slashing.rs

// This file is part of Substrate.

// Copyright (C) 2019-2021 Parity Technologies (UK) Ltd.
// SPDX-License-Identifier: Apache-2.0

// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// 	http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

//! A slashing implementation for NPoS systems.
//!
//! For the purposes of the economic model, it is easiest to think of each validator as a nominator
//! which nominates only its own identity.
//!
//! The act of nomination signals intent to unify economic identity with the validator - to take
//! part in the rewards of a job well done, and to take part in the punishment of a job done badly.
//!
//! There are 3 main difficulties to account for with slashing in NPoS:
//!   - A nominator can nominate multiple validators and be slashed via any of them.
//!   - Until slashed, stake is reused from era to era. Nominating with N coins for E eras in a row
//!     does not mean you have N*E coins to be slashed - you've only ever had N.
//!   - Slashable offences can be found after the fact and out of order.
//!
//! The algorithm implemented in this module tries to balance these 3 difficulties.
//!
//! First, we only slash participants for the _maximum_ slash they receive in some time period,
//! rather than the sum. This ensures a protection from overslashing.
//!
//! Second, we do not want the time period (or "span") that the maximum is computed
//! over to last indefinitely. That would allow participants to begin acting with
//! impunity after some point, fearing no further repercussions. For that reason, we
//! automatically "chill" validators and withdraw a nominator's nomination after a slashing event,
//! requiring them to re-enlist voluntarily (acknowledging the slash) and begin a new
//! slashing span.
//!
//! Typically, you will have a single slashing event per slashing span. Only in the case
//! where a validator releases many misbehaviors at once, or goes "back in time" to misbehave in
//! eras that have already passed, would you encounter situations where a slashing span
//! has multiple misbehaviors. However, accounting for such cases is necessary
//! to deter a class of "rage-quit" attacks.
//!
//! Based on research at <https://w3f-research.readthedocs.io/en/latest/polkadot/slashing/npos.html>

use crate::{
	BalanceOf, Config, EraIndex, Error, Exposure, NegativeImbalanceOf, Pallet, Perbill,
	SessionInterface, Store, UnappliedSlash,
};
use codec::{Decode, Encode};
use frame_support::{
	ensure,
	traits::{Currency, Get, Imbalance, OnUnbalanced},
};
use scale_info::TypeInfo;
use sp_runtime::{
	traits::{Saturating, Zero},
	DispatchResult, RuntimeDebug,
};
use sp_std::vec::Vec;

/// The proportion of the slashing reward to be paid out on the first slashing detection.
/// This is f_1 in the paper.
const REWARD_F1: Perbill = Perbill::from_percent(50);

/// The index of a slashing span - unique to each stash.
pub type SpanIndex = u32;

// A range of start..end eras for a slashing span.
#[derive(Encode, Decode, TypeInfo)]
#[cfg_attr(test, derive(Debug, PartialEq))]
pub(crate) struct SlashingSpan {
	pub(crate) index: SpanIndex,
	pub(crate) start: EraIndex,
	pub(crate) length: Option<EraIndex>, // the ongoing slashing span has indeterminate length.
}

impl SlashingSpan {
	fn contains_era(&self, era: EraIndex) -> bool {
		self.start <= era && self.length.map_or(true, |l| self.start + l > era)
	}
}

/// An encoding of all of a nominator's slashing spans.
#[derive(Encode, Decode, RuntimeDebug, TypeInfo)]
pub struct SlashingSpans {
	// the index of the current slashing span of the nominator. different for
	// every stash, resets when the account hits free balance 0.
	span_index: SpanIndex,
	// the start era of the most recent (ongoing) slashing span.
	last_start: EraIndex,
	// the last era at which a non-zero slash occurred.
	last_nonzero_slash: EraIndex,
	// all prior slashing spans' start indices, in reverse order (most recent first)
	// encoded as offsets relative to the slashing span after it.
	prior: Vec<EraIndex>,
}

impl SlashingSpans {
	// creates a new record of slashing spans for a stash, starting at the beginning
	// of the bonding period, relative to now.
	pub(crate) fn new(window_start: EraIndex) -> Self {
		SlashingSpans {
			span_index: 0,
			last_start: window_start,
			// initialize to zero, as this structure is lazily created until
			// the first slash is applied. setting equal to `window_start` would
			// put a time limit on nominations.
			last_nonzero_slash: 0,
			prior: Vec::new(),
		}
	}

