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Vitalik Buterin 2019-01-07 18:53:33 -06:00
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specs/core/0_beacon-chain.md
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@ -45,7 +45,6 @@
- [`BeaconState`](#beaconstate)
- [`ValidatorRecord`](#validatorrecord)
- [`CrosslinkRecord`](#crosslinkrecord)
- [`ShardCommittee`](#shardcommittee)
- [`DepositRootVote`](#depositrootvote)
- [`PendingAttestationRecord`](#pendingattestationrecord)
- [`ForkData`](#forkdata)
@ -66,7 +65,10 @@
- [`get_active_validator_indices`](#get_active_validator_indices)
- [`shuffle`](#shuffle)
- [`split`](#split)
- [`get_committees_per_slot`](#get_committees_per_slot)
- [`get_shuffling`](#get_shuffling)
- [`get_prev_epoch_committees_per_slot`](#get_prev_epoch_committees_per_slot)
- [`get_cur_epoch_committees_per_slot`](#get_cur_epoch_committees_per_slot)
- [`get_shard_committees_at_slot`](#get_shard_committees_at_slot)
- [`get_block_root`](#get_block_root)
- [`get_beacon_proposer_index`](#get_beacon_proposer_index)
@ -478,7 +480,10 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
# Randomness and committees
'latest_randao_mixes': ['hash32'],
'latest_vdf_outputs': ['hash32'],
'shard_committees_at_slots': [[ShardCommittee]],
'prev_epoch_start_shard': 'uint64',
'cur_epoch_start_shard': 'uint64',
'prev_epoch_calculation_slot': 'uint64',
'cur_epoch_calculation_slot': 'uint64',
# Custody challenges
'custody_challenges': [CustodyChallenge],
@ -546,19 +551,6 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
}
```
#### `ShardCommittee`
```python
{
# Shard number
'shard': 'uint64',
# Validator indices
'committee': ['uint24'],
# Total validator count (for custody challenges)
'total_validator_count': 'uint64',
}
```
#### `DepositRootVote`
```python
@ -854,15 +846,29 @@ def split(values: List[Any], split_count: int) -> List[Any]:
]
```
#### `get_committees_per_slot`
```python
def get_committees_per_slot(active_validator_count: int):
return max(
1,
min(
SHARD_COUNT // EPOCH_LENGTH,
len(active_validator_indices) // EPOCH_LENGTH // TARGET_COMMITTEE_SIZE,
)
)
```
#### `get_shuffling`
```python
def get_shuffling(seed: Hash32,
validators: List[ValidatorRecord],
crosslinking_start_shard: int,
slot: int) -> List[List[ShardCommittee]]:
slot: int) -> List[List[int]]
"""
Shuffles ``validators`` into shard committees using ``seed`` as entropy.
Shuffles ``validators`` into shard committees using ``seed`` as entropy. Returns a list of
``EPOCH_LENGTH * committees_per_slot`` committees where each committee is itself a list of
validator indices.
"""
# Normalizes slot to start of epoch boundary
@ -870,59 +876,67 @@ def get_shuffling(seed: Hash32,
active_validator_indices = get_active_validator_indices(validators, slot)
committees_per_slot = max(
1,
min(
SHARD_COUNT // EPOCH_LENGTH,
len(active_validator_indices) // EPOCH_LENGTH // TARGET_COMMITTEE_SIZE,
)
)
committees_per_slot = get_committees_per_slot(len(active_validator_indices))
# Shuffle with seed
shuffled_active_validator_indices = shuffle(active_validator_indices, seed)
# Split the shuffled list into epoch_length pieces
validators_per_slot = split(shuffled_active_validator_indices, EPOCH_LENGTH)
output = []
for slot, slot_indices in enumerate(validators_per_slot):
# Split the shuffled list into committees_per_slot pieces
shard_indices = split(slot_indices, committees_per_slot)
shard_id_start = crosslinking_start_shard + slot * committees_per_slot
shard_committees = [
ShardCommittee(
shard=(shard_id_start + shard_position) % SHARD_COUNT,
committee=indices,
total_validator_count=len(active_validator_indices),
)
for shard_position, indices in enumerate(shard_indices)
]
output.append(shard_committees)
return output
# Split the shuffled list into epoch_length * committees_per_slot pieces
return split(shuffled_active_validator_indices, committees_per_slot * EPOCH_LENGTH)
```
**Invariant**: if `get_shuffling(seed, validators, shard, slot)` returns some value `x`, it should return the same value `x` for the same `seed` and `shard` and possible future modifications of `validators` forever in phase 0, and until the ~1 year deletion delay in phase 2 and in the future.
