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Update 0_beacon-chain.md

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@ -76,7 +76,7 @@
- [`is_power_of_two`](#is_power_of_two) - [`is_power_of_two`](#is_power_of_two)
- [`int_to_bytes1`, `int_to_bytes2`, ...](#int_to_bytes1-int_to_bytes2-) - [`int_to_bytes1`, `int_to_bytes2`, ...](#int_to_bytes1-int_to_bytes2-)
- [`get_effective_balance`](#get_effective_balance) - [`get_effective_balance`](#get_effective_balance)
- [`total_balance`](#total_balance) - [`get_total_balance`](#get_total_balance)
- [`get_fork_version`](#get_fork_version) - [`get_fork_version`](#get_fork_version)
- [`get_domain`](#get_domain) - [`get_domain`](#get_domain)
- [`get_bitfield_bit`](#get_bitfield_bit) - [`get_bitfield_bit`](#get_bitfield_bit)
@ -1028,10 +1028,10 @@ def get_effective_balance(state: State, index: ValidatorIndex) -> Gwei:
return min(state.validator_balances[index], MAX_DEPOSIT_AMOUNT) return min(state.validator_balances[index], MAX_DEPOSIT_AMOUNT)
``` ```
### `total_balance` ### `get_total_balance`
```python ```python
def total_balance(state: BeaconState, validators: List[ValidatorIndex]) -> Gwei: def get_total_balance(state: BeaconState, validators: List[ValidatorIndex]) -> Gwei:
""" """
Return the combined effective balance of an array of validators. Return the combined effective balance of an array of validators.
""" """
@ -1843,31 +1843,31 @@ The steps below happen when `(state.slot + 1) % EPOCH_LENGTH == 0`.
[Validators](#dfn-Validator) attesting during the current epoch: [Validators](#dfn-Validator) attesting during the current epoch:
* Let `current_total_balance = total_balance(state, get_active_validator_indices(state.validator_registry, current_epoch))`. * Let `current_total_balance = get_total_balance(state, get_active_validator_indices(state.validator_registry, current_epoch))`.
* Let `current_epoch_attestations = [a for a in state.latest_attestations if current_epoch == slot_to_epoch(a.data.slot)]`. (Note: this is the set of attestations of slots in the epoch `current_epoch`, _not_ attestations that got included in the chain during the epoch `current_epoch`.) * Let `current_epoch_attestations = [a for a in state.latest_attestations if current_epoch == slot_to_epoch(a.data.slot)]`. (Note: this is the set of attestations of slots in the epoch `current_epoch`, _not_ attestations that got included in the chain during the epoch `current_epoch`.)
* Validators justifying the epoch boundary block at the start of the current epoch: * Validators justifying the epoch boundary block at the start of the current epoch:
* Let `current_epoch_boundary_attestations = [a for a in current_epoch_attestations if a.data.epoch_boundary_root == get_block_root(state, get_epoch_start_slot(current_epoch)) and a.data.justified_epoch == state.justified_epoch]`. * Let `current_epoch_boundary_attestations = [a for a in current_epoch_attestations if a.data.epoch_boundary_root == get_block_root(state, get_epoch_start_slot(current_epoch)) and a.data.justified_epoch == state.justified_epoch]`.
* Let `current_epoch_boundary_attester_indices` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in current_epoch_boundary_attestations]`. * Let `current_epoch_boundary_attester_indices` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in current_epoch_boundary_attestations]`.
* Let `current_epoch_boundary_attesting_balance = total_balance(state, current_epoch_boundary_attester_indices)`. * Let `current_epoch_boundary_attesting_balance = get_total_balance(state, current_epoch_boundary_attester_indices)`.
[Validators](#dfn-Validator) attesting during the previous epoch: [Validators](#dfn-Validator) attesting during the previous epoch:
* Let `previous_total_balance = total_balance(state, get_active_validator_indices(state.validator_registry, previous_epoch))`. * Let `previous_total_balance = get_total_balance(state, get_active_validator_indices(state.validator_registry, previous_epoch))`.
