12165272839

Committed 04 Dec 2024 05:35PM UTC coverage: 58.978% (+0.2%) from 58.789%

Build # 12165272839

Build Type

Pull #9316

github

Committed by

ziggie1984

Commit Message

docs: add release-notes.

Pull Request Pull Request #9316: routing: fix mc blinded path behaviour.

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91.06

/routing/pathfind.go

package routing

import (
        "bytes"
        "container/heap"
        "errors"
        "fmt"
        "math"
        "sort"
        "time"

        "github.com/btcsuite/btcd/btcutil"
        sphinx "github.com/lightningnetwork/lightning-onion"
        "github.com/lightningnetwork/lnd/feature"
        "github.com/lightningnetwork/lnd/fn"
        graphdb "github.com/lightningnetwork/lnd/graph/db"
        "github.com/lightningnetwork/lnd/graph/db/models"
        "github.com/lightningnetwork/lnd/lnutils"
        "github.com/lightningnetwork/lnd/lnwire"
        "github.com/lightningnetwork/lnd/record"
        "github.com/lightningnetwork/lnd/routing/route"
)

const (
        // infinity is used as a starting distance in our shortest path search.
        infinity = math.MaxInt64

        // RiskFactorBillionths controls the influence of time lock delta
        // of a channel on route selection. It is expressed as billionths
        // of msat per msat sent through the channel per time lock delta
        // block. See edgeWeight function below for more details.
        // The chosen value is based on the previous incorrect weight function
        // 1 + timelock + fee * fee. In this function, the fee penalty
        // diminishes the time lock penalty for all but the smallest amounts.
        // To not change the behaviour of path finding too drastically, a
        // relatively small value is chosen which is still big enough to give
        // some effect with smaller time lock values. The value may need
        // tweaking and/or be made configurable in the future.
        RiskFactorBillionths = 15

        // estimatedNodeCount is used to preallocate the path finding structures
        // 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.
type pathFinder = func(g *graphParams, r *RestrictParams,
        cfg *PathFindingConfig, self, source, target route.Vertex,
        amt lnwire.MilliSatoshi, timePref float64, finalHtlcExpiry int32) (
        []*unifiedEdge, float64, error)

var (
        // DefaultEstimator is the default estimator used for computing
        // probabilities in pathfinding.
        DefaultEstimator = AprioriEstimatorName

        // DefaultAttemptCost is the default fixed virtual cost in path finding
        // of a failed payment attempt. It is used to trade off potentially
        // better routes against their probability of succeeding.
        DefaultAttemptCost = lnwire.NewMSatFromSatoshis(100)

        // DefaultAttemptCostPPM is the default proportional virtual cost in
        // path finding weight units of executing a payment attempt that fails.
        // It is used to trade off potentially better routes against their
        // probability of succeeding. This parameter is expressed in parts per
        // million of the payment amount.
        //
        // It is impossible to pick a perfect default value. The current value
        // of 0.1% is based on the idea that a transaction fee of 1% is within
        // reasonable territory and that a payment shouldn't need more than 10
        // attempts.
        DefaultAttemptCostPPM = int64(1000)

        // DefaultMinRouteProbability is the default minimum probability for routes
        // returned from findPath.
        DefaultMinRouteProbability = float64(0.01)

        // DefaultAprioriHopProbability is the default a priori probability for
        // a hop.
        DefaultAprioriHopProbability = float64(0.6)
)

// edgePolicyWithSource is a helper struct to keep track of the source node
// of a channel edge. ChannelEdgePolicy only contains to destination node
// of the edge.
type edgePolicyWithSource struct {
        sourceNode route.Vertex
        edge       AdditionalEdge
}

// finalHopParams encapsulates various parameters for route construction that
// apply to the final hop in a route. These features include basic payment data
// such as amounts and cltvs, as well as more complex features like destination
// custom records and payment address.
type finalHopParams struct {
        amt      lnwire.MilliSatoshi
        totalAmt lnwire.MilliSatoshi

        // cltvDelta is the final hop's minimum CLTV expiry delta.
        //
        // NOTE that in the case of paying to a blinded path, this value will
        // be set to a duplicate of the blinded path's accumulated CLTV value.
        // We would then only need to use this value in the case where the
        // introduction node of the path is also the destination node.
        cltvDelta uint16

        records     record.CustomSet
        paymentAddr fn.Option[[32]byte]

        // metadata is additional data that is sent along with the payment to
        // the payee.
        metadata []byte
}

// newRoute constructs a route using the provided path and final hop constraints.
// Any destination specific fields from the final hop params  will be attached
// assuming the destination's feature vector signals support, otherwise this
// method will fail.  If the route is too long, or the selected path cannot
// support the fully payment including fees, then a non-nil error is returned.
// If the route is to a blinded path, the blindedPath parameter is used to
// back fill additional fields that are required for a blinded payment. This is
// done in a separate pass to keep our route construction simple, as blinded
// paths require zero expiry and amount values for intermediate hops (which
// makes calculating the totals during route construction difficult if we
// include blinded paths on the first pass).
//
// NOTE: The passed slice of unified edges MUST be sorted in forward order: from
// the source to the target node of the path finding attempt. It is assumed that
// any feature vectors on all hops have been validated for transitive
// dependencies.
// NOTE: If a non-nil blinded path is provided it is assumed to have been
// validated by the caller.
func newRoute(sourceVertex route.Vertex,
        pathEdges []*unifiedEdge, currentHeight uint32, finalHop finalHopParams,
        blindedPathSet *BlindedPaymentPathSet) (*route.Route, error) {

        var (
                hops []*route.Hop

                // totalTimeLock will accumulate the cumulative time lock
                // across the entire route. This value represents how long the
                // sender will need to wait in the *worst* case.
                totalTimeLock = currentHeight

                // nextIncomingAmount is the amount that will need to flow into
                // the *next* hop. Since we're going to be walking the route
                // backwards below, this next hop gets closer and closer to the
                // sender of the payment.
                nextIncomingAmount lnwire.MilliSatoshi

                blindedPayment *BlindedPayment
        )

        pathLength := len(pathEdges)