	// update the slashing spans to reflect the start of a new span at the era after `now`
	// returns `true` if a new span was started, `false` otherwise. `false` indicates
	// that internal state is unchanged.
	pub(crate) fn end_span(&mut self, now: EraIndex) -> bool {
		let next_start = now + 1;
		if next_start <= self.last_start {
			return false
		}

		let last_length = next_start - self.last_start;
		self.prior.insert(0, last_length);
		self.last_start = next_start;
		self.span_index += 1;
		true
	}

	// an iterator over all slashing spans in _reverse_ order - most recent first.
	pub(crate) fn iter(&'_ self) -> impl Iterator<Item = SlashingSpan> + '_ {
		let mut last_start = self.last_start;
		let mut index = self.span_index;
		let last = SlashingSpan { index, start: last_start, length: None };
		let prior = self.prior.iter().cloned().map(move |length| {
			let start = last_start - length;
			last_start = start;
			index -= 1;

			SlashingSpan { index, start, length: Some(length) }
		});

		sp_std::iter::once(last).chain(prior)
	}

	/// Yields the era index where the most recent non-zero slash occurred.
	pub fn last_nonzero_slash(&self) -> EraIndex {
		self.last_nonzero_slash
	}

	// prune the slashing spans against a window, whose start era index is given.
	//
	// If this returns `Some`, then it includes a range start..end of all the span
	// indices which were pruned.
	fn prune(&mut self, window_start: EraIndex) -> Option<(SpanIndex, SpanIndex)> {
		let old_idx = self
			.iter()
			.skip(1) // skip ongoing span.
			.position(|span| span.length.map_or(false, |len| span.start + len <= window_start));

		let earliest_span_index = self.span_index - self.prior.len() as SpanIndex;
		let pruned = match old_idx {
			Some(o) => {
				self.prior.truncate(o);
				let new_earliest = self.span_index - self.prior.len() as SpanIndex;
				Some((earliest_span_index, new_earliest))
			},
			None => None,
		};

		// readjust the ongoing span, if it started before the beginning of the window.
		self.last_start = sp_std::cmp::max(self.last_start, window_start);
		pruned
	}
}

/// A slashing-span record for a particular stash.
#[derive(Encode, Decode, Default, TypeInfo)]
pub(crate) struct SpanRecord<Balance> {
	slashed: Balance,
	paid_out: Balance,
}

impl<Balance> SpanRecord<Balance> {
	/// The value of stash balance slashed in this span.
	#[cfg(test)]
	pub(crate) fn amount_slashed(&self) -> &Balance {
		&self.slashed
	}
}

/// Parameters for performing a slash.
#[derive(Clone)]
pub(crate) struct SlashParams<'a, T: 'a + Config> {
	/// The stash account being slashed.
	pub(crate) stash: &'a T::AccountId,
	/// The proportion of the slash.
	pub(crate) slash: Perbill,
	/// The exposure of the stash and all nominators.
	pub(crate) exposure: &'a Exposure<T::AccountId, BalanceOf<T>>,
	/// The era where the offence occurred.
	pub(crate) slash_era: EraIndex,
	/// The first era in the current bonding period.
	pub(crate) window_start: EraIndex,
	/// The current era.
	pub(crate) now: EraIndex,
	/// The maximum percentage of a slash that ever gets paid out.
	/// This is f_inf in the paper.
	pub(crate) reward_proportion: Perbill,
}