* Validators that made an attestation during the previous epoch: * Validators that made an attestation during the previous epoch:
* Let `previous_epoch_attestations = [a for a in state.latest_attestations if previous_epoch == slot_to_epoch(a.data.slot)]`. * Let `previous_epoch_attestations = [a for a in state.latest_attestations if previous_epoch == slot_to_epoch(a.data.slot)]`.
* Let `previous_epoch_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_attestations]`. * Let `previous_epoch_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_attestations]`.
* Validators targeting the previous justified slot: * Validators targeting the previous justified slot:
* Let `previous_epoch_justified_attestations = [a for a in current_epoch_attestations + previous_epoch_attestations if a.data.justified_epoch == state.previous_justified_epoch]`. * Let `previous_epoch_justified_attestations = [a for a in current_epoch_attestations + previous_epoch_attestations if a.data.justified_epoch == state.previous_justified_epoch]`.
* Let `previous_epoch_justified_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_justified_attestations]`. * Let `previous_epoch_justified_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_justified_attestations]`.
* Let `previous_epoch_justified_attesting_balance = total_balance(state, previous_epoch_justified_attester_indices)`. * Let `previous_epoch_justified_attesting_balance = get_total_balance(state, previous_epoch_justified_attester_indices)`.
* Validators justifying the epoch boundary block at the start of the previous epoch: * Validators justifying the epoch boundary block at the start of the previous epoch:
* Let `previous_epoch_boundary_attestations = [a for a in previous_epoch_justified_attestations if a.data.epoch_boundary_root == get_block_root(state, get_epoch_start_slot(previous_epoch))]`. * Let `previous_epoch_boundary_attestations = [a for a in previous_epoch_justified_attestations if a.data.epoch_boundary_root == get_block_root(state, get_epoch_start_slot(previous_epoch))]`.
* Let `previous_epoch_boundary_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_boundary_attestations]`. * Let `previous_epoch_boundary_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_boundary_attestations]`.
* Let `previous_epoch_boundary_attesting_balance = total_balance(state, previous_epoch_boundary_attester_indices)`. * Let `previous_epoch_boundary_attesting_balance = get_total_balance(state, previous_epoch_boundary_attester_indices)`.
* Validators attesting to the expected beacon chain head during the previous epoch: * Validators attesting to the expected beacon chain head during the previous epoch:
* Let `previous_epoch_head_attestations = [a for a in previous_epoch_attestations if a.data.beacon_block_root == get_block_root(state, a.data.slot)]`. * Let `previous_epoch_head_attestations = [a for a in previous_epoch_attestations if a.data.beacon_block_root == get_block_root(state, a.data.slot)]`.
* Let `previous_epoch_head_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_head_attestations]`. * Let `previous_epoch_head_attester_indices` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in previous_epoch_head_attestations]`.
* Let `previous_epoch_head_attesting_balance = total_balance(state, previous_epoch_head_attester_indices)`. * Let `previous_epoch_head_attesting_balance = get_total_balance(state, previous_epoch_head_attester_indices)`.
**Note**: `previous_total_balance` and `previous_epoch_boundary_attesting_balance` balance might be marginally different than the actual balances during previous epoch transition. Due to the tight bound on validator churn each epoch and small per-epoch rewards/penalties, the potential balance difference is very low and only marginally affects consensus safety. **Note**: `previous_total_balance` and `previous_epoch_boundary_attesting_balance` balance might be marginally different than the actual balances during previous epoch transition. Due to the tight bound on validator churn each epoch and small per-epoch rewards/penalties, the potential balance difference is very low and only marginally affects consensus safety.
@ -1875,9 +1875,9 @@ For every `slot in range(get_epoch_start_slot(previous_epoch), get_epoch_start_s
* Let `shard_block_root` be `state.latest_crosslinks[shard].shard_block_root` * Let `shard_block_root` be `state.latest_crosslinks[shard].shard_block_root`
* Let `attesting_validator_indices(crosslink_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.data.shard == shard and a.data.shard_block_root == shard_block_root]`. * Let `attesting_validator_indices(crosslink_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.aggregation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.data.shard == shard and a.data.shard_block_root == shard_block_root]`.
