Buffer Insertion Basics - Computer Engineering & Systems Group ...

Algorithm: GiLa(T u )/GiLa(T u,v )
Input: Subtree T u rooted at node u or edge (u, v)
Output: A set of candidate solutions Γ u
Global: Routing tree T and buffer library B
1. if u is a leaf, Γ u = (C u , q u , λ u , 0)
2. else if node u has one child node v or the input is T u,v
2.1 Γ v = GiLa(T v )
2.2 Γ u = ∪ γ∈Γv (addWire((u, v), γ))
2.3 Γ b = ∅
2.4 for each b in B
2.4.1 Γ = ∪ γ∈Γu (addBuffer(γ, b))
2.4.2 prune Γ
2.4.3 Γ b = Γ b ∪ Γ
2.5 Γ u = Γ u ∪ Γ b
// Γ u ≡ {Γ x , ...,Γ y }, x, y indicate latency
2.6 if u is source
2.6.1 if x > 0, exit: the net is not feasible
2.6.2 if y < 0, // insert −y more flops in Γ u
2.6.2.1 Γ u = ReFlop(T u , −y)
3. else if u has two child edges (u, v) and (u, z)
3.1 Γ u,v = GiLa(T u,v ), Γ u,z = GiLa(T u,z )
3.2 //Γ u,v ≡ {Γ x , ...,Γ y }, Γ u,z ≡ {Γ m , ...,Γ n }
3.3 if y < m // insert m − y more flops in Γ u,v
3.3.1 Γ u,v = ReFlop(T u,v , m − y)
3.4 if n < x // insert x − n more flops in Γ u,z
3.4.1 Γ u,z = ReFlop(T u,z , x − n)
3.5 Γ u = Γ u ∪ merge(Γ u,v , Γ u,z )
4. prune Γ u
5. return Γ u
Figure 13: The GiLa algorithm.
Shi [41] proposed a simple O(mn) algorithms for m-pin nets. The speedup is achieved by the
property explored in [40], convex pruning, a clever bookkeeping method and an innovative linked
list that allow O(1) time update for adding a wire or a candidate.
In the following subsections, new pruning techniques, efficient way to find the best candidates
when adding a buffer, and implicit data representations are presented. They are the basic component
of many recent speedup algorithms.
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