        // When paying to a blinded route we might have appened a dummy hop at
        // the end to make MPP payment possible via the whole path. Before
        // sending out the onion payload we make sure we remove this hop again.
        //
        // NOTE: The path length is always at least 1 because there must be one
        // edge from the source to the destination. However we check for > 0
        // just for robustness here.
        if blindedPathSet != nil && pathLength > 0 {
                finalBlindedPubKey := pathEdges[pathLength-1].policy.
                        ToNodePubKey()

                if isBlindedRouteNUMSTargetKey(finalBlindedPubKey[:]) {
                        // If the last hop is the NUMS key for blinded paths, we
                        // remove the dummy hop from the route.
                        pathEdges = pathEdges[:pathLength-1]
                        pathLength--
                }
        }

        for i := pathLength - 1; i >= 0; i-- {
                // Now we'll start to calculate the items within the per-hop
                // payload for the hop this edge is leading to.
                edge := pathEdges[i].policy

                // If this is an edge from a blinded path and the
                // blindedPayment variable has not been set yet, then set it now
                // by extracting the corresponding blinded payment from the
                // edge.
                isBlindedEdge := pathEdges[i].blindedPayment != nil
                if isBlindedEdge && blindedPayment == nil {
                        blindedPayment = pathEdges[i].blindedPayment
                }

                // We'll calculate the amounts, timelocks, and fees for each hop
                // in the route. The base case is the final hop which includes
                // their amount and timelocks. These values will accumulate
                // contributions from the preceding hops back to the sender as
                // we compute the route in reverse.
                var (
                        amtToForward        lnwire.MilliSatoshi
                        fee                 int64
                        totalAmtMsatBlinded lnwire.MilliSatoshi
                        outgoingTimeLock    uint32
                        customRecords       record.CustomSet
                        mpp                 *record.MPP
                        metadata            []byte
                )

                // Define a helper function that checks this edge's feature
                // vector for support for a given feature. We assume at this
                // point that the feature vectors transitive dependencies have
                // been validated.
                supports := func(feature lnwire.FeatureBit) bool {
                        // If this edge comes from router hints, the features
                        // could be nil.
                        if edge.ToNodeFeatures == nil {
                                return false
                        }
                        return edge.ToNodeFeatures.HasFeature(feature)
                }

                if i == len(pathEdges)-1 {
                        // If this is the last hop, then the hop payload will
                        // contain the exact amount. In BOLT #4: Onion Routing
                        // Protocol / "Payload for the Last Node", this is
                        // detailed.
                        amtToForward = finalHop.amt

                        // Fee is not part of the hop payload, but only used for
                        // reporting through RPC. Set to zero for the final hop.
                        fee = 0

                        if blindedPathSet == nil {
                                totalTimeLock += uint32(finalHop.cltvDelta)
                        } else {
                                totalTimeLock += uint32(
                                        blindedPathSet.FinalCLTVDelta(),
                                )
                        }
                        outgoingTimeLock = totalTimeLock

                        // Attach any custom records to the final hop.
                        customRecords = finalHop.records

                        // If we're attaching a payment addr but the receiver
                        // doesn't support both TLV and payment addrs, fail.
                        payAddr := supports(lnwire.PaymentAddrOptional)
                        if !payAddr && finalHop.paymentAddr.IsSome() {
                                return nil, errors.New("cannot attach " +
                                        "payment addr")
                        }

                        // Otherwise attach the mpp record if it exists.
                        // TODO(halseth): move this to payment life cycle,
                        // where AMP options are set.
                        finalHop.paymentAddr.WhenSome(func(addr [32]byte) {
                                mpp = record.NewMPP(finalHop.totalAmt, addr)
                        })

                        metadata = finalHop.metadata

                        if blindedPathSet != nil {
                                totalAmtMsatBlinded = finalHop.totalAmt
                        }
                } else {
                        // The amount that the current hop needs to forward is
                        // equal to the incoming amount of the next hop.
                        amtToForward = nextIncomingAmount

                        // The fee that needs to be paid to the current hop is
                        // based on the amount that this hop needs to forward
                        // and its policy for the outgoing channel. This policy
                        // is stored as part of the incoming channel of
                        // the next hop.
                        outboundFee := pathEdges[i+1].policy.ComputeFee(
                                amtToForward,
                        )

                        inboundFee := pathEdges[i].inboundFees.CalcFee(
                                amtToForward + outboundFee,
                        )

                        fee = int64(outboundFee) + inboundFee
                        if fee < 0 {
                                fee = 0
                        }

                        // We'll take the total timelock of the preceding hop as
                        // the outgoing timelock or this hop. Then we'll
                        // increment the total timelock incurred by this hop.
                        outgoingTimeLock = totalTimeLock
                        totalTimeLock += uint32(
                                pathEdges[i+1].policy.TimeLockDelta,
                        )
                }

                // Since we're traversing the path backwards atm, we prepend
                // each new hop such that, the final slice of hops will be in
                // the forwards order.
                currentHop := &route.Hop{
                        PubKeyBytes:      edge.ToNodePubKey(),
                        ChannelID:        edge.ChannelID,
                        AmtToForward:     amtToForward,
                        OutgoingTimeLock: outgoingTimeLock,
                        CustomRecords:    customRecords,
                        MPP:              mpp,
                        Metadata:         metadata,
                        TotalAmtMsat:     totalAmtMsatBlinded,
                }

                hops = append([]*route.Hop{currentHop}, hops...)

                // Finally, we update the amount that needs to flow into the
                // *next* hop, which is the amount this hop needs to forward,
                // accounting for the fee that it takes.
                nextIncomingAmount = amtToForward + lnwire.MilliSatoshi(fee)
        }

        // If we are creating a route to a blinded path, we need to add some
        // additional data to the route that is required for blinded forwarding.
        // We do another pass on our edges to append this data.
        if blindedPathSet != nil {
                // If the passed in BlindedPaymentPathSet is non-nil but no
                // edge had a BlindedPayment attached, it means that the path
                // chosen was an introduction-node-only path. So in this case,
                // we can assume the relevant payment is the only one in the
                // payment set.
                if blindedPayment == nil {
                        var err error
                        blindedPayment, err = blindedPathSet.IntroNodeOnlyPath()
                        if err != nil {
                                return nil, err
                        }
                }

                var (
                        inBlindedRoute bool
                        dataIndex      = 0

