Merge pull request #2723 from jkczyz/2023-11-direct-connect

[rust-lightning] / lightning / src / routing / scoring.rs

// This file is Copyright its original authors, visible in version control
// history.
//
// This file is licensed under the Apache License, Version 2.0 <LICENSE-APACHE
// or http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your option.
// You may not use this file except in accordance with one or both of these
// licenses.

//! Utilities for scoring payment channels.
//!
//! [`ProbabilisticScorer`] may be given to [`find_route`] to score payment channels during path
//! finding when a custom [`ScoreLookUp`] implementation is not needed.
//!
//! # Example
//!
//! ```
//! # extern crate bitcoin;
//! #
//! # use lightning::routing::gossip::NetworkGraph;
//! # use lightning::routing::router::{RouteParameters, find_route};
//! # use lightning::routing::scoring::{ProbabilisticScorer, ProbabilisticScoringFeeParameters, ProbabilisticScoringDecayParameters};
//! # use lightning::sign::KeysManager;
//! # use lightning::util::logger::{Logger, Record};
//! # use bitcoin::secp256k1::PublicKey;
//! #
//! # struct FakeLogger {};
//! # impl Logger for FakeLogger {
//! #     fn log(&self, record: Record) { unimplemented!() }
//! # }
//! # fn find_scored_route(payer: PublicKey, route_params: RouteParameters, network_graph: NetworkGraph<&FakeLogger>) {
//! # let logger = FakeLogger {};
//! #
//! // Use the default channel penalties.
//! let params = ProbabilisticScoringFeeParameters::default();
//! let decay_params = ProbabilisticScoringDecayParameters::default();
//! let scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
//!
//! // Or use custom channel penalties.
//! let params = ProbabilisticScoringFeeParameters {
//!     liquidity_penalty_multiplier_msat: 2 * 1000,
//!     ..ProbabilisticScoringFeeParameters::default()
//! };
//! let decay_params = ProbabilisticScoringDecayParameters::default();
//! let scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
//! # let random_seed_bytes = [42u8; 32];
//!
//! let route = find_route(&payer, &route_params, &network_graph, None, &logger, &scorer, &params, &random_seed_bytes);
//! # }
//! ```
//!
//! # Note
//!
//! Persisting when built with feature `no-std` and restoring without it, or vice versa, uses
//! different types and thus is undefined.
//!
//! [`find_route`]: crate::routing::router::find_route

use crate::ln::msgs::DecodeError;
use crate::routing::gossip::{EffectiveCapacity, NetworkGraph, NodeId};
use crate::routing::router::{Path, CandidateRouteHop};
use crate::util::ser::{Readable, ReadableArgs, Writeable, Writer};
use crate::util::logger::Logger;
use crate::util::time::Time;

use crate::prelude::*;
use core::{cmp, fmt};
use core::cell::{RefCell, RefMut, Ref};
use core::convert::TryInto;
use core::ops::{Deref, DerefMut};
use core::time::Duration;
use crate::io::{self, Read};
use crate::sync::{Mutex, MutexGuard, RwLock, RwLockReadGuard, RwLockWriteGuard};

/// We define Score ever-so-slightly differently based on whether we are being built for C bindings
/// or not. For users, `LockableScore` must somehow be writeable to disk. For Rust users, this is
/// no problem - you move a `Score` that implements `Writeable` into a `Mutex`, lock it, and now
/// you have the original, concrete, `Score` type, which presumably implements `Writeable`.
///
/// For C users, once you've moved the `Score` into a `LockableScore` all you have after locking it
/// is an opaque trait object with an opaque pointer with no type info. Users could take the unsafe
/// approach of blindly casting that opaque pointer to a concrete type and calling `Writeable` from
/// there, but other languages downstream of the C bindings (e.g. Java) can't even do that.
/// Instead, we really want `Score` and `LockableScore` to implement `Writeable` directly, which we
/// do here by defining `Score` differently for `cfg(c_bindings)`.
macro_rules! define_score { ($($supertrait: path)*) => {
/// An interface used to score payment channels for path finding.
///
/// `ScoreLookUp` is used to determine the penalty for a given channel.
///
/// Scoring is in terms of fees willing to be paid in order to avoid routing through a channel.
pub trait ScoreLookUp {
        /// A configurable type which should contain various passed-in parameters for configuring the scorer,
        /// on a per-routefinding-call basis through to the scorer methods,
        /// which are used to determine the parameters for the suitability of channels for use.
        type ScoreParams;
        /// Returns the fee in msats willing to be paid to avoid routing `send_amt_msat` through the
        /// given channel in the direction from `source` to `target`.
        ///
        /// The channel's capacity (less any other MPP parts that are also being considered for use in
        /// the same payment) is given by `capacity_msat`. It may be determined from various sources
        /// such as a chain data, network gossip, or invoice hints. For invoice hints, a capacity near
        /// [`u64::max_value`] is given to indicate sufficient capacity for the invoice's full amount.
        /// Thus, implementations should be overflow-safe.
        fn channel_penalty_msat(
                &self, candidate: &CandidateRouteHop, usage: ChannelUsage, score_params: &Self::ScoreParams
        ) -> u64;
}

/// `ScoreUpdate` is used to update the scorer's internal state after a payment attempt.
pub trait ScoreUpdate {
        /// Handles updating channel penalties after failing to route through a channel.
        fn payment_path_failed(&mut self, path: &Path, short_channel_id: u64);

        /// Handles updating channel penalties after successfully routing along a path.
        fn payment_path_successful(&mut self, path: &Path);

        /// Handles updating channel penalties after a probe over the given path failed.
        fn probe_failed(&mut self, path: &Path, short_channel_id: u64);

        /// Handles updating channel penalties after a probe over the given path succeeded.
        fn probe_successful(&mut self, path: &Path);
}

/// A trait which can both lookup and update routing channel penalty scores.
///
/// This is used in places where both bounds are required and implemented for all types which
/// implement [`ScoreLookUp`] and [`ScoreUpdate`].
///
/// Bindings users may need to manually implement this for their custom scoring implementations.
pub trait Score : ScoreLookUp + ScoreUpdate $(+ $supertrait)* {}

#[cfg(not(c_bindings))]
impl<T: ScoreLookUp + ScoreUpdate $(+ $supertrait)*> Score for T {}

#[cfg(not(c_bindings))]
impl<S: ScoreLookUp, T: Deref<Target=S>> ScoreLookUp for T {
        type ScoreParams = S::ScoreParams;
        fn channel_penalty_msat(
                &self, candidate: &CandidateRouteHop, usage: ChannelUsage, score_params: &Self::ScoreParams
        ) -> u64 {
                self.deref().channel_penalty_msat(candidate, usage, score_params)
        }
}

#[cfg(not(c_bindings))]
impl<S: ScoreUpdate, T: DerefMut<Target=S>> ScoreUpdate for T {
        fn payment_path_failed(&mut self, path: &Path, short_channel_id: u64) {
                self.deref_mut().payment_path_failed(path, short_channel_id)
        }

        fn payment_path_successful(&mut self, path: &Path) {
                self.deref_mut().payment_path_successful(path)
        }

        fn probe_failed(&mut self, path: &Path, short_channel_id: u64) {
                self.deref_mut().probe_failed(path, short_channel_id)
        }

        fn probe_successful(&mut self, path: &Path) {
                self.deref_mut().probe_successful(path)
        }
}
} }

#[cfg(c_bindings)]
define_score!(Writeable);

#[cfg(not(c_bindings))]
define_score!();

/// A scorer that is accessed under a lock.
///
/// Needed so that calls to [`ScoreLookUp::channel_penalty_msat`] in [`find_route`] can be made while
/// having shared ownership of a scorer but without requiring internal locking in [`ScoreUpdate`]
/// implementations. Internal locking would be detrimental to route finding performance and could
/// result in [`ScoreLookUp::channel_penalty_msat`] returning a different value for the same channel.
///
/// [`find_route`]: crate::routing::router::find_route
pub trait LockableScore<'a> {
        /// The [`ScoreUpdate`] type.
        type ScoreUpdate: 'a + ScoreUpdate;
        /// The [`ScoreLookUp`] type.
        type ScoreLookUp: 'a + ScoreLookUp;

        /// The write locked [`ScoreUpdate`] type.
        type WriteLocked: DerefMut<Target = Self::ScoreUpdate> + Sized;

        /// The read locked [`ScoreLookUp`] type.
        type ReadLocked: Deref<Target = Self::ScoreLookUp> + Sized;

        /// Returns read locked scorer.
        fn read_lock(&'a self) -> Self::ReadLocked;

        /// Returns write locked scorer.
        fn write_lock(&'a self) -> Self::WriteLocked;
}

/// Refers to a scorer that is accessible under lock and also writeable to disk
///
/// We need this trait to be able to pass in a scorer to `lightning-background-processor` that will enable us to
/// use the Persister to persist it.
pub trait WriteableScore<'a>: LockableScore<'a> + Writeable {}

#[cfg(not(c_bindings))]
impl<'a, T> WriteableScore<'a> for T where T: LockableScore<'a> + Writeable {}
#[cfg(not(c_bindings))]
impl<'a, T: Score + 'a> LockableScore<'a> for Mutex<T> {
        type ScoreUpdate = T;
        type ScoreLookUp = T;

        type WriteLocked = MutexGuard<'a, Self::ScoreUpdate>;
        type ReadLocked = MutexGuard<'a, Self::ScoreLookUp>;

        fn read_lock(&'a self) -> Self::ReadLocked {
                Mutex::lock(self).unwrap()
        }

        fn write_lock(&'a self) -> Self::WriteLocked {
                Mutex::lock(self).unwrap()
        }
}

#[cfg(not(c_bindings))]
impl<'a, T: Score + 'a> LockableScore<'a> for RefCell<T> {
        type ScoreUpdate = T;
        type ScoreLookUp = T;

        type WriteLocked = RefMut<'a, Self::ScoreUpdate>;
        type ReadLocked = Ref<'a, Self::ScoreLookUp>;

        fn write_lock(&'a self) -> Self::WriteLocked {
                self.borrow_mut()
        }

        fn read_lock(&'a self) -> Self::ReadLocked {
                self.borrow()
        }
}

#[cfg(not(c_bindings))]
impl<'a, T: Score + 'a> LockableScore<'a> for RwLock<T> {
        type ScoreUpdate = T;
        type ScoreLookUp = T;

        type WriteLocked = RwLockWriteGuard<'a, Self::ScoreLookUp>;
        type ReadLocked = RwLockReadGuard<'a, Self::ScoreUpdate>;

        fn read_lock(&'a self) -> Self::ReadLocked {
                RwLock::read(self).unwrap()
        }

        fn write_lock(&'a self) -> Self::WriteLocked {
                RwLock::write(self).unwrap()
        }
}

#[cfg(c_bindings)]
/// A concrete implementation of [`LockableScore`] which supports multi-threading.
pub struct MultiThreadedLockableScore<T: Score> {
        score: RwLock<T>,
}

#[cfg(c_bindings)]
impl<'a, T: Score + 'a> LockableScore<'a> for MultiThreadedLockableScore<T> {
        type ScoreUpdate = T;
        type ScoreLookUp = T;
        type WriteLocked = MultiThreadedScoreLockWrite<'a, Self::ScoreUpdate>;
        type ReadLocked = MultiThreadedScoreLockRead<'a, Self::ScoreLookUp>;

        fn read_lock(&'a self) -> Self::ReadLocked {
                MultiThreadedScoreLockRead(self.score.read().unwrap())
        }

        fn write_lock(&'a self) -> Self::WriteLocked {
                MultiThreadedScoreLockWrite(self.score.write().unwrap())
        }
}

#[cfg(c_bindings)]
impl<T: Score> Writeable for MultiThreadedLockableScore<T> {
        fn write<W: Writer>(&self, writer: &mut W) -> Result<(), io::Error> {
                self.score.read().unwrap().write(writer)
        }
}

#[cfg(c_bindings)]
impl<'a, T: Score + 'a> WriteableScore<'a> for MultiThreadedLockableScore<T> {}

#[cfg(c_bindings)]
impl<T: Score> MultiThreadedLockableScore<T> {
        /// Creates a new [`MultiThreadedLockableScore`] given an underlying [`Score`].
        pub fn new(score: T) -> Self {
                MultiThreadedLockableScore { score: RwLock::new(score) }
        }
}

#[cfg(c_bindings)]
/// A locked `MultiThreadedLockableScore`.
pub struct MultiThreadedScoreLockRead<'a, T: Score>(RwLockReadGuard<'a, T>);

#[cfg(c_bindings)]
/// A locked `MultiThreadedLockableScore`.
pub struct MultiThreadedScoreLockWrite<'a, T: Score>(RwLockWriteGuard<'a, T>);

#[cfg(c_bindings)]
impl<'a, T: 'a + Score> Deref for MultiThreadedScoreLockRead<'a, T> {
        type Target = T;

        fn deref(&self) -> &Self::Target {
                self.0.deref()
        }
}

#[cfg(c_bindings)]
impl<'a, T: Score> ScoreLookUp for MultiThreadedScoreLockRead<'a, T> {
        type ScoreParams = T::ScoreParams;
        fn channel_penalty_msat(&self, candidate:&CandidateRouteHop, usage: ChannelUsage, score_params: &Self::ScoreParams
        ) -> u64 {
                self.0.channel_penalty_msat(candidate, usage, score_params)
        }
}

#[cfg(c_bindings)]
impl<'a, T: Score> Writeable for MultiThreadedScoreLockWrite<'a, T> {
        fn write<W: Writer>(&self, writer: &mut W) -> Result<(), io::Error> {
                self.0.write(writer)
        }
}

#[cfg(c_bindings)]
impl<'a, T: 'a + Score> Deref for MultiThreadedScoreLockWrite<'a, T> {
        type Target = T;

        fn deref(&self) -> &Self::Target {
                self.0.deref()
        }
}

#[cfg(c_bindings)]
impl<'a, T: 'a + Score> DerefMut for MultiThreadedScoreLockWrite<'a, T> {
        fn deref_mut(&mut self) -> &mut Self::Target {
                self.0.deref_mut()
        }
}

#[cfg(c_bindings)]
impl<'a, T: Score> ScoreUpdate for MultiThreadedScoreLockWrite<'a, T> {
        fn payment_path_failed(&mut self, path: &Path, short_channel_id: u64) {
                self.0.payment_path_failed(path, short_channel_id)
        }

        fn payment_path_successful(&mut self, path: &Path) {
                self.0.payment_path_successful(path)
        }

        fn probe_failed(&mut self, path: &Path, short_channel_id: u64) {
                self.0.probe_failed(path, short_channel_id)
        }

        fn probe_successful(&mut self, path: &Path) {
                self.0.probe_successful(path)
        }
}


/// Proposed use of a channel passed as a parameter to [`ScoreLookUp::channel_penalty_msat`].
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct ChannelUsage {
        /// The amount to send through the channel, denominated in millisatoshis.
        pub amount_msat: u64,

        /// Total amount, denominated in millisatoshis, already allocated to send through the channel
        /// as part of a multi-path payment.
        pub inflight_htlc_msat: u64,

        /// The effective capacity of the channel.
        pub effective_capacity: EffectiveCapacity,
}

#[derive(Clone)]
/// [`ScoreLookUp`] implementation that uses a fixed penalty.
pub struct FixedPenaltyScorer {
        penalty_msat: u64,
}

impl FixedPenaltyScorer {
        /// Creates a new scorer using `penalty_msat`.
        pub fn with_penalty(penalty_msat: u64) -> Self {
                Self { penalty_msat }
        }
}

impl ScoreLookUp for FixedPenaltyScorer {
        type ScoreParams = ();
        fn channel_penalty_msat(&self, _: &CandidateRouteHop, _: ChannelUsage, _score_params: &Self::ScoreParams) -> u64 {
                self.penalty_msat
        }
}

impl ScoreUpdate for FixedPenaltyScorer {
        fn payment_path_failed(&mut self, _path: &Path, _short_channel_id: u64) {}

        fn payment_path_successful(&mut self, _path: &Path) {}

        fn probe_failed(&mut self, _path: &Path, _short_channel_id: u64) {}

        fn probe_successful(&mut self, _path: &Path) {}
}

impl Writeable for FixedPenaltyScorer {
        #[inline]
        fn write<W: Writer>(&self, w: &mut W) -> Result<(), io::Error> {
                write_tlv_fields!(w, {});
                Ok(())
        }
}

impl ReadableArgs<u64> for FixedPenaltyScorer {
        #[inline]
        fn read<R: Read>(r: &mut R, penalty_msat: u64) -> Result<Self, DecodeError> {
                read_tlv_fields!(r, {});
                Ok(Self { penalty_msat })
        }
}

#[cfg(not(feature = "no-std"))]
type ConfiguredTime = crate::util::time::MonotonicTime;
#[cfg(feature = "no-std")]
use crate::util::time::Eternity;
#[cfg(feature = "no-std")]
type ConfiguredTime = Eternity;

