feat: add deterministic regional scheduler

simulation/regional/AnalyticalRegionalUpdates.gd

@@ -0,0 +1,59 @@
+class_name AnalyticalRegionalUpdates
+extends RefCounted
+
+
+static func linear_value(
+	current_value: float,
+	rate_per_tick: float,
+	elapsed_ticks: int,
+	minimum: float = -INF,
+	maximum: float = INF
+) -> float:
+	if elapsed_ticks <= 0 or not is_finite(current_value) or not is_finite(rate_per_tick):
+		return clampf(current_value, minimum, maximum)
+	return clampf(current_value + rate_per_tick * elapsed_ticks, minimum, maximum)
+
+
+static func exponential_value(
+	current_value: float,
+	multiplier_per_tick: float,
+	elapsed_ticks: int,
+	minimum: float = -INF,
+	maximum: float = INF
+) -> float:
+	if (
+		elapsed_ticks <= 0
+		or not is_finite(current_value)
+		or not is_finite(multiplier_per_tick)
+		or multiplier_per_tick < 0.0
+	):
+		return clampf(current_value, minimum, maximum)
+	return clampf(current_value * pow(multiplier_per_tick, elapsed_ticks), minimum, maximum)
+
+
+static func periodic_occurrences(
+	first_due_tick: int, interval_ticks: int, through_tick: int
+) -> int:
+	if first_due_tick < 0 or interval_ticks <= 0 or through_tick < first_due_tick:
+		return 0
+	return (through_tick - first_due_tick) / interval_ticks + 1
+
+
+static func transfer_amount(
+	available: float,
+	demand: float,
+	rate_per_tick: float,
+	elapsed_ticks: int,
+	loss_fraction: float = 0.0
+) -> Dictionary:
+	var sent := minf(
+		maxf(available, 0.0),
+		minf(maxf(demand, 0.0), maxf(rate_per_tick, 0.0) * maxi(elapsed_ticks, 0))
+	)
+	var received := sent * (1.0 - clampf(loss_fraction, 0.0, 1.0))
+	return {
+		"sent": sent,
+		"received": received,
+		"remaining_available": maxf(available - sent, 0.0),
+		"remaining_demand": maxf(demand - received, 0.0),
+	}