                        blindedPath = blindedPayment.BlindedPath
                        introVertex = route.NewVertex(
                                blindedPath.IntroductionPoint,
                        )
                )

                for i, hop := range hops {
                        // Once we locate our introduction node, we know that
                        // every hop after this is part of the blinded route.
                        if bytes.Equal(hop.PubKeyBytes[:], introVertex[:]) {
                                inBlindedRoute = true
                                hop.BlindingPoint = blindedPath.BlindingPoint
                        }

                        // We don't need to modify edges outside of our blinded
                        // route.
                        if !inBlindedRoute {
                                continue
                        }

                        payload := blindedPath.BlindedHops[dataIndex].CipherText
                        hop.EncryptedData = payload

                        // All of the hops in a blinded route *except* the
                        // final hop should have zero amounts / time locks.
                        if i != len(hops)-1 {
                                hop.AmtToForward = 0
                                hop.OutgoingTimeLock = 0
                        }

                        dataIndex++
                }
        }

        // With the base routing data expressed as hops, build the full route
        newRoute, err := route.NewRouteFromHops(
                nextIncomingAmount, totalTimeLock, route.Vertex(sourceVertex),
                hops,
        )
        if err != nil {
                return nil, err
        }

        return newRoute, nil
}

// edgeWeight computes the weight of an edge. This value is used when searching
// for the shortest path within the channel graph between two nodes. Weight is
// is the fee itself plus a time lock penalty added to it. This benefits
// channels with shorter time lock deltas and shorter (hops) routes in general.
// RiskFactor controls the influence of time lock on route selection. This is
// currently a fixed value, but might be configurable in the future.
func edgeWeight(lockedAmt lnwire.MilliSatoshi, fee lnwire.MilliSatoshi,
        timeLockDelta uint16) int64 {
        // timeLockPenalty is the penalty for the time lock delta of this channel.
        // It is controlled by RiskFactorBillionths and scales proportional
        // to the amount that will pass through channel. Rationale is that it if
        // a twice as large amount gets locked up, it is twice as bad.
        timeLockPenalty := int64(lockedAmt) * int64(timeLockDelta) *
                RiskFactorBillionths / 1000000000

        return int64(fee) + timeLockPenalty
}

// graphParams wraps the set of graph parameters passed to findPath.
type graphParams struct {
        // graph is the ChannelGraph to be used during path finding.
        graph Graph

        // additionalEdges is an optional set of edges that should be
        // considered during path finding, that is not already found in the
        // channel graph. These can either be private edges for bolt 11 invoices
        // or blinded edges when a payment to a blinded path is made.
        additionalEdges map[route.Vertex][]AdditionalEdge

        // bandwidthHints is an interface that provides bandwidth hints that
        // can provide a better estimate of the current channel bandwidth than
        // what is found in the graph. It will override the capacities and
        // disabled flags found in the graph for local channels when doing
        // path finding if it has updated values for that channel. In
        // particular, it should be set to the current available sending
        // bandwidth for active local channels, and 0 for inactive channels.
        bandwidthHints bandwidthHints
}

// RestrictParams wraps the set of restrictions passed to findPath that the
// found path must adhere to.
type RestrictParams struct {
        // ProbabilitySource is a callback that is expected to return the
        // success probability of traversing the channel from the node.
        ProbabilitySource func(route.Vertex, route.Vertex,
                lnwire.MilliSatoshi, btcutil.Amount) float64

        // FeeLimit is a maximum fee amount allowed to be used on the path from
        // the source to the target.
        FeeLimit lnwire.MilliSatoshi

        // OutgoingChannelIDs is the list of channels that are allowed for the
        // first hop. If nil, any channel may be used.
        OutgoingChannelIDs []uint64

        // LastHop is the pubkey of the last node before the final destination
        // is reached. If nil, any node may be used.
        LastHop *route.Vertex

        // CltvLimit is the maximum time lock of the route excluding the final
        // ctlv. After path finding is complete, the caller needs to increase
        // all cltv expiry heights with the required final cltv delta.
        CltvLimit uint32

        // DestCustomRecords contains the custom records to drop off at the
        // final hop, if any.
        DestCustomRecords record.CustomSet

        // DestFeatures is a feature vector describing what the final hop
        // supports. If none are provided, pathfinding will try to inspect any
        // features on the node announcement instead.
        DestFeatures *lnwire.FeatureVector

        // PaymentAddr is a random 32-byte value generated by the receiver to
        // mitigate probing vectors and payment sniping attacks on overpaid
        // invoices.
        PaymentAddr fn.Option[[32]byte]

        // Amp signals to the pathfinder that this payment is an AMP payment
        // and therefore it needs to account for additional AMP data in the
        // final hop payload size calculation.
        Amp *AMPOptions

        // Metadata is additional data that is sent along with the payment to
        // the payee.
        Metadata []byte

        // BlindedPaymentPathSet is necessary to determine the hop size of the
        // last/exit hop.
        BlindedPaymentPathSet *BlindedPaymentPathSet

        // FirstHopCustomRecords includes any records that should be included in
        // the update_add_htlc message towards our peer.
        FirstHopCustomRecords lnwire.CustomRecords
}

// PathFindingConfig defines global parameters that control the trade-off in
// path finding between fees and probability.
type PathFindingConfig struct {
        // AttemptCost is the fixed virtual cost in path finding of a failed
        // payment attempt. It is used to trade off potentially better routes
        // against their probability of succeeding.
        AttemptCost lnwire.MilliSatoshi

        // AttemptCostPPM is the proportional virtual cost in path finding of a
        // failed payment attempt. It is used to trade off potentially better
        // routes against their probability of succeeding. This parameter is
        // expressed in parts per million of the total payment amount.
        AttemptCostPPM int64

        // MinProbability defines the minimum success probability of the
        // returned route.
        MinProbability float64
}

// getOutgoingBalance returns the maximum available balance in any of the
// channels of the given node. The second return parameters is the total
// available balance.
func getOutgoingBalance(node route.Vertex, outgoingChans map[uint64]struct{},
        bandwidthHints bandwidthHints,
        g Graph) (lnwire.MilliSatoshi, lnwire.MilliSatoshi, error) {

        var max, total lnwire.MilliSatoshi
        cb := func(channel *graphdb.DirectedChannel) error {
                if !channel.OutPolicySet {
                        return nil
                }

                chanID := channel.ChannelID

                // Enforce outgoing channel restriction.
                if outgoingChans != nil {
                        if _, ok := outgoingChans[chanID]; !ok {
                                return nil
                        }
                }

                bandwidth, ok := bandwidthHints.availableChanBandwidth(
                        chanID, 0,
                )