* Let `winning_root(crosslink_committee)` be equal to the value of `shard_block_root` such that `total_balance(state, attesting_validator_indices(crosslink_committee, shard_block_root))` is maximized (ties broken by favoring lower `shard_block_root` values). * Let `winning_root(crosslink_committee)` be equal to the value of `shard_block_root` such that `get_total_balance(state, attesting_validator_indices(crosslink_committee, shard_block_root))` is maximized (ties broken by favoring lower `shard_block_root` values).
* Let `attesting_validators(crosslink_committee)` be equal to `attesting_validator_indices(crosslink_committee, winning_root(crosslink_committee))` for convenience. * Let `attesting_validators(crosslink_committee)` be equal to `attesting_validator_indices(crosslink_committee, winning_root(crosslink_committee))` for convenience.
* Let `total_attesting_balance(crosslink_committee) = total_balance(state, attesting_validators(crosslink_committee))`. * Let `total_attesting_balance(crosslink_committee) = get_total_balance(state, attesting_validators(crosslink_committee))`.
Define the following helpers to process attestation inclusion rewards and inclusion distance reward/penalty. For every attestation `a` in `previous_epoch_attestations`: Define the following helpers to process attestation inclusion rewards and inclusion distance reward/penalty. For every attestation `a` in `previous_epoch_attestations`:
@ -1916,7 +1916,7 @@ Finally, update the following:
For every `slot in range(get_epoch_start_slot(previous_epoch), get_epoch_start_slot(next_epoch))`, let `crosslink_committees_at_slot = get_crosslink_committees_at_slot(state, slot)`. For every `(crosslink_committee, shard)` in `crosslink_committees_at_slot`, compute: For every `slot in range(get_epoch_start_slot(previous_epoch), get_epoch_start_slot(next_epoch))`, let `crosslink_committees_at_slot = get_crosslink_committees_at_slot(state, slot)`. For every `(crosslink_committee, shard)` in `crosslink_committees_at_slot`, compute:
* Set `state.latest_crosslinks[shard] = Crosslink(epoch=current_epoch, shard_block_root=winning_root(crosslink_committee))` if `3 * total_attesting_balance(crosslink_committee) >= 2 * total_balance(crosslink_committee)`. * Set `state.latest_crosslinks[shard] = Crosslink(epoch=current_epoch, shard_block_root=winning_root(crosslink_committee))` if `3 * total_attesting_balance(crosslink_committee) >= 2 * get_total_balance(crosslink_committee)`.
#### Rewards and penalties #### Rewards and penalties
@ -1964,7 +1964,7 @@ For every `slot in range(get_epoch_start_slot(previous_epoch), get_epoch_start_s
* Let `crosslink_committees_at_slot = get_crosslink_committees_at_slot(state, slot)`. * Let `crosslink_committees_at_slot = get_crosslink_committees_at_slot(state, slot)`.
* For every `(crosslink_committee, shard)` in `crosslink_committees_at_slot`: * For every `(crosslink_committee, shard)` in `crosslink_committees_at_slot`:
* If `index in attesting_validators(crosslink_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(crosslink_committee) // total_balance(crosslink_committee))`. * If `index in attesting_validators(crosslink_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(crosslink_committee) // get_total_balance(state, crosslink_committee))`.
* If `index not in attesting_validators(crosslink_committee)`, `state.validator_balances[index] -= base_reward(state, index)`. * If `index not in attesting_validators(crosslink_committee)`, `state.validator_balances[index] -= base_reward(state, index)`.
#### Ejections #### Ejections
@ -2007,7 +2007,7 @@ def update_validator_registry(state: BeaconState) -> None:
# The active validators # The active validators
active_validator_indices = get_active_validator_indices(state.validator_registry, current_epoch) active_validator_indices = get_active_validator_indices(state.validator_registry, current_epoch)
# The total effective balance of active validators # The total effective balance of active validators
total_balance = total_balance(state, active_validator_indices) total_balance = get_total_balance(state, active_validator_indices)
# The maximum balance churn in Gwei (for deposits and exits separately) # The maximum balance churn in Gwei (for deposits and exits separately)
max_balance_churn = max( max_balance_churn = max(