/// [`ScoreLookUp`] implementation using channel success probability distributions.
///
/// Channels are tracked with upper and lower liquidity bounds - when an HTLC fails at a channel,
/// we learn that the upper-bound on the available liquidity is lower than the amount of the HTLC.
/// When a payment is forwarded through a channel (but fails later in the route), we learn the
/// lower-bound on the channel's available liquidity must be at least the value of the HTLC.
///
/// These bounds are then used to determine a success probability using the formula from
/// *Optimally Reliable & Cheap Payment Flows on the Lightning Network* by Rene Pickhardt
/// and Stefan Richter [[1]] (i.e. `(upper_bound - payment_amount) / (upper_bound - lower_bound)`).
///
/// This probability is combined with the [`liquidity_penalty_multiplier_msat`] and
/// [`liquidity_penalty_amount_multiplier_msat`] parameters to calculate a concrete penalty in
/// milli-satoshis. The penalties, when added across all hops, have the property of being linear in
/// terms of the entire path's success probability. This allows the router to directly compare
/// penalties for different paths. See the documentation of those parameters for the exact formulas.
///
/// The liquidity bounds are decayed by halving them every [`liquidity_offset_half_life`].
///
/// Further, we track the history of our upper and lower liquidity bounds for each channel,
/// allowing us to assign a second penalty (using [`historical_liquidity_penalty_multiplier_msat`]
/// and [`historical_liquidity_penalty_amount_multiplier_msat`]) based on the same probability
/// formula, but using the history of a channel rather than our latest estimates for the liquidity
/// bounds.
///
/// # Note
///
/// Mixing the `no-std` feature between serialization and deserialization results in undefined
/// behavior.
///
/// [1]: https://arxiv.org/abs/2107.05322
/// [`liquidity_penalty_multiplier_msat`]: ProbabilisticScoringFeeParameters::liquidity_penalty_multiplier_msat
/// [`liquidity_penalty_amount_multiplier_msat`]: ProbabilisticScoringFeeParameters::liquidity_penalty_amount_multiplier_msat
/// [`liquidity_offset_half_life`]: ProbabilisticScoringDecayParameters::liquidity_offset_half_life
/// [`historical_liquidity_penalty_multiplier_msat`]: ProbabilisticScoringFeeParameters::historical_liquidity_penalty_multiplier_msat
/// [`historical_liquidity_penalty_amount_multiplier_msat`]: ProbabilisticScoringFeeParameters::historical_liquidity_penalty_amount_multiplier_msat
pub type ProbabilisticScorer<G, L> = ProbabilisticScorerUsingTime::<G, L, ConfiguredTime>;

/// Probabilistic [`ScoreLookUp`] implementation.
///
/// This is not exported to bindings users generally all users should use the [`ProbabilisticScorer`] type alias.
pub struct ProbabilisticScorerUsingTime<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time>
where L::Target: Logger {
        decay_params: ProbabilisticScoringDecayParameters,
        network_graph: G,
        logger: L,
        // TODO: Remove entries of closed channels.
        channel_liquidities: HashMap<u64, ChannelLiquidity<T>>,
}

/// Parameters for configuring [`ProbabilisticScorer`].
///
/// Used to configure base, liquidity, and amount penalties, the sum of which comprises the channel
/// penalty (i.e., the amount in msats willing to be paid to avoid routing through the channel).
///
/// The penalty applied to any channel by the [`ProbabilisticScorer`] is the sum of each of the
/// parameters here.
#[derive(Clone)]
pub struct ProbabilisticScoringFeeParameters {
        /// A fixed penalty in msats to apply to each channel.
        ///
        /// Default value: 500 msat
        pub base_penalty_msat: u64,

        /// A multiplier used with the total amount flowing over a channel to calculate a fixed penalty
        /// applied to each channel, in excess of the [`base_penalty_msat`].
        ///
        /// The purpose of the amount penalty is to avoid having fees dominate the channel cost (i.e.,
        /// fees plus penalty) for large payments. The penalty is computed as the product of this
        /// multiplier and `2^30`ths of the total amount flowing over a channel (i.e. the payment
        /// amount plus the amount of any other HTLCs flowing we sent over the same channel).
        ///
        /// ie `base_penalty_amount_multiplier_msat * amount_msat / 2^30`
        ///
        /// Default value: 8,192 msat
        ///
        /// [`base_penalty_msat`]: Self::base_penalty_msat
        pub base_penalty_amount_multiplier_msat: u64,

        /// A multiplier used in conjunction with the negative `log10` of the channel's success
        /// probability for a payment, as determined by our latest estimates of the channel's
        /// liquidity, to determine the liquidity penalty.
        ///
        /// The penalty is based in part on the knowledge learned from prior successful and unsuccessful
        /// payments. This knowledge is decayed over time based on [`liquidity_offset_half_life`]. The
        /// penalty is effectively limited to `2 * liquidity_penalty_multiplier_msat` (corresponding to
        /// lower bounding the success probability to `0.01`) when the amount falls within the
        /// uncertainty bounds of the channel liquidity balance. Amounts above the upper bound will
        /// result in a `u64::max_value` penalty, however.
        ///
        /// `-log10(success_probability) * liquidity_penalty_multiplier_msat`
        ///
        /// Default value: 30,000 msat
        ///
        /// [`liquidity_offset_half_life`]: ProbabilisticScoringDecayParameters::liquidity_offset_half_life
        pub liquidity_penalty_multiplier_msat: u64,

        /// A multiplier used in conjunction with the total amount flowing over a channel and the
        /// negative `log10` of the channel's success probability for the payment, as determined by our
        /// latest estimates of the channel's liquidity, to determine the amount penalty.
        ///
        /// The purpose of the amount penalty is to avoid having fees dominate the channel cost (i.e.,
        /// fees plus penalty) for large payments. The penalty is computed as the product of this
        /// multiplier and `2^20`ths of the amount flowing over this channel, weighted by the negative
        /// `log10` of the success probability.
        ///
        /// `-log10(success_probability) * liquidity_penalty_amount_multiplier_msat * amount_msat / 2^20`
        ///
        /// In practice, this means for 0.1 success probability (`-log10(0.1) == 1`) each `2^20`th of
        /// the amount will result in a penalty of the multiplier. And, as the success probability
        /// decreases, the negative `log10` weighting will increase dramatically. For higher success
        /// probabilities, the multiplier will have a decreasing effect as the negative `log10` will
        /// fall below `1`.
        ///
        /// Default value: 192 msat
        pub liquidity_penalty_amount_multiplier_msat: u64,

        /// A multiplier used in conjunction with the negative `log10` of the channel's success
        /// probability for the payment, as determined based on the history of our estimates of the
        /// channel's available liquidity, to determine a penalty.
        ///
        /// This penalty is similar to [`liquidity_penalty_multiplier_msat`], however, instead of using
        /// only our latest estimate for the current liquidity available in the channel, it estimates
        /// success probability based on the estimated liquidity available in the channel through
        /// history. Specifically, every time we update our liquidity bounds on a given channel, we
        /// track which of several buckets those bounds fall into, exponentially decaying the
        /// probability of each bucket as new samples are added.
        ///
        /// Default value: 10,000 msat
        ///
        /// [`liquidity_penalty_multiplier_msat`]: Self::liquidity_penalty_multiplier_msat
        pub historical_liquidity_penalty_multiplier_msat: u64,

        /// A multiplier used in conjunction with the total amount flowing over a channel and the
        /// negative `log10` of the channel's success probability for the payment, as determined based
        /// on the history of our estimates of the channel's available liquidity, to determine a
        /// penalty.
        ///
        /// The purpose of the amount penalty is to avoid having fees dominate the channel cost for
        /// large payments. The penalty is computed as the product of this multiplier and `2^20`ths
        /// of the amount flowing over this channel, weighted by the negative `log10` of the success
        /// probability.
        ///
        /// This penalty is similar to [`liquidity_penalty_amount_multiplier_msat`], however, instead
        /// of using only our latest estimate for the current liquidity available in the channel, it
        /// estimates success probability based on the estimated liquidity available in the channel
        /// through history. Specifically, every time we update our liquidity bounds on a given
        /// channel, we track which of several buckets those bounds fall into, exponentially decaying
        /// the probability of each bucket as new samples are added.
        ///
        /// Default value: 64 msat
        ///
        /// [`liquidity_penalty_amount_multiplier_msat`]: Self::liquidity_penalty_amount_multiplier_msat
        pub historical_liquidity_penalty_amount_multiplier_msat: u64,

        /// Manual penalties used for the given nodes. Allows to set a particular penalty for a given
        /// node. Note that a manual penalty of `u64::max_value()` means the node would not ever be
        /// considered during path finding.
        ///
        /// This is not exported to bindings users
        pub manual_node_penalties: HashMap<NodeId, u64>,

        /// This penalty is applied when `htlc_maximum_msat` is equal to or larger than half of the
        /// channel's capacity, (ie. htlc_maximum_msat >= 0.5 * channel_capacity) which makes us
        /// prefer nodes with a smaller `htlc_maximum_msat`. We treat such nodes preferentially
        /// as this makes balance discovery attacks harder to execute, thereby creating an incentive
        /// to restrict `htlc_maximum_msat` and improve privacy.
        ///
        /// Default value: 250 msat
        pub anti_probing_penalty_msat: u64,

        /// This penalty is applied when the total amount flowing over a channel exceeds our current
        /// estimate of the channel's available liquidity. The total amount is the amount of the
        /// current HTLC plus any HTLCs which we've sent over the same channel.
        ///
        /// Note that in this case all other penalties, including the
        /// [`liquidity_penalty_multiplier_msat`] and [`liquidity_penalty_amount_multiplier_msat`]-based
        /// penalties, as well as the [`base_penalty_msat`] and the [`anti_probing_penalty_msat`], if
        /// applicable, are still included in the overall penalty.
        ///
        /// If you wish to avoid creating paths with such channels entirely, setting this to a value of
        /// `u64::max_value()` will guarantee that.
        ///
        /// Default value: 1_0000_0000_000 msat (1 Bitcoin)
        ///
        /// [`liquidity_penalty_multiplier_msat`]: Self::liquidity_penalty_multiplier_msat
        /// [`liquidity_penalty_amount_multiplier_msat`]: Self::liquidity_penalty_amount_multiplier_msat
        /// [`base_penalty_msat`]: Self::base_penalty_msat
        /// [`anti_probing_penalty_msat`]: Self::anti_probing_penalty_msat
        pub considered_impossible_penalty_msat: u64,

        /// In order to calculate most of the scores above, we must first convert a lower and upper
        /// bound on the available liquidity in a channel into the probability that we think a payment
        /// will succeed. That probability is derived from a Probability Density Function for where we
        /// think the liquidity in a channel likely lies, given such bounds.
        ///
        /// If this flag is set, that PDF is simply a constant - we assume that the actual available
        /// liquidity in a channel is just as likely to be at any point between our lower and upper
        /// bounds.
        ///
        /// If this flag is *not* set, that PDF is `(x - 0.5*capacity) ^ 2`. That is, we use an
        /// exponential curve which expects the liquidity of a channel to lie "at the edges". This
        /// matches experimental results - most routing nodes do not aggressively rebalance their
        /// channels and flows in the network are often unbalanced, leaving liquidity usually
        /// unavailable.
        ///
        /// Thus, for the "best" routes, leave this flag `false`. However, the flag does imply a number
        /// of floating-point multiplications in the hottest routing code, which may lead to routing
        /// performance degradation on some machines.
        ///
        /// Default value: false
        pub linear_success_probability: bool,
}

impl Default for ProbabilisticScoringFeeParameters {
        fn default() -> Self {
                Self {
                        base_penalty_msat: 500,
                        base_penalty_amount_multiplier_msat: 8192,
                        liquidity_penalty_multiplier_msat: 30_000,
                        liquidity_penalty_amount_multiplier_msat: 192,
                        manual_node_penalties: HashMap::new(),
                        anti_probing_penalty_msat: 250,
                        considered_impossible_penalty_msat: 1_0000_0000_000,
                        historical_liquidity_penalty_multiplier_msat: 10_000,
                        historical_liquidity_penalty_amount_multiplier_msat: 64,
                        linear_success_probability: false,
                }
        }
}

impl ProbabilisticScoringFeeParameters {
        /// Marks the node with the given `node_id` as banned,
        /// i.e it will be avoided during path finding.
        pub fn add_banned(&mut self, node_id: &NodeId) {
                self.manual_node_penalties.insert(*node_id, u64::max_value());
        }

        /// Marks all nodes in the given list as banned, i.e.,
        /// they will be avoided during path finding.
        pub fn add_banned_from_list(&mut self, node_ids: Vec<NodeId>) {
                for id in node_ids {
                        self.manual_node_penalties.insert(id, u64::max_value());
                }
        }

        /// Removes the node with the given `node_id` from the list of nodes to avoid.
        pub fn remove_banned(&mut self, node_id: &NodeId) {
                self.manual_node_penalties.remove(node_id);
        }

        /// Sets a manual penalty for the given node.
        pub fn set_manual_penalty(&mut self, node_id: &NodeId, penalty: u64) {
                self.manual_node_penalties.insert(*node_id, penalty);
        }

        /// Removes the node with the given `node_id` from the list of manual penalties.
        pub fn remove_manual_penalty(&mut self, node_id: &NodeId) {
                self.manual_node_penalties.remove(node_id);
        }

        /// Clears the list of manual penalties that are applied during path finding.
        pub fn clear_manual_penalties(&mut self) {
                self.manual_node_penalties = HashMap::new();
        }
}

#[cfg(test)]
impl ProbabilisticScoringFeeParameters {
        fn zero_penalty() -> Self {
                Self {
                        base_penalty_msat: 0,
                        base_penalty_amount_multiplier_msat: 0,
                        liquidity_penalty_multiplier_msat: 0,
                        liquidity_penalty_amount_multiplier_msat: 0,
                        historical_liquidity_penalty_multiplier_msat: 0,
                        historical_liquidity_penalty_amount_multiplier_msat: 0,
                        manual_node_penalties: HashMap::new(),
                        anti_probing_penalty_msat: 0,
                        considered_impossible_penalty_msat: 0,
                        linear_success_probability: true,
                }
        }
}

/// Parameters for configuring [`ProbabilisticScorer`].
///
/// Used to configure decay parameters that are static throughout the lifetime of the scorer.
/// these decay parameters affect the score of the channel penalty and are not changed on a
/// per-route penalty cost call.
#[derive(Copy, Clone)]
pub struct ProbabilisticScoringDecayParameters {
        /// If we aren't learning any new datapoints for a channel, the historical liquidity bounds
        /// tracking can simply live on with increasingly stale data. Instead, when a channel has not
        /// seen a liquidity estimate update for this amount of time, the historical datapoints are
        /// decayed by half.
        /// For an example of historical_no_updates_half_life being used see [`historical_estimated_channel_liquidity_probabilities`]
        ///
        /// Note that after 16 or more half lives all historical data will be completely gone.
        ///
        /// Default value: 14 days
        ///
        /// [`historical_estimated_channel_liquidity_probabilities`]: ProbabilisticScorerUsingTime::historical_estimated_channel_liquidity_probabilities
        pub historical_no_updates_half_life: Duration,

        /// Whenever this amount of time elapses since the last update to a channel's liquidity bounds,
        /// the distance from the bounds to "zero" is cut in half. In other words, the lower-bound on
        /// the available liquidity is halved and the upper-bound moves half-way to the channel's total
        /// capacity.
        ///
        /// Because halving the liquidity bounds grows the uncertainty on the channel's liquidity,
        /// the penalty for an amount within the new bounds may change. See the [`ProbabilisticScorer`]
        /// struct documentation for more info on the way the liquidity bounds are used.
        ///
        /// For example, if the channel's capacity is 1 million sats, and the current upper and lower
        /// liquidity bounds are 200,000 sats and 600,000 sats, after this amount of time the upper
        /// and lower liquidity bounds will be decayed to 100,000 and 800,000 sats.
        ///
        /// Default value: 6 hours
        ///
        /// # Note
        ///
        /// When built with the `no-std` feature, time will never elapse. Therefore, the channel
        /// liquidity knowledge will never decay except when the bounds cross.
        pub liquidity_offset_half_life: Duration,
}

impl Default for ProbabilisticScoringDecayParameters {
        fn default() -> Self {
                Self {
                        liquidity_offset_half_life: Duration::from_secs(6 * 60 * 60),
                        historical_no_updates_half_life: Duration::from_secs(60 * 60 * 24 * 14),
                }
        }
}

#[cfg(test)]
impl ProbabilisticScoringDecayParameters {
        fn zero_penalty() -> Self {
                Self {
                        liquidity_offset_half_life: Duration::from_secs(6 * 60 * 60),
                        historical_no_updates_half_life: Duration::from_secs(60 * 60 * 24 * 14),
                }
        }
}

/// Accounting for channel liquidity balance uncertainty.
///
/// Direction is defined in terms of [`NodeId`] partial ordering, where the source node is the
/// first node in the ordering of the channel's counterparties. Thus, swapping the two liquidity
/// offset fields gives the opposite direction.
struct ChannelLiquidity<T: Time> {
        /// Lower channel liquidity bound in terms of an offset from zero.
        min_liquidity_offset_msat: u64,

        /// Upper channel liquidity bound in terms of an offset from the effective capacity.
        max_liquidity_offset_msat: u64,

        /// Time when the liquidity bounds were last modified.
        last_updated: T,

        min_liquidity_offset_history: HistoricalBucketRangeTracker,
        max_liquidity_offset_history: HistoricalBucketRangeTracker,
}

/// A snapshot of [`ChannelLiquidity`] in one direction assuming a certain channel capacity and
/// decayed with a given half life.
struct DirectedChannelLiquidity<L: Deref<Target = u64>, BRT: Deref<Target = HistoricalBucketRangeTracker>, T: Time, U: Deref<Target = T>> {
        min_liquidity_offset_msat: L,
        max_liquidity_offset_msat: L,
        liquidity_history: HistoricalMinMaxBuckets<BRT>,
        capacity_msat: u64,
        last_updated: U,
        now: T,
        decay_params: ProbabilisticScoringDecayParameters,
}

impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time> ProbabilisticScorerUsingTime<G, L, T> where L::Target: Logger {
        /// Creates a new scorer using the given scoring parameters for sending payments from a node
        /// through a network graph.
        pub fn new(decay_params: ProbabilisticScoringDecayParameters, network_graph: G, logger: L) -> Self {
                Self {
                        decay_params,
                        network_graph,
                        logger,
                        channel_liquidities: HashMap::new(),
                }
        }