                // If the bandwidth is not available, use the channel capacity.
                // This can happen when a channel is added to the graph after
                // we've already queried the bandwidth hints.
                if !ok {
                        bandwidth = lnwire.NewMSatFromSatoshis(channel.Capacity)
                }

                if bandwidth > max {
                        max = bandwidth
                }

                var overflow bool
                total, overflow = overflowSafeAdd(total, bandwidth)
                if overflow {
                        // If the current total and the bandwidth would
                        // overflow the maximum value, we set the total to the
                        // maximum value. Which is more milli-satoshis than are
                        // in existence anyway, so the actual value is
                        // irrelevant.
                        total = lnwire.MilliSatoshi(math.MaxUint64)
                }

                return nil
        }

        // Iterate over all channels of the to node.
        err := g.ForEachNodeChannel(node, cb)
        if err != nil {
                return 0, 0, err
        }
        return max, total, err
}

// findPath attempts to find a path from the source node within the ChannelGraph
// to the target node that's capable of supporting a payment of `amt` value. The
// current approach implemented is modified version of Dijkstra's algorithm to
// find a single shortest path between the source node and the destination. The
// distance metric used for edges is related to the time-lock+fee costs along a
// particular edge. If a path is found, this function returns a slice of
// ChannelHop structs which encoded the chosen path from the target to the
// source. The search is performed backwards from destination node back to
// source. This is to properly accumulate fees that need to be paid along the
// path and accurately check the amount to forward at every node against the
// available bandwidth.
func findPath(g *graphParams, r *RestrictParams, cfg *PathFindingConfig,
        self, source, target route.Vertex, amt lnwire.MilliSatoshi,
        timePref float64, finalHtlcExpiry int32) ([]*unifiedEdge, float64,
        error) {

        // Pathfinding can be a significant portion of the total payment
        // latency, especially on low-powered devices. Log several metrics to
        // aid in the analysis performance problems in this area.
        start := time.Now()
        nodesVisited := 0
        edgesExpanded := 0
        defer func() {
                timeElapsed := time.Since(start)
                log.Debugf("Pathfinding perf metrics: nodes=%v, edges=%v, "+
                        "time=%v", nodesVisited, edgesExpanded, timeElapsed)
        }()

        // If no destination features are provided, we will load what features
        // we have for the target node from our graph.
        features := r.DestFeatures
        if features == nil {
                var err error
                features, err = g.graph.FetchNodeFeatures(target)
                if err != nil {
                        return nil, 0, err
                }
        }

        // Ensure that the destination's features don't include unknown
        // required features.
        err := feature.ValidateRequired(features)
        if err != nil {
                log.Warnf("Pathfinding destination node features: %v", err)
                return nil, 0, errUnknownRequiredFeature
        }

        // Ensure that all transitive dependencies are set.
        err = feature.ValidateDeps(features)
        if err != nil {
                log.Warnf("Pathfinding destination node features: %v", err)
                return nil, 0, errMissingDependentFeature
        }

        // Now that we know the feature vector is well-formed, we'll proceed in
        // checking that it supports the features we need. If the caller has a
        // payment address to attach, check that our destination feature vector
        // supports them.
        if r.PaymentAddr.IsSome() &&
                !features.HasFeature(lnwire.PaymentAddrOptional) {

                return nil, 0, errNoPaymentAddr
        }

        // Set up outgoing channel map for quicker access.
        var outgoingChanMap map[uint64]struct{}
        if len(r.OutgoingChannelIDs) > 0 {
                outgoingChanMap = make(map[uint64]struct{})
                for _, outChan := range r.OutgoingChannelIDs {
                        outgoingChanMap[outChan] = struct{}{}
                }
        }

        // If we are routing from ourselves, check that we have enough local
        // balance available.
        if source == self {
                max, total, err := getOutgoingBalance(
                        self, outgoingChanMap, g.bandwidthHints, g.graph,
                )
                if err != nil {
                        return nil, 0, err
                }

                // If the total outgoing balance isn't sufficient, it will be
                // impossible to complete the payment.
                if total < amt {
                        log.Warnf("Not enough outbound balance to send "+
                                "htlc of amount: %v, only have local "+
                                "balance: %v", amt, total)

                        return nil, 0, errInsufficientBalance
                }

                // If there is only not enough capacity on a single route, it
                // may still be possible to complete the payment by splitting.
                if max < amt {
                        return nil, 0, errNoPathFound
                }
        }

        // First we'll initialize an empty heap which'll help us to quickly
        // locate the next edge we should visit next during our graph
        // traversal.
        nodeHeap := newDistanceHeap(estimatedNodeCount)

        // Holds the current best distance for a given node.
        distance := make(map[route.Vertex]*nodeWithDist, estimatedNodeCount)

        additionalEdgesWithSrc := make(map[route.Vertex][]*edgePolicyWithSource)
        for vertex, additionalEdges := range g.additionalEdges {
                // Edges connected to self are always included in the graph,
                // therefore can be skipped. This prevents us from trying
                // routes to malformed hop hints.
                if vertex == self {
                        continue
                }

                // Build reverse lookup to find incoming edges. Needed because
                // search is taken place from target to source.
                for _, additionalEdge := range additionalEdges {
                        outgoingEdgePolicy := additionalEdge.EdgePolicy()
                        toVertex := outgoingEdgePolicy.ToNodePubKey()

                        incomingEdgePolicy := &edgePolicyWithSource{
                                sourceNode: vertex,
                                edge:       additionalEdge,
                        }

                        additionalEdgesWithSrc[toVertex] =
                                append(additionalEdgesWithSrc[toVertex],
                                        incomingEdgePolicy)
                }
        }

        // The payload size of the final hop differ from intermediate hops
        // and depends on whether the destination is blinded or not.
        lastHopPayloadSize := lastHopPayloadSize(r, finalHtlcExpiry, amt)

        // We can't always assume that the end destination is publicly
        // advertised to the network so we'll manually include the target node.
        // The target node charges no fee. Distance is set to 0, because this is
        // the starting point of the graph traversal. We are searching backwards
        // to get the fees first time right and correctly match channel
        // bandwidth.
        //
        // Don't record the initial partial path in the distance map and reserve
        // that key for the source key in the case we route to ourselves.
        partialPath := &nodeWithDist{
                dist:              0,
                weight:            0,
                node:              target,
                netAmountReceived: amt,
                incomingCltv:      finalHtlcExpiry,
                probability:       1,
                routingInfoSize:   lastHopPayloadSize,
        }