Here's a diagram of what is going on:
**Note**: this definition and the next few definitions will make heavy use of repetitive computing. Real life implementations are expected to appropriately use caching/memoization to avoid redoing work.
![](http://vitalik.ca/files/ShuffleAndAssign.png?1)
#### `get_prev_epoch_committees_per_slot`
```python
def get_prev_epoch_committees_per_slot(state: BeaconState):
prev_active_validators = get_active_validator_indices(validators, state.prev_epoch_calculation_slot)
return get_committees_per_slot(len(prev_active_validators))
```
#### `get_cur_epoch_committees_per_slot`
```python
def get_cur_epoch_committees_per_slot(state: BeaconState):
cur_active_validators = get_active_validator_indices(validators, state.cur_epoch_calculation_slot)
return get_committees_per_slot(len(cur_active_validators))
```
#### `get_shard_committees_at_slot`
```python
def get_shard_committees_at_slot(state: BeaconState,
slot: int) -> List[ShardCommittee]:
slot: int) -> (List[List[int]], int):
"""
Returns the ``ShardCommittee`` for the ``slot``.
Returns (i) the list of committees and (ii) the shard associated with the first committee for the ``slot``.
"""
earliest_slot_in_array = state.slot - (state.slot % EPOCH_LENGTH) - EPOCH_LENGTH
assert earliest_slot_in_array <= slot < earliest_slot_in_array + EPOCH_LENGTH * 2
return state.shard_committees_at_slots[slot - earliest_slot_in_array]
earliest_slot = state.slot - (state.slot % EPOCH_LENGTH) - EPOCH_LENGTH
assert earliest_slot <= slot < earliest_slot + EPOCH_LENGTH * 2
offset = slot % EPOCH_LENGTH
if slot < earliest_slot + EPOCH_LENGTH:
committees_per_slot = get_prev_epoch_committees_per_slot(state)
shuffling = get_shuffling(state.latest_randao_mixes[state.prev_epoch_calculation_slot % LATEST_RANDAO_MIXES_LENGTH],
state.validator_registry,
state.slot - (state.slot % EPOCH_LENGTH) - EPOCH_LENGTH)
start_shard = state.prev_epoch_start_shard
else:
committees_per_slot = get_cur_epoch_committees_per_slot(state)
shuffling = get_shuffling(state.latest_randao_mixes[state.cur_epoch_calculation_slot % LATEST_RANDAO_MIXES_LENGTH],
state.validator_registry,
state.slot - (state.slot % EPOCH_LENGTH))
start_shard = state.cur_epoch_start_shard
return shuffling[committees_per_slot * offset: committees_per_slot * (offset + 1)], \
(start_shard + committees_per_slot * offset) % SHARD_COUNT
```
**Note**: we plan to replace the shuffling algorithm with a pointwise-evaluable shuffle (see https://github.com/ethereum/eth2.0-specs/issues/323), which will allow calculation of the committees for each slot individually.
#### `get_block_root`
```python
@ -946,8 +960,8 @@ def get_beacon_proposer_index(state: BeaconState,
"""
Returns the beacon proposer index for the ``slot``.
"""
first_committee = get_shard_committees_at_slot(state, slot)[0].committee
return first_committee[slot % len(first_committee)]
committees, shard = get_shard_committees_at_slot(state, slot)
return committees[0][slot % len(committees[0])]
```
#### `merkle_root`
@ -974,13 +988,13 @@ def get_attestation_participants(state: BeaconState,
"""
# Find the relevant committee
shard_committees = get_shard_committees_at_slot(state, attestation_data.slot)
shard_committee = [x for x in shard_committees if x.shard == attestation_data.shard][0]
assert len(participation_bitfield) == ceil_div8(len(shard_committee.committee))
shard_committees, start_shard = get_shard_committees_at_slot(state, attestation_data.slot)
shard_committee = shard_committee[(attestation_data.shard - start_shard) % SHARD_COUNT]
assert len(participation_bitfield) == ceil_div8(len(shard_committee))
# Find the participating attesters in the committee
participants = []
for i, validator_index in enumerate(shard_committee.committee):
for i, validator_index in enumerate(shard_committee):
participation_bit = (participation_bitfield[i//8] >> (7 - (i % 8))) % 2
if participation_bit == 1:
participants.append(validator_index)
@ -1165,7 +1179,10 @@ def get_initial_beacon_state(initial_validator_deposits: List[Deposit],
# Randomness and committees
latest_randao_mixes=[ZERO_HASH for _ in range(LATEST_RANDAO_MIXES_LENGTH)],
latest_vdf_outputs=[ZERO_HASH for _ in range(LATEST_RANDAO_MIXES_LENGTH // EPOCH_LENGTH)],
shard_committees_at_slots=[],
prev_epoch_start_shard=0,
cur_epoch_start_shard=0,
prev_epoch_calculation_slot=GENESIS_SLOT,
cur_epoch_calculation_slot=GENESIS_SLOT,
# Custody challenges
custody_challenges=[],
@ -1205,10 +1222,6 @@ def get_initial_beacon_state(initial_validator_deposits: List[Deposit],
if get_effective_balance(state, validator_index) >= MAX_DEPOSIT * GWEI_PER_ETH:
activate_validator(state, validator_index, True)
# Set initial committee shuffling
initial_shuffling = get_shuffling(ZERO_HASH, state.validator_registry, 0, GENESIS_SLOT)
state.shard_committees_at_slots = initial_shuffling + initial_shuffling
return state
```
@ -1554,14 +1567,14 @@ All [validators](#dfn-validator):
**Note**: `previous_epoch_boundary_attesting_balance` balance might be marginally different than `current_epoch_boundary_attesting_balance` during the 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.
