routing: add capacity to special edges

Having a capacity available is important for liquidity estimation.

* We add a dummy capacity to hop hints. Hop hints specify neither the
  capacity nor a maxHTLC size, which is why we assume the channel to
  have a high capacity relative to the amount we send.

* We add a capacity to local edges. These channels should always have a
  capacity associated with them, even in the neutrino case (a fallback
  to maxHTLC is not necessary). This is just for completeness, as the
  probability calculation for local channels is done separately.

routing/pathfind.go

@@ -37,6 +37,11 @@ const (
 	// to avoid resizing and copies. It should be number on the same order as
 	// the number of active nodes in the network.
 	estimatedNodeCount = 10000
+
+	// fakeHopHintCapacity is the capacity we assume for hop hint channels.
+	// This is a high number, which expresses that a hop hint channel should
+	// be able to route payments.
+	fakeHopHintCapacity = btcutil.Amount(10 * btcutil.SatoshiPerBitcoin)
 )
 
 // pathFinder defines the interface of a path finding algorithm.
@@ -863,8 +868,17 @@ func findPath(g *graphParams, r *RestrictParams, cfg *PathFindingConfig,
 			return nil, 0, err
 		}
 
+		// We add hop hints that were supplied externally.
 		for _, reverseEdge := range additionalEdgesWithSrc[pivot] {
-			u.addPolicy(reverseEdge.sourceNode, reverseEdge.edge, 0)
+			// Hop hints don't contain a capacity. We set one here,
+			// since a capacity is needed for probability
+			// calculations. We set a high capacity to act as if
+			// there is enough liquidity, otherwise the hint would
+			// not have been added by a wallet.
+			u.addPolicy(
+				reverseEdge.sourceNode, reverseEdge.edge,
+				fakeHopHintCapacity,
+			)
 		}
 
 		amtToSend := partialPath.amountToReceive

routing/probability_bimodal.go

@@ -28,9 +28,12 @@ const (
 	// the timescale of about a week.
 	DefaultBimodalDecayTime = 7 * 24 * time.Hour
 
-	// BimodalScaleMsatLimit is the maximum value for BimodalScaleMsat to
+	// BimodalScaleMsatMax is the maximum value for BimodalScaleMsat. We
-	// avoid numerical issues.
+	// limit it here to the fakeHopHintCapacity to avoid issues with hop
-	BimodalScaleMsatMax = lnwire.MilliSatoshi(21e17)
+	// hint probability calculations.
+	BimodalScaleMsatMax = lnwire.MilliSatoshi(
+		1000 * fakeHopHintCapacity / 4,
+	)
 
 	// BimodalEstimatorName is used to identify the bimodal estimator.
 	BimodalEstimatorName = "bimodal"

routing/unified_edges.go

@@ -218,7 +218,10 @@ func (u *edgeUnifier) getEdgeLocal(amt lnwire.MilliSatoshi,
 		maxBandwidth = bandwidth
 
 		// Update best edge.
-		bestEdge = &unifiedEdge{policy: edge.policy}
+		bestEdge = &unifiedEdge{
+			policy:   edge.policy,
+			capacity: edge.capacity,
+		}
 	}
 
 	return bestEdge