        #[cfg(test)]
        fn with_channel(mut self, short_channel_id: u64, liquidity: ChannelLiquidity<T>) -> Self {
                assert!(self.channel_liquidities.insert(short_channel_id, liquidity).is_none());
                self
        }

        /// Dump the contents of this scorer into the configured logger.
        ///
        /// Note that this writes roughly one line per channel for which we have a liquidity estimate,
        /// which may be a substantial amount of log output.
        pub fn debug_log_liquidity_stats(&self) {
                let now = T::now();

                let graph = self.network_graph.read_only();
                for (scid, liq) in self.channel_liquidities.iter() {
                        if let Some(chan_debug) = graph.channels().get(scid) {
                                let log_direction = |source, target| {
                                        if let Some((directed_info, _)) = chan_debug.as_directed_to(target) {
                                                let amt = directed_info.effective_capacity().as_msat();
                                                let dir_liq = liq.as_directed(source, target, amt, self.decay_params);

                                                let (min_buckets, max_buckets) = dir_liq.liquidity_history
                                                        .get_decayed_buckets(now, *dir_liq.last_updated,
                                                                self.decay_params.historical_no_updates_half_life)
                                                        .unwrap_or(([0; 32], [0; 32]));

                                                log_debug!(self.logger, core::concat!(
                                                        "Liquidity from {} to {} via {} is in the range ({}, {}).\n",
                                                        "\tHistorical min liquidity bucket relative probabilities:\n",
                                                        "\t\t{} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {}\n",
                                                        "\tHistorical max liquidity bucket relative probabilities:\n",
                                                        "\t\t{} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {}"),
                                                        source, target, scid, dir_liq.min_liquidity_msat(), dir_liq.max_liquidity_msat(),
                                                        min_buckets[ 0], min_buckets[ 1], min_buckets[ 2], min_buckets[ 3],
                                                        min_buckets[ 4], min_buckets[ 5], min_buckets[ 6], min_buckets[ 7],
                                                        min_buckets[ 8], min_buckets[ 9], min_buckets[10], min_buckets[11],
                                                        min_buckets[12], min_buckets[13], min_buckets[14], min_buckets[15],
                                                        min_buckets[16], min_buckets[17], min_buckets[18], min_buckets[19],
                                                        min_buckets[20], min_buckets[21], min_buckets[22], min_buckets[23],
                                                        min_buckets[24], min_buckets[25], min_buckets[26], min_buckets[27],
                                                        min_buckets[28], min_buckets[29], min_buckets[30], min_buckets[31],
                                                        // Note that the liquidity buckets are an offset from the edge, so we
                                                        // inverse the max order to get the probabilities from zero.
                                                        max_buckets[31], max_buckets[30], max_buckets[29], max_buckets[28],
                                                        max_buckets[27], max_buckets[26], max_buckets[25], max_buckets[24],
                                                        max_buckets[23], max_buckets[22], max_buckets[21], max_buckets[20],
                                                        max_buckets[19], max_buckets[18], max_buckets[17], max_buckets[16],
                                                        max_buckets[15], max_buckets[14], max_buckets[13], max_buckets[12],
                                                        max_buckets[11], max_buckets[10], max_buckets[ 9], max_buckets[ 8],
                                                        max_buckets[ 7], max_buckets[ 6], max_buckets[ 5], max_buckets[ 4],
                                                        max_buckets[ 3], max_buckets[ 2], max_buckets[ 1], max_buckets[ 0]);
                                        } else {
                                                log_debug!(self.logger, "No amount known for SCID {} from {:?} to {:?}", scid, source, target);
                                        }
                                };

                                log_direction(&chan_debug.node_one, &chan_debug.node_two);
                                log_direction(&chan_debug.node_two, &chan_debug.node_one);
                        } else {
                                log_debug!(self.logger, "No network graph entry for SCID {}", scid);
                        }
                }
        }

        /// Query the estimated minimum and maximum liquidity available for sending a payment over the
        /// channel with `scid` towards the given `target` node.
        pub fn estimated_channel_liquidity_range(&self, scid: u64, target: &NodeId) -> Option<(u64, u64)> {
                let graph = self.network_graph.read_only();

                if let Some(chan) = graph.channels().get(&scid) {
                        if let Some(liq) = self.channel_liquidities.get(&scid) {
                                if let Some((directed_info, source)) = chan.as_directed_to(target) {
                                        let amt = directed_info.effective_capacity().as_msat();
                                        let dir_liq = liq.as_directed(source, target, amt, self.decay_params);
                                        return Some((dir_liq.min_liquidity_msat(), dir_liq.max_liquidity_msat()));
                                }
                        }
                }
                None
        }

        /// Query the historical estimated minimum and maximum liquidity available for sending a
        /// payment over the channel with `scid` towards the given `target` node.
        ///
        /// Returns two sets of 32 buckets. The first set describes the lower-bound liquidity history,
        /// the second set describes the upper-bound liquidity history. Each bucket describes the
        /// relative frequency at which we've seen a liquidity bound in the bucket's range relative to
        /// the channel's total capacity, on an arbitrary scale. Because the values are slowly decayed,
        /// more recent data points are weighted more heavily than older datapoints.
        ///
        /// Note that the range of each bucket varies by its location to provide more granular results
        /// at the edges of a channel's capacity, where it is more likely to sit.
        ///
        /// When scoring, the estimated probability that an upper-/lower-bound lies in a given bucket
        /// is calculated by dividing that bucket's value with the total value of all buckets.
        ///
        /// For example, using a lower bucket count for illustrative purposes, a value of
        /// `[0, 0, 0, ..., 0, 32]` indicates that we believe the probability of a bound being very
        /// close to the channel's capacity to be 100%, and have never (recently) seen it in any other
        /// bucket. A value of `[31, 0, 0, ..., 0, 0, 32]` indicates we've seen the bound being both
        /// in the top and bottom bucket, and roughly with similar (recent) frequency.
        ///
        /// Because the datapoints are decayed slowly over time, values will eventually return to
        /// `Some(([1; 32], [1; 32]))` and then to `None` once no datapoints remain.
        ///
        /// In order to fetch a single success probability from the buckets provided here, as used in
        /// the scoring model, see [`Self::historical_estimated_payment_success_probability`].
        pub fn historical_estimated_channel_liquidity_probabilities(&self, scid: u64, target: &NodeId)
        -> Option<([u16; 32], [u16; 32])> {
                let graph = self.network_graph.read_only();

                if let Some(chan) = graph.channels().get(&scid) {
                        if let Some(liq) = self.channel_liquidities.get(&scid) {
                                if let Some((directed_info, source)) = chan.as_directed_to(target) {
                                        let amt = directed_info.effective_capacity().as_msat();
                                        let dir_liq = liq.as_directed(source, target, amt, self.decay_params);

                                        let (min_buckets, mut max_buckets) =
                                                dir_liq.liquidity_history.get_decayed_buckets(
                                                        dir_liq.now, *dir_liq.last_updated,
                                                        self.decay_params.historical_no_updates_half_life
                                                )?;

                                        // Note that the liquidity buckets are an offset from the edge, so we inverse
                                        // the max order to get the probabilities from zero.
                                        max_buckets.reverse();
                                        return Some((min_buckets, max_buckets));
                                }
                        }
                }
                None
        }

        /// Query the probability of payment success sending the given `amount_msat` over the channel
        /// with `scid` towards the given `target` node, based on the historical estimated liquidity
        /// bounds.
        ///
        /// These are the same bounds as returned by
        /// [`Self::historical_estimated_channel_liquidity_probabilities`] (but not those returned by
        /// [`Self::estimated_channel_liquidity_range`]).
        pub fn historical_estimated_payment_success_probability(
                &self, scid: u64, target: &NodeId, amount_msat: u64, params: &ProbabilisticScoringFeeParameters)
        -> Option<f64> {
                let graph = self.network_graph.read_only();

                if let Some(chan) = graph.channels().get(&scid) {
                        if let Some(liq) = self.channel_liquidities.get(&scid) {
                                if let Some((directed_info, source)) = chan.as_directed_to(target) {
                                        let capacity_msat = directed_info.effective_capacity().as_msat();
                                        let dir_liq = liq.as_directed(source, target, capacity_msat, self.decay_params);

                                        return dir_liq.liquidity_history.calculate_success_probability_times_billion(
                                                dir_liq.now, *dir_liq.last_updated,
                                                self.decay_params.historical_no_updates_half_life, &params, amount_msat,
                                                capacity_msat
                                        ).map(|p| p as f64 / (1024 * 1024 * 1024) as f64);
                                }
                        }
                }
                None
        }
}

impl<T: Time> ChannelLiquidity<T> {
        #[inline]
        fn new() -> Self {
                Self {
                        min_liquidity_offset_msat: 0,
                        max_liquidity_offset_msat: 0,
                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                        last_updated: T::now(),
                }
        }

        /// Returns a view of the channel liquidity directed from `source` to `target` assuming
        /// `capacity_msat`.
        fn as_directed(
                &self, source: &NodeId, target: &NodeId, capacity_msat: u64, decay_params: ProbabilisticScoringDecayParameters
        ) -> DirectedChannelLiquidity<&u64, &HistoricalBucketRangeTracker, T, &T> {
                let (min_liquidity_offset_msat, max_liquidity_offset_msat, min_liquidity_offset_history, max_liquidity_offset_history) =
                        if source < target {
                                (&self.min_liquidity_offset_msat, &self.max_liquidity_offset_msat,
                                        &self.min_liquidity_offset_history, &self.max_liquidity_offset_history)
                        } else {
                                (&self.max_liquidity_offset_msat, &self.min_liquidity_offset_msat,
                                        &self.max_liquidity_offset_history, &self.min_liquidity_offset_history)
                        };

                DirectedChannelLiquidity {
                        min_liquidity_offset_msat,
                        max_liquidity_offset_msat,
                        liquidity_history: HistoricalMinMaxBuckets {
                                min_liquidity_offset_history,
                                max_liquidity_offset_history,
                        },
                        capacity_msat,
                        last_updated: &self.last_updated,
                        now: T::now(),
                        decay_params: decay_params,
                }
        }

        /// Returns a mutable view of the channel liquidity directed from `source` to `target` assuming
        /// `capacity_msat`.
        fn as_directed_mut(
                &mut self, source: &NodeId, target: &NodeId, capacity_msat: u64, decay_params: ProbabilisticScoringDecayParameters
        ) -> DirectedChannelLiquidity<&mut u64, &mut HistoricalBucketRangeTracker, T, &mut T> {
                let (min_liquidity_offset_msat, max_liquidity_offset_msat, min_liquidity_offset_history, max_liquidity_offset_history) =
                        if source < target {
                                (&mut self.min_liquidity_offset_msat, &mut self.max_liquidity_offset_msat,
                                        &mut self.min_liquidity_offset_history, &mut self.max_liquidity_offset_history)
                        } else {
                                (&mut self.max_liquidity_offset_msat, &mut self.min_liquidity_offset_msat,
                                        &mut self.max_liquidity_offset_history, &mut self.min_liquidity_offset_history)
                        };

                DirectedChannelLiquidity {
                        min_liquidity_offset_msat,
                        max_liquidity_offset_msat,
                        liquidity_history: HistoricalMinMaxBuckets {
                                min_liquidity_offset_history,
                                max_liquidity_offset_history,
                        },
                        capacity_msat,
                        last_updated: &mut self.last_updated,
                        now: T::now(),
                        decay_params: decay_params,
                }
        }
}

/// Bounds `-log10` to avoid excessive liquidity penalties for payments with low success
/// probabilities.
const NEGATIVE_LOG10_UPPER_BOUND: u64 = 2;

/// The rough cutoff at which our precision falls off and we should stop bothering to try to log a
/// ratio, as X in 1/X.
const PRECISION_LOWER_BOUND_DENOMINATOR: u64 = approx::LOWER_BITS_BOUND;

/// The divisor used when computing the amount penalty.
const AMOUNT_PENALTY_DIVISOR: u64 = 1 << 20;
const BASE_AMOUNT_PENALTY_DIVISOR: u64 = 1 << 30;

/// Raises three `f64`s to the 3rd power, without `powi` because it requires `std` (dunno why).
#[inline(always)]
fn three_f64_pow_3(a: f64, b: f64, c: f64) -> (f64, f64, f64) {
        (a * a * a, b * b * b, c * c * c)
}

/// Given liquidity bounds, calculates the success probability (in the form of a numerator and
/// denominator) of an HTLC. This is a key assumption in our scoring models.
///
/// Must not return a numerator or denominator greater than 2^31 for arguments less than 2^31.
///
/// min_zero_implies_no_successes signals that a `min_liquidity_msat` of 0 means we've not
/// (recently) seen an HTLC successfully complete over this channel.
#[inline(always)]
fn success_probability(
        amount_msat: u64, min_liquidity_msat: u64, max_liquidity_msat: u64, capacity_msat: u64,
        params: &ProbabilisticScoringFeeParameters, min_zero_implies_no_successes: bool,
) -> (u64, u64) {
        debug_assert!(min_liquidity_msat <= amount_msat);
        debug_assert!(amount_msat < max_liquidity_msat);
        debug_assert!(max_liquidity_msat <= capacity_msat);

        let (numerator, mut denominator) =
                if params.linear_success_probability {
                        (max_liquidity_msat - amount_msat,
                                (max_liquidity_msat - min_liquidity_msat).saturating_add(1))
                } else {
                        let capacity = capacity_msat as f64;
                        let min = (min_liquidity_msat as f64) / capacity;
                        let max = (max_liquidity_msat as f64) / capacity;
                        let amount = (amount_msat as f64) / capacity;

                        // Assume the channel has a probability density function of (x - 0.5)^2 for values from
                        // 0 to 1 (where 1 is the channel's full capacity). The success probability given some
                        // liquidity bounds is thus the integral under the curve from the amount to maximum
                        // estimated liquidity, divided by the same integral from the minimum to the maximum
                        // estimated liquidity bounds.
                        //
                        // Because the integral from x to y is simply (y - 0.5)^3 - (x - 0.5)^3, we can
                        // calculate the cumulative density function between the min/max bounds trivially. Note
                        // that we don't bother to normalize the CDF to total to 1, as it will come out in the
                        // division of num / den.
                        let (max_pow, amt_pow, min_pow) = three_f64_pow_3(max - 0.5, amount - 0.5, min - 0.5);
                        let num = max_pow - amt_pow;
                        let den = max_pow - min_pow;

                        // Because our numerator and denominator max out at 0.5^3 we need to multiply them by
                        // quite a large factor to get something useful (ideally in the 2^30 range).
                        const BILLIONISH: f64 = 1024.0 * 1024.0 * 1024.0;
                        let numerator = (num * BILLIONISH) as u64 + 1;
                        let denominator = (den * BILLIONISH) as u64 + 1;
                        debug_assert!(numerator <= 1 << 30, "Got large numerator ({}) from float {}.", numerator, num);
                        debug_assert!(denominator <= 1 << 30, "Got large denominator ({}) from float {}.", denominator, den);
                        (numerator, denominator)
                };

        if min_zero_implies_no_successes && min_liquidity_msat == 0 &&
                denominator < u64::max_value() / 21
        {
                // If we have no knowledge of the channel, scale probability down by ~75%
                // Note that we prefer to increase the denominator rather than decrease the numerator as
                // the denominator is more likely to be larger and thus provide greater precision. This is
                // mostly an overoptimization but makes a large difference in tests.
                denominator = denominator * 21 / 16
        }

