Why it matters

The idea behind depth-based derating can be tested directly: draw a delay for each stage from a normal distribution, add them up, and measure the spread of the totals. This is a model of independent random variation only; it says nothing about systematic effects.

Simulation

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import random, statistics
rng = random.Random(2024)             # fixed seed: deterministic
def rel_sigma(n, samples=4000):
    totals = [sum(rng.gauss(0.10, 0.005) for _ in range(n)) for _ in range(samples)]
    return statistics.pstdev(totals) / statistics.fmean(totals)
r = {n: rel_sigma(n) for n in (1, 4, 16)}
assert 0.045 < r[1] < 0.056                      # expected 0.05 for one stage
assert 3.7 < r[1] / r[16] < 4.4                  # expected 4 = sqrt(16)
assert 1.8 < r[1] / r[4] < 2.2                   # expected 2 = sqrt(4)
print("PASS: relative sigma by stages", {n: round(v, 4) for n, v in r.items()}, "; ratio 1 to 16:", round(r[1] / r[16], 2))

Each stage has a mean of 0.10 ns and a sigma of 0.005 ns, so a single stage has 5% relative spread. Four stages give about half of that and sixteen stages a quarter, matching 1 over the square root of n. The simulation confirms the formula behind the depth-based table. It also marks the limit of the method: if stage variations are correlated (a common supply or temperature effect), the spread does not shrink this way.

What the review looks for

• The depth-based tables reflect independent random variation; systematic effects are carried by corners and other margins.

• Stage counting matches the way the tables were built.

• Any use of depth credit on a path dominated by a few cells (long wires, a macro) is questioned.

Related topics

• Depth-Based Derating

• Next: Short Paths Versus Long