miller loop

[zlemon819]

Hi, i have a question about the miller loop implementation in the bn128_pairing.py file.

From article(https://eprint.iacr.org/2019/077.pdf), your code excluded blow lines seems to be the classic miller loop,

# assert R == multiply(Q, ate_loop_count)                                                                      
Q1 = (Q[0] ** field_modulus, Q[1] ** field_modulus)
# assert is_on_curve(Q1, b12)
nQ2 = (Q1[0] ** field_modulus, -Q1[1] ** field_modulus)
# assert is_on_curve(nQ2, b12)
f = f * linefunc(R, Q1, P)
R = add(R, Q1)
f = f * linefunc(R, nQ2, P)
# R = add(R, nQ2) This line is in many specifications but it technically does nothing`

then what is your idea of these adding lines? is that a variant of classic miller loop? Coud you point the paper or source? Thank you.