        (numerator, denominator)
}

impl<L: Deref<Target = u64>, BRT: Deref<Target = HistoricalBucketRangeTracker>, T: Time, U: Deref<Target = T>> DirectedChannelLiquidity< L, BRT, T, U> {
        /// Returns a liquidity penalty for routing the given HTLC `amount_msat` through the channel in
        /// this direction.
        fn penalty_msat(&self, amount_msat: u64, score_params: &ProbabilisticScoringFeeParameters) -> u64 {
                let available_capacity = self.capacity_msat;
                let max_liquidity_msat = self.max_liquidity_msat();
                let min_liquidity_msat = core::cmp::min(self.min_liquidity_msat(), max_liquidity_msat);

                let mut res = if amount_msat <= min_liquidity_msat {
                        0
                } else if amount_msat >= max_liquidity_msat {
                        // Equivalent to hitting the else clause below with the amount equal to the effective
                        // capacity and without any certainty on the liquidity upper bound, plus the
                        // impossibility penalty.
                        let negative_log10_times_2048 = NEGATIVE_LOG10_UPPER_BOUND * 2048;
                        Self::combined_penalty_msat(amount_msat, negative_log10_times_2048,
                                        score_params.liquidity_penalty_multiplier_msat,
                                        score_params.liquidity_penalty_amount_multiplier_msat)
                                .saturating_add(score_params.considered_impossible_penalty_msat)
                } else {
                        let (numerator, denominator) = success_probability(amount_msat,
                                min_liquidity_msat, max_liquidity_msat, available_capacity, score_params, false);
                        if denominator - numerator < denominator / PRECISION_LOWER_BOUND_DENOMINATOR {
                                // If the failure probability is < 1.5625% (as 1 - numerator/denominator < 1/64),
                                // don't bother trying to use the log approximation as it gets too noisy to be
                                // particularly helpful, instead just round down to 0.
                                0
                        } else {
                                let negative_log10_times_2048 =
                                        approx::negative_log10_times_2048(numerator, denominator);
                                Self::combined_penalty_msat(amount_msat, negative_log10_times_2048,
                                        score_params.liquidity_penalty_multiplier_msat,
                                        score_params.liquidity_penalty_amount_multiplier_msat)
                        }
                };

                if amount_msat >= available_capacity {
                        // We're trying to send more than the capacity, use a max penalty.
                        res = res.saturating_add(Self::combined_penalty_msat(amount_msat,
                                NEGATIVE_LOG10_UPPER_BOUND * 2048,
                                score_params.historical_liquidity_penalty_multiplier_msat,
                                score_params.historical_liquidity_penalty_amount_multiplier_msat));
                        return res;
                }

                if score_params.historical_liquidity_penalty_multiplier_msat != 0 ||
                   score_params.historical_liquidity_penalty_amount_multiplier_msat != 0 {
                        if let Some(cumulative_success_prob_times_billion) = self.liquidity_history
                                .calculate_success_probability_times_billion(self.now, *self.last_updated,
                                        self.decay_params.historical_no_updates_half_life, score_params, amount_msat,
                                        self.capacity_msat)
                        {
                                let historical_negative_log10_times_2048 = approx::negative_log10_times_2048(cumulative_success_prob_times_billion + 1, 1024 * 1024 * 1024);
                                res = res.saturating_add(Self::combined_penalty_msat(amount_msat,
                                        historical_negative_log10_times_2048, score_params.historical_liquidity_penalty_multiplier_msat,
                                        score_params.historical_liquidity_penalty_amount_multiplier_msat));
                        } else {
                                // If we don't have any valid points (or, once decayed, we have less than a full
                                // point), redo the non-historical calculation with no liquidity bounds tracked and
                                // the historical penalty multipliers.
                                let (numerator, denominator) = success_probability(amount_msat, 0,
                                        available_capacity, available_capacity, score_params, true);
                                let negative_log10_times_2048 =
                                        approx::negative_log10_times_2048(numerator, denominator);
                                res = res.saturating_add(Self::combined_penalty_msat(amount_msat, negative_log10_times_2048,
                                        score_params.historical_liquidity_penalty_multiplier_msat,
                                        score_params.historical_liquidity_penalty_amount_multiplier_msat));
                        }
                }

                res
        }

        /// Computes the liquidity penalty from the penalty multipliers.
        #[inline(always)]
        fn combined_penalty_msat(amount_msat: u64, mut negative_log10_times_2048: u64,
                liquidity_penalty_multiplier_msat: u64, liquidity_penalty_amount_multiplier_msat: u64,
        ) -> u64 {
                negative_log10_times_2048 =
                        negative_log10_times_2048.min(NEGATIVE_LOG10_UPPER_BOUND * 2048);

                // Upper bound the liquidity penalty to ensure some channel is selected.
                let liquidity_penalty_msat = negative_log10_times_2048
                        .saturating_mul(liquidity_penalty_multiplier_msat) / 2048;
                let amount_penalty_msat = negative_log10_times_2048
                        .saturating_mul(liquidity_penalty_amount_multiplier_msat)
                        .saturating_mul(amount_msat) / 2048 / AMOUNT_PENALTY_DIVISOR;

                liquidity_penalty_msat.saturating_add(amount_penalty_msat)
        }

        /// Returns the lower bound of the channel liquidity balance in this direction.
        #[inline(always)]
        fn min_liquidity_msat(&self) -> u64 {
                self.decayed_offset_msat(*self.min_liquidity_offset_msat)
        }

        /// Returns the upper bound of the channel liquidity balance in this direction.
        #[inline(always)]
        fn max_liquidity_msat(&self) -> u64 {
                self.capacity_msat
                        .saturating_sub(self.decayed_offset_msat(*self.max_liquidity_offset_msat))
        }

        fn decayed_offset_msat(&self, offset_msat: u64) -> u64 {
                let half_life = self.decay_params.liquidity_offset_half_life.as_secs();
                if half_life != 0 {
                        // Decay the offset by the appropriate number of half lives. If half of the next half
                        // life has passed, approximate an additional three-quarter life to help smooth out the
                        // decay.
                        let elapsed_time = self.now.duration_since(*self.last_updated).as_secs();
                        let half_decays = elapsed_time / (half_life / 2);
                        let decays = half_decays / 2;
                        let decayed_offset_msat = offset_msat.checked_shr(decays as u32).unwrap_or(0);
                        if half_decays % 2 == 0 {
                                decayed_offset_msat
                        } else {
                                // 11_585 / 16_384 ~= core::f64::consts::FRAC_1_SQRT_2
                                // 16_384 == 2^14
                                (decayed_offset_msat as u128 * 11_585 / 16_384) as u64
                        }
                } else {
                        0
                }
        }
}

impl<L: DerefMut<Target = u64>, BRT: DerefMut<Target = HistoricalBucketRangeTracker>, T: Time, U: DerefMut<Target = T>> DirectedChannelLiquidity<L, BRT, T, U> {
        /// Adjusts the channel liquidity balance bounds when failing to route `amount_msat`.
        fn failed_at_channel<Log: Deref>(&mut self, amount_msat: u64, chan_descr: fmt::Arguments, logger: &Log) where Log::Target: Logger {
                let existing_max_msat = self.max_liquidity_msat();
                if amount_msat < existing_max_msat {
                        log_debug!(logger, "Setting max liquidity of {} from {} to {}", chan_descr, existing_max_msat, amount_msat);
                        self.set_max_liquidity_msat(amount_msat);
                } else {
                        log_trace!(logger, "Max liquidity of {} is {} (already less than or equal to {})",
                                chan_descr, existing_max_msat, amount_msat);
                }
                self.update_history_buckets(0);
        }

        /// Adjusts the channel liquidity balance bounds when failing to route `amount_msat` downstream.
        fn failed_downstream<Log: Deref>(&mut self, amount_msat: u64, chan_descr: fmt::Arguments, logger: &Log) where Log::Target: Logger {
                let existing_min_msat = self.min_liquidity_msat();
                if amount_msat > existing_min_msat {
                        log_debug!(logger, "Setting min liquidity of {} from {} to {}", existing_min_msat, chan_descr, amount_msat);
                        self.set_min_liquidity_msat(amount_msat);
                } else {
                        log_trace!(logger, "Min liquidity of {} is {} (already greater than or equal to {})",
                                chan_descr, existing_min_msat, amount_msat);
                }
                self.update_history_buckets(0);
        }

        /// Adjusts the channel liquidity balance bounds when successfully routing `amount_msat`.
        fn successful<Log: Deref>(&mut self, amount_msat: u64, chan_descr: fmt::Arguments, logger: &Log) where Log::Target: Logger {
                let max_liquidity_msat = self.max_liquidity_msat().checked_sub(amount_msat).unwrap_or(0);
                log_debug!(logger, "Subtracting {} from max liquidity of {} (setting it to {})", amount_msat, chan_descr, max_liquidity_msat);
                self.set_max_liquidity_msat(max_liquidity_msat);
                self.update_history_buckets(amount_msat);
        }

        /// Updates the history buckets for this channel. Because the history buckets track what we now
        /// know about the channel's state *prior to our payment* (i.e. what we assume is "steady
        /// state"), we allow the caller to set an offset applied to our liquidity bounds which
        /// represents the amount of the successful payment we just made.
        fn update_history_buckets(&mut self, bucket_offset_msat: u64) {
                let half_lives = self.now.duration_since(*self.last_updated).as_secs()
                        .checked_div(self.decay_params.historical_no_updates_half_life.as_secs())
                        .map(|v| v.try_into().unwrap_or(u32::max_value())).unwrap_or(u32::max_value());
                self.liquidity_history.min_liquidity_offset_history.time_decay_data(half_lives);
                self.liquidity_history.max_liquidity_offset_history.time_decay_data(half_lives);

                let min_liquidity_offset_msat = self.decayed_offset_msat(*self.min_liquidity_offset_msat);
                self.liquidity_history.min_liquidity_offset_history.track_datapoint(
                        min_liquidity_offset_msat + bucket_offset_msat, self.capacity_msat
                );
                let max_liquidity_offset_msat = self.decayed_offset_msat(*self.max_liquidity_offset_msat);
                self.liquidity_history.max_liquidity_offset_history.track_datapoint(
                        max_liquidity_offset_msat.saturating_sub(bucket_offset_msat), self.capacity_msat
                );
        }

        /// Adjusts the lower bound of the channel liquidity balance in this direction.
        fn set_min_liquidity_msat(&mut self, amount_msat: u64) {
                *self.min_liquidity_offset_msat = amount_msat;
                *self.max_liquidity_offset_msat = if amount_msat > self.max_liquidity_msat() {
                        0
                } else {
                        self.decayed_offset_msat(*self.max_liquidity_offset_msat)
                };
                *self.last_updated = self.now;
        }

        /// Adjusts the upper bound of the channel liquidity balance in this direction.
        fn set_max_liquidity_msat(&mut self, amount_msat: u64) {
                *self.max_liquidity_offset_msat = self.capacity_msat.checked_sub(amount_msat).unwrap_or(0);
                *self.min_liquidity_offset_msat = if amount_msat < self.min_liquidity_msat() {
                        0
                } else {
                        self.decayed_offset_msat(*self.min_liquidity_offset_msat)
                };
                *self.last_updated = self.now;
        }
}

impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time> ScoreLookUp for ProbabilisticScorerUsingTime<G, L, T> where L::Target: Logger {
        type ScoreParams = ProbabilisticScoringFeeParameters;
        fn channel_penalty_msat(
                &self, candidate: &CandidateRouteHop, usage: ChannelUsage, score_params: &ProbabilisticScoringFeeParameters
        ) -> u64 {
                let scid = match candidate.short_channel_id() {
                        Some(scid) => scid,
                        None => return 0,
                };
                let target = match candidate.target() {
                        Some(target) => target,
                        None => return 0,
                };
                let source = candidate.source();
                if let Some(penalty) = score_params.manual_node_penalties.get(&target) {
                        return *penalty;
                }

                let base_penalty_msat = score_params.base_penalty_msat.saturating_add(
                        score_params.base_penalty_amount_multiplier_msat
                                .saturating_mul(usage.amount_msat) / BASE_AMOUNT_PENALTY_DIVISOR);

                let mut anti_probing_penalty_msat = 0;
                match usage.effective_capacity {
                        EffectiveCapacity::ExactLiquidity { liquidity_msat: amount_msat } |
                                EffectiveCapacity::HintMaxHTLC { amount_msat } =>
                        {
                                if usage.amount_msat > amount_msat {
                                        return u64::max_value();
                                } else {
                                        return base_penalty_msat;
                                }
                        },
                        EffectiveCapacity::Total { capacity_msat, htlc_maximum_msat } => {
                                if htlc_maximum_msat >= capacity_msat/2 {
                                        anti_probing_penalty_msat = score_params.anti_probing_penalty_msat;
                                }
                        },
                        _ => {},
                }

                let amount_msat = usage.amount_msat.saturating_add(usage.inflight_htlc_msat);
                let capacity_msat = usage.effective_capacity.as_msat();
                self.channel_liquidities
                        .get(&scid)
                        .unwrap_or(&ChannelLiquidity::new())
                        .as_directed(&source, &target, capacity_msat, self.decay_params)
                        .penalty_msat(amount_msat, score_params)
                        .saturating_add(anti_probing_penalty_msat)
                        .saturating_add(base_penalty_msat)
        }
}

impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time> ScoreUpdate for ProbabilisticScorerUsingTime<G, L, T> where L::Target: Logger {
        fn payment_path_failed(&mut self, path: &Path, short_channel_id: u64) {
                let amount_msat = path.final_value_msat();
                log_trace!(self.logger, "Scoring path through to SCID {} as having failed at {} msat", short_channel_id, amount_msat);
                let network_graph = self.network_graph.read_only();
                for (hop_idx, hop) in path.hops.iter().enumerate() {
                        let target = NodeId::from_pubkey(&hop.pubkey);
                        let channel_directed_from_source = network_graph.channels()
                                .get(&hop.short_channel_id)
                                .and_then(|channel| channel.as_directed_to(&target));

                        let at_failed_channel = hop.short_channel_id == short_channel_id;
                        if at_failed_channel && hop_idx == 0 {
                                log_warn!(self.logger, "Payment failed at the first hop - we do not attempt to learn channel info in such cases as we can directly observe local state.\n\tBecause we know the local state, we should generally not see failures here - this may be an indication that your channel peer on channel {} is broken and you may wish to close the channel.", hop.short_channel_id);
                        }

                        // Only score announced channels.
                        if let Some((channel, source)) = channel_directed_from_source {
                                let capacity_msat = channel.effective_capacity().as_msat();
                                if at_failed_channel {
                                        self.channel_liquidities
                                                .entry(hop.short_channel_id)
                                                .or_insert_with(ChannelLiquidity::new)
                                                .as_directed_mut(source, &target, capacity_msat, self.decay_params)
                                                .failed_at_channel(amount_msat, format_args!("SCID {}, towards {:?}", hop.short_channel_id, target), &self.logger);
                                } else {
                                        self.channel_liquidities
                                                .entry(hop.short_channel_id)
                                                .or_insert_with(ChannelLiquidity::new)
                                                .as_directed_mut(source, &target, capacity_msat, self.decay_params)
                                                .failed_downstream(amount_msat, format_args!("SCID {}, towards {:?}", hop.short_channel_id, target), &self.logger);
                                }
                        } else {
                                log_debug!(self.logger, "Not able to penalize channel with SCID {} as we do not have graph info for it (likely a route-hint last-hop).",
                                        hop.short_channel_id);
                        }
                        if at_failed_channel { break; }
                }
        }

        fn payment_path_successful(&mut self, path: &Path) {
                let amount_msat = path.final_value_msat();
                log_trace!(self.logger, "Scoring path through SCID {} as having succeeded at {} msat.",
                        path.hops.split_last().map(|(hop, _)| hop.short_channel_id).unwrap_or(0), amount_msat);
                let network_graph = self.network_graph.read_only();
                for hop in &path.hops {
                        let target = NodeId::from_pubkey(&hop.pubkey);
                        let channel_directed_from_source = network_graph.channels()
                                .get(&hop.short_channel_id)
                                .and_then(|channel| channel.as_directed_to(&target));

                        // Only score announced channels.
                        if let Some((channel, source)) = channel_directed_from_source {
                                let capacity_msat = channel.effective_capacity().as_msat();
                                self.channel_liquidities
                                        .entry(hop.short_channel_id)
                                        .or_insert_with(ChannelLiquidity::new)
                                        .as_directed_mut(source, &target, capacity_msat, self.decay_params)
                                        .successful(amount_msat, format_args!("SCID {}, towards {:?}", hop.short_channel_id, target), &self.logger);
                        } else {
                                log_debug!(self.logger, "Not able to learn for channel with SCID {} as we do not have graph info for it (likely a route-hint last-hop).",
                                        hop.short_channel_id);
                        }
                }
        }

        fn probe_failed(&mut self, path: &Path, short_channel_id: u64) {
                self.payment_path_failed(path, short_channel_id)
        }

        fn probe_successful(&mut self, path: &Path) {
                self.payment_path_failed(path, u64::max_value())
        }
}

#[cfg(c_bindings)]
impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time> Score for ProbabilisticScorerUsingTime<G, L, T>
where L::Target: Logger {}

mod approx {
        const BITS: u32 = 64;
        const HIGHEST_BIT: u32 = BITS - 1;
        const LOWER_BITS: u32 = 6;
        pub(super) const LOWER_BITS_BOUND: u64 = 1 << LOWER_BITS;
        const LOWER_BITMASK: u64 = (1 << LOWER_BITS) - 1;