For every `shard_committee_at_slot` in `state.shard_committees_at_slots` and for every `shard_committee` in `shard_committee_at_slot`:
For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `shard_committee_at_slot, start_shard = get_shard_committees_at_slot(slot)`. For every `index in range(len(shard_committee_at_slot))`, let `shard_committee = shard_committee_at_slot[index]`, `shard = (start_shard + index) % SHARD_COUNT`, and compute:
* Let `shard_block_root` be `state.latest_crosslinks[shard_committee.shard].shard_block_root`
* Let `attesting_validator_indices(shard_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.participation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.shard == shard_committee.shard and a.shard_block_root == shard_block_root]`.
* Let `shard_block_root` be `state.latest_crosslinks[shard].shard_block_root`
* Let `attesting_validator_indices(shard_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.participation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.shard == shard and a.shard_block_root == shard_block_root]`.
* Let `winning_root(shard_committee)` be equal to the value of `shard_block_root` such that `sum([get_effective_balance(state, i) for i in attesting_validator_indices(shard_committee, shard_block_root)])` is maximized (ties broken by favoring lower `shard_block_root` values).
* Let `attesting_validators(shard_committee)` be equal to `attesting_validator_indices(shard_committee, winning_root(shard_committee))` for convenience.
* Let `total_attesting_balance(shard_committee) = sum([get_effective_balance(state, i) for i in attesting_validators(shard_committee)])`.
* Let `total_balance(shard_committee) = sum([get_effective_balance(state, i) for i in shard_committee.committee])`.
* Let `total_balance(shard_committee) = sum([get_effective_balance(state, i) for i in shard_committee])`.
* Let `inclusion_slot(state, index) = a.slot_included` for the attestation `a` where `index` is in `get_attestation_participants(state, a.data, a.participation_bitfield)`.
* Let `inclusion_distance(state, index) = a.slot_included - a.data.slot` where `a` is the above attestation.
@ -1587,9 +1600,9 @@ Set `state.finalized_slot = state.previous_justified_slot` if any of the followi
### Crosslinks
For every `shard_committee_at_slot` in `state.shard_committees_at_slots` and for every `shard_committee`in `shard_committee_at_slot`:
For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `shard_committee_at_slot, start_shard = get_shard_committees_at_slot(slot)`. For every `index in range(len(shard_committee_at_slot))`, let `shard_committee = shard_committee_at_slot[index]`, `shard = (start_shard + index) % SHARD_COUNT`, and compute:
* Set `state.latest_crosslinks[shard_committee.shard] = CrosslinkRecord(slot=state.slot, shard_block_root=winning_root(shard_committee))` if `3 * total_attesting_balance(shard_committee) >= 2 * total_balance(shard_committee)`.
* Set `state.latest_crosslinks[shard] = CrosslinkRecord(slot=state.slot, shard_block_root=winning_root(shard_committee))` if `3 * total_attesting_balance(shard_committee) >= 2 * total_balance(shard_committee)`.
