Analysis of Fast Radix-10 Digit Recurrence Algorithms for Fixed-Point and Floating-Point Dividers on FPGAs

Algorithm 2

Algorithm for the calculation of the type2 ROM entries.

(1) compute 𝐿_𝑘(𝑑_𝑖) and 𝑈_𝑘(𝑑_𝑖) for each 𝑑_𝑖 ∈

 {0.40,0.41,…,0.99} and 𝑘∈{−8,…,+8} according

  to (12a) and (12b)

(2) for all 10⋅𝑤_𝑛∈{−8.8,−8.7,…,+8.8} with |𝑤|≤

 𝜌⋅𝑑_max=0.88 compute the quotient digits 𝑧 as

 follows:

  if 10⋅𝑤_𝑛≥𝑈₇−𝜖=𝑈₇−0.2 then 𝑧=8

  else if 10⋅𝑤_𝑛≥𝑈₆−0.2 then 𝑧=7

    ⋮

  else if 10⋅𝑤_𝑛≥𝑈₀−0.2 then 𝑧=1

  else if 10⋅𝑤_𝑛≥𝐿₀ then 𝑧=0

    ⋮

  else if 10⋅𝑤_𝑛≥𝐿₋₈ then 𝑧=−8