        /// Look-up table for `log10(x) * 2048` where row `i` is used for each `x` having `i` as the
        /// most significant bit. The next 4 bits of `x`, if applicable, are used for the second index.
        const LOG10_TIMES_2048: [[u16; (LOWER_BITS_BOUND) as usize]; BITS as usize] = [
                [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                [617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617,
                        617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617, 617,
                        977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977,
                        977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977, 977],
                [1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233, 1233,
                        1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431, 1431,
                        1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594, 1594,
                        1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731, 1731],
                [1850, 1850, 1850, 1850, 1850, 1850, 1850, 1850, 1954, 1954, 1954, 1954, 1954, 1954, 1954, 1954,
                        2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2133, 2133, 2133, 2133, 2133, 2133, 2133, 2133,
                        2210, 2210, 2210, 2210, 2210, 2210, 2210, 2210, 2281, 2281, 2281, 2281, 2281, 2281, 2281, 2281,
                        2347, 2347, 2347, 2347, 2347, 2347, 2347, 2347, 2409, 2409, 2409, 2409, 2409, 2409, 2409, 2409],
                [2466, 2466, 2466, 2466, 2520, 2520, 2520, 2520, 2571, 2571, 2571, 2571, 2619, 2619, 2619, 2619,
                        2665, 2665, 2665, 2665, 2708, 2708, 2708, 2708, 2749, 2749, 2749, 2749, 2789, 2789, 2789, 2789,
                        2827, 2827, 2827, 2827, 2863, 2863, 2863, 2863, 2898, 2898, 2898, 2898, 2931, 2931, 2931, 2931,
                        2964, 2964, 2964, 2964, 2995, 2995, 2995, 2995, 3025, 3025, 3025, 3025, 3054, 3054, 3054, 3054],
                [3083, 3083, 3110, 3110, 3136, 3136, 3162, 3162, 3187, 3187, 3212, 3212, 3235, 3235, 3259, 3259,
                        3281, 3281, 3303, 3303, 3324, 3324, 3345, 3345, 3366, 3366, 3386, 3386, 3405, 3405, 3424, 3424,
                        3443, 3443, 3462, 3462, 3479, 3479, 3497, 3497, 3514, 3514, 3531, 3531, 3548, 3548, 3564, 3564,
                        3580, 3580, 3596, 3596, 3612, 3612, 3627, 3627, 3642, 3642, 3656, 3656, 3671, 3671, 3685, 3685],
                [3699, 3713, 3726, 3740, 3753, 3766, 3779, 3791, 3804, 3816, 3828, 3840, 3852, 3864, 3875, 3886,
                        3898, 3909, 3919, 3930, 3941, 3951, 3962, 3972, 3982, 3992, 4002, 4012, 4022, 4031, 4041, 4050,
                        4060, 4069, 4078, 4087, 4096, 4105, 4114, 4122, 4131, 4139, 4148, 4156, 4164, 4173, 4181, 4189,
                        4197, 4205, 4213, 4220, 4228, 4236, 4243, 4251, 4258, 4266, 4273, 4280, 4287, 4294, 4302, 4309],
                [4316, 4329, 4343, 4356, 4369, 4382, 4395, 4408, 4420, 4433, 4445, 4457, 4468, 4480, 4492, 4503,
                        4514, 4525, 4536, 4547, 4557, 4568, 4578, 4589, 4599, 4609, 4619, 4629, 4638, 4648, 4657, 4667,
                        4676, 4685, 4695, 4704, 4713, 4721, 4730, 4739, 4747, 4756, 4764, 4773, 4781, 4789, 4797, 4805,
                        4813, 4821, 4829, 4837, 4845, 4852, 4860, 4867, 4875, 4882, 4889, 4897, 4904, 4911, 4918, 4925],
                [4932, 4946, 4959, 4973, 4986, 4999, 5012, 5024, 5037, 5049, 5061, 5073, 5085, 5097, 5108, 5119,
                        5131, 5142, 5153, 5163, 5174, 5184, 5195, 5205, 5215, 5225, 5235, 5245, 5255, 5264, 5274, 5283,
                        5293, 5302, 5311, 5320, 5329, 5338, 5347, 5355, 5364, 5372, 5381, 5389, 5397, 5406, 5414, 5422,
                        5430, 5438, 5446, 5453, 5461, 5469, 5476, 5484, 5491, 5499, 5506, 5513, 5520, 5527, 5535, 5542],
                [5549, 5562, 5576, 5589, 5603, 5615, 5628, 5641, 5653, 5666, 5678, 5690, 5701, 5713, 5725, 5736,
                        5747, 5758, 5769, 5780, 5790, 5801, 5811, 5822, 5832, 5842, 5852, 5862, 5871, 5881, 5890, 5900,
                        5909, 5918, 5928, 5937, 5946, 5954, 5963, 5972, 5980, 5989, 5997, 6006, 6014, 6022, 6030, 6038,
                        6046, 6054, 6062, 6070, 6078, 6085, 6093, 6100, 6108, 6115, 6122, 6130, 6137, 6144, 6151, 6158],
                [6165, 6179, 6192, 6206, 6219, 6232, 6245, 6257, 6270, 6282, 6294, 6306, 6318, 6330, 6341, 6352,
                        6364, 6375, 6386, 6396, 6407, 6417, 6428, 6438, 6448, 6458, 6468, 6478, 6488, 6497, 6507, 6516,
                        6526, 6535, 6544, 6553, 6562, 6571, 6580, 6588, 6597, 6605, 6614, 6622, 6630, 6639, 6647, 6655,
                        6663, 6671, 6679, 6686, 6694, 6702, 6709, 6717, 6724, 6732, 6739, 6746, 6753, 6761, 6768, 6775],
                [6782, 6795, 6809, 6822, 6836, 6849, 6861, 6874, 6886, 6899, 6911, 6923, 6934, 6946, 6958, 6969,
                        6980, 6991, 7002, 7013, 7023, 7034, 7044, 7055, 7065, 7075, 7085, 7095, 7104, 7114, 7124, 7133,
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                        31323, 31331, 31339, 31347, 31354, 31362, 31370, 31377, 31385, 31392, 31399, 31407, 31414, 31421, 31428, 31435],
                [31442, 31456, 31469, 31483, 31496, 31509, 31522, 31534, 31547, 31559, 31571, 31583, 31595, 31606, 31618, 31629,
                        31640, 31652, 31662, 31673, 31684, 31694, 31705, 31715, 31725, 31735, 31745, 31755, 31765, 31774, 31784, 31793,
                        31803, 31812, 31821, 31830, 31839, 31848, 31857, 31865, 31874, 31882, 31891, 31899, 31907, 31916, 31924, 31932,
                        31940, 31948, 31955, 31963, 31971, 31979, 31986, 31994, 32001, 32008, 32016, 32023, 32030, 32037, 32044, 32052],
                [32058, 32072, 32086, 32099, 32112, 32125, 32138, 32151, 32163, 32176, 32188, 32200, 32211, 32223, 32234, 32246,
                        32257, 32268, 32279, 32290, 32300, 32311, 32321, 32332, 32342, 32352, 32362, 32372, 32381, 32391, 32400, 32410,
                        32419, 32428, 32437, 32446, 32455, 32464, 32473, 32482, 32490, 32499, 32507, 32516, 32524, 32532, 32540, 32548,
                        32556, 32564, 32572, 32580, 32587, 32595, 32603, 32610, 32618, 32625, 32632, 32640, 32647, 32654, 32661, 32668],
                [32675, 32689, 32702, 32716, 32729, 32742, 32755, 32767, 32780, 32792, 32804, 32816, 32828, 32839, 32851, 32862,
                        32873, 32885, 32895, 32906, 32917, 32927, 32938, 32948, 32958, 32968, 32978, 32988, 32998, 33007, 33017, 33026,
                        33036, 33045, 33054, 33063, 33072, 33081, 33090, 33098, 33107, 33115, 33124, 33132, 33140, 33149, 33157, 33165,
                        33173, 33181, 33188, 33196, 33204, 33212, 33219, 33227, 33234, 33241, 33249, 33256, 33263, 33270, 33278, 33285],
                [33292, 33305, 33319, 33332, 33345, 33358, 33371, 33384, 33396, 33409, 33421, 33433, 33444, 33456, 33467, 33479,
                        33490, 33501, 33512, 33523, 33533, 33544, 33554, 33565, 33575, 33585, 33595, 33605, 33614, 33624, 33633, 33643,
                        33652, 33661, 33670, 33680, 33688, 33697, 33706, 33715, 33723, 33732, 33740, 33749, 33757, 33765, 33773, 33781,
                        33789, 33797, 33805, 33813, 33820, 33828, 33836, 33843, 33851, 33858, 33865, 33873, 33880, 33887, 33894, 33901],
                [33908, 33922, 33935, 33949, 33962, 33975, 33988, 34000, 34013, 34025, 34037, 34049, 34061, 34072, 34084, 34095,
                        34106, 34118, 34128, 34139, 34150, 34160, 34171, 34181, 34191, 34201, 34211, 34221, 34231, 34240, 34250, 34259,
                        34269, 34278, 34287, 34296, 34305, 34314, 34323, 34331, 34340, 34348, 34357, 34365, 34373, 34382, 34390, 34398,
                        34406, 34414, 34422, 34429, 34437, 34445, 34452, 34460, 34467, 34475, 34482, 34489, 34496, 34503, 34511, 34518],
                [34525, 34538, 34552, 34565, 34578, 34591, 34604, 34617, 34629, 34642, 34654, 34666, 34677, 34689, 34700, 34712,
                        34723, 34734, 34745, 34756, 34766, 34777, 34787, 34798, 34808, 34818, 34828, 34838, 34847, 34857, 34866, 34876,
                        34885, 34894, 34904, 34913, 34921, 34930, 34939, 34948, 34956, 34965, 34973, 34982, 34990, 34998, 35006, 35014,
                        35022, 35030, 35038, 35046, 35053, 35061, 35069, 35076, 35084, 35091, 35098, 35106, 35113, 35120, 35127, 35134],
                [35141, 35155, 35168, 35182, 35195, 35208, 35221, 35233, 35246, 35258, 35270, 35282, 35294, 35306, 35317, 35328,
                        35340, 35351, 35361, 35372, 35383, 35393, 35404, 35414, 35424, 35434, 35444, 35454, 35464, 35473, 35483, 35492,
                        35502, 35511, 35520, 35529, 35538, 35547, 35556, 35564, 35573, 35581, 35590, 35598, 35606, 35615, 35623, 35631,
                        35639, 35647, 35655, 35662, 35670, 35678, 35685, 35693, 35700, 35708, 35715, 35722, 35729, 35736, 35744, 35751],
                [35758, 35771, 35785, 35798, 35811, 35824, 35837, 35850, 35862, 35875, 35887, 35899, 35910, 35922, 35934, 35945,
                        35956, 35967, 35978, 35989, 35999, 36010, 36020, 36031, 36041, 36051, 36061, 36071, 36080, 36090, 36099, 36109,
                        36118, 36127, 36137, 36146, 36154, 36163, 36172, 36181, 36189, 36198, 36206, 36215, 36223, 36231, 36239, 36247,
                        36255, 36263, 36271, 36279, 36287, 36294, 36302, 36309, 36317, 36324, 36331, 36339, 36346, 36353, 36360, 36367],
                [36374, 36388, 36401, 36415, 36428, 36441, 36454, 36466, 36479, 36491, 36503, 36515, 36527, 36539, 36550, 36561,
                        36573, 36584, 36594, 36605, 36616, 36626, 36637, 36647, 36657, 36667, 36677, 36687, 36697, 36706, 36716, 36725,
                        36735, 36744, 36753, 36762, 36771, 36780, 36789, 36797, 36806, 36814, 36823, 36831, 36839, 36848, 36856, 36864,
                        36872, 36880, 36888, 36895, 36903, 36911, 36918, 36926, 36933, 36941, 36948, 36955, 36962, 36969, 36977, 36984],
                [36991, 37004, 37018, 37031, 37044, 37057, 37070, 37083, 37095, 37108, 37120, 37132, 37143, 37155, 37167, 37178,
                        37189, 37200, 37211, 37222, 37232, 37243, 37253, 37264, 37274, 37284, 37294, 37304, 37313, 37323, 37332, 37342,
                        37351, 37360, 37370, 37379, 37388, 37396, 37405, 37414, 37422, 37431, 37439, 37448, 37456, 37464, 37472, 37480,
                        37488, 37496, 37504, 37512, 37520, 37527, 37535, 37542, 37550, 37557, 37564, 37572, 37579, 37586, 37593, 37600],
                [37607, 37621, 37634, 37648, 37661, 37674, 37687, 37699, 37712, 37724, 37736, 37748, 37760, 37772, 37783, 37794,
                        37806, 37817, 37828, 37838, 37849, 37859, 37870, 37880, 37890, 37900, 37910, 37920, 37930, 37939, 37949, 37958,
                        37968, 37977, 37986, 37995, 38004, 38013, 38022, 38030, 38039, 38047, 38056, 38064, 38072, 38081, 38089, 38097,
                        38105, 38113, 38121, 38128, 38136, 38144, 38151, 38159, 38166, 38174, 38181, 38188, 38195, 38202, 38210, 38217],
                [38224, 38237, 38251, 38264, 38278, 38290, 38303, 38316, 38328, 38341, 38353, 38365, 38376, 38388, 38400, 38411,
                        38422, 38433, 38444, 38455, 38465, 38476, 38486, 38497, 38507, 38517, 38527, 38537, 38546, 38556, 38565, 38575,
                        38584, 38593, 38603, 38612, 38621, 38629, 38638, 38647, 38655, 38664, 38672, 38681, 38689, 38697, 38705, 38713,
                        38721, 38729, 38737, 38745, 38753, 38760, 38768, 38775, 38783, 38790, 38797, 38805, 38812, 38819, 38826, 38833],
                [38840, 38854, 38867, 38881, 38894, 38907, 38920, 38932, 38945, 38957, 38969, 38981, 38993, 39005, 39016, 39027,
                        39039, 39050, 39061, 39071, 39082, 39092, 39103, 39113, 39123, 39133, 39143, 39153, 39163, 39172, 39182, 39191,
                        39201, 39210, 39219, 39228, 39237, 39246, 39255, 39263, 39272, 39280, 39289, 39297, 39305, 39314, 39322, 39330,
                        39338, 39346, 39354, 39361, 39369, 39377, 39384, 39392, 39399, 39407, 39414, 39421, 39428, 39436, 39443, 39450],
        ];

        /// Approximate `log10(numerator / denominator) * 2048` using a look-up table.
        #[inline]
        pub fn negative_log10_times_2048(numerator: u64, denominator: u64) -> u64 {
                // Multiply the -1 through to avoid needing to use signed numbers.
                (log10_times_2048(denominator) - log10_times_2048(numerator)) as u64
        }

        #[inline]
        fn log10_times_2048(x: u64) -> u16 {
                debug_assert_ne!(x, 0);
                let most_significant_bit = HIGHEST_BIT - x.leading_zeros();
                let lower_bits = (x >> most_significant_bit.saturating_sub(LOWER_BITS)) & LOWER_BITMASK;
                LOG10_TIMES_2048[most_significant_bit as usize][lower_bits as usize]
        }

        #[cfg(test)]
        mod tests {
                use super::*;

                #[test]
                fn prints_negative_log10_times_2048_lookup_table() {
                        for msb in 0..BITS {
                                for i in 0..LOWER_BITS_BOUND {
                                        let x = ((LOWER_BITS_BOUND + i) << (HIGHEST_BIT - LOWER_BITS)) >> (HIGHEST_BIT - msb);
                                        let log10_times_2048 = ((x as f64).log10() * 2048.0).round() as u16;
                                        assert_eq!(log10_times_2048, LOG10_TIMES_2048[msb as usize][i as usize]);

                                        if i % LOWER_BITS_BOUND == 0 {
                                                print!("\t\t[{}, ", log10_times_2048);
                                        } else if i % LOWER_BITS_BOUND == LOWER_BITS_BOUND - 1 {
                                                println!("{}],", log10_times_2048);
                                        } else if i % (LOWER_BITS_BOUND/4) == LOWER_BITS_BOUND/4 - 1 {
                                                print!("{},\n\t\t\t", log10_times_2048);
                                        } else {
                                                print!("{}, ", log10_times_2048);
                                        }
                                }
                        }
                }
        }
}

mod bucketed_history {
        use super::*;

        // Because liquidity is often skewed heavily in one direction, we store historical state
        // distribution in buckets of different size. For backwards compatibility, buckets of size 1/8th
        // must fit evenly into the buckets here.
        //
        // The smallest bucket is 2^-14th of the channel, for each of our 32 buckets here we define the
        // width of the bucket in 2^14'ths of the channel. This increases exponentially until we reach
        // a full 16th of the channel's capacity, which is reapeated a few times for backwards
        // compatibility. The four middle buckets represent full octiles of the channel's capacity.
        //
        // For a 1 BTC channel, this let's us differentiate between failures in the bottom 6k sats, or
        // between the 12,000th sat and 24,000th sat, while only needing to store and operate on 32
        // buckets in total.

        const BUCKET_START_POS: [u16; 33] = [
                0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 3072, 4096, 6144, 8192, 10240, 12288,
                13312, 14336, 15360, 15872, 16128, 16256, 16320, 16352, 16368, 16376, 16380, 16382, 16383, 16384,
        ];

        const LEGACY_TO_BUCKET_RANGE: [(u8, u8); 8] = [
                (0, 12), (12, 14), (14, 15), (15, 16), (16, 17), (17, 18), (18, 20), (20, 32)
        ];

        const POSITION_TICKS: u16 = 1 << 14;

        fn pos_to_bucket(pos: u16) -> usize {
                for bucket in 0..32 {
                        if pos < BUCKET_START_POS[bucket + 1] {
                                return bucket;
                        }
                }
                debug_assert!(false);
                return 32;
        }

        #[cfg(test)]
        #[test]
        fn check_bucket_maps() {
                const BUCKET_WIDTH_IN_16384S: [u16; 32] = [
                        1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 1024, 1024, 2048, 2048,
                        2048, 2048, 1024, 1024, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 1];

                let mut min_size_iter = 0;
                let mut legacy_bucket_iter = 0;
                for (bucket, width) in BUCKET_WIDTH_IN_16384S.iter().enumerate() {
                        assert_eq!(BUCKET_START_POS[bucket], min_size_iter);
                        for i in 0..*width {
                                assert_eq!(pos_to_bucket(min_size_iter + i) as usize, bucket);
                        }
                        min_size_iter += *width;
                        if min_size_iter % (POSITION_TICKS / 8) == 0 {
                                assert_eq!(LEGACY_TO_BUCKET_RANGE[legacy_bucket_iter].1 as usize, bucket + 1);
                                if legacy_bucket_iter + 1 < 8 {
                                        assert_eq!(LEGACY_TO_BUCKET_RANGE[legacy_bucket_iter + 1].0 as usize, bucket + 1);
                                }
                                legacy_bucket_iter += 1;
                        }
                }
                assert_eq!(BUCKET_START_POS[32], POSITION_TICKS);
                assert_eq!(min_size_iter, POSITION_TICKS);
        }

