eth2.0-specs/specs/altair/beacon-chain.md

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# Ethereum 2.0 Altair Beacon chain changes
## Table of contents
<!-- TOC -->
<!-- START doctoc generated TOC please keep comment here to allow auto update -->
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- [Introduction](#introduction)
- [Custom types](#custom-types)
- [Constants](#constants)
- [Participation flag indices](#participation-flag-indices)
- [Participation flag fractions](#participation-flag-fractions)
- [Misc](#misc)
- [Configuration](#configuration)
- [Updated penalty values](#updated-penalty-values)
- [Misc](#misc-1)
- [Time parameters](#time-parameters)
- [Domain types](#domain-types)
- [Containers](#containers)
- [Modified containers](#modified-containers)
- [`BeaconBlockBody`](#beaconblockbody)
- [`BeaconState`](#beaconstate)
- [New containers](#new-containers)
- [`SyncCommittee`](#synccommittee)
- [Helper functions](#helper-functions)
- [`Predicates`](#predicates)
- [`eth2_fast_aggregate_verify`](#eth2_fast_aggregate_verify)
- [Misc](#misc-2)
- [`get_flag_indices_and_numerators`](#get_flag_indices_and_numerators)
- [`add_flag`](#add_flag)
- [`has_flag`](#has_flag)
- [Beacon state accessors](#beacon-state-accessors)
- [`get_sync_committee_indices`](#get_sync_committee_indices)
- [`get_sync_committee`](#get_sync_committee)
- [`get_base_reward`](#get_base_reward)
- [`get_unslashed_participating_indices`](#get_unslashed_participating_indices)
- [`get_flag_index_deltas`](#get_flag_index_deltas)
- [Modified `get_inactivity_penalty_deltas`](#modified-get_inactivity_penalty_deltas)
- [Beacon state mutators](#beacon-state-mutators)
- [Modified `slash_validator`](#modified-slash_validator)
- [Block processing](#block-processing)
- [Modified `process_attestation`](#modified-process_attestation)
- [Modified `process_deposit`](#modified-process_deposit)
- [Sync committee processing](#sync-committee-processing)
- [Epoch processing](#epoch-processing)
- [Justification and finalization](#justification-and-finalization)
- [Inactivity scores](#inactivity-scores)
- [Rewards and penalties](#rewards-and-penalties)
- [Slashings](#slashings)
- [Participation flags updates](#participation-flags-updates)
- [Sync committee updates](#sync-committee-updates)
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## Introduction
Altair is the first beacon chain hard fork. Its main features are:
* sync committees to support light clients
* incentive accounting reforms to reduce spec complexity
* penalty parameter updates to move them to their planned maximally punitive configuration
## Custom types
| Name | SSZ equivalent | Description |
| - | - | - |
| `ParticipationFlags` | `uint8` | a succinct representation of 8 boolean participation flags |
## Constants
### Participation flag indices
| Name | Value |
| - | - |
| `TIMELY_HEAD_FLAG_INDEX` | `0` |
| `TIMELY_SOURCE_FLAG_INDEX` | `1` |
| `TIMELY_TARGET_FLAG_INDEX` | `2` |
### Participation flag fractions
| Name | Value |
| - | - |
| `TIMELY_HEAD_FLAG_NUMERATOR` | `12` |
| `TIMELY_SOURCE_FLAG_NUMERATOR` | `12` |
| `TIMELY_TARGET_FLAG_NUMERATOR` | `32` |
| `FLAG_DENOMINATOR` | `64` |
**Note**: The sum of the participatition flag fractions (7/8) plus the proposer reward fraction (1/8) equals 1.
### Misc
| Name | Value |
| - | - |
| `G2_POINT_AT_INFINITY` | `BLSSignature(b'\xc0' + b'\x00' * 95)` |
## Configuration
### Updated penalty values
This patch updates a few configuration values to move penalty parameters toward their final, maxmium security values.
