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

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Ethereum 2.0 Altair Beacon chain changes

Table of contents

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 towards their planned maximally punitive values

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

Incentivization weights

Name Value
TIMELY_HEAD_WEIGHT uint64(12)
TIMELY_SOURCE_WEIGHT uint64(12)
TIMELY_TARGET_WEIGHT uint64(24)
SYNC_REWARD_WEIGHT uint64(8)
PROPOSER_WEIGHT uint64(8)
WEIGHT_DENOMINATOR uint64(64)

Note: The sum of the weights equal WEIGHT_DENOMINATOR.

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, maximum security values.

Note: The spec does not override previous configuration values but instead creates new values and replaces usage throughout.

Name Value
INACTIVITY_PENALTY_QUOTIENT_ALTAIR uint64(3 * 2**24) (= 50,331,648)
MIN_SLASHING_PENALTY_QUOTIENT_ALTAIR uint64(2**6) (= 64)
PROPORTIONAL_SLASHING_MULTIPLIER_ALTAIR uint64(2)

Misc

Name Value
SYNC_COMMITTEE_SIZE uint64(2**10) (= 1,024)
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')
DOMAIN_SYNC_COMMITTEE_SELECTION_PROOF DomainType('0x08000000')
DOMAIN_CONTRIBUTION_AND_PROOF DomainType('0x09000000')

Containers

Modified containers

BeaconBlockBody

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]
    # [New in Altair]
    sync_aggregate: SyncAggregate

BeaconState

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

SyncAggregate

class SyncAggregate(Container):
    sync_committee_bits: Bitvector[SYNC_COMMITTEE_SIZE]
    sync_committee_signature: BLSSignature

SyncCommittee

class SyncCommittee(Container):
    pubkeys: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE]
    aggregate_pubkey: BLSPubkey

Helper functions

Predicates

eth2_fast_aggregate_verify

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_weights

def get_flag_indices_and_weights() -> Sequence[Tuple[int, uint64]]:
    """
    Return paired tuples of participation flag indices along with associated incentivization weights.
    """
    return (
        (TIMELY_HEAD_FLAG_INDEX, TIMELY_HEAD_WEIGHT),
        (TIMELY_SOURCE_FLAG_INDEX, TIMELY_SOURCE_WEIGHT),
        (TIMELY_TARGET_FLAG_INDEX, TIMELY_TARGET_WEIGHT),
    )

add_flag

def add_flag(flags: ParticipationFlags, flag_index: int) -> ParticipationFlags:
    """
    Return a new ``ParticipationFlags`` adding ``flag_index`` to ``flags``.
    """
    flag = ParticipationFlags(2**flag_index)
    return flags | flag

has_flag

def has_flag(flags: ParticipationFlags, flag_index: int) -> bool:
    """
    Return whether ``flags`` has ``flag_index`` set.
    """
    flag = ParticipationFlags(2**flag_index)
    return flags & flag == flag

Beacon state accessors

get_sync_committee_indices

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

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]
    aggregate_pubkey = bls.AggregatePKs(pubkeys)
    return SyncCommittee(pubkeys=pubkeys, aggregate_pubkey=aggregate_pubkey)

get_base_reward_per_increment

def get_base_reward_per_increment(state: BeaconState) -> Gwei:
    return Gwei(EFFECTIVE_BALANCE_INCREMENT * BASE_REWARD_FACTOR // integer_squareroot(get_total_active_balance(state)))

get_base_reward

Note: The function get_base_reward is modified with the removal of BASE_REWARDS_PER_EPOCH and the use of increment based accounting.

def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
    """
    Return the base reward for the validator defined by ``index`` with respect to the current ``state``.

    Note: A validator can optimally earn one base reward per epoch over a long time horizon.
    This takes into account both per-epoch (e.g. attestation) and intermittent duties (e.g. block proposal
    and sync committees).
    """
    increments = state.validators[index].effective_balance // EFFECTIVE_BALANCE_INCREMENT
    return Gwei(increments * get_base_reward_per_increment(state))

get_unslashed_participating_indices

def get_unslashed_participating_indices(state: BeaconState, flag_index: int, epoch: Epoch) -> Set[ValidatorIndex]:
    """
    Return the set of validator indices that are both active and unslashed for the given ``flag_index`` and ``epoch``.
    """
    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

def get_flag_index_deltas(state: BeaconState, flag_index: int, weight: uint64) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Return the deltas for a given ``flag_index`` scaled by ``weight`` 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 * weight // WEIGHT_DENOMINATOR)
            else:
                reward_numerator = base_reward * weight * unslashed_participating_increments
                rewards[index] += Gwei(reward_numerator // (active_increments * WEIGHT_DENOMINATOR))
        else:
            penalties[index] += Gwei(base_reward * weight // WEIGHT_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.

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 (_, weight) in get_flag_indices_and_weights():
                # This inactivity penalty cancels the flag reward corresponding to the flag index
                penalties[index] += Gwei(get_base_reward(state, index) * weight // WEIGHT_DENOMINATOR)
            if index not in matching_target_indices:
                penalty_numerator = state.validators[index].effective_balance * state.inactivity_scores[index]
                penalty_denominator = INACTIVITY_SCORE_BIAS * INACTIVITY_PENALTY_QUOTIENT_ALTAIR
                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 MIN_SLASHING_PENALTY_QUOTIENT_ALTAIR and use PROPOSER_WEIGHT when calculating the proposer reward.

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 // MIN_SLASHING_PENALTY_QUOTIENT_ALTAIR)

    # 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_WEIGHT // WEIGHT_DENOMINATOR)
    increase_balance(state, proposer_index, proposer_reward)
    increase_balance(state, whistleblower_index, Gwei(whistleblower_reward - proposer_reward))

Block processing

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.sync_aggregate)  # [New in Altair]

Modified process_attestation

Note: The function process_attestation is modified to do incentive accounting with epoch participation flags.

