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Replace cycles with epochs 

Also adjusted constants to keep interest rates and the quadratic leak period the same.

Also, did some simplifications of the cycle calculation procedure. Make the decision to remove automatic registration of a validator as a proposer when they join, because that can just happen on its own due to the reshuffling procedure.
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specs/core/0_beacon-chain.md
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@ -41,15 +41,14 @@ The primary source of load on the beacon chain are "attestations". Attestations
| `GENESIS_TIME` | **TBD** | seconds | | `GENESIS_TIME` | **TBD** | seconds |
| `SLOT_DURATION` | 2**4 (= 16) | seconds | | `SLOT_DURATION` | 2**4 (= 16) | seconds |
| `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~17 minutes | | `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~17 minutes |
| `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~1.1 hours |
| `RANDAO_SLOTS_PER_LAYER` | 2**12 (= 4096) | slots | ~18 hours | | `RANDAO_SLOTS_PER_LAYER` | 2**12 (= 4096) | slots | ~18 hours |
| `SQRT_E_DROP_TIME` | 2**16 (= 65,536) | slots | ~12 days | | `SQRT_E_DROP_TIME` | 2**10 (= 1,024) | cycles | ~12 days |
| `MIN_WITHDRAWAL_PERIOD` | 2**12 (= 4096) | slots | ~18 hours | | `MIN_WITHDRAWAL_PERIOD` | 2**12 (= 4096) | slots | ~18 hours |
| `WITHDRAWALS_PER_CYCLE` | 8 | - | 4.3m ETH in ~6 months | | `WITHDRAWALS_PER_CYCLE` | 8 | - | 4.3m ETH in ~6 months |
| `COLLECTIVE_PENALTY_CALCULATION_PERIOD` | 2**19 (= 524,288) | slots | ~3 months | | `COLLECTIVE_PENALTY_CALCULATION_PERIOD` | 2**19 (= 524,288) | slots | ~3 months |
| `DELETION_PERIOD` | 2**21 (= 2,097,152) | slots | ~1.06 years | | `DELETION_PERIOD` | 2**21 (= 2,097,152) | slots | ~1.06 years |
| `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**16 (= 65,536) | slots | ~12 days | | `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**16 (= 65,536) | slots | ~12 days |
| `BASE_REWARD_QUOTIENT` | 2**15 (= 32,768) | — | | `BASE_REWARD_QUOTIENT` | 2**9 (= 512) | — |
| `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — | | `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — |
| `POW_HASH_VOTING_PERIOD` | 2**10 (=1024) | - | | `POW_HASH_VOTING_PERIOD` | 2**10 (=1024) | - |
| `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (=32) | - | | `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (=32) | - |
@ -61,7 +60,7 @@ The primary source of load on the beacon chain are "attestations". Attestations
* See a recommended min committee size of 111 here https://vitalik.ca/files/Ithaca201807_Sharding.pdf); our algorithm will generally ensure the committee size is at least half the target. * See a recommended min committee size of 111 here https://vitalik.ca/files/Ithaca201807_Sharding.pdf); our algorithm will generally ensure the committee size is at least half the target.
* The `SQRT_E_DROP_TIME` constant is the amount of time it takes for the quadratic leak to cut deposits of non-participating validators by ~39.4%. * The `SQRT_E_DROP_TIME` constant is the amount of time it takes for the quadratic leak to cut deposits of non-participating validators by ~39.4%.
* The `BASE_REWARD_QUOTIENT` constant is the per-slot interest rate assuming all validators are participating, assuming total deposits of 1 ETH. It corresponds to ~3.88% annual interest assuming 10 million participating ETH. * The `BASE_REWARD_QUOTIENT` constant is the per-cycle interest rate assuming all validators are participating, assuming total deposits of 1 ETH. It corresponds to ~3.88% annual interest assuming 10 million participating ETH.
* At most `1/MAX_VALIDATOR_CHURN_QUOTIENT` of the validators can change during each validator set change. * At most `1/MAX_VALIDATOR_CHURN_QUOTIENT` of the validators can change during each validator set change.