*Note*: The spec does *not* override previous configuration values but instead creates new values and replaces usage throughout.
| Name | Value |
| - | - |
| `ALTAIR_INACTIVITY_PENALTY_QUOTIENT` | `uint64(3 * 2**24)` (= 50,331,648) |
| `ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT` | `uint64(2**6)` (= 64) |
| `ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER` | `uint64(2)` |
### Misc
| Name | Value |
| - | - |
| `SYNC_COMMITTEE_SIZE` | `uint64(2**10)` (= 1,024) |
| `SYNC_SUBCOMMITTEE_SIZE` | `uint64(2**6)` (= 64) |
| `INACTIVITY_SCORE_BIAS` | `uint64(4)` |
### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `EPOCHS_PER_SYNC_COMMITTEE_PERIOD` | `Epoch(2**8)` (= 256) | epochs | ~27 hours |
### Domain types
| Name | Value |
| - | - |
| `DOMAIN_SYNC_COMMITTEE` | `DomainType('0x07000000')` |
## Containers
### Modified containers
#### `BeaconBlockBody`
```python
class BeaconBlockBody(Container):
randao_reveal: BLSSignature
eth1_data: Eth1Data # Eth1 data vote
graffiti: Bytes32 # Arbitrary data
# Operations
proposer_slashings: List[ProposerSlashing, MAX_PROPOSER_SLASHINGS]
attester_slashings: List[AttesterSlashing, MAX_ATTESTER_SLASHINGS]
attestations: List[Attestation, MAX_ATTESTATIONS]
deposits: List[Deposit, MAX_DEPOSITS]
voluntary_exits: List[SignedVoluntaryExit, MAX_VOLUNTARY_EXITS]
# Sync committee aggregate signature
sync_committee_bits: Bitvector[SYNC_COMMITTEE_SIZE] # [New in Altair]
sync_committee_signature: BLSSignature # [New in Altair]
```
#### `BeaconState`
```python
class BeaconState(Container):
# Versioning
genesis_time: uint64
genesis_validators_root: Root
slot: Slot
fork: Fork
# History
latest_block_header: BeaconBlockHeader
block_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
state_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
historical_roots: List[Root, HISTORICAL_ROOTS_LIMIT]
# Eth1
eth1_data: Eth1Data
eth1_data_votes: List[Eth1Data, EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH]
eth1_deposit_index: uint64
# Registry
validators: List[Validator, VALIDATOR_REGISTRY_LIMIT]
balances: List[Gwei, VALIDATOR_REGISTRY_LIMIT]
# Randomness
randao_mixes: Vector[Bytes32, EPOCHS_PER_HISTORICAL_VECTOR]
# Slashings
slashings: Vector[Gwei, EPOCHS_PER_SLASHINGS_VECTOR] # Per-epoch sums of slashed effective balances
# Participation
previous_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT] # [Modified in Altair]
current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT] # [Modified in Altair]
# Finality
justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH] # Bit set for every recent justified epoch
previous_justified_checkpoint: Checkpoint
current_justified_checkpoint: Checkpoint
finalized_checkpoint: Checkpoint
# Inactivity
inactivity_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT] # [New in Altair]
# Sync
current_sync_committee: SyncCommittee # [New in Altair]
next_sync_committee: SyncCommittee # [New in Altair]
```
### New containers
#### `SyncCommittee`
```python
class SyncCommittee(Container):
pubkeys: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE]
pubkey_aggregates: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE // SYNC_SUBCOMMITTEE_SIZE]
```
## Helper functions
### `Predicates`
#### `eth2_fast_aggregate_verify`
```python
def eth2_fast_aggregate_verify(pubkeys: Sequence[BLSPubkey], message: Bytes32, signature: BLSSignature) -> bool:
"""
Wrapper to ``bls.FastAggregateVerify`` accepting the ``G2_POINT_AT_INFINITY`` signature when ``pubkeys`` is empty.
