python - How do I decompose a number into powers of 2?

Question

I'm trying to create a function that receives a number as an argument and performs actions on that number to find out its closest powers of 2 that will then add up to that number. For example, if the user enters 4, the function will append 4 because it is already a power of 2. If the user enters a 14 the function should see that 14 is not a power of 2 and the closest powers of 2 that make up 14 are 2,4, and 8.

Key notes: I am only going up to 2^9.

What i have so far:

def powers_finder(n):
    powers=[]
    i=0
    total=0
    while i<10:
         value=2**i
         total=total+value
         i=i+1
         #This if statement is for if the user enters a power of 2 as n
         #Then the number will be appended right away into my powers list.
         if value==n:
            powers.append(value)

The problem here being if the user enters in lets say 5 as (n) 5 is made up of the power 2^2=4 and 2^0=1 4+1=5. How can i extend my function to include this process?

thank you!

Answer 1

Most efficient way of doing this:

def myfunc(x):
    powers = []
    i = 1
    while i <= x:
        if i & x:
            powers.append(i)
        i <<= 1
    return powers