        // Calculate the absolute cltv limit. Use uint64 to prevent an overflow
        // if the cltv limit is MaxUint32.
        absoluteCltvLimit := uint64(r.CltvLimit) + uint64(finalHtlcExpiry)

        // Calculate the default attempt cost as configured globally.
        defaultAttemptCost := float64(
                cfg.AttemptCost +
                        amt*lnwire.MilliSatoshi(cfg.AttemptCostPPM)/1000000,
        )

        // Validate time preference value.
        if math.Abs(timePref) > 1 {
                return nil, 0, fmt.Errorf("time preference %v out of range "+
                        "[-1, 1]", timePref)
        }

        // Scale to avoid the extremes -1 and 1 which run into infinity issues.
        timePref *= 0.9

        // Apply time preference. At 0, the default attempt cost will
        // be used.
        absoluteAttemptCost := defaultAttemptCost * (1/(0.5-timePref/2) - 1)

        log.Debugf("Pathfinding absolute attempt cost: %v sats",
                absoluteAttemptCost/1000)

        // processEdge is a helper closure that will be used to make sure edges
        // satisfy our specific requirements.
        processEdge := func(fromVertex route.Vertex,
                edge *unifiedEdge, toNodeDist *nodeWithDist) {

                edgesExpanded++

                // Calculate inbound fee charged by "to" node. The exit hop
                // doesn't charge inbound fees. If the "to" node is the exit
                // hop, its inbound fees have already been set to zero by
                // nodeEdgeUnifier.
                inboundFee := edge.inboundFees.CalcFee(
                        toNodeDist.netAmountReceived,
                )

                // Make sure that the node total fee is never negative.
                // Routing nodes treat a total fee that turns out
                // negative as a zero fee and pathfinding should do the
                // same.
                minInboundFee := -int64(toNodeDist.outboundFee)
                if inboundFee < minInboundFee {
                        inboundFee = minInboundFee
                }

                // Calculate amount that the candidate node would have to send
                // out.
                amountToSend := toNodeDist.netAmountReceived +
                        lnwire.MilliSatoshi(inboundFee)

                // Check if accumulated fees would exceed fee limit when this
                // node would be added to the path.
                totalFee := int64(amountToSend) - int64(amt)

                log.Trace(lnutils.NewLogClosure(func() string {
                        return fmt.Sprintf(
                                "Checking fromVertex (%v) with "+
                                        "minInboundFee=%v, inboundFee=%v, "+
                                        "amountToSend=%v, amt=%v, totalFee=%v",
                                fromVertex, minInboundFee, inboundFee,
                                amountToSend, amt, totalFee,
                        )
                }))

                if totalFee > 0 && lnwire.MilliSatoshi(totalFee) > r.FeeLimit {
                        return
                }

                // Request the success probability for this edge.
                edgeProbability := r.ProbabilitySource(
                        fromVertex, toNodeDist.node, amountToSend,
                        edge.capacity,
                )

                log.Trace(lnutils.NewLogClosure(func() string {
                        return fmt.Sprintf("path finding probability: fromnode=%v,"+
                                " tonode=%v, amt=%v, cap=%v, probability=%v",
                                fromVertex, toNodeDist.node, amountToSend,
                                edge.capacity, edgeProbability)
                }))

                // If the probability is zero, there is no point in trying.
                if edgeProbability == 0 {
                        return
                }

                // Compute fee that fromVertex is charging. It is based on the
                // amount that needs to be sent to the next node in the route.
                //
                // Source node has no predecessor to pay a fee. Therefore set
                // fee to zero, because it should not be included in the fee
                // limit check and edge weight.
                //
                // Also determine the time lock delta that will be added to the
                // route if fromVertex is selected. If fromVertex is the source
                // node, no additional timelock is required.
                var (
                        timeLockDelta uint16
                        outboundFee   int64
                )

                if fromVertex != source {
                        outboundFee = int64(
                                edge.policy.ComputeFee(amountToSend),
                        )
                        timeLockDelta = edge.policy.TimeLockDelta
                }

                incomingCltv := toNodeDist.incomingCltv + int32(timeLockDelta)

                // Check that we are within our CLTV limit.
                if uint64(incomingCltv) > absoluteCltvLimit {
                        return
                }

                // netAmountToReceive is the amount that the node that is added
                // to the distance map needs to receive from a (to be found)
                // previous node in the route. The inbound fee of the receiving
                // node is already subtracted from this value. The previous node
                // will need to pay the amount that this node forwards plus the
                // fee it charges plus this node's inbound fee.
                netAmountToReceive := amountToSend +
                        lnwire.MilliSatoshi(outboundFee)

                // Calculate total probability of successfully reaching target
                // by multiplying the probabilities. Both this edge and the rest
                // of the route must succeed.
                probability := toNodeDist.probability * edgeProbability

                // If the probability is below the specified lower bound, we can
                // abandon this direction. Adding further nodes can only lower
                // the probability more.
                if probability < cfg.MinProbability {
                        return
                }

                // Calculate the combined fee for this edge. Dijkstra does not
                // support negative edge weights. Because this fee feeds into
                // the edge weight calculation, we don't allow it to be
                // negative.
                signedFee := inboundFee + outboundFee
                fee := lnwire.MilliSatoshi(0)
                if signedFee > 0 {
                        fee = lnwire.MilliSatoshi(signedFee)
                }

                // By adding fromVertex in the route, there will be an extra
                // weight composed of the fee that this node will charge and
                // the amount that will be locked for timeLockDelta blocks in
                // the HTLC that is handed out to fromVertex.
                weight := edgeWeight(amountToSend, fee, timeLockDelta)

                // Compute the tentative weight to this new channel/edge
                // which is the weight from our toNode to the target node
                // plus the weight of this edge.
                tempWeight := toNodeDist.weight + weight

                // Add an extra factor to the weight to take into account the
                // probability. Another reason why we rounded the fee up to zero
                // is to prevent a highly negative fee from cancelling out the
                // extra factor. We don't want an always-failing node to attract
                // traffic using a highly negative fee and escape penalization.
                tempDist := getProbabilityBasedDist(
                        tempWeight, probability,
                        absoluteAttemptCost,
                )

