“…It is more difficult to skip normalization during division, because the quotient digit q used in each "multiply and subtract" step is a guess. Early routines ( [3,4,5,6,8]) used integer arithmetic to estimate q. Bailey used double precision to estimate q, which made the probability of an incorrect q much smaller. Brent used Newton iteration and multiplication to avoid the long-division algorithm, but this made division much slower than multiplication.…”