I want to classify the runtime of this function in big O notation. This function is multiplying two whole numbers and checks the in binary digits of the multiplicand. And adding the multiplier to the product a specific number of times if the bit is '1', dependent on the weigth of that bit.
I'm trying to figure out the classifcation of the for-loop. Since the while-loop will go through all bits of the multiplicand the while-loop will probably have a runtime of $O(n)$ whereas $n = \#digits$. The inner loop will execute $2^0, 2^1, 2^2, 2^3, 2^4...=1, 2, 4, 8, 16,...$ if the bit will be a '1'. So in total the for-loop will execute $\sum_{i=0}^{n-1}2^i$ steps, in the worst-case (if all bits are ones).
My question is, how do I write this for-loop in big O notation?
def mul(multiplier,multiplicand):
product = 0
pot = 1 # power of two
while (multiplicand > 0):
q = divtwo(multiplicand)
q1 = (q + q)
if (q1 != multiplicand): # is odd => bit 1
for i in range(0,pot):
product = (product + multiplier)
multiplicand = q
pot = (pot + pot)
return product
P.S.: I'm not allowed to use "/" or "*". Only "+" and "-".
