Why it matters

Slack is usually quoted at endpoints, but it is defined at every node. That generalisation is what lets a tool say which cells and nets lie on a failing path and where along it the margin is lost. It also explains why every node on one critical path shows the same slack.

Definitions

arrival(n)  = max over predecessors p of ( arrival(p) + delay(p -> n) )     (setup, latest)
required(n) = min over successors  s of ( required(s) - delay(n -> s) )      (setup, earliest limit)
slack(n)    = required(n) - arrival(n)
at an endpoint: required = capture edge arrival - setup - uncertainty

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# Graph: ck -> a (0.4), a -> b (0.3), a -> c (0.5), b -> d (0.2), c -> d (0.1), d -> end (0.0)
edges = {("ck","a"):0.4, ("a","b"):0.3, ("a","c"):0.5, ("b","d"):0.2, ("c","d"):0.1, ("d","end"):0.0}
order = ["ck","a","b","c","d","end"]
arr = {"ck": 0.0}
for n in order[1:]:
    arr[n] = max(arr[p] + w for (p, m), w in edges.items() if m == n)
T_req = 1.5                              # required time at the endpoint
req = {"end": T_req}
for n in reversed(order[:-1]):
    req[n] = min(req[m] - w for (p, m), w in edges.items() if p == n)
slack = {n: round(req[n] - arr[n], 6) for n in order}
assert abs(arr["end"] - 1.0) < 1e-9          # 0.4 + 0.5 + 0.1
assert abs(slack["end"] - 0.5) < 1e-9
# nodes on the critical path (ck, a, c, d, end) share the endpoint's slack; b has more
assert all(abs(slack[n] - 0.5) < 1e-9 for n in ("ck", "a", "c", "d", "end"))
assert slack["b"] > slack["c"]
print("PASS: slack per node", slack)

The critical route is ck-a-c-d-end with total 1.0 ns, so the endpoint slack is 1.5 - 1.0 = 0.5 ns. Every node on that route has slack 0.5 because required and arrival differ by the same amount along it. Node b is off the critical route: its slack is 0.6 ns, 0.1 ns larger, because the route through b (0.9 ns in total) is 0.1 ns faster than the route through c (1.0 ns).

What the review looks for

• A path report's slack equals the endpoint slack; per-node slack in a graph view identifies where a fix would help.

• Fixing a node on the critical path improves the endpoint slack until another route becomes critical (a path wall).

• Hold uses the same structure with earliest arrivals and the hold requirement.

Related topics

• Next: Forward and Backward Propagation

• The Timing Graph