For the largest divisions, a block-wise Barrett division algorithm is used. Here, the divisor is inverted to a precision determined by the relative size of the dividend and divisor. Blocks of quotient limbs are then generated by multiplying blocks from the dividend by the inverse.
Our block-wise algorithm computes a smaller inverse than in the plain Barrett algorithm. For a 2n/n division, the inverse will be just ceil(n/2) limbs.