Why it matters

When sizing and buffering are exhausted, the remaining lever is logic structure: re-associating an expression, moving a late input closer to the output, duplicating logic to cut fanout. These changes can save hundreds of picoseconds but alter the netlist, so function equivalence must be proven afterwards.

Worked example (illustrative)

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import heapq
gate = 40.0                                   # ps per 2-input gate
arrivals = [0.0] * 7 + [100.0]                # eight inputs, the last arriving 100 ps late
def chain(arr):
    t = arr[0]
    for a in arr[1:]:
        t = max(t, a) + gate
    return t
def balanced(arr):                            # fixed balanced tree, inputs paired in order
    level = list(arr)
    while len(level) > 1:
        level = [max(level[i], level[i + 1]) + gate for i in range(0, len(level), 2)]
    return level[0]
def arrival_aware(arr):                       # always combine the two earliest signals
    h = list(arr); heapq.heapify(h)
    while len(h) > 1:
        a, b = heapq.heappop(h), heapq.heappop(h)
        heapq.heappush(h, max(a, b) + gate)
    return h[0]
res = (chain(arrivals), balanced(arrivals), arrival_aware(arrivals))
assert res == (280.0, 220.0, 160.0)
print("PASS: output arrival for chain, balanced and arrival-aware trees:", res)

The same function (an 8-input associative operation) arrives at 280 ps as a chain, 220 ps as a balanced tree and 160 ps when the late input is combined last. The arrival-aware tree is 120 ps faster than the chain and 60 ps faster than the textbook-balanced one, because depth is measured from the latest input. Only associative and commutative functions can be re-associated freely; for anything else the change must preserve the exact function.

What the review looks for

• Equivalence checking before and after the change, run on the final netlist and not on a model.

• New logic is placed and routed in the same flow as everything else; timing, SI and power are rerun.

• Logical ECOs are limited to cones with timing evidence; changing logic for convenience reopens verification.

Related topics

• Buffering and Layers

• Next: ECO Risk Ladder