"""
if len(pubkeys) == 0 and signature == G2_POINT_AT_INFINITY:
return True
return bls.FastAggregateVerify(pubkeys, message, signature)
```
### Misc
#### `get_flag_indices_and_numerators`
```python
def get_flag_indices_and_numerators() -> Sequence[Tuple[int, int]]:
return (
(TIMELY_HEAD_FLAG_INDEX, TIMELY_HEAD_FLAG_NUMERATOR),
(TIMELY_SOURCE_FLAG_INDEX, TIMELY_SOURCE_FLAG_NUMERATOR),
(TIMELY_TARGET_FLAG_INDEX, TIMELY_TARGET_FLAG_NUMERATOR),
)
```
#### `add_flag`
```python
def add_flag(flags: ParticipationFlags, flag_index: int) -> ParticipationFlags:
flag = ParticipationFlags(2**flag_index)
return flags | flag
```
#### `has_flag`
```python
def has_flag(flags: ParticipationFlags, flag_index: int) -> bool:
flag = ParticipationFlags(2**flag_index)
return flags & flag == flag
```
### Beacon state accessors
#### `get_sync_committee_indices`
```python
def get_sync_committee_indices(state: BeaconState, epoch: Epoch) -> Sequence[ValidatorIndex]:
"""
Return the sequence of sync committee indices (which may include duplicate indices) for a given state and epoch.
"""
MAX_RANDOM_BYTE = 2**8 - 1
base_epoch = Epoch((max(epoch // EPOCHS_PER_SYNC_COMMITTEE_PERIOD, 1) - 1) * EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
active_validator_indices = get_active_validator_indices(state, base_epoch)
active_validator_count = uint64(len(active_validator_indices))
seed = get_seed(state, base_epoch, DOMAIN_SYNC_COMMITTEE)
i = 0
sync_committee_indices: List[ValidatorIndex] = []
while len(sync_committee_indices) < SYNC_COMMITTEE_SIZE:
shuffled_index = compute_shuffled_index(uint64(i % active_validator_count), active_validator_count, seed)
candidate_index = active_validator_indices[shuffled_index]
random_byte = hash(seed + uint_to_bytes(uint64(i // 32)))[i % 32]
effective_balance = state.validators[candidate_index].effective_balance
if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte: # Sample with replacement
sync_committee_indices.append(candidate_index)
i += 1
return sync_committee_indices
```
#### `get_sync_committee`
```python
def get_sync_committee(state: BeaconState, epoch: Epoch) -> SyncCommittee:
"""
Return the sync committee for a given state and epoch.
"""
indices = get_sync_committee_indices(state, epoch)
pubkeys = [state.validators[index].pubkey for index in indices]
subcommitees = [pubkeys[i:i + SYNC_SUBCOMMITTEE_SIZE] for i in range(0, len(pubkeys), SYNC_SUBCOMMITTEE_SIZE)]
pubkey_aggregates = [bls.AggregatePKs(subcommitee) for subcommitee in subcommitees]
return SyncCommittee(pubkeys=pubkeys, pubkey_aggregates=pubkey_aggregates)
```
#### `get_base_reward`
*Note*: The function `get_base_reward` is modified with the removal of `BASE_REWARDS_PER_EPOCH`.
```python
def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
total_balance = get_total_active_balance(state)
effective_balance = state.validators[index].effective_balance
return Gwei(effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance))
```
#### `get_unslashed_participating_indices`
```python
def get_unslashed_participating_indices(state: BeaconState, flag_index: int, epoch: Epoch) -> Set[ValidatorIndex]:
"""
Return the active and unslashed validator indices for the given epoch and flag index.
"""
assert epoch in (get_previous_epoch(state), get_current_epoch(state))
if epoch == get_current_epoch(state):
epoch_participation = state.current_epoch_participation
else:
epoch_participation = state.previous_epoch_participation
active_validator_indices = get_active_validator_indices(state, epoch)
participating_indices = [i for i in active_validator_indices if has_flag(epoch_participation[i], flag_index)]
return set(filter(lambda index: not state.validators[index].slashed, participating_indices))
```
#### `get_flag_index_deltas`
```python
def get_flag_index_deltas(state: BeaconState,
flag_index: int,
numerator: uint64) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return the deltas for a given flag index by scanning through the participation flags.