/// Computes a slash of a validator and nominators. It returns an unapplied
/// record to be applied at some later point. Slashing metadata is updated in storage,
/// since unapplied records are only rarely intended to be dropped.
///
/// The pending slash record returned does not have initialized reporters. Those have
/// to be set at a higher level, if any.
pub(crate) fn compute_slash<T: Config>(
	params: SlashParams<T>,
) -> Option<UnappliedSlash<T::AccountId, BalanceOf<T>>> {
	let SlashParams { stash, slash, exposure, slash_era, window_start, now, reward_proportion } =
		params.clone();

	let mut reward_payout = Zero::zero();
	let mut val_slashed = Zero::zero();

	// is the slash amount here a maximum for the era?
	let own_slash = slash * exposure.own;
	if slash * exposure.total == Zero::zero() {
		// kick out the validator even if they won't be slashed,
		// as long as the misbehavior is from their most recent slashing span.
		kick_out_if_recent::<T>(params);
		return None
	}

	let (prior_slash_p, _era_slash) =
		<Pallet<T> as Store>::ValidatorSlashInEra::get(&slash_era, stash)
			.unwrap_or((Perbill::zero(), Zero::zero()));

	// compare slash proportions rather than slash values to avoid issues due to rounding
	// error.
	if slash.deconstruct() > prior_slash_p.deconstruct() {
		<Pallet<T> as Store>::ValidatorSlashInEra::insert(&slash_era, stash, &(slash, own_slash));
	} else {
		// we slash based on the max in era - this new event is not the max,
		// so neither the validator or any nominators will need an update.
		//
		// this does lead to a divergence of our system from the paper, which
		// pays out some reward even if the latest report is not max-in-era.
		// we opt to avoid the nominator lookups and edits and leave more rewards
		// for more drastic misbehavior.
		return None
	}

	// apply slash to validator.
	{
		let mut spans = fetch_spans::<T>(
			stash,
			window_start,
			&mut reward_payout,
			&mut val_slashed,
			reward_proportion,
		);

		let target_span = spans.compare_and_update_span_slash(slash_era, own_slash);

		if target_span == Some(spans.span_index()) {
			// misbehavior occurred within the current slashing span - take appropriate
			// actions.

			// chill the validator - it misbehaved in the current span and should
			// not continue in the next election. also end the slashing span.
			spans.end_span(now);
			<Pallet<T>>::chill_stash(stash);
		}
	}

	// add the validator to the offenders list and make sure it is disabled for
	// the duration of the era
	add_offending_validator::<T>(params.stash, true);

	let mut nominators_slashed = Vec::new();
	reward_payout += slash_nominators::<T>(params, prior_slash_p, &mut nominators_slashed);

	Some(UnappliedSlash {
		validator: stash.clone(),
		own: val_slashed,
		others: nominators_slashed,
		reporters: Vec::new(),
		payout: reward_payout,
	})
}

// doesn't apply any slash, but kicks out the validator if the misbehavior is from
// the most recent slashing span.
fn kick_out_if_recent<T: Config>(params: SlashParams<T>) {
	// these are not updated by era-span or end-span.
	let mut reward_payout = Zero::zero();
	let mut val_slashed = Zero::zero();
	let mut spans = fetch_spans::<T>(
		params.stash,
		params.window_start,
		&mut reward_payout,
		&mut val_slashed,
		params.reward_proportion,
	);

	if spans.era_span(params.slash_era).map(|s| s.index) == Some(spans.span_index()) {
		spans.end_span(params.now);
		<Pallet<T>>::chill_stash(params.stash);
	}

	// add the validator to the offenders list but since there's no slash being
	// applied there's no need to disable the validator
	add_offending_validator::<T>(params.stash, false);
}

