Programming Loop Invariants

This second python programming assignment is about loop invariants. You will write a function eExp(left,right) that computes exponentials left ** right in a similar fashion as the egyptian_multiplication function computes products, as discussed in the loop invariants lecture.

The starter code contains some skeleton code. Study egyptian multiplication in the lecture slides. The program logic in egyptian_multiplication, and thus the loop invariant is based on the fact that

and that e stepwise gathers the exponential.

Your job is to complete the code INCLUDING the correct assert statements to check the loop invariant, loop test and their combination, as indicated in the skeleton code. Leave the print statements in place. Be sure to use the invariant function, as we will call this directly with different values to check that it is correct. A correct implementation of eExp:

Given code:

import sys

def invariant(n, k, e, left, right): return True

def eExp(left, right): # precondition: left>0 AND right>0 if left

if __name__ == "__main__": print("program:", sys.argv[0], sys.argv[1], sys.argv[2]) n = int(sys.argv[1]) k = int(sys.argv[2]) e = eExp(n,k) print(n,"**",k,"=",e)

Picture:

a + b = if odd (a): b = (a//2)* (b*2) else: (a//2)* (b*2) python3 eExp.py 2 11 produces program: eExp.py 2 11 n: 2 k: 11 e: 1 n: 4 k: 5 e: 2 n: 16 k: 2 e: 8 n: 256 k: 1 e: 8 k: 0 e: 2048 2 ** 11 = 2048 1 2 import sys 3 4 def invariant(n, k, e, left, right): 5 return True 6 7 def eExp(left, right): 8 # precondition: left> AND right> 9 if left AND right> 9 if left