"""
rewards = [Gwei(0)] * len(state.validators)
penalties = [Gwei(0)] * len(state.validators)
unslashed_participating_indices = get_unslashed_participating_indices(state, flag_index, get_previous_epoch(state))
increment = EFFECTIVE_BALANCE_INCREMENT # Factored out from balances to avoid uint64 overflow
unslashed_participating_increments = get_total_balance(state, unslashed_participating_indices) // increment
active_increments = get_total_active_balance(state) // increment
for index in get_eligible_validator_indices(state):
base_reward = get_base_reward(state, index)
if index in unslashed_participating_indices:
if is_in_inactivity_leak(state):
# This flag reward cancels the inactivity penalty corresponding to the flag index
rewards[index] += Gwei(base_reward * numerator // FLAG_DENOMINATOR)
else:
reward_numerator = base_reward * numerator * unslashed_participating_increments
rewards[index] += Gwei(reward_numerator // (active_increments * FLAG_DENOMINATOR))
else:
penalties[index] += Gwei(base_reward * numerator // FLAG_DENOMINATOR)
return rewards, penalties
```
#### Modified `get_inactivity_penalty_deltas`
*Note*: The function `get_inactivity_penalty_deltas` is modified in the selection of matching target indices
and the removal of `BASE_REWARDS_PER_EPOCH`.
```python
def get_inactivity_penalty_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return the inactivity penalty deltas by considering timely target participation flags and inactivity scores.
"""
rewards = [Gwei(0) for _ in range(len(state.validators))]
penalties = [Gwei(0) for _ in range(len(state.validators))]
if is_in_inactivity_leak(state):
previous_epoch = get_previous_epoch(state)
matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, previous_epoch)
for index in get_eligible_validator_indices(state):
for (_, numerator) in get_flag_indices_and_numerators():
# This inactivity penalty cancels the flag reward corresponding to the flag index
penalties[index] += Gwei(get_base_reward(state, index) * numerator // FLAG_DENOMINATOR)
if index not in matching_target_indices:
penalty_numerator = state.validators[index].effective_balance * state.inactivity_scores[index]
penalty_denominator = INACTIVITY_SCORE_BIAS * ALTAIR_INACTIVITY_PENALTY_QUOTIENT
penalties[index] += Gwei(penalty_numerator // penalty_denominator)
return rewards, penalties
```
### Beacon state mutators
#### Modified `slash_validator`
*Note*: The function `slash_validator` is modified to use `ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT`.
```python
def slash_validator(state: BeaconState,
slashed_index: ValidatorIndex,
whistleblower_index: ValidatorIndex=None) -> None:
"""
Slash the validator with index ``slashed_index``.
"""
epoch = get_current_epoch(state)
initiate_validator_exit(state, slashed_index)
validator = state.validators[slashed_index]
validator.slashed = True
validator.withdrawable_epoch = max(validator.withdrawable_epoch, Epoch(epoch + EPOCHS_PER_SLASHINGS_VECTOR))
state.slashings[epoch % EPOCHS_PER_SLASHINGS_VECTOR] += validator.effective_balance
decrease_balance(state, slashed_index, validator.effective_balance // ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT)
# Apply proposer and whistleblower rewards
proposer_index = get_beacon_proposer_index(state)
if whistleblower_index is None:
whistleblower_index = proposer_index
whistleblower_reward = Gwei(validator.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT)
proposer_reward = Gwei(whistleblower_reward // PROPOSER_REWARD_QUOTIENT)
increase_balance(state, proposer_index, proposer_reward)
increase_balance(state, whistleblower_index, Gwei(whistleblower_reward - proposer_reward))
```
### Block processing
```python
def process_block(state: BeaconState, block: BeaconBlock) -> None:
process_block_header(state, block)
process_randao(state, block.body)
process_eth1_data(state, block.body)
process_operations(state, block.body) # [Modified in Altair]
process_sync_committee(state, block.body) # [New in Altair]
```
#### Modified `process_attestation`
*Note*: The function `process_attestation` is modified to do incentive accounting with epoch participation flags.