/// Add the given validator to the offenders list and optionally disable it.
/// If after adding the validator `OffendingValidatorsThreshold` is reached
/// a new era will be forced.
fn add_offending_validator<T: Config>(stash: &T::AccountId, disable: bool) {
	<Pallet<T> as Store>::OffendingValidators::mutate(|offending| {
		let validators = T::SessionInterface::validators();
		let validator_index = match validators.iter().position(|i| i == stash) {
			Some(index) => index,
			None => return,
		};

		let validator_index_u32 = validator_index as u32;

		match offending.binary_search_by_key(&validator_index_u32, |(index, _)| *index) {
			// this is a new offending validator
			Err(index) => {
				offending.insert(index, (validator_index_u32, disable));

				let offending_threshold =
					T::OffendingValidatorsThreshold::get() * validators.len() as u32;

				if offending.len() >= offending_threshold as usize {
					// force a new era, to select a new validator set
					<Pallet<T>>::ensure_new_era()
				}

				if disable {
					T::SessionInterface::disable_validator(validator_index_u32);
				}
			},
			Ok(index) => {
				if disable && !offending[index].1 {
					// the validator had previously offended without being disabled,
					// let's make sure we disable it now
					offending[index].1 = true;
					T::SessionInterface::disable_validator(validator_index_u32);
				}
			},
		}
	});
}

/// Slash nominators. Accepts general parameters and the prior slash percentage of the validator.
///
/// Returns the amount of reward to pay out.
fn slash_nominators<T: Config>(
	params: SlashParams<T>,
	prior_slash_p: Perbill,
	nominators_slashed: &mut Vec<(T::AccountId, BalanceOf<T>)>,
) -> BalanceOf<T> {
	let SlashParams { stash: _, slash, exposure, slash_era, window_start, now, reward_proportion } =
		params;

	let mut reward_payout = Zero::zero();

	nominators_slashed.reserve(exposure.others.len());
	for nominator in &exposure.others {
		let stash = &nominator.who;
		let mut nom_slashed = Zero::zero();

		// the era slash of a nominator always grows, if the validator
		// had a new max slash for the era.
		let era_slash = {
			let own_slash_prior = prior_slash_p * nominator.value;
			let own_slash_by_validator = slash * nominator.value;
			let own_slash_difference = own_slash_by_validator.saturating_sub(own_slash_prior);

			let mut era_slash = <Pallet<T> as Store>::NominatorSlashInEra::get(&slash_era, stash)
				.unwrap_or_else(|| Zero::zero());

			era_slash += own_slash_difference;

			<Pallet<T> as Store>::NominatorSlashInEra::insert(&slash_era, stash, &era_slash);

			era_slash
		};

		// compare the era slash against other eras in the same span.
		{
			let mut spans = fetch_spans::<T>(
				stash,
				window_start,
				&mut reward_payout,
				&mut nom_slashed,
				reward_proportion,
			);

			let target_span = spans.compare_and_update_span_slash(slash_era, era_slash);

			if target_span == Some(spans.span_index()) {
				// End the span, but don't chill the nominator. its nomination
				// on this validator will be ignored in the future.
				spans.end_span(now);
			}
		}

		nominators_slashed.push((stash.clone(), nom_slashed));
	}

	reward_payout
}

// helper struct for managing a set of spans we are currently inspecting.
// writes alterations to disk on drop, but only if a slash has been carried out.
//
// NOTE: alterations to slashing metadata should not be done after this is dropped.
// dropping this struct applies any necessary slashes, which can lead to free balance
// being 0, and the account being garbage-collected -- a dead account should get no new
// metadata.
struct InspectingSpans<'a, T: Config + 'a> {
	dirty: bool,
	window_start: EraIndex,
	stash: &'a T::AccountId,
	spans: SlashingSpans,
	paid_out: &'a mut BalanceOf<T>,
	slash_of: &'a mut BalanceOf<T>,
	reward_proportion: Perbill,
	_marker: sp_std::marker::PhantomData<T>,
}

// fetches the slashing spans record for a stash account, initializing it if necessary.
fn fetch_spans<'a, T: Config + 'a>(
	stash: &'a T::AccountId,
	window_start: EraIndex,
	paid_out: &'a mut BalanceOf<T>,
	slash_of: &'a mut BalanceOf<T>,
	reward_proportion: Perbill,
) -> InspectingSpans<'a, T> {
	let spans = <Pallet<T> as Store>::SlashingSpans::get(stash).unwrap_or_else(|| {
		let spans = SlashingSpans::new(window_start);
		<Pallet<T> as Store>::SlashingSpans::insert(stash, &spans);
		spans
	});