        #[inline]
        fn amount_to_pos(amount_msat: u64, capacity_msat: u64) -> u16 {
                let pos = if amount_msat < u64::max_value() / (POSITION_TICKS as u64) {
                        (amount_msat * (POSITION_TICKS as u64) / capacity_msat.saturating_add(1))
                                .try_into().unwrap_or(POSITION_TICKS)
                } else {
                        // Only use 128-bit arithmetic when multiplication will overflow to avoid 128-bit
                        // division. This branch should only be hit in fuzz testing since the amount would
                        // need to be over 2.88 million BTC in practice.
                        ((amount_msat as u128) * (POSITION_TICKS as u128)
                                        / (capacity_msat as u128).saturating_add(1))
                                .try_into().unwrap_or(POSITION_TICKS)
                };
                // If we are running in a client that doesn't validate gossip, its possible for a channel's
                // capacity to change due to a `channel_update` message which, if received while a payment
                // is in-flight, could cause this to fail. Thus, we only assert in test.
                #[cfg(test)]
                debug_assert!(pos < POSITION_TICKS);
                pos
        }

        /// Prior to LDK 0.0.117 we used eight buckets which were split evenly across the either
        /// octiles. This was changed to use 32 buckets for accuracy reasons in 0.0.117, however we
        /// support reading the legacy values here for backwards compatibility.
        pub(super) struct LegacyHistoricalBucketRangeTracker {
                buckets: [u16; 8],
        }

        impl LegacyHistoricalBucketRangeTracker {
                pub(crate) fn into_current(&self) -> HistoricalBucketRangeTracker {
                        let mut buckets = [0; 32];
                        for (idx, legacy_bucket) in self.buckets.iter().enumerate() {
                                let mut new_val = *legacy_bucket;
                                let (start, end) = LEGACY_TO_BUCKET_RANGE[idx];
                                new_val /= (end - start) as u16;
                                for i in start..end {
                                        buckets[i as usize] = new_val;
                                }
                        }
                        HistoricalBucketRangeTracker { buckets }
                }
        }

        /// Tracks the historical state of a distribution as a weighted average of how much time was spent
        /// in each of 32 buckets.
        #[derive(Clone, Copy)]
        pub(super) struct HistoricalBucketRangeTracker {
                buckets: [u16; 32],
        }

        /// Buckets are stored in fixed point numbers with a 5 bit fractional part. Thus, the value
        /// "one" is 32, or this constant.
        pub const BUCKET_FIXED_POINT_ONE: u16 = 32;

        impl HistoricalBucketRangeTracker {
                pub(super) fn new() -> Self { Self { buckets: [0; 32] } }
                pub(super) fn track_datapoint(&mut self, liquidity_offset_msat: u64, capacity_msat: u64) {
                        // We have 32 leaky buckets for min and max liquidity. Each bucket tracks the amount of time
                        // we spend in each bucket as a 16-bit fixed-point number with a 5 bit fractional part.
                        //
                        // Each time we update our liquidity estimate, we add 32 (1.0 in our fixed-point system) to
                        // the buckets for the current min and max liquidity offset positions.
                        //
                        // We then decay each bucket by multiplying by 2047/2048 (avoiding dividing by a
                        // non-power-of-two). This ensures we can't actually overflow the u16 - when we get to
                        // 63,457 adding 32 and decaying by 2047/2048 leaves us back at 63,457.
                        //
                        // In total, this allows us to track data for the last 8,000 or so payments across a given
                        // channel.
                        //
                        // These constants are a balance - we try to fit in 2 bytes per bucket to reduce overhead,
                        // and need to balance having more bits in the decimal part (to ensure decay isn't too
                        // non-linear) with having too few bits in the mantissa, causing us to not store very many
                        // datapoints.
                        //
                        // The constants were picked experimentally, selecting a decay amount that restricts us
                        // from overflowing buckets without having to cap them manually.

                        let pos: u16 = amount_to_pos(liquidity_offset_msat, capacity_msat);
                        if pos < POSITION_TICKS {
                                for e in self.buckets.iter_mut() {
                                        *e = ((*e as u32) * 2047 / 2048) as u16;
                                }
                                let bucket = pos_to_bucket(pos);
                                self.buckets[bucket] = self.buckets[bucket].saturating_add(BUCKET_FIXED_POINT_ONE);
                        }
                }
                /// Decay all buckets by the given number of half-lives. Used to more aggressively remove old
                /// datapoints as we receive newer information.
                #[inline]
                pub(super) fn time_decay_data(&mut self, half_lives: u32) {
                        for e in self.buckets.iter_mut() {
                                *e = e.checked_shr(half_lives).unwrap_or(0);
                        }
                }
        }

        impl_writeable_tlv_based!(HistoricalBucketRangeTracker, { (0, buckets, required) });
        impl_writeable_tlv_based!(LegacyHistoricalBucketRangeTracker, { (0, buckets, required) });

        /// A set of buckets representing the history of where we've seen the minimum- and maximum-
        /// liquidity bounds for a given channel.
        pub(super) struct HistoricalMinMaxBuckets<D: Deref<Target = HistoricalBucketRangeTracker>> {
                /// Buckets tracking where and how often we've seen the minimum liquidity bound for a
                /// channel.
                pub(super) min_liquidity_offset_history: D,
                /// Buckets tracking where and how often we've seen the maximum liquidity bound for a
                /// channel.
                pub(super) max_liquidity_offset_history: D,
        }

        impl<D: Deref<Target = HistoricalBucketRangeTracker>> HistoricalMinMaxBuckets<D> {
                pub(super) fn get_decayed_buckets<T: Time>(&self, now: T, last_updated: T, half_life: Duration)
                -> Option<([u16; 32], [u16; 32])> {
                        let (_, required_decays) = self.get_total_valid_points(now, last_updated, half_life)?;

                        let mut min_buckets = *self.min_liquidity_offset_history;
                        min_buckets.time_decay_data(required_decays);
                        let mut max_buckets = *self.max_liquidity_offset_history;
                        max_buckets.time_decay_data(required_decays);
                        Some((min_buckets.buckets, max_buckets.buckets))
                }
                #[inline]
                pub(super) fn get_total_valid_points<T: Time>(&self, now: T, last_updated: T, half_life: Duration)
                -> Option<(u64, u32)> {
                        let required_decays = now.duration_since(last_updated).as_secs()
                                .checked_div(half_life.as_secs())
                                .map_or(u32::max_value(), |decays| cmp::min(decays, u32::max_value() as u64) as u32);

                        let mut total_valid_points_tracked = 0;
                        for (min_idx, min_bucket) in self.min_liquidity_offset_history.buckets.iter().enumerate() {
                                for max_bucket in self.max_liquidity_offset_history.buckets.iter().take(32 - min_idx) {
                                        total_valid_points_tracked += (*min_bucket as u64) * (*max_bucket as u64);
                                }
                        }

                        // If the total valid points is smaller than 1.0 (i.e. 32 in our fixed-point scheme),
                        // treat it as if we were fully decayed.
                        const FULLY_DECAYED: u16 = BUCKET_FIXED_POINT_ONE * BUCKET_FIXED_POINT_ONE;
                        if total_valid_points_tracked.checked_shr(required_decays).unwrap_or(0) < FULLY_DECAYED.into() {
                                return None;
                        }

                        Some((total_valid_points_tracked, required_decays))
                }

                #[inline]
                pub(super) fn calculate_success_probability_times_billion<T: Time>(
                        &self, now: T, last_updated: T, half_life: Duration,
                        params: &ProbabilisticScoringFeeParameters, amount_msat: u64, capacity_msat: u64
                ) -> Option<u64> {
                        // If historical penalties are enabled, we try to calculate a probability of success
                        // given our historical distribution of min- and max-liquidity bounds in a channel.
                        // To do so, we walk the set of historical liquidity bucket (min, max) combinations
                        // (where min_idx < max_idx, as having a minimum above our maximum is an invalid
                        // state). For each pair, we calculate the probability as if the bucket's corresponding
                        // min- and max- liquidity bounds were our current liquidity bounds and then multiply
                        // that probability by the weight of the selected buckets.
                        let payment_pos = amount_to_pos(amount_msat, capacity_msat);
                        if payment_pos >= POSITION_TICKS { return None; }

                        // Check if all our buckets are zero, once decayed and treat it as if we had no data. We
                        // don't actually use the decayed buckets, though, as that would lose precision.
                        let (total_valid_points_tracked, _)
                                = self.get_total_valid_points(now, last_updated, half_life)?;

                        let mut cumulative_success_prob_times_billion = 0;
                        // Special-case the 0th min bucket - it generally means we failed a payment, so only
                        // consider the highest (i.e. largest-offset-from-max-capacity) max bucket for all
                        // points against the 0th min bucket. This avoids the case where we fail to route
                        // increasingly lower values over a channel, but treat each failure as a separate
                        // datapoint, many of which may have relatively high maximum-available-liquidity
                        // values, which will result in us thinking we have some nontrivial probability of
                        // routing up to that amount.
                        if self.min_liquidity_offset_history.buckets[0] != 0 {
                                let mut highest_max_bucket_with_points = 0; // The highest max-bucket with any data
                                let mut total_max_points = 0; // Total points in max-buckets to consider
                                for (max_idx, max_bucket) in self.max_liquidity_offset_history.buckets.iter().enumerate() {
                                        if *max_bucket >= BUCKET_FIXED_POINT_ONE {
                                                highest_max_bucket_with_points = cmp::max(highest_max_bucket_with_points, max_idx);
                                        }
                                        total_max_points += *max_bucket as u64;
                                }
                                let max_bucket_end_pos = BUCKET_START_POS[32 - highest_max_bucket_with_points] - 1;
                                if payment_pos < max_bucket_end_pos {
                                        let (numerator, denominator) = success_probability(payment_pos as u64, 0,
                                                max_bucket_end_pos as u64, POSITION_TICKS as u64 - 1, params, true);
                                        let bucket_prob_times_billion =
                                                (self.min_liquidity_offset_history.buckets[0] as u64) * total_max_points
                                                        * 1024 * 1024 * 1024 / total_valid_points_tracked;
                                        cumulative_success_prob_times_billion += bucket_prob_times_billion *
                                                numerator / denominator;
                                }
                        }

                        for (min_idx, min_bucket) in self.min_liquidity_offset_history.buckets.iter().enumerate().skip(1) {
                                let min_bucket_start_pos = BUCKET_START_POS[min_idx];
                                for (max_idx, max_bucket) in self.max_liquidity_offset_history.buckets.iter().enumerate().take(32 - min_idx) {
                                        let max_bucket_end_pos = BUCKET_START_POS[32 - max_idx] - 1;
                                        // Note that this multiply can only barely not overflow - two 16 bit ints plus
                                        // 30 bits is 62 bits.
                                        let bucket_prob_times_billion = (*min_bucket as u64) * (*max_bucket as u64)
                                                * 1024 * 1024 * 1024 / total_valid_points_tracked;
                                        if payment_pos >= max_bucket_end_pos {
                                                // Success probability 0, the payment amount may be above the max liquidity
                                                break;
                                        } else if payment_pos < min_bucket_start_pos {
                                                cumulative_success_prob_times_billion += bucket_prob_times_billion;
                                        } else {
                                                let (numerator, denominator) = success_probability(payment_pos as u64,
                                                        min_bucket_start_pos as u64, max_bucket_end_pos as u64,
                                                        POSITION_TICKS as u64 - 1, params, true);
                                                cumulative_success_prob_times_billion += bucket_prob_times_billion *
                                                        numerator / denominator;
                                        }
                                }
                        }

                        Some(cumulative_success_prob_times_billion)
                }
        }
}
use bucketed_history::{LegacyHistoricalBucketRangeTracker, HistoricalBucketRangeTracker, HistoricalMinMaxBuckets};

impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time> Writeable for ProbabilisticScorerUsingTime<G, L, T> where L::Target: Logger {
        #[inline]
        fn write<W: Writer>(&self, w: &mut W) -> Result<(), io::Error> {
                write_tlv_fields!(w, {
                        (0, self.channel_liquidities, required),
                });
                Ok(())
        }
}

impl<G: Deref<Target = NetworkGraph<L>>, L: Deref, T: Time>
ReadableArgs<(ProbabilisticScoringDecayParameters, G, L)> for ProbabilisticScorerUsingTime<G, L, T> where L::Target: Logger {
        #[inline]
        fn read<R: Read>(
                r: &mut R, args: (ProbabilisticScoringDecayParameters, G, L)
        ) -> Result<Self, DecodeError> {
                let (decay_params, network_graph, logger) = args;
                let mut channel_liquidities = HashMap::new();
                read_tlv_fields!(r, {
                        (0, channel_liquidities, required),
                });
                Ok(Self {
                        decay_params,
                        network_graph,
                        logger,
                        channel_liquidities,
                })
        }
}

impl<T: Time> Writeable for ChannelLiquidity<T> {
        #[inline]
        fn write<W: Writer>(&self, w: &mut W) -> Result<(), io::Error> {
                let duration_since_epoch = T::duration_since_epoch() - self.last_updated.elapsed();
                write_tlv_fields!(w, {
                        (0, self.min_liquidity_offset_msat, required),
                        // 1 was the min_liquidity_offset_history in octile form
                        (2, self.max_liquidity_offset_msat, required),
                        // 3 was the max_liquidity_offset_history in octile form
                        (4, duration_since_epoch, required),
                        (5, Some(self.min_liquidity_offset_history), option),
                        (7, Some(self.max_liquidity_offset_history), option),
                });
                Ok(())
        }
}

impl<T: Time> Readable for ChannelLiquidity<T> {
        #[inline]
        fn read<R: Read>(r: &mut R) -> Result<Self, DecodeError> {
                let mut min_liquidity_offset_msat = 0;
                let mut max_liquidity_offset_msat = 0;
                let mut legacy_min_liq_offset_history: Option<LegacyHistoricalBucketRangeTracker> = None;
                let mut legacy_max_liq_offset_history: Option<LegacyHistoricalBucketRangeTracker> = None;
                let mut min_liquidity_offset_history: Option<HistoricalBucketRangeTracker> = None;
                let mut max_liquidity_offset_history: Option<HistoricalBucketRangeTracker> = None;
                let mut duration_since_epoch = Duration::from_secs(0);
                read_tlv_fields!(r, {
                        (0, min_liquidity_offset_msat, required),
                        (1, legacy_min_liq_offset_history, option),
                        (2, max_liquidity_offset_msat, required),
                        (3, legacy_max_liq_offset_history, option),
                        (4, duration_since_epoch, required),
                        (5, min_liquidity_offset_history, option),
                        (7, max_liquidity_offset_history, option),
                });
                // On rust prior to 1.60 `Instant::duration_since` will panic if time goes backwards.
                // We write `last_updated` as wallclock time even though its ultimately an `Instant` (which
                // is a time from a monotonic clock usually represented as an offset against boot time).
                // Thus, we have to construct an `Instant` by subtracting the difference in wallclock time
                // from the one that was written. However, because `Instant` can panic if we construct one
                // in the future, we must handle wallclock time jumping backwards, which we do by simply
                // using `Instant::now()` in that case.
                let wall_clock_now = T::duration_since_epoch();
                let now = T::now();
                let last_updated = if wall_clock_now > duration_since_epoch {
                        now - (wall_clock_now - duration_since_epoch)
                } else { now };
                if min_liquidity_offset_history.is_none() {
                        if let Some(legacy_buckets) = legacy_min_liq_offset_history {
                                min_liquidity_offset_history = Some(legacy_buckets.into_current());
                        } else {
                                min_liquidity_offset_history = Some(HistoricalBucketRangeTracker::new());
                        }
                }
                if max_liquidity_offset_history.is_none() {
                        if let Some(legacy_buckets) = legacy_max_liq_offset_history {
                                max_liquidity_offset_history = Some(legacy_buckets.into_current());
                        } else {
                                max_liquidity_offset_history = Some(HistoricalBucketRangeTracker::new());
                        }
                }
                Ok(Self {
                        min_liquidity_offset_msat,
                        max_liquidity_offset_msat,
                        min_liquidity_offset_history: min_liquidity_offset_history.unwrap(),
                        max_liquidity_offset_history: max_liquidity_offset_history.unwrap(),
                        last_updated,
                })
        }
}

#[cfg(test)]
mod tests {
        use super::{ChannelLiquidity, HistoricalBucketRangeTracker, ProbabilisticScoringFeeParameters, ProbabilisticScoringDecayParameters, ProbabilisticScorerUsingTime};
        use crate::blinded_path::{BlindedHop, BlindedPath};
        use crate::util::config::UserConfig;
        use crate::util::time::Time;
        use crate::util::time::tests::SinceEpoch;

        use crate::ln::channelmanager;
        use crate::ln::msgs::{ChannelAnnouncement, ChannelUpdate, UnsignedChannelAnnouncement, UnsignedChannelUpdate};
        use crate::routing::gossip::{EffectiveCapacity, NetworkGraph, NodeId};
        use crate::routing::router::{BlindedTail, Path, RouteHop, CandidateRouteHop};
        use crate::routing::scoring::{ChannelUsage, ScoreLookUp, ScoreUpdate};
        use crate::util::ser::{ReadableArgs, Writeable};
        use crate::util::test_utils::{self, TestLogger};

        use bitcoin::blockdata::constants::ChainHash;
        use bitcoin::hashes::Hash;
        use bitcoin::hashes::sha256d::Hash as Sha256dHash;
        use bitcoin::network::constants::Network;
        use bitcoin::secp256k1::{PublicKey, Secp256k1, SecretKey};
        use core::time::Duration;
        use crate::io;

        fn source_privkey() -> SecretKey {
                SecretKey::from_slice(&[42; 32]).unwrap()
        }

        fn target_privkey() -> SecretKey {
                SecretKey::from_slice(&[43; 32]).unwrap()
        }

        fn source_pubkey() -> PublicKey {
                let secp_ctx = Secp256k1::new();
                PublicKey::from_secret_key(&secp_ctx, &source_privkey())
        }

        fn target_pubkey() -> PublicKey {
                let secp_ctx = Secp256k1::new();
                PublicKey::from_secret_key(&secp_ctx, &target_privkey())
        }

        fn source_node_id() -> NodeId {
                NodeId::from_pubkey(&source_pubkey())
        }

        fn target_node_id() -> NodeId {
                NodeId::from_pubkey(&target_pubkey())
        }