                // If there is already a best route stored, compare this
                // candidate route with the best route so far.
                current, ok := distance[fromVertex]
                if ok {
                        // If this route is worse than what we already found,
                        // skip this route.
                        if tempDist > current.dist {
                                return
                        }

                        // If the route is equally good and the probability
                        // isn't better, skip this route. It is important to
                        // also return if both cost and probability are equal,
                        // because otherwise the algorithm could run into an
                        // endless loop.
                        probNotBetter := probability <= current.probability
                        if tempDist == current.dist && probNotBetter {
                                return
                        }
                }

                // Calculate the total routing info size if this hop were to be
                // included. If we are coming from the source hop, the payload
                // size is zero, because the original htlc isn't in the onion
                // blob.
                var payloadSize uint64
                ToPubKey := edge.policy.ToNodePubKey()

                // If the edge points to the NUMS key we don't need to consider
                // the payload size again because we already added the size of
                // the dummy hop which will be removed after the route is found.
                // The dummy target hop has the same cipher text length as the
                // real last blinded target hop.
                if fromVertex != source &&
                        !isBlindedRouteNUMSTargetKey(ToPubKey[:]) {
                        // In case the unifiedEdge does not have a payload size
                        // function supplied we request a graceful shutdown
                        // because this should never happen.
                        if edge.hopPayloadSizeFn == nil {
                                log.Criticalf("No payload size function "+
                                        "available for edge=%v unable to "+
                                        "determine payload size: %v", edge,
                                        ErrNoPayLoadSizeFunc)

                                return
                        }

                        payloadSize = edge.hopPayloadSizeFn(
                                amountToSend,
                                uint32(toNodeDist.incomingCltv),
                                edge.policy.ChannelID,
                        )
                }

                routingInfoSize := toNodeDist.routingInfoSize + payloadSize
                // Skip paths that would exceed the maximum routing info size.
                if routingInfoSize > sphinx.MaxPayloadSize {
                        return
                }

                // All conditions are met and this new tentative distance is
                // better than the current best known distance to this node.
                // The new better distance is recorded, and also our "next hop"
                // map is populated with this edge.
                withDist := &nodeWithDist{
                        dist:              tempDist,
                        weight:            tempWeight,
                        node:              fromVertex,
                        netAmountReceived: netAmountToReceive,
                        outboundFee:       lnwire.MilliSatoshi(outboundFee),
                        incomingCltv:      incomingCltv,
                        probability:       probability,
                        nextHop:           edge,
                        routingInfoSize:   routingInfoSize,
                }
                distance[fromVertex] = withDist

                // Either push withDist onto the heap if the node
                // represented by fromVertex is not already on the heap OR adjust
                // its position within the heap via heap.Fix.
                nodeHeap.PushOrFix(withDist)
        }

        // TODO(roasbeef): also add path caching
        //  * similar to route caching, but doesn't factor in the amount

        // Cache features because we visit nodes multiple times.
        featureCache := make(map[route.Vertex]*lnwire.FeatureVector)

        // getGraphFeatures returns (cached) node features from the graph.
        getGraphFeatures := func(node route.Vertex) (*lnwire.FeatureVector,
                error) {

                // Check cache for features of the fromNode.
                fromFeatures, ok := featureCache[node]
                if ok {
                        return fromFeatures, nil
                }

                // Fetch node features fresh from the graph.
                fromFeatures, err := g.graph.FetchNodeFeatures(node)
                if err != nil {
                        return nil, err
                }

                // Don't route through nodes that contain unknown required
                // features and mark as nil in the cache.
                err = feature.ValidateRequired(fromFeatures)
                if err != nil {
                        featureCache[node] = nil
                        return nil, nil
                }

                // Don't route through nodes that don't properly set all
                // transitive feature dependencies and mark as nil in the cache.
                err = feature.ValidateDeps(fromFeatures)
                if err != nil {
                        featureCache[node] = nil
                        return nil, nil
                }

                // Update cache.
                featureCache[node] = fromFeatures

                return fromFeatures, nil
        }

        routeToSelf := source == target
        for {
                nodesVisited++

                pivot := partialPath.node
                isExitHop := partialPath.nextHop == nil

                // Create unified policies for all incoming connections. Don't
                // use inbound fees for the exit hop.
                u := newNodeEdgeUnifier(
                        self, pivot, !isExitHop, outgoingChanMap,
                )

                err := u.addGraphPolicies(g.graph)
                if err != nil {
                        return nil, 0, err
                }

                // We add hop hints that were supplied externally.
                for _, reverseEdge := range additionalEdgesWithSrc[pivot] {
                        // Assume zero inbound fees for route hints. If inbound
                        // fees would apply, they couldn't be communicated in
                        // bolt11 invoices currently.
                        inboundFee := models.InboundFee{}

                        // 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.
                        // We also pass the payload size function to the
                        // graph data so that we calculate the exact payload
                        // size when evaluating this hop for a route.
                        u.addPolicy(
                                reverseEdge.sourceNode,
                                reverseEdge.edge.EdgePolicy(),
                                inboundFee,
                                fakeHopHintCapacity,
                                reverseEdge.edge.IntermediatePayloadSize,
                                reverseEdge.edge.BlindedPayment(),
                        )
                }

                netAmountReceived := partialPath.netAmountReceived

                // Expand all connections using the optimal policy for each
                // connection.
                for fromNode, edgeUnifier := range u.edgeUnifiers {
                        // The target node is not recorded in the distance map.
                        // Therefore we need to have this check to prevent
                        // creating a cycle. Only when we intend to route to
                        // self, we allow this cycle to form. In that case we'll
                        // also break out of the search loop below.
                        if !routeToSelf && fromNode == target {
                                continue
                        }

                        // Apply last hop restriction if set.
                        if r.LastHop != nil &&
                                pivot == target && fromNode != *r.LastHop {

                                continue
                        }

                        edge := edgeUnifier.getEdge(
                                netAmountReceived, g.bandwidthHints,
                                partialPath.outboundFee,
                        )

                        if edge == nil {
                                continue
                        }

                        // Get feature vector for fromNode.
                        fromFeatures, err := getGraphFeatures(fromNode)
                        if err != nil {
                                return nil, 0, err
                        }

