (bitshift-right) operator has higher precedence than the & operator, so this calculation is done first. The last step to calculating the list value is performing a logical & of the bitshifted value and the value 1. This step requires some thinking, but what it does is it returns the last bit of our bitshifted value.

This is easier if you actually do the steps on a piece of paper. See, how the only time the last bit of our computation is 1 is if we shift the bit value of 2 to the right by one place (hence the list entry at index 1 is a 1 and the rest are 0's):

Index 0: 2 (dec) = 10 (bin) -> >> 0 -> 10 (bin) -> 10 & 01 = 00 (bin) = 0 (dec)
Index 1: 2 (dec) = 10 (bin) -> >> 1 -> 01 (bin) -> 01 & 01 = 01 (bin) = 1 (dec)
Index 2: 2 (dec) = 10 (bin) -> >> 2 -> 00 (bin) -> 00 & 01 = 00 (bin) = 0 (dec)
# From here on it will be the same as index 2, because we are only shifting 0's

I hope this helps you understanding what is going on.