**Validator status codes** **Validator status codes**
@ -200,8 +199,6 @@ The `BeaconState` has the following fields:
'last_finalized_slot': 'uint64', 'last_finalized_slot': 'uint64',
# Last justified slot # Last justified slot
'last_justified_slot': 'uint64', 'last_justified_slot': 'uint64',
# Number of consecutive justified slots
'justified_streak': 'uint64',
# Committee members and their assigned shard, per slot # Committee members and their assigned shard, per slot
'shard_and_committee_for_slots': [[ShardAndCommittee]], 'shard_and_committee_for_slots': [[ShardAndCommittee]],
# Persistent shard committees # Persistent shard committees
@ -692,13 +689,14 @@ def add_validator(validators: List[ValidatorRecord],
exit_slot=0, exit_slot=0,
exit_seq=0 exit_seq=0
) )
# Add the validator
index = min_empty_validator(validators) index = min_empty_validator(validators)
if index is None: if index is None:
validators.append(rec) validators.append(rec)
return len(validators) - 1 index = len(validators) - 1
else: else:
validators[index] = rec validators[index] = rec
return index return index
``` ```
### Routine for removing a validator ### Routine for removing a validator
@ -709,6 +707,11 @@ def exit_validator(index, state, penalize, current_slot):
validator.exit_slot = current_slot validator.exit_slot = current_slot
validator.exit_seq = state.current_exit_seq validator.exit_seq = state.current_exit_seq
state.current_exit_seq += 1 state.current_exit_seq += 1
for committee in state.persistent_committees:
for i, vindex in committee:
if vindex == index:
committee.pop(i)
break
if penalize: if penalize:
validator.status = PENALIZED validator.status = PENALIZED
state.deposits_penalized_in_period[current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD] += validator.balance state.deposits_penalized_in_period[current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD] += validator.balance
@ -906,18 +909,15 @@ Verify that `deposit_data.msg_value == DEPOSIT_SIZE` and `block.slot - (deposit_
Run `add_validator(validators, deposit_data.deposit_params.pubkey, deposit_data.deposit_params.proof_of_possession, deposit_data.deposit_params.withdrawal_shard, data.deposit_params.withdrawal_address, deposit_data.deposit_params.randao_commitment, PENDING_ACTIVATION, block.slot)`. Run `add_validator(validators, deposit_data.deposit_params.pubkey, deposit_data.deposit_params.proof_of_possession, deposit_data.deposit_params.withdrawal_shard, data.deposit_params.withdrawal_address, deposit_data.deposit_params.randao_commitment, PENDING_ACTIVATION, block.slot)`.
## State recalculations (every `CYCLE_LENGTH` slots) ## Cycle boundary processing (every `CYCLE_LENGTH` slots)
Repeat while `slot - last_state_recalculation_slot >= CYCLE_LENGTH`: Repeat the steps in this section while `block.slot - last_state_recalculation_slot >= CYCLE_LENGTH`. For simplicity, we'll use `s` as `last_state_recalculation_slot`.
#### Adjust justified slots and crosslink status #### Adjust justified slots and crosslink status
For every slot `s` in the range `last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`:
* Let `total_balance` be the total balance of active validators. * Let `total_balance` be the total balance of active validators.
* Let `total_balance_attesting_at_s` be the total balance of validators that attested to the beacon block at slot `s`. * Let `total_balance_attesting_at_s` be the total balance of validators that attested to the beacon block at slot `s`.
* If `3 * total_balance_attesting_at_s >= 2 * total_balance` set `last_justified_slot = max(last_justified_slot, s)` and `justified_streak += 1`. Otherwise set `justified_streak = 0`. * If `3 * total_balance_attesting_at_s >= 2 * total_balance` then first (i) if `last_justified_slot == s - CYCLE_LENGTH`, set `last_finalized_slot = last_justified_slot`, then (ii) set `last_justified_slot = s`.
* If `justified_streak >= CYCLE_LENGTH + 1` set `last_finalized_slot = max(last_finalized_slot, s - CYCLE_LENGTH - 1)`.
For every `(shard, shard_block_hash)` tuple: For every `(shard, shard_block_hash)` tuple:
@ -932,12 +932,11 @@ Note: When applying penalties in the following balance recalculations implemente
* Let `total_balance` be the total balance of active validators. * Let `total_balance` be the total balance of active validators.
* Let `total_balance_in_eth = total_balance // GWEI_PER_ETH`. * Let `total_balance_in_eth = total_balance // GWEI_PER_ETH`.
* Let `reward_quotient = BASE_REWARD_QUOTIENT * int_sqrt(total_balance_in_eth)`. (The per-slot maximum interest rate is `1/reward_quotient`.) * Let `reward_quotient = BASE_REWARD_QUOTIENT * int_sqrt(total_balance_in_eth)`. (The per-slot maximum interest rate is `1/reward_quotient`.)
* Let `quadratic_penalty_quotient = SQRT_E_DROP_TIME**2`. (The portion lost by offline validators after `D` slots is about `D*D/2/quadratic