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_source = data.source == justified_checkpoint
    is_matching_target = is_matching_source and data.target.root == get_block_root(state, data.target.epoch)
    is_matching_head = is_matching_target and data.beacon_block_root == get_block_root_at_slot(state, data.slot)
    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_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)
    if is_matching_head and state.slot == data.slot + MIN_ATTESTATION_INCLUSION_DELAY:
        participation_flag_indices.append(TIMELY_HEAD_FLAG_INDEX)

    # Update epoch participation flags
    proposer_reward_numerator = 0
    for index in get_attesting_indices(state, data, attestation.aggregation_bits):
        for flag_index, weight in get_flag_indices_and_weights():
            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) * weight

    # Reward proposer
    proposer_reward_denominator = (WEIGHT_DENOMINATOR - PROPOSER_WEIGHT) * WEIGHT_DENOMINATOR // PROPOSER_WEIGHT
    proposer_reward = Gwei(proposer_reward_numerator // proposer_reward_denominator)
    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, and current_epoch_participation.

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(uint64(0))
    else:
        # Increase balance by deposit amount
        index = ValidatorIndex(validator_pubkeys.index(pubkey))
        increase_balance(state, index, amount)

Sync committee processing

def process_sync_committee(state: BeaconState, aggregate: SyncAggregate) -> None:
    # Verify sync committee aggregate signature signing over the previous slot block root
    committee_pubkeys = state.current_sync_committee.pubkeys
    participant_pubkeys = [pubkey for pubkey, bit in zip(committee_pubkeys, aggregate.sync_committee_bits) if bit]
    previous_slot = max(state.slot, Slot(1)) - Slot(1)
    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, aggregate.sync_committee_signature)

    # Compute participant and proposer rewards
    total_active_increments = get_total_active_balance(state) // EFFECTIVE_BALANCE_INCREMENT
    total_base_rewards = Gwei(get_base_reward_per_increment(state) * total_active_increments)
    max_participant_rewards = Gwei(total_base_rewards * SYNC_REWARD_WEIGHT // WEIGHT_DENOMINATOR // SLOTS_PER_EPOCH)
    participant_reward = Gwei(max_participant_rewards // SYNC_COMMITTEE_SIZE)
    proposer_reward = Gwei(participant_reward * PROPOSER_WEIGHT // (WEIGHT_DENOMINATOR - PROPOSER_WEIGHT))

    # Apply participant and proposer rewards
    committee_indices = get_sync_committee_indices(state, get_current_epoch(state))
    participant_indices = [index for index, bit in zip(committee_indices, aggregate.sync_committee_bits) if bit]
    for participant_index in participant_indices:
        increase_balance(state, participant_index, participant_reward)
        increase_balance(state, get_beacon_proposer_index(state), proposer_reward)

Epoch processing

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 to adapt to the new participation records.

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_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state))
    current_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_current_epoch(state))
    total_active_balance = get_total_active_balance(state)
    previous_target_balance = get_total_balance(state, previous_indices)
    current_target_balance = get_total_balance(state, current_indices)
    weigh_justification_and_finalization(state, total_active_balance, previous_target_balance, current_target_balance)

Inactivity scores

Note: The function process_inactivity_updates is new.

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.

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_weights()
    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 PROPORTIONAL_SLASHING_MULTIPLIER_ALTAIR.

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) * PROPORTIONAL_SLASHING_MULTIPLIER_ALTAIR, 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.

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.

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)

Initialize state for pure Altair testnets and test vectors

This helper function is only for initializing the state for pure Altair testnets and tests.

Note: The function initialize_beacon_state_from_eth1 is modified: (1) using ALTAIR_FORK_VERSION as the current fork version, (2) utilizing the Altair BeaconBlockBody when constructing the initial latest_block_header, and (3) adding initial sync committees.

def initialize_beacon_state_from_eth1(eth1_block_hash: Bytes32,
                                      eth1_timestamp: uint64,
                                      deposits: Sequence[Deposit]) -> BeaconState:
    fork = Fork(
        previous_version=GENESIS_FORK_VERSION,
        current_version=ALTAIR_FORK_VERSION,  # [Modified in Altair]
        epoch=GENESIS_EPOCH,
    )
    state = BeaconState(
        genesis_time=eth1_timestamp + GENESIS_DELAY,
        fork=fork,
        eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=uint64(len(deposits))),
        latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
        randao_mixes=[eth1_block_hash] * EPOCHS_PER_HISTORICAL_VECTOR,  # Seed RANDAO with Eth1 entropy
    )

    # Process deposits
    leaves = list(map(lambda deposit: deposit.data, deposits))
    for index, deposit in enumerate(deposits):
        deposit_data_list = List[DepositData, 2**DEPOSIT_CONTRACT_TREE_DEPTH](*leaves[:index + 1])
        state.eth1_data.deposit_root = hash_tree_root(deposit_data_list)
        process_deposit(state, deposit)

    # Process activations
    for index, validator in enumerate(state.validators):
        balance = state.balances[index]
        validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
        if validator.effective_balance == MAX_EFFECTIVE_BALANCE:
            validator.activation_eligibility_epoch = GENESIS_EPOCH
            validator.activation_epoch = GENESIS_EPOCH

    # Set genesis validators root for domain separation and chain versioning
    state.genesis_validators_root = hash_tree_root(state.validators)

    # [New in Altair] Fill in sync committees
    state.current_sync_committee = get_sync_committee(state, get_current_epoch(state))
    state.next_sync_committee = get_sync_committee(state, get_current_epoch(state) + EPOCHS_PER_SYNC_COMMITTEE_PERIOD)

    return state