```python
def process_attestation(state: BeaconState, attestation: Attestation) -> None:
data = attestation.data
assert data.target.epoch in (get_previous_epoch(state), get_current_epoch(state))
assert data.target.epoch == compute_epoch_at_slot(data.slot)
assert data.slot + MIN_ATTESTATION_INCLUSION_DELAY <= state.slot <= data.slot + SLOTS_PER_EPOCH
assert data.index < get_committee_count_per_slot(state, data.target.epoch)
committee = get_beacon_committee(state, data.slot, data.index)
assert len(attestation.aggregation_bits) == len(committee)
if data.target.epoch == get_current_epoch(state):
epoch_participation = state.current_epoch_participation
justified_checkpoint = state.current_justified_checkpoint
else:
epoch_participation = state.previous_epoch_participation
justified_checkpoint = state.previous_justified_checkpoint
# Matching roots
is_matching_head = data.beacon_block_root == get_block_root_at_slot(state, data.slot)
is_matching_source = data.source == justified_checkpoint
is_matching_target = data.target.root == get_block_root(state, data.target.epoch)
assert is_matching_source
# Verify signature
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
# Participation flag indices
participation_flag_indices = []
if is_matching_head and is_matching_target and state.slot <= data.slot + MIN_ATTESTATION_INCLUSION_DELAY:
participation_flag_indices.append(TIMELY_HEAD_FLAG_INDEX)
if is_matching_source and state.slot <= data.slot + integer_squareroot(SLOTS_PER_EPOCH):
participation_flag_indices.append(TIMELY_SOURCE_FLAG_INDEX)
if is_matching_target and state.slot <= data.slot + SLOTS_PER_EPOCH:
participation_flag_indices.append(TIMELY_TARGET_FLAG_INDEX)
# Update epoch participation flags
proposer_reward_numerator = 0
for index in get_attesting_indices(state, data, attestation.aggregation_bits):
for flag_index, flag_numerator in get_flag_indices_and_numerators():
if flag_index in participation_flag_indices and not has_flag(epoch_participation[index], flag_index):
epoch_participation[index] = add_flag(epoch_participation[index], flag_index)
proposer_reward_numerator += get_base_reward(state, index) * flag_numerator
# Reward proposer
proposer_reward = Gwei(proposer_reward_numerator // (FLAG_DENOMINATOR * PROPOSER_REWARD_QUOTIENT))
increase_balance(state, get_beacon_proposer_index(state), proposer_reward)
```
#### Modified `process_deposit`
*Note*: The function `process_deposit` is modified to initialize `inactivity_scores`, `previous_epoch_participation`, `current_epoch_participation`.
```python
def process_deposit(state: BeaconState, deposit: Deposit) -> None:
# Verify the Merkle branch
assert is_valid_merkle_branch(
leaf=hash_tree_root(deposit.data),
branch=deposit.proof,
depth=DEPOSIT_CONTRACT_TREE_DEPTH + 1, # Add 1 for the List length mix-in
index=state.eth1_deposit_index,
root=state.eth1_data.deposit_root,
)
# Deposits must be processed in order
state.eth1_deposit_index += 1
pubkey = deposit.data.pubkey
amount = deposit.data.amount
validator_pubkeys = [validator.pubkey for validator in state.validators]
if pubkey not in validator_pubkeys:
# Verify the deposit signature (proof of possession) which is not checked by the deposit contract
deposit_message = DepositMessage(
pubkey=deposit.data.pubkey,