                        // If there are no valid features, skip this node.
                        if fromFeatures == nil {
                                continue
                        }

                        // Check if this candidate node is better than what we
                        // already have.
                        processEdge(fromNode, edge, partialPath)
                }

                if nodeHeap.Len() == 0 {
                        break
                }

                // Fetch the node within the smallest distance from our source
                // from the heap.
                partialPath = heap.Pop(&nodeHeap).(*nodeWithDist)

                // If we've reached our source (or we don't have any incoming
                // edges), then we're done here and can exit the graph
                // traversal early.
                if partialPath.node == source {
                        break
                }
        }

        // Use the distance map to unravel the forward path from source to
        // target.
        var pathEdges []*unifiedEdge
        currentNode := source
        for {
                // Determine the next hop forward using the next map.
                currentNodeWithDist, ok := distance[currentNode]
                if !ok {
                        // If the node doesn't have a next hop it means we
                        // didn't find a path.
                        return nil, 0, errNoPathFound
                }

                // Add the next hop to the list of path edges.
                pathEdges = append(pathEdges, currentNodeWithDist.nextHop)

                // Advance current node.
                currentNode = currentNodeWithDist.nextHop.policy.ToNodePubKey()

                // Check stop condition at the end of this loop. This prevents
                // breaking out too soon for self-payments that have target set
                // to source.
                if currentNode == target {
                        break
                }
        }

        // For the final hop, we'll set the node features to those determined
        // above. These are either taken from the destination features, e.g.
        // virtual or invoice features, or loaded as a fallback from the graph.
        // The transitive dependencies were already validated above, so no need
        // to do so now.
        //
        // NOTE: This may overwrite features loaded from the graph if
        // destination features were provided. This is fine though, since our
        // route construction does not care where the features are actually
        // taken from. In the future we may wish to do route construction within
        // findPath, and avoid using ChannelEdgePolicy altogether.
        pathEdges[len(pathEdges)-1].policy.ToNodeFeatures = features

        log.Debugf("Found route: probability=%v, hops=%v, fee=%v",
                distance[source].probability, len(pathEdges),
                distance[source].netAmountReceived-amt)

        return pathEdges, distance[source].probability, nil
}

// blindedPathRestrictions are a set of constraints to adhere to when
// choosing a set of blinded paths to this node.
type blindedPathRestrictions struct {
        // minNumHops is the minimum number of hops to include in a blinded
        // path. This doesn't include our node, so if the minimum is 1, then
        // the path will contain at minimum our node along with an introduction
        // node hop. A minimum of 0 will include paths where this node is the
        // introduction node and so should be used with caution.
        minNumHops uint8

        // maxNumHops is the maximum number of hops to include in a blinded
        // path. This doesn't include our node, so if the maximum is 1, then
        // the path will contain our node along with an introduction node hop.
        maxNumHops uint8

        // nodeOmissionSet holds a set of node IDs of nodes that we should
        // ignore during blinded path selection.
        nodeOmissionSet fn.Set[route.Vertex]
}

// blindedHop holds the information about a hop we have selected for a blinded
// path.
type blindedHop struct {
        vertex       route.Vertex
        channelID    uint64
        edgeCapacity btcutil.Amount
}

// findBlindedPaths does a depth first search from the target node to find a set
// of blinded paths to the target node given the set of restrictions. This
// function will select and return any candidate path. A candidate path is a
// path to the target node with a size determined by the given hop number
// constraints where all the nodes on the path signal the route blinding feature
// _and_ the introduction node for the path has more than one public channel.
// Any filtering of paths based on payment value or success probabilities is
// left to the caller.
func findBlindedPaths(g Graph, target route.Vertex,
        restrictions *blindedPathRestrictions) ([][]blindedHop, error) {

        // Sanity check the restrictions.
        if restrictions.minNumHops > restrictions.maxNumHops {
                return nil, fmt.Errorf("maximum number of blinded path hops "+
                        "(%d) must be greater than or equal to the minimum "+
                        "number of hops (%d)", restrictions.maxNumHops,
                        restrictions.minNumHops)
        }

        // If the node is not the destination node, then it is required that the
        // node advertise the route blinding feature-bit in order for it to be
        // chosen as a node on the blinded path.
        supportsRouteBlinding := func(node route.Vertex) (bool, error) {
                if node == target {
                        return true, nil
                }

                features, err := g.FetchNodeFeatures(node)
                if err != nil {
                        return false, err
                }

                return features.HasFeature(lnwire.RouteBlindingOptional), nil
        }

        // This function will have some recursion. We will spin out from the
        // target node & append edges to the paths until we reach various exit
        // conditions such as: The maxHops number being reached or reaching
        // a node that doesn't have any other edges - in that final case, the
        // whole path should be ignored.
        paths, _, err := processNodeForBlindedPath(
                g, target, supportsRouteBlinding, nil, restrictions,
        )
        if err != nil {
                return nil, err
        }

        // Reverse each path so that the order is correct (from introduction
        // node to last hop node) and then append this node on as the
        // destination of each path.
        orderedPaths := make([][]blindedHop, len(paths))
        for i, path := range paths {
                sort.Slice(path, func(i, j int) bool {
                        return j < i
                })

                orderedPaths[i] = append(path, blindedHop{vertex: target})
        }

        // Handle the special case that allows a blinded path with the
        // introduction node as the destination node.
        if restrictions.minNumHops == 0 {
                singleHopPath := [][]blindedHop{{{vertex: target}}}

                //nolint:makezero
                orderedPaths = append(
                        orderedPaths, singleHopPath...,
                )
        }

        return orderedPaths, err
}

// processNodeForBlindedPath is a recursive function that traverses the graph
// in a depth first manner searching for a set of blinded paths to the given
// node.
func processNodeForBlindedPath(g Graph, node route.Vertex,
        supportsRouteBlinding func(vertex route.Vertex) (bool, error),
        alreadyVisited map[route.Vertex]bool,
        restrictions *blindedPathRestrictions) ([][]blindedHop, bool, error) {

        // If we have already visited the maximum number of hops, then this path
        // is complete and we can exit now.
        if len(alreadyVisited) > int(restrictions.maxNumHops) {
                return nil, false, nil
        }

        // If we have already visited this peer on this path, then we skip
        // processing it again.
        if alreadyVisited[node] {
                return nil, false, nil
        }