### Rewards and penalties
@ -1633,7 +1646,7 @@ For each `index` in `previous_epoch_attester_indices`, we determine the proposer
#### Crosslinks
For every `shard_committee_at_slot` in `state.shard_committees_at_slots[:EPOCH_LENGTH]` (i.e. the objects corresponding to the epoch before the current one), for each `shard_committee` in `shard_committee_at_slot`, and for each `index` in `shard_committee.committee`, adjust balances as follows:
For every `i in range(state.slot - 2 * EPOCH_LENGTH, state.slot - EPOCH_LENGTH)`, let `shard_committee_at_slot, start_shard = get_shard_committees_at_slot(i)`. For every `j in range(len(shard_committee_at_slot))`, let `shard_committee = shard_committee_at_slot[j]`, `shard = (start_shard + j) % SHARD_COUNT`, and compute:
* If `index in attesting_validators(shard_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(shard_committee) // total_balance(shard_committee))`.
* If `index not in attesting_validators(shard_committee)`, `state.validator_balances[index] -= base_reward(state, index)`.
@ -1658,7 +1671,7 @@ def process_ejections(state: BeaconState) -> None:
If the following are satisfied:
* `state.finalized_slot > state.validator_registry_latest_change_slot`
* `state.latest_crosslinks[shard].slot > state.validator_registry_latest_change_slot` for every shard number `shard` in `state.shard_committees_at_slots`
* `state.latest_crosslinks[shard].slot > state.validator_registry_latest_change_slot` for every shard number `shard` in `[(state.cur_epoch_start_shard + i) % SHARD_COUNT for i in range(get_cur_epoch_committees_per_slot(state) * EPOCH_LENGTH)]` (that is, for every shard in the current committees)
update the validator registry and associated fields by running
@ -1706,7 +1719,21 @@ def update_validator_registry(state: BeaconState) -> None:
state.validator_registry_latest_change_slot = state.slot
```
Regardless of whether the above conditions are satisfied, run the following:
and perform the following updates:
* Set `state.prev_epoch_calculation_slot = state.cur_epoch_calculation_slot`
* Set `state.prev_epoch_start_shard = state.cur_epoch_start_shard`
* Set `state.cur_epoch_calculation_slot = state.slot`
* Set `state.cur_epoch_start_shard = (state.cur_epoch_start_shard + get_cur_epoch_committees_per_slot(state) * EPOCH_LENGTH) % SHARD_COUNT`
If a validator registry update does _not_ happen do the following:
* Set `state.prev_epoch_calculation_slot = state.cur_epoch_calculation_slot`
* Set `state.prev_epoch_start_shard = state.cur_epoch_start_shard`
* Let `epochs_since_last_registry_change = (state.slot - state.validator_registry_latest_change_slot) // EPOCH_LENGTH`.
* If `epochs_since_last_registry_change` is an exact power of 2, set `state.cur_epoch_calculation_slot = state.slot`. Note that `state.cur_epoch_start_shard` is left unchanged.
Regardless of whether or not a validator set change happens, run the following:
```python
def process_penalties_and_exits(state: BeaconState) -> None:
@ -1744,18 +1771,6 @@ def process_penalties_and_exits(state: BeaconState) -> None:
break
```
Also perform the following updates:
* Set `state.shard_committees_at_slots[:EPOCH_LENGTH] = state.shard_committees_at_slots[EPOCH_LENGTH:]`.
* Set `state.shard_committees_at_slots[EPOCH_LENGTH:] = get_shuffling(state.latest_randao_mixes[(state.slot - SEED_LOOKAHEAD) % LATEST_RANDAO_MIXES_LENGTH], state.validator_registry, next_start_shard, state.slot)` where `next_start_shard = (state.shard_committees_at_slots[-1][-1].shard + 1) % SHARD_COUNT`.
If a validator registry update does _not_ happen do the following:
* Set `state.shard_committees_at_slots[:EPOCH_LENGTH] = state.shard_committees_at_slots[EPOCH_LENGTH:]`.
* Let `epochs_since_last_registry_change = (state.slot - state.validator_registry_latest_change_slot) // EPOCH_LENGTH`.
* Let `start_shard = state.shard_committees_at_slots[0][0].shard`.
* If `epochs_since_last_registry_change` is an exact power of 2, set `state.shard_committees_at_slots[EPOCH_LENGTH:] = get_shuffling(state.latest_randao_mixes[(state.slot - SEED_LOOKAHEAD) % LATEST_RANDAO_MIXES_LENGTH], state.validator_registry, start_shard, state.slot)`. Note that `start_shard` is not changed from the last epoch.
### Final updates
* Let `e = state.slot // EPOCH_LENGTH`. Set `state.latest_penalized_exit_balances[(e+1) % LATEST_PENALIZED_EXIT_LENGTH] = state.latest_penalized_exit_balances[e % LATEST_PENALIZED_EXIT_LENGTH]`