        // `ProbabilisticScorer` tests

        /// A probabilistic scorer for testing with time that can be manually advanced.
        type ProbabilisticScorer<'a> = ProbabilisticScorerUsingTime::<&'a NetworkGraph<&'a TestLogger>, &'a TestLogger, SinceEpoch>;

        fn sender_privkey() -> SecretKey {
                SecretKey::from_slice(&[41; 32]).unwrap()
        }

        fn recipient_privkey() -> SecretKey {
                SecretKey::from_slice(&[45; 32]).unwrap()
        }

        fn sender_pubkey() -> PublicKey {
                let secp_ctx = Secp256k1::new();
                PublicKey::from_secret_key(&secp_ctx, &sender_privkey())
        }

        fn recipient_pubkey() -> PublicKey {
                let secp_ctx = Secp256k1::new();
                PublicKey::from_secret_key(&secp_ctx, &recipient_privkey())
        }

        fn sender_node_id() -> NodeId {
                NodeId::from_pubkey(&sender_pubkey())
        }

        fn recipient_node_id() -> NodeId {
                NodeId::from_pubkey(&recipient_pubkey())
        }

        fn network_graph(logger: &TestLogger) -> NetworkGraph<&TestLogger> {
                let mut network_graph = NetworkGraph::new(Network::Testnet, logger);
                add_channel(&mut network_graph, 42, source_privkey(), target_privkey());
                add_channel(&mut network_graph, 43, target_privkey(), recipient_privkey());

                network_graph
        }

        fn add_channel(
                network_graph: &mut NetworkGraph<&TestLogger>, short_channel_id: u64, node_1_key: SecretKey,
                node_2_key: SecretKey
        ) {
                let genesis_hash = ChainHash::using_genesis_block(Network::Testnet);
                let node_1_secret = &SecretKey::from_slice(&[39; 32]).unwrap();
                let node_2_secret = &SecretKey::from_slice(&[40; 32]).unwrap();
                let secp_ctx = Secp256k1::new();
                let unsigned_announcement = UnsignedChannelAnnouncement {
                        features: channelmanager::provided_channel_features(&UserConfig::default()),
                        chain_hash: genesis_hash,
                        short_channel_id,
                        node_id_1: NodeId::from_pubkey(&PublicKey::from_secret_key(&secp_ctx, &node_1_key)),
                        node_id_2: NodeId::from_pubkey(&PublicKey::from_secret_key(&secp_ctx, &node_2_key)),
                        bitcoin_key_1: NodeId::from_pubkey(&PublicKey::from_secret_key(&secp_ctx, &node_1_secret)),
                        bitcoin_key_2: NodeId::from_pubkey(&PublicKey::from_secret_key(&secp_ctx, &node_2_secret)),
                        excess_data: Vec::new(),
                };
                let msghash = hash_to_message!(&Sha256dHash::hash(&unsigned_announcement.encode()[..])[..]);
                let signed_announcement = ChannelAnnouncement {
                        node_signature_1: secp_ctx.sign_ecdsa(&msghash, &node_1_key),
                        node_signature_2: secp_ctx.sign_ecdsa(&msghash, &node_2_key),
                        bitcoin_signature_1: secp_ctx.sign_ecdsa(&msghash, &node_1_secret),
                        bitcoin_signature_2: secp_ctx.sign_ecdsa(&msghash, &node_2_secret),
                        contents: unsigned_announcement,
                };
                let chain_source: Option<&crate::util::test_utils::TestChainSource> = None;
                network_graph.update_channel_from_announcement(
                        &signed_announcement, &chain_source).unwrap();
                update_channel(network_graph, short_channel_id, node_1_key, 0, 1_000, 100);
                update_channel(network_graph, short_channel_id, node_2_key, 1, 0, 100);
        }

        fn update_channel(
                network_graph: &mut NetworkGraph<&TestLogger>, short_channel_id: u64, node_key: SecretKey,
                flags: u8, htlc_maximum_msat: u64, timestamp: u32,
        ) {
                let genesis_hash = ChainHash::using_genesis_block(Network::Testnet);
                let secp_ctx = Secp256k1::new();
                let unsigned_update = UnsignedChannelUpdate {
                        chain_hash: genesis_hash,
                        short_channel_id,
                        timestamp,
                        flags,
                        cltv_expiry_delta: 18,
                        htlc_minimum_msat: 0,
                        htlc_maximum_msat,
                        fee_base_msat: 1,
                        fee_proportional_millionths: 0,
                        excess_data: Vec::new(),
                };
                let msghash = hash_to_message!(&Sha256dHash::hash(&unsigned_update.encode()[..])[..]);
                let signed_update = ChannelUpdate {
                        signature: secp_ctx.sign_ecdsa(&msghash, &node_key),
                        contents: unsigned_update,
                };
                network_graph.update_channel(&signed_update).unwrap();
        }

        fn path_hop(pubkey: PublicKey, short_channel_id: u64, fee_msat: u64) -> RouteHop {
                let config = UserConfig::default();
                RouteHop {
                        pubkey,
                        node_features: channelmanager::provided_node_features(&config),
                        short_channel_id,
                        channel_features: channelmanager::provided_channel_features(&config),
                        fee_msat,
                        cltv_expiry_delta: 18,
                        maybe_announced_channel: true,
                }
        }

        fn payment_path_for_amount(amount_msat: u64) -> Path {
                Path {
                        hops: vec![
                                path_hop(source_pubkey(), 41, 1),
                                path_hop(target_pubkey(), 42, 2),
                                path_hop(recipient_pubkey(), 43, amount_msat),
                        ], blinded_tail: None,
                }
        }

        #[test]
        fn liquidity_bounds_directed_from_lowest_node_id() {
                let logger = TestLogger::new();
                let last_updated = SinceEpoch::now();
                let network_graph = network_graph(&logger);
                let decay_params = ProbabilisticScoringDecayParameters::default();
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger)
                        .with_channel(42,
                                ChannelLiquidity {
                                        min_liquidity_offset_msat: 700, max_liquidity_offset_msat: 100, last_updated,
                                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                })
                        .with_channel(43,
                                ChannelLiquidity {
                                        min_liquidity_offset_msat: 700, max_liquidity_offset_msat: 100, last_updated,
                                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                });
                let source = source_node_id();
                let target = target_node_id();
                let recipient = recipient_node_id();
                assert!(source > target);
                assert!(target < recipient);

                // Update minimum liquidity.

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 100);
                assert_eq!(liquidity.max_liquidity_msat(), 300);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 700);
                assert_eq!(liquidity.max_liquidity_msat(), 900);

                scorer.channel_liquidities.get_mut(&42).unwrap()
                        .as_directed_mut(&source, &target, 1_000, decay_params)
                        .set_min_liquidity_msat(200);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 200);
                assert_eq!(liquidity.max_liquidity_msat(), 300);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 700);
                assert_eq!(liquidity.max_liquidity_msat(), 800);

                // Update maximum liquidity.

                let liquidity = scorer.channel_liquidities.get(&43).unwrap()
                        .as_directed(&target, &recipient, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 700);
                assert_eq!(liquidity.max_liquidity_msat(), 900);

                let liquidity = scorer.channel_liquidities.get(&43).unwrap()
                        .as_directed(&recipient, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 100);
                assert_eq!(liquidity.max_liquidity_msat(), 300);

                scorer.channel_liquidities.get_mut(&43).unwrap()
                        .as_directed_mut(&target, &recipient, 1_000, decay_params)
                        .set_max_liquidity_msat(200);

                let liquidity = scorer.channel_liquidities.get(&43).unwrap()
                        .as_directed(&target, &recipient, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 0);
                assert_eq!(liquidity.max_liquidity_msat(), 200);

                let liquidity = scorer.channel_liquidities.get(&43).unwrap()
                        .as_directed(&recipient, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 800);
                assert_eq!(liquidity.max_liquidity_msat(), 1000);
        }

        #[test]
        fn resets_liquidity_upper_bound_when_crossed_by_lower_bound() {
                let logger = TestLogger::new();
                let last_updated = SinceEpoch::now();
                let network_graph = network_graph(&logger);
                let decay_params = ProbabilisticScoringDecayParameters::default();
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger)
                        .with_channel(42,
                                ChannelLiquidity {
                                        min_liquidity_offset_msat: 200, max_liquidity_offset_msat: 400, last_updated,
                                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                });
                let source = source_node_id();
                let target = target_node_id();
                assert!(source > target);

                // Check initial bounds.
                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 400);
                assert_eq!(liquidity.max_liquidity_msat(), 800);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 200);
                assert_eq!(liquidity.max_liquidity_msat(), 600);

                // Reset from source to target.
                scorer.channel_liquidities.get_mut(&42).unwrap()
                        .as_directed_mut(&source, &target, 1_000, decay_params)
                        .set_min_liquidity_msat(900);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 900);
                assert_eq!(liquidity.max_liquidity_msat(), 1_000);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 0);
                assert_eq!(liquidity.max_liquidity_msat(), 100);

                // Reset from target to source.
                scorer.channel_liquidities.get_mut(&42).unwrap()
                        .as_directed_mut(&target, &source, 1_000, decay_params)
                        .set_min_liquidity_msat(400);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 0);
                assert_eq!(liquidity.max_liquidity_msat(), 600);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 400);
                assert_eq!(liquidity.max_liquidity_msat(), 1_000);
        }

        #[test]
        fn resets_liquidity_lower_bound_when_crossed_by_upper_bound() {
                let logger = TestLogger::new();
                let last_updated = SinceEpoch::now();
                let network_graph = network_graph(&logger);
                let decay_params = ProbabilisticScoringDecayParameters::default();
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger)
                        .with_channel(42,
                                ChannelLiquidity {
                                        min_liquidity_offset_msat: 200, max_liquidity_offset_msat: 400, last_updated,
                                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                });
                let source = source_node_id();
                let target = target_node_id();
                assert!(source > target);

                // Check initial bounds.
                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 400);
                assert_eq!(liquidity.max_liquidity_msat(), 800);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 200);
                assert_eq!(liquidity.max_liquidity_msat(), 600);

                // Reset from source to target.
                scorer.channel_liquidities.get_mut(&42).unwrap()
                        .as_directed_mut(&source, &target, 1_000, decay_params)
                        .set_max_liquidity_msat(300);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 0);
                assert_eq!(liquidity.max_liquidity_msat(), 300);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 700);
                assert_eq!(liquidity.max_liquidity_msat(), 1_000);

                // Reset from target to source.
                scorer.channel_liquidities.get_mut(&42).unwrap()
                        .as_directed_mut(&target, &source, 1_000, decay_params)
                        .set_max_liquidity_msat(600);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 400);
                assert_eq!(liquidity.max_liquidity_msat(), 1_000);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&target, &source, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 0);
                assert_eq!(liquidity.max_liquidity_msat(), 600);
        }

        #[test]
        fn increased_penalty_nearing_liquidity_upper_bound() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters::default();
                let scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 1_024,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 1_000 },
                };
                let network_graph = network_graph.read_only();
                let channel = network_graph.channel(42).unwrap();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 10_240, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 102_400, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 47);
                let usage = ChannelUsage { amount_msat: 1_023_999, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2_000);

                let usage = ChannelUsage {
                        amount_msat: 128,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_000 },
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 58);
                let usage = ChannelUsage { amount_msat: 256, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 125);
                let usage = ChannelUsage { amount_msat: 374, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 198);
                let usage = ChannelUsage { amount_msat: 512, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);
                let usage = ChannelUsage { amount_msat: 640, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 425);
                let usage = ChannelUsage { amount_msat: 768, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 602);
                let usage = ChannelUsage { amount_msat: 896, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 902);
        }

        #[test]
        fn constant_penalty_outside_liquidity_bounds() {
                let logger = TestLogger::new();
                let last_updated = SinceEpoch::now();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        ..ProbabilisticScoringDecayParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger)
                        .with_channel(42,
                                ChannelLiquidity {
                                        min_liquidity_offset_msat: 40, max_liquidity_offset_msat: 40, last_updated,
                                        min_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                        max_liquidity_offset_history: HistoricalBucketRangeTracker::new(),
                                });
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 39,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 100, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 50, ..usage };
                assert_ne!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                assert_ne!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
                let usage = ChannelUsage { amount_msat: 61, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
        }

        #[test]
        fn does_not_further_penalize_own_channel() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 500,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let failed_path = payment_path_for_amount(500);
                let successful_path = payment_path_for_amount(200);
                let channel = &network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 41,
                };

                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 301);

                scorer.payment_path_failed(&failed_path, 41);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 301);

                scorer.payment_path_successful(&successful_path);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 301);
        }

        #[test]
        fn sets_liquidity_lower_bound_on_downstream_failure() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();
                let path = payment_path_for_amount(500);

                let usage = ChannelUsage {
                        amount_msat: 250,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
                let usage = ChannelUsage { amount_msat: 500, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 301);
                let usage = ChannelUsage { amount_msat: 750, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 602);

                scorer.payment_path_failed(&path, 43);

                let usage = ChannelUsage { amount_msat: 250, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 500, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 750, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);
        }

        #[test]
        fn sets_liquidity_upper_bound_on_failure() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();
                let path = payment_path_for_amount(500);

                let usage = ChannelUsage {
                        amount_msat: 250,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
                let usage = ChannelUsage { amount_msat: 500, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 301);
                let usage = ChannelUsage { amount_msat: 750, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 602);

                scorer.payment_path_failed(&path, 42);

                let usage = ChannelUsage { amount_msat: 250, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);
                let usage = ChannelUsage { amount_msat: 500, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
                let usage = ChannelUsage { amount_msat: 750, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
        }

        #[test]
        fn ignores_channels_after_removed_failed_channel() {
                // Previously, if we'd tried to send over a channel which was removed from the network
                // graph before we call `payment_path_failed` (which is the default if the we get a "no
                // such channel" error in the `InvoicePayer`), we would call `failed_downstream` on all
                // channels in the route, even ones which they payment never reached. This tests to ensure
                // we do not score such channels.
                let secp_ctx = Secp256k1::new();
                let logger = TestLogger::new();
                let mut network_graph = NetworkGraph::new(Network::Testnet, &logger);
                let secret_a = SecretKey::from_slice(&[42; 32]).unwrap();
                let secret_b = SecretKey::from_slice(&[43; 32]).unwrap();
                let secret_c = SecretKey::from_slice(&[44; 32]).unwrap();
                let secret_d = SecretKey::from_slice(&[45; 32]).unwrap();
                add_channel(&mut network_graph, 42, secret_a, secret_b);
                // Don't add the channel from B -> C.
                add_channel(&mut network_graph, 44, secret_c, secret_d);

                let pub_a = PublicKey::from_secret_key(&secp_ctx, &secret_a);
                let pub_b = PublicKey::from_secret_key(&secp_ctx, &secret_b);
                let pub_c = PublicKey::from_secret_key(&secp_ctx, &secret_c);
                let pub_d = PublicKey::from_secret_key(&secp_ctx, &secret_d);

                let path = vec![
                        path_hop(pub_b, 42, 1),
                        path_hop(pub_c, 43, 2),
                        path_hop(pub_d, 44, 100),
                ];

                let node_a = NodeId::from_pubkey(&pub_a);
                let node_b = NodeId::from_pubkey(&pub_b);
                let node_c = NodeId::from_pubkey(&pub_c);

                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);

                let usage = ChannelUsage {
                        amount_msat: 250,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_a).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
                // Note that a default liquidity bound is used for B -> C as no channel exists
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_b).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 43,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
                let channel = network_graph.read_only().channel(44).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_c).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 44,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);

                scorer.payment_path_failed(&Path { hops: path, blinded_tail: None }, 43);

                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_a).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 80);
                // Note that a default liquidity bound is used for B -> C as no channel exists
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_b).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 43,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
                let channel = network_graph.read_only().channel(44).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&node_c).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 44,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 128);
        }

        #[test]
        fn reduces_liquidity_upper_bound_along_path_on_success() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 250,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let network_graph = network_graph.read_only().channels().clone();
                let channel_42 = network_graph.get(&42).unwrap();
                let channel_43 = network_graph.get(&43).unwrap();
                let (info, _) = channel_42.as_directed_from(&source).unwrap();
                let candidate_41 = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 41,
                };
                let (info, target) = channel_42.as_directed_from(&source).unwrap();
                let candidate_42 = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                let (info, _) = channel_43.as_directed_from(&target).unwrap();
                let candidate_43 = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 43,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate_41, usage, &params), 128);
                assert_eq!(scorer.channel_penalty_msat(&candidate_42, usage, &params), 128);
                assert_eq!(scorer.channel_penalty_msat(&candidate_43, usage, &params), 128);

                scorer.payment_path_successful(&payment_path_for_amount(500));

                assert_eq!(scorer.channel_penalty_msat(&candidate_41, usage, &params), 128);
                assert_eq!(scorer.channel_penalty_msat(&candidate_42, usage, &params), 300);
                assert_eq!(scorer.channel_penalty_msat(&candidate_43, usage, &params), 300);
        }

