Generate carry in Carry-lookahead adder

Recently, I am implementing an 8-bit Carry-lookahead adder. But unfortunately, almost all materials in the Internet only provide the formula to get C1 toC4, so I write a simple python script to generate all carries:

#!/usr/bin/python3

import sys
num = 8

if len(sys.argv) != 1:
    num = int(sys.argv[1])

dict = {'C0': 'C0'}
for i in range(1, num + 1):
    dict['C' + str(i)] = 'G' + str(i - 1) + \
                        '+' + \
                        '+'.join([x + "*P" + str(i - 1) for x in dict['C' + str(i - 1)].split('+')])

for i in range(0, num + 1):
    key = 'C' + str(i)
    print(key, "=", dict[key])

By default, it will generate C1 to C8:

$ ./CarryFormulaInLookAheadAdder.py
C0 = C0
C1 = G0+C0*P0
C2 = G1+G0*P1+C0*P0*P1
C3 = G2+G1*P2+G0*P1*P2+C0*P0*P1*P2
C4 = G3+G2*P3+G1*P2*P3+G0*P1*P2*P3+C0*P0*P1*P2*P3
C5 = G4+G3*P4+G2*P3*P4+G1*P2*P3*P4+G0*P1*P2*P3*P4+C0*P0*P1*P2*P3*P4
C6 = G5+G4*P5+G3*P4*P5+G2*P3*P4*P5+G1*P2*P3*P4*P5+G0*P1*P2*P3*P4*P5+C0*P0*P1*P2*P3*P4*P5
C7 = G6+G5*P6+G4*P5*P6+G3*P4*P5*P6+G2*P3*P4*P5*P6+G1*P2*P3*P4*P5*P6+G0*P1*P2*P3*P4*P5*P6+C0*P0*P1*P2*P3*P4*P5*P6
C8 = G7+G6*P7+G5*P6*P7+G4*P5*P6*P7+G3*P4*P5*P6*P7+G2*P3*P4*P5*P6*P7+G1*P2*P3*P4*P5*P6*P7+G0*P1*P2*P3*P4*P5*P6*P7+C0*P0*P1*P2*P3*P4*P5*P6*P7

But you can pass a parameter to tell how many carries you want:

$ ./CarryFormulaInLookAheadAdder.py 6
C0 = C0
C1 = G0+C0*P0
C2 = G1+G0*P1+C0*P0*P1
C3 = G2+G1*P2+G0*P1*P2+C0*P0*P1*P2
C4 = G3+G2*P3+G1*P2*P3+G0*P1*P2*P3+C0*P0*P1*P2*P3
C5 = G4+G3*P4+G2*P3*P4+G1*P2*P3*P4+G0*P1*P2*P3*P4+C0*P0*P1*P2*P3*P4
C6 = G5+G4*P5+G3*P4*P5+G2*P3*P4*P5+G1*P2*P3*P4*P5+G0*P1*P2*P3*P4*P5+C0*P0*P1*P2*P3*P4*P5

P.S., the full code is here.