OpenSTA activity propagation is incomplete

[hongted]

OpenSTA computes power here

OpenSTA/power/Power.cc

Lines 670 to 694 in c4b94c3

	float
	Power::evalBddActivity(DdNode *bdd,
	const Instance *inst)
	{
	float density = 0.0;
	for (const auto [port, var_node] : bdd_.portVarMap()) {
	const Pin *pin = findLinkPin(inst, port);
	if (pin) {
	PwrActivity var_activity = findActivity(pin);
	unsigned int var_index = Cudd_NodeReadIndex(var_node);
	DdNode *diff = Cudd_bddBooleanDiff(bdd_.cuddMgr(), bdd, var_index);
	Cudd_Ref(diff);
	float diff_duty = evalBddDuty(diff, inst);
	Cudd_RecursiveDeref(bdd_.cuddMgr(), diff);
	float var_density = var_activity.density() * diff_duty;
	density += var_density;
	debugPrint(debug_, "power_activity", 3, "var %s %.3e * %.3f = %.3e",
	port->name(),
	var_activity.density(),
	diff_duty,
	var_density);
	}
	}
	return density;
	}

according to the following method:

Density Output = Sum ( Probability(Output switches given input signal Xi switches) * Probability(Xi switches))

where Probability(Output switches given input signal Xi switches) is Duty(BooleanDiff for Xi)).

This incorrectly propagates probability as it does not take into account that multiple inputs may switch simultaneously.

---

Consider a 2-input NAND gate Z=!(AB), with Density 0.5/cycle and Duty 0.5 at both inputs. OpenSTA computes the output density at 0.5/cycle. Instead it should be 0.375/cycle all other assumptions other than propagation being equal:

All input transitions XX to YY are equally likely at 1/16.
There are 6 possible input transitions that cause the output to switch: 00->11, 01->11, 10->11, 11->00, 11->01, 11->10.
So output density is 6/16 = 0.375.

[akashlevy]

Can you provide a test case that demonstrates this more clearly?