withdrawal_credentials=deposit.data.withdrawal_credentials,
amount=deposit.data.amount,
)
domain = compute_domain(DOMAIN_DEPOSIT) # Fork-agnostic domain since deposits are valid across forks
signing_root = compute_signing_root(deposit_message, domain)
# Initialize validator if the deposit signature is valid
if bls.Verify(pubkey, signing_root, deposit.data.signature):
state.validators.append(get_validator_from_deposit(state, deposit))
state.balances.append(amount)
state.previous_epoch_participation.append(ParticipationFlags(0b0000_0000))
state.current_epoch_participation.append(ParticipationFlags(0b0000_0000))
state.inactivity_scores.append(0)
else:
# Increase balance by deposit amount
index = ValidatorIndex(validator_pubkeys.index(pubkey))
increase_balance(state, index, amount)
```
#### Sync committee processing
```python
def process_sync_committee(state: BeaconState, body: BeaconBlockBody) -> None:
# Verify sync committee aggregate signature signing over the previous slot block root
previous_slot = Slot(max(int(state.slot), 1) - 1)
committee_indices = get_sync_committee_indices(state, get_current_epoch(state))
participant_indices = [index for index, bit in zip(committee_indices, body.sync_committee_bits) if bit]
committee_pubkeys = state.current_sync_committee.pubkeys
participant_pubkeys = [pubkey for pubkey, bit in zip(committee_pubkeys, body.sync_committee_bits) if bit]
domain = get_domain(state, DOMAIN_SYNC_COMMITTEE, compute_epoch_at_slot(previous_slot))
signing_root = compute_signing_root(get_block_root_at_slot(state, previous_slot), domain)
assert eth2_fast_aggregate_verify(participant_pubkeys, signing_root, body.sync_committee_signature)
# Reward sync committee participants
proposer_rewards = Gwei(0)
active_validator_count = uint64(len(get_active_validator_indices(state, get_current_epoch(state))))
for participant_index in participant_indices:
proposer_reward = get_proposer_reward(state, participant_index)
proposer_rewards += proposer_reward
base_reward = get_base_reward(state, participant_index)
max_participant_reward = base_reward - proposer_reward
reward = Gwei(max_participant_reward * active_validator_count // (len(committee_indices) * SLOTS_PER_EPOCH))
increase_balance(state, participant_index, reward)
# Reward beacon proposer
increase_balance(state, get_beacon_proposer_index(state), proposer_rewards)
```
### Epoch processing
```python
def process_epoch(state: BeaconState) -> None:
process_justification_and_finalization(state) # [Modified in Altair]
process_inactivity_updates(state) # [New in Altair]
process_rewards_and_penalties(state) # [Modified in Altair]
process_registry_updates(state)
process_slashings(state) # [Modified in Altair]
process_eth1_data_reset(state)
process_effective_balance_updates(state)
process_slashings_reset(state)
process_randao_mixes_reset(state)
process_historical_roots_update(state)
process_participation_flag_updates(state) # [New in Altair]
process_sync_committee_updates(state) # [New in Altair]
```
#### Justification and finalization
*Note*: The function `process_justification_and_finalization` is modified with `matching_target_attestations` replaced by `matching_target_indices`.
```python
def process_justification_and_finalization(state: BeaconState) -> None:
# Initial FFG checkpoint values have a `0x00` stub for `root`.
# Skip FFG updates in the first two epochs to avoid corner cases that might result in modifying this stub.
if get_current_epoch(state) <= GENESIS_EPOCH + 1:
return
previous_epoch = get_previous_epoch(state)
current_epoch = get_current_epoch(state)
old_previous_justified_checkpoint = state.previous_justified_checkpoint
old_current_justified_checkpoint = state.current_justified_checkpoint
# Process justifications
state.previous_justified_checkpoint = state.current_justified_checkpoint
state.justification_bits[1:] = state.justification_bits[:JUSTIFICATION_BITS_LENGTH - 1]
state.justification_bits[0] = 0b0
matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, previous_epoch)
if get_total_balance(state, matching_target_indices) * 3 >= get_total_active_balance(state) * 2:
state.current_justified_checkpoint = Checkpoint(epoch=previous_epoch,
root=get_block_root(state, previous_epoch))
state.justification_bits[1] = 0b1
matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, current_epoch)
if get_total_balance(state, matching_target_indices) * 3 >= get_total_active_balance(state) * 2:
state.current_justified_checkpoint = Checkpoint(epoch=current_epoch,
root=get_block_root(state, current_epoch))
state.justification_bits[0] = 0b1
# Process finalizations
bits = state.justification_bits
# The 2nd/3rd/4th most recent epochs are justified, the 2nd using the 4th as source
if all(bits[1:4]) and old_previous_justified_checkpoint.epoch + 3 == current_epoch:
state.finalized_checkpoint = old_previous_justified_checkpoint
# The 2nd/3rd most recent epochs are justified, the 2nd using the 3rd as source
if all(bits[1:3]) and old_previous_justified_checkpoint.epoch + 2 == current_epoch:
state.finalized_checkpoint = old_previous_justified_checkpoint
# The 1st/2nd/3rd most recent epochs are justified, the 1st using the 3rd as source
if all(bits[0:3]) and old_current_justified_checkpoint.epoch + 2 == current_epoch:
state.finalized_checkpoint = old_current_justified_checkpoint
# The 1st/2nd most recent epochs are justified, the 1st using the 2nd as source
if all(bits[0:2]) and old_current_justified_checkpoint.epoch + 1 == current_epoch:
state.finalized_checkpoint = old_current_justified_checkpoint
```
#### Inactivity scores
*Note*: The function `process_inactivity_updates` is new.
```python
def process_inactivity_updates(state: BeaconState) -> None:
for index in get_eligible_validator_indices(state):
if index in get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state)):
if state.inactivity_scores[index] > 0:
state.inactivity_scores[index] -= 1
elif is_in_inactivity_leak(state):
state.inactivity_scores[index] += INACTIVITY_SCORE_BIAS
```
#### Rewards and penalties
*Note*: The function `process_rewards_and_penalties` is modified to support the incentive accounting reforms.
```python
def process_rewards_and_penalties(state: BeaconState) -> None:
# No rewards are applied at the end of `GENESIS_EPOCH` because rewards are for work done in the previous epoch
if get_current_epoch(state) == GENESIS_EPOCH:
return
flag_indices_and_numerators = get_flag_indices_and_numerators()
flag_deltas = [get_flag_index_deltas(state, index, numerator) for (index, numerator) in flag_indices_and_numerators]
deltas = flag_deltas + [get_inactivity_penalty_deltas(state)]
for (rewards, penalties) in deltas:
for index in range(len(state.validators)):
increase_balance(state, ValidatorIndex(index), rewards[index])
decrease_balance(state, ValidatorIndex(index), penalties[index])
```
#### Slashings
*Note*: The function `process_slashings` is modified to use `ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER`.
```python
def process_slashings(state: BeaconState) -> None:
epoch = get_current_epoch(state)
total_balance = get_total_active_balance(state)
adjusted_total_slashing_balance = min(sum(state.slashings) * ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER, total_balance)
for index, validator in enumerate(state.validators):
if validator.slashed and epoch + EPOCHS_PER_SLASHINGS_VECTOR // 2 == validator.withdrawable_epoch:
increment = EFFECTIVE_BALANCE_INCREMENT # Factored out from penalty numerator to avoid uint64 overflow
penalty_numerator = validator.effective_balance // increment * adjusted_total_slashing_balance
penalty = penalty_numerator // total_balance * increment
decrease_balance(state, ValidatorIndex(index), penalty)
```
#### Participation flags updates
*Note*: The function `process_participation_flag_updates` is new.
```python
def process_participation_flag_updates(state: BeaconState) -> None:
state.previous_epoch_participation = state.current_epoch_participation
state.current_epoch_participation = [ParticipationFlags(0b0000_0000) for _ in range(len(state.validators))]
```
#### Sync committee updates
*Note*: The function `process_sync_committee_updates` is new.
```python
def process_sync_committee_updates(state: BeaconState) -> None:
next_epoch = get_current_epoch(state) + Epoch(1)
if next_epoch % EPOCHS_PER_SYNC_COMMITTEE_PERIOD == 0:
state.current_sync_committee = state.next_sync_committee
state.next_sync_committee = get_sync_committee(state, next_epoch + EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
```