	InspectingSpans {
		dirty: false,
		window_start,
		stash,
		spans,
		slash_of,
		paid_out,
		reward_proportion,
		_marker: sp_std::marker::PhantomData,
	}
}

impl<'a, T: 'a + Config> InspectingSpans<'a, T> {
	fn span_index(&self) -> SpanIndex {
		self.spans.span_index
	}

	fn end_span(&mut self, now: EraIndex) {
		self.dirty = self.spans.end_span(now) || self.dirty;
	}

	// add some value to the slash of the staker.
	// invariant: the staker is being slashed for non-zero value here
	// although `amount` may be zero, as it is only a difference.
	fn add_slash(&mut self, amount: BalanceOf<T>, slash_era: EraIndex) {
		*self.slash_of += amount;
		self.spans.last_nonzero_slash = sp_std::cmp::max(self.spans.last_nonzero_slash, slash_era);
	}

	// find the span index of the given era, if covered.
	fn era_span(&self, era: EraIndex) -> Option<SlashingSpan> {
		self.spans.iter().find(|span| span.contains_era(era))
	}

	// compares the slash in an era to the overall current span slash.
	// if it's higher, applies the difference of the slashes and then updates the span on disk.
	//
	// returns the span index of the era where the slash occurred, if any.
	fn compare_and_update_span_slash(
		&mut self,
		slash_era: EraIndex,
		slash: BalanceOf<T>,
	) -> Option<SpanIndex> {
		let target_span = self.era_span(slash_era)?;
		let span_slash_key = (self.stash.clone(), target_span.index);
		let mut span_record = <Pallet<T> as Store>::SpanSlash::get(&span_slash_key);
		let mut changed = false;

		let reward = if span_record.slashed < slash {
			// new maximum span slash. apply the difference.
			let difference = slash - span_record.slashed;
			span_record.slashed = slash;

			// compute reward.
			let reward =
				REWARD_F1 * (self.reward_proportion * slash).saturating_sub(span_record.paid_out);

			self.add_slash(difference, slash_era);
			changed = true;

			reward
		} else if span_record.slashed == slash {
			// compute reward. no slash difference to apply.
			REWARD_F1 * (self.reward_proportion * slash).saturating_sub(span_record.paid_out)
		} else {
			Zero::zero()
		};

		if !reward.is_zero() {
			changed = true;
			span_record.paid_out += reward;
			*self.paid_out += reward;
		}

		if changed {
			self.dirty = true;
			<Pallet<T> as Store>::SpanSlash::insert(&span_slash_key, &span_record);
		}

		Some(target_span.index)
	}
}

impl<'a, T: 'a + Config> Drop for InspectingSpans<'a, T> {
	fn drop(&mut self) {
		// only update on disk if we slashed this account.
		if !self.dirty {
			return
		}

		if let Some((start, end)) = self.spans.prune(self.window_start) {
			for span_index in start..end {
				<Pallet<T> as Store>::SpanSlash::remove(&(self.stash.clone(), span_index));
			}
		}

		<Pallet<T> as Store>::SlashingSpans::insert(self.stash, &self.spans);
	}
}

/// Clear slashing metadata for an obsolete era.
pub(crate) fn clear_era_metadata<T: Config>(obsolete_era: EraIndex) {
	<Pallet<T> as Store>::ValidatorSlashInEra::remove_prefix(&obsolete_era, None);
	<Pallet<T> as Store>::NominatorSlashInEra::remove_prefix(&obsolete_era, None);
}

/// Clear slashing metadata for a dead account.
pub(crate) fn clear_stash_metadata<T: Config>(
	stash: &T::AccountId,
	num_slashing_spans: u32,
) -> DispatchResult {
	let spans = match <Pallet<T> as Store>::SlashingSpans::get(stash) {
		None => return Ok(()),
		Some(s) => s,
	};

	ensure!(
		num_slashing_spans as usize >= spans.iter().count(),
		Error::<T>::IncorrectSlashingSpans
	);

	<Pallet<T> as Store>::SlashingSpans::remove(stash);

	// kill slashing-span metadata for account.
	//
	// this can only happen while the account is staked _if_ they are completely slashed.
	// in that case, they may re-bond, but it would count again as span 0. Further ancient
	// slashes would slash into this new bond, since metadata has now been cleared.
	for span in spans.iter() {
		<Pallet<T> as Store>::SpanSlash::remove(&(stash.clone(), span.index));
	}

	Ok(())
}

// apply the slash to a stash account, deducting any missing funds from the reward
// payout, saturating at 0. this is mildly unfair but also an edge-case that
// can only occur when overlapping locked funds have been slashed.
pub fn do_slash<T: Config>(
	stash: &T::AccountId,
	value: BalanceOf<T>,
	reward_payout: &mut BalanceOf<T>,
	slashed_imbalance: &mut NegativeImbalanceOf<T>,
) {
	let controller = match <Pallet<T>>::bonded(stash) {
		None => return, // defensive: should always exist.
		Some(c) => c,
	};

	let mut ledger = match <Pallet<T>>::ledger(&controller) {
		Some(ledger) => ledger,
		None => return, // nothing to do.
	};

	let value = ledger.slash(value, T::Currency::minimum_balance());

	if !value.is_zero() {
		let (imbalance, missing) = T::Currency::slash(stash, value);
		slashed_imbalance.subsume(imbalance);

		if !missing.is_zero() {
			// deduct overslash from the reward payout
			*reward_payout = reward_payout.saturating_sub(missing);
		}

		<Pallet<T>>::update_ledger(&controller, &ledger);

		// trigger the event
		<Pallet<T>>::deposit_event(super::Event::<T>::Slashed(stash.clone(), value));
	}
}

/// Apply a previously-unapplied slash.
pub(crate) fn apply_slash<T: Config>(unapplied_slash: UnappliedSlash<T::AccountId, BalanceOf<T>>) {
	let mut slashed_imbalance = NegativeImbalanceOf::<T>::zero();
	let mut reward_payout = unapplied_slash.payout;

	do_slash::<T>(
		&unapplied_slash.validator,
		unapplied_slash.own,
		&mut reward_payout,
		&mut slashed_imbalance,
	);

	for &(ref nominator, nominator_slash) in &unapplied_slash.others {
		do_slash::<T>(&nominator, nominator_slash, &mut reward_payout, &mut slashed_imbalance);
	}

	pay_reporters::<T>(reward_payout, slashed_imbalance, &unapplied_slash.reporters);
}

/// Apply a reward payout to some reporters, paying the rewards out of the slashed imbalance.
fn pay_reporters<T: Config>(
	reward_payout: BalanceOf<T>,
	slashed_imbalance: NegativeImbalanceOf<T>,
	reporters: &[T::AccountId],
) {
	if reward_payout.is_zero() || reporters.is_empty() {
		// nobody to pay out to or nothing to pay;
		// just treat the whole value as slashed.
		T::Slash::on_unbalanced(slashed_imbalance);
		return
	}

	// take rewards out of the slashed imbalance.
	let reward_payout = reward_payout.min(slashed_imbalance.peek());
	let (mut reward_payout, mut value_slashed) = slashed_imbalance.split(reward_payout);

	let per_reporter = reward_payout.peek() / (reporters.len() as u32).into();
	for reporter in reporters {
		let (reporter_reward, rest) = reward_payout.split(per_reporter);
		reward_payout = rest;

		// this cancels out the reporter reward imbalance internally, leading
		// to no change in total issuance.
		T::Currency::resolve_creating(reporter, reporter_reward);
	}

	// the rest goes to the on-slash imbalance handler (e.g. treasury)
	value_slashed.subsume(reward_payout); // remainder of reward division remains.
	T::Slash::on_unbalanced(value_slashed);
}

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

	#[test]
	fn span_contains_era() {
		// unbounded end
		let span = SlashingSpan { index: 0, start: 1000, length: None };
		assert!(!span.contains_era(0));
		assert!(!span.contains_era(999));

		assert!(span.contains_era(1000));
		assert!(span.contains_era(1001));
		assert!(span.contains_era(10000));

		// bounded end - non-inclusive range.
		let span = SlashingSpan { index: 0, start: 1000, length: Some(10) };
		assert!(!span.contains_era(0));
		assert!(!span.contains_era(999));

		assert!(span.contains_era(1000));
		assert!(span.contains_era(1001));
		assert!(span.contains_era(1009));
		assert!(!span.contains_era(1010));
		assert!(!span.contains_era(1011));
	}

	#[test]
	fn single_slashing_span() {
		let spans = SlashingSpans {
			span_index: 0,
			last_start: 1000,
			last_nonzero_slash: 0,
			prior: Vec::new(),
		};

		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![SlashingSpan { index: 0, start: 1000, length: None }],
		);
	}

	#[test]
	fn many_prior_spans() {
		let spans = SlashingSpans {
			span_index: 10,
			last_start: 1000,
			last_nonzero_slash: 0,
			prior: vec![10, 9, 8, 10],
		};

		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 10, start: 1000, length: None },
				SlashingSpan { index: 9, start: 990, length: Some(10) },
				SlashingSpan { index: 8, start: 981, length: Some(9) },
				SlashingSpan { index: 7, start: 973, length: Some(8) },
				SlashingSpan { index: 6, start: 963, length: Some(10) },
			],
		)
	}

	#[test]
	fn pruning_spans() {
		let mut spans = SlashingSpans {
			span_index: 10,
			last_start: 1000,
			last_nonzero_slash: 0,
			prior: vec![10, 9, 8, 10],
		};

		assert_eq!(spans.prune(981), Some((6, 8)));
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 10, start: 1000, length: None },
				SlashingSpan { index: 9, start: 990, length: Some(10) },
				SlashingSpan { index: 8, start: 981, length: Some(9) },
			],
		);

		assert_eq!(spans.prune(982), None);
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 10, start: 1000, length: None },
				SlashingSpan { index: 9, start: 990, length: Some(10) },
				SlashingSpan { index: 8, start: 981, length: Some(9) },
			],
		);

		assert_eq!(spans.prune(989), None);
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 10, start: 1000, length: None },
				SlashingSpan { index: 9, start: 990, length: Some(10) },
				SlashingSpan { index: 8, start: 981, length: Some(9) },
			],
		);

		assert_eq!(spans.prune(1000), Some((8, 10)));
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![SlashingSpan { index: 10, start: 1000, length: None },],
		);

		assert_eq!(spans.prune(2000), None);
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![SlashingSpan { index: 10, start: 2000, length: None },],
		);

		// now all in one shot.
		let mut spans = SlashingSpans {
			span_index: 10,
			last_start: 1000,
			last_nonzero_slash: 0,
			prior: vec![10, 9, 8, 10],
		};
		assert_eq!(spans.prune(2000), Some((6, 10)));
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![SlashingSpan { index: 10, start: 2000, length: None },],
		);
	}

	#[test]
	fn ending_span() {
		let mut spans = SlashingSpans {
			span_index: 1,
			last_start: 10,
			last_nonzero_slash: 0,
			prior: Vec::new(),
		};

		assert!(spans.end_span(10));

		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 2, start: 11, length: None },
				SlashingSpan { index: 1, start: 10, length: Some(1) },
			],
		);

		assert!(spans.end_span(15));
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 3, start: 16, length: None },
				SlashingSpan { index: 2, start: 11, length: Some(5) },
				SlashingSpan { index: 1, start: 10, length: Some(1) },
			],
		);

		// does nothing if not a valid end.
		assert!(!spans.end_span(15));
		assert_eq!(
			spans.iter().collect::<Vec<_>>(),
			vec![
				SlashingSpan { index: 3, start: 16, length: None },
				SlashingSpan { index: 2, start: 11, length: Some(5) },
				SlashingSpan { index: 1, start: 10, length: Some(1) },
			],
		);
	}
}