        // If we have explicitly been told to ignore this node for blinded paths
        // then we skip it too.
        if restrictions.nodeOmissionSet.Contains(node) {
                return nil, false, nil
        }

        supports, err := supportsRouteBlinding(node)
        if err != nil {
                return nil, false, err
        }
        if !supports {
                return nil, false, nil
        }

        // At this point, copy the alreadyVisited map.
        visited := make(map[route.Vertex]bool, len(alreadyVisited))
        for r := range alreadyVisited {
                visited[r] = true
        }

        // Add this node the visited set.
        visited[node] = true

        var (
                hopSets   [][]blindedHop
                chanCount int
        )

        // Now, iterate over the node's channels in search for paths to this
        // node that can be used for blinded paths
        err = g.ForEachNodeChannel(node,
                func(channel *graphdb.DirectedChannel) error {
                        // Keep track of how many incoming channels this node
                        // has. We only use a node as an introduction node if it
                        // has channels other than the one that lead us to it.
                        chanCount++

                        // Process each channel peer to gather any paths that
                        // lead to the peer.
                        nextPaths, hasMoreChans, err := processNodeForBlindedPath( //nolint:ll
                                g, channel.OtherNode, supportsRouteBlinding,
                                visited, restrictions,
                        )
                        if err != nil {
                                return err
                        }

                        hop := blindedHop{
                                vertex:       channel.OtherNode,
                                channelID:    channel.ChannelID,
                                edgeCapacity: channel.Capacity,
                        }

                        // For each of the paths returned, unwrap them and
                        // append this hop to them.
                        for _, path := range nextPaths {
                                hopSets = append(
                                        hopSets,
                                        append([]blindedHop{hop}, path...),
                                )
                        }

                        // If this node does have channels other than the one
                        // that lead to it, and if the hop count up to this node
                        // meets the minHop requirement, then we also add a
                        // path that starts at this node.
                        if hasMoreChans &&
                                len(visited) >= int(restrictions.minNumHops) {

                                hopSets = append(hopSets, []blindedHop{hop})
                        }

                        return nil
                },
        )
        if err != nil {
                return nil, false, err
        }

        return hopSets, chanCount > 1, nil
}

// getProbabilityBasedDist converts a weight into a distance that takes into
// account the success probability and the (virtual) cost of a failed payment
// attempt.
//
// Derivation:
//
// Suppose there are two routes A and B with fees Fa and Fb and success
// probabilities Pa and Pb.
//
// Is the expected cost of trying route A first and then B lower than trying the
// other way around?
//
// The expected cost of A-then-B is: Pa*Fa + (1-Pa)*Pb*(c+Fb)
//
// The expected cost of B-then-A is: Pb*Fb + (1-Pb)*Pa*(c+Fa)
//
// In these equations, the term representing the case where both A and B fail is
// left out because its value would be the same in both cases.
//
// Pa*Fa + (1-Pa)*Pb*(c+Fb) < Pb*Fb + (1-Pb)*Pa*(c+Fa)
//
// Pa*Fa + Pb*c + Pb*Fb - Pa*Pb*c - Pa*Pb*Fb < Pb*Fb + Pa*c + Pa*Fa - Pa*Pb*c - Pa*Pb*Fa
//
// Removing terms that cancel out:
// Pb*c - Pa*Pb*Fb < Pa*c - Pa*Pb*Fa
//
// Divide by Pa*Pb:
// c/Pa - Fb < c/Pb - Fa
//
// Move terms around:
// Fa + c/Pa < Fb + c/Pb
//
// So the value of F + c/P can be used to compare routes.
func getProbabilityBasedDist(weight int64, probability float64,
        penalty float64) int64 {

        // Prevent divide by zero by returning early.
        if probability == 0 {
                return infinity
        }

        // Calculate distance.
        dist := float64(weight) + penalty/probability

        // Avoid cast if an overflow would occur. The maxFloat constant is
        // chosen to stay well below the maximum float64 value that is still
        // convertible to int64.
        const maxFloat = 9000000000000000000
        if dist > maxFloat {
                return infinity
        }

        return int64(dist)
}

// lastHopPayloadSize calculates the payload size of the final hop in a route.
// It depends on the tlv types which are present and also whether the hop is
// part of a blinded route or not.
func lastHopPayloadSize(r *RestrictParams, finalHtlcExpiry int32,
        amount lnwire.MilliSatoshi) uint64 {

        if r.BlindedPaymentPathSet != nil {
                paymentPath := r.BlindedPaymentPathSet.
                        LargestLastHopPayloadPath()
                blindedPath := paymentPath.BlindedPath.BlindedHops
                blindedPoint := paymentPath.BlindedPath.BlindingPoint

                encryptedData := blindedPath[len(blindedPath)-1].CipherText
                finalHop := route.Hop{
                        AmtToForward:     amount,
                        OutgoingTimeLock: uint32(finalHtlcExpiry),
                        EncryptedData:    encryptedData,
                }
                if len(blindedPath) == 1 {
                        finalHop.BlindingPoint = blindedPoint
                }

                // The final hop does not have a short chanID set.
                return finalHop.PayloadSize(0)
        }

        var mpp *record.MPP
        r.PaymentAddr.WhenSome(func(addr [32]byte) {
                mpp = record.NewMPP(amount, addr)
        })

        var amp *record.AMP
        if r.Amp != nil {
                // The AMP payload is not easy accessible at this point but we
                // are only interested in the size of the payload so we just use
                // the AMP record dummy.
                amp = &record.MaxAmpPayLoadSize
        }

        finalHop := route.Hop{
                AmtToForward:     amount,
                OutgoingTimeLock: uint32(finalHtlcExpiry),
                CustomRecords:    r.DestCustomRecords,
                MPP:              mpp,
                AMP:              amp,
                Metadata:         r.Metadata,
        }

        // The final hop does not have a short chanID set.
        return finalHop.PayloadSize(0)
}

// overflowSafeAdd adds two MilliSatoshi values and returns the result. If an
// overflow could occur, zero is returned instead and the boolean is set to
// true.
func overflowSafeAdd(x, y lnwire.MilliSatoshi) (lnwire.MilliSatoshi, bool) {
        if y > math.MaxUint64-x {
                // Overflow would occur, return 0 and set overflow flag.
                return 0, true
        }

        return x + y, false
}

lightningnetwork / lnd / 12165272839

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