        #[test]
        fn decays_liquidity_bounds_over_time() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 0,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_024 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, target) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 1_023, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2_000);

                scorer.payment_path_failed(&payment_path_for_amount(768), 42);
                scorer.payment_path_failed(&payment_path_for_amount(128), 43);

                // Initial penalties
                let usage = ChannelUsage { amount_msat: 128, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 256, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 93);
                let usage = ChannelUsage { amount_msat: 768, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 1_479);
                let usage = ChannelUsage { amount_msat: 896, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                // No decay
                SinceEpoch::advance(Duration::from_secs(4));
                let usage = ChannelUsage { amount_msat: 128, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 256, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 93);
                let usage = ChannelUsage { amount_msat: 768, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 1_479);
                let usage = ChannelUsage { amount_msat: 896, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                // Half decay (i.e., three-quarter life)
                SinceEpoch::advance(Duration::from_secs(1));
                let usage = ChannelUsage { amount_msat: 128, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 22);
                let usage = ChannelUsage { amount_msat: 256, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 106);
                let usage = ChannelUsage { amount_msat: 768, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 921);
                let usage = ChannelUsage { amount_msat: 896, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                // One decay (i.e., half life)
                SinceEpoch::advance(Duration::from_secs(5));
                let usage = ChannelUsage { amount_msat: 64, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 128, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 34);
                let usage = ChannelUsage { amount_msat: 896, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 1_970);
                let usage = ChannelUsage { amount_msat: 960, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                // Fully decay liquidity lower bound.
                SinceEpoch::advance(Duration::from_secs(10 * 7));
                let usage = ChannelUsage { amount_msat: 0, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 1, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 1_023, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2_000);
                let usage = ChannelUsage { amount_msat: 1_024, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                // Fully decay liquidity upper bound.
                SinceEpoch::advance(Duration::from_secs(10));
                let usage = ChannelUsage { amount_msat: 0, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 1_024, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                SinceEpoch::advance(Duration::from_secs(10));
                let usage = ChannelUsage { amount_msat: 0, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
                let usage = ChannelUsage { amount_msat: 1_024, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
        }

        #[test]
        fn decays_liquidity_bounds_without_shift_overflow() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::default()
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 256,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, target) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 125);

                scorer.payment_path_failed(&payment_path_for_amount(512), 42);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 281);

                // An unchecked right shift 64 bits or more in DirectedChannelLiquidity::decayed_offset_msat
                // would cause an overflow.
                SinceEpoch::advance(Duration::from_secs(10 * 64));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 125);

                SinceEpoch::advance(Duration::from_secs(10));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 125);
        }

        #[test]
        fn restricts_liquidity_bounds_after_decay() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::default()
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 512,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };

                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);

                // More knowledge gives higher confidence (256, 768), meaning a lower penalty.
                scorer.payment_path_failed(&payment_path_for_amount(768), 42);
                scorer.payment_path_failed(&payment_path_for_amount(256), 43);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 281);

                // Decaying knowledge gives less confidence (128, 896), meaning a higher penalty.
                SinceEpoch::advance(Duration::from_secs(10));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 291);

                // Reducing the upper bound gives more confidence (128, 832) that the payment amount (512)
                // is closer to the upper bound, meaning a higher penalty.
                scorer.payment_path_successful(&payment_path_for_amount(64));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 331);

                // Increasing the lower bound gives more confidence (256, 832) that the payment amount (512)
                // is closer to the lower bound, meaning a lower penalty.
                scorer.payment_path_failed(&payment_path_for_amount(256), 43);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 245);

                // Further decaying affects the lower bound more than the upper bound (128, 928).
                SinceEpoch::advance(Duration::from_secs(10));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 280);
        }

        #[test]
        fn restores_persisted_liquidity_bounds() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::default()
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 500,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };

                scorer.payment_path_failed(&payment_path_for_amount(500), 42);
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                SinceEpoch::advance(Duration::from_secs(10));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 473);

                scorer.payment_path_failed(&payment_path_for_amount(250), 43);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);

                let mut serialized_scorer = Vec::new();
                scorer.write(&mut serialized_scorer).unwrap();

                let mut serialized_scorer = io::Cursor::new(&serialized_scorer);
                let deserialized_scorer =
                        <ProbabilisticScorer>::read(&mut serialized_scorer, (decay_params, &network_graph, &logger)).unwrap();
                assert_eq!(deserialized_scorer.channel_penalty_msat(&candidate, usage, &params), 300);
        }

        #[test]
        fn decays_persisted_liquidity_bounds() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::zero_penalty()
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 500,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };

                scorer.payment_path_failed(&payment_path_for_amount(500), 42);
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                let mut serialized_scorer = Vec::new();
                scorer.write(&mut serialized_scorer).unwrap();

                SinceEpoch::advance(Duration::from_secs(10));

                let mut serialized_scorer = io::Cursor::new(&serialized_scorer);
                let deserialized_scorer =
                        <ProbabilisticScorer>::read(&mut serialized_scorer, (decay_params, &network_graph, &logger)).unwrap();
                assert_eq!(deserialized_scorer.channel_penalty_msat(&candidate, usage, &params), 473);

                scorer.payment_path_failed(&payment_path_for_amount(250), 43);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);

                SinceEpoch::advance(Duration::from_secs(10));
                assert_eq!(deserialized_scorer.channel_penalty_msat(&candidate, usage, &params), 370);
        }

        #[test]
        fn scores_realistic_payments() {
                // Shows the scores of "realistic" sends of 100k sats over channels of 1-10m sats (with a
                // 50k sat reserve).
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters::default();
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 100_000_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 950_000_000, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 11497);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 7408);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 2_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 6151);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 3_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 5427);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 4_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4955);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 5_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4736);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 6_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4484);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 7_450_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4484);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 7_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4263);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 8_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4263);
                let usage = ChannelUsage {
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 9_950_000_000, htlc_maximum_msat: 1_000 }, ..usage
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 4044);
        }

        #[test]
        fn adds_base_penalty_to_liquidity_penalty() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 128,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_000 },
                };

                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 58);

                let params = ProbabilisticScoringFeeParameters {
                        base_penalty_msat: 500, liquidity_penalty_multiplier_msat: 1_000,
                        anti_probing_penalty_msat: 0, ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 558);

                let params = ProbabilisticScoringFeeParameters {
                        base_penalty_msat: 500, liquidity_penalty_multiplier_msat: 1_000,
                        base_penalty_amount_multiplier_msat: (1 << 30),
                        anti_probing_penalty_msat: 0, ..ProbabilisticScoringFeeParameters::zero_penalty()
                };

                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 558 + 128);
        }

        #[test]
        fn adds_amount_penalty_to_liquidity_penalty() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 512_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 1_000 },
                };

                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        liquidity_penalty_amount_multiplier_msat: 0,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);

                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        liquidity_penalty_amount_multiplier_msat: 256,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 337);
        }

        #[test]
        fn calculates_log10_without_overflowing_u64_max_value() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: u64::max_value(),
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Infinite,
                };
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 40_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters::zero_penalty();
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                let scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 80_000);
        }

        #[test]
        fn accounts_for_inflight_htlc_usage() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        considered_impossible_penalty_msat: u64::max_value(),
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 750,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_000, htlc_maximum_msat: 1_000 },
                };
                let network_graph = network_graph.read_only();
                let channel = network_graph.channel(42).unwrap();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_ne!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());

                let usage = ChannelUsage { inflight_htlc_msat: 251, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
        }

        #[test]
        fn removes_uncertainity_when_exact_liquidity_known() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters::default();
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);
                let source = source_node_id();

                let base_penalty_msat = params.base_penalty_msat;
                let usage = ChannelUsage {
                        amount_msat: 750,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::ExactLiquidity { liquidity_msat: 1_000 },
                };
                let network_graph = network_graph.read_only();
                let channel = network_graph.channel(42).unwrap();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), base_penalty_msat);

                let usage = ChannelUsage { amount_msat: 1_000, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), base_penalty_msat);

                let usage = ChannelUsage { amount_msat: 1_001, ..usage };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), u64::max_value());
        }

        fn remembers_historical_failures() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        historical_liquidity_penalty_multiplier_msat: 1024,
                        historical_liquidity_penalty_amount_multiplier_msat: 1024,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(60 * 60),
                        historical_no_updates_half_life: Duration::from_secs(10),
                };
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();

                let usage = ChannelUsage {
                        amount_msat: 100,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_024 },
                };
                let usage_1 = ChannelUsage {
                        amount_msat: 1,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_024 },
                };
                let network_graph = network_graph.read_only();
                let channel = network_graph.channel(42).unwrap();
                let (info, target) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };

                // With no historical data the normal liquidity penalty calculation is used.
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 168);
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                None);
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, 42, &params),
                None);

                scorer.payment_path_failed(&payment_path_for_amount(1), 42);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2048);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage_1, &params), 249);
                // The "it failed" increment is 32, where the probability should lie several buckets into
                // the first octile.
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        Some(([32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                                [0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])));
                assert!(scorer.historical_estimated_payment_success_probability(42, &target, 1, &params)
                        .unwrap() > 0.35);
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, 500, &params),
                        Some(0.0));

                // Even after we tell the scorer we definitely have enough available liquidity, it will
                // still remember that there was some failure in the past, and assign a non-0 penalty.
                scorer.payment_path_failed(&payment_path_for_amount(1000), 43);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 105);
                // The first points should be decayed just slightly and the last bucket has a new point.
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        Some(([31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0],
                                [0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32])));

                // The exact success probability is a bit complicated and involves integer rounding, so we
                // simply check bounds here.
                let five_hundred_prob =
                        scorer.historical_estimated_payment_success_probability(42, &target, 500, &params).unwrap();
                assert!(five_hundred_prob > 0.59);
                assert!(five_hundred_prob < 0.60);
                let one_prob =
                        scorer.historical_estimated_payment_success_probability(42, &target, 1, &params).unwrap();
                assert!(one_prob < 0.85);
                assert!(one_prob > 0.84);

                // Advance the time forward 16 half-lives (which the docs claim will ensure all data is
                // gone), and check that we're back to where we started.
                SinceEpoch::advance(Duration::from_secs(10 * 16));
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 168);
                // Once fully decayed we still have data, but its all-0s. In the future we may remove the
                // data entirely instead.
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        None);
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, 1, &params), None);

                let mut usage = ChannelUsage {
                        amount_msat: 100,
                        inflight_htlc_msat: 1024,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_024 },
                };
                scorer.payment_path_failed(&payment_path_for_amount(1), 42);
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2050);
                usage.inflight_htlc_msat = 0;
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 866);

                let usage = ChannelUsage {
                        amount_msat: 1,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::AdvertisedMaxHTLC { amount_msat: 0 },
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 2048);

                // Advance to decay all liquidity offsets to zero.
                SinceEpoch::advance(Duration::from_secs(60 * 60 * 10));

                // Use a path in the opposite direction, which have zero for htlc_maximum_msat. This will
                // ensure that the effective capacity is zero to test division-by-zero edge cases.
                let path = vec![
                        path_hop(target_pubkey(), 43, 2),
                        path_hop(source_pubkey(), 42, 1),
                        path_hop(sender_pubkey(), 41, 0),
                ];
                scorer.payment_path_failed(&Path { hops: path, blinded_tail: None }, 42);
        }

        #[test]
        fn adds_anti_probing_penalty() {
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let source = source_node_id();
                let params = ProbabilisticScoringFeeParameters {
                        anti_probing_penalty_msat: 500,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let scorer = ProbabilisticScorer::new(ProbabilisticScoringDecayParameters::default(), &network_graph, &logger);

                // Check we receive no penalty for a low htlc_maximum_msat.
                let usage = ChannelUsage {
                        amount_msat: 512_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 1_000 },
                };
                let network_graph = network_graph.read_only();
                let channel = network_graph.channel(42).unwrap();
                let (info, _) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);

                // Check we receive anti-probing penalty for htlc_maximum_msat == channel_capacity.
                let usage = ChannelUsage {
                        amount_msat: 512_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 1_024_000 },
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 500);

                // Check we receive anti-probing penalty for htlc_maximum_msat == channel_capacity/2.
                let usage = ChannelUsage {
                        amount_msat: 512_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 512_000 },
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 500);

                // Check we receive no anti-probing penalty for htlc_maximum_msat == channel_capacity/2 - 1.
                let usage = ChannelUsage {
                        amount_msat: 512_000,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024_000, htlc_maximum_msat: 511_999 },
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 0);
        }

        #[test]
        fn scores_with_blinded_path() {
                // Make sure we'll account for a blinded path's final_value_msat in scoring
                let logger = TestLogger::new();
                let network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        liquidity_penalty_multiplier_msat: 1_000,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters::default();
                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();
                let usage = ChannelUsage {
                        amount_msat: 512,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat: 1_024, htlc_maximum_msat: 1_000 },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, target) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 300);

                let mut path = payment_path_for_amount(768);
                let recipient_hop = path.hops.pop().unwrap();
                let blinded_path = BlindedPath {
                        introduction_node_id: path.hops.last().as_ref().unwrap().pubkey,
                        blinding_point: test_utils::pubkey(42),
                        blinded_hops: vec![
                                BlindedHop { blinded_node_id: test_utils::pubkey(44), encrypted_payload: Vec::new() }
                        ],
                };
                path.blinded_tail = Some(BlindedTail {
                        hops: blinded_path.blinded_hops,
                        blinding_point: blinded_path.blinding_point,
                        excess_final_cltv_expiry_delta: recipient_hop.cltv_expiry_delta,
                        final_value_msat: recipient_hop.fee_msat,
                });

                // Check the liquidity before and after scoring payment failures to ensure the blinded path's
                // final value is taken into account.
                assert!(scorer.channel_liquidities.get(&42).is_none());

                scorer.payment_path_failed(&path, 42);
                path.blinded_tail.as_mut().unwrap().final_value_msat = 256;
                scorer.payment_path_failed(&path, 43);

                let liquidity = scorer.channel_liquidities.get(&42).unwrap()
                        .as_directed(&source, &target, 1_000, decay_params);
                assert_eq!(liquidity.min_liquidity_msat(), 256);
                assert_eq!(liquidity.max_liquidity_msat(), 768);
        }

        #[test]
        fn realistic_historical_failures() {
                // The motivation for the unequal sized buckets came largely from attempting to pay 10k
                // sats over a one bitcoin channel. This tests that case explicitly, ensuring that we score
                // properly.
                let logger = TestLogger::new();
                let mut network_graph = network_graph(&logger);
                let params = ProbabilisticScoringFeeParameters {
                        historical_liquidity_penalty_multiplier_msat: 1024,
                        historical_liquidity_penalty_amount_multiplier_msat: 1024,
                        ..ProbabilisticScoringFeeParameters::zero_penalty()
                };
                let decay_params = ProbabilisticScoringDecayParameters {
                        liquidity_offset_half_life: Duration::from_secs(60 * 60),
                        historical_no_updates_half_life: Duration::from_secs(10),
                        ..ProbabilisticScoringDecayParameters::default()
                };

                let capacity_msat = 100_000_000_000;
                update_channel(&mut network_graph, 42, source_privkey(), 0, capacity_msat, 200);
                update_channel(&mut network_graph, 42, target_privkey(), 1, capacity_msat, 200);

                let mut scorer = ProbabilisticScorer::new(decay_params, &network_graph, &logger);
                let source = source_node_id();

                let mut amount_msat = 10_000_000;
                let usage = ChannelUsage {
                        amount_msat,
                        inflight_htlc_msat: 0,
                        effective_capacity: EffectiveCapacity::Total { capacity_msat, htlc_maximum_msat: capacity_msat },
                };
                let channel = network_graph.read_only().channel(42).unwrap().to_owned();
                let (info, target) = channel.as_directed_from(&source).unwrap();
                let candidate = CandidateRouteHop::PublicHop {
                        info,
                        short_channel_id: 42,
                };
                // With no historical data the normal liquidity penalty calculation is used, which results
                // in a success probability of ~75%.
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params), 1269);
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        None);
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, 42, &params),
                        None);

                // Fail to pay once, and then check the buckets and penalty.
                scorer.payment_path_failed(&payment_path_for_amount(amount_msat), 42);
                // The penalty should be the maximum penalty, as the payment we're scoring is now in the
                // same bucket which is the only maximum datapoint.
                assert_eq!(scorer.channel_penalty_msat(&candidate, usage, &params),
                        2048 + 2048 * amount_msat / super::AMOUNT_PENALTY_DIVISOR);
                // The "it failed" increment is 32, which we should apply to the first upper-bound (between
                // 6k sats and 12k sats).
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        Some(([32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                                [0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])));
                // The success probability estimate itself should be zero.
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, amount_msat, &params),
                        Some(0.0));

                // Now test again with the amount in the bottom bucket.
                amount_msat /= 2;
                // The new amount is entirely within the only minimum bucket with score, so the probability
                // we assign is 1/2.
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, amount_msat, &params),
                        Some(0.5));

                // ...but once we see a failure, we consider the payment to be substantially less likely,
                // even though not a probability of zero as we still look at the second max bucket which
                // now shows 31.
                scorer.payment_path_failed(&payment_path_for_amount(amount_msat), 42);
                assert_eq!(scorer.historical_estimated_channel_liquidity_probabilities(42, &target),
                        Some(([63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                                [32, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])));
                assert_eq!(scorer.historical_estimated_payment_success_probability(42, &target, amount_msat, &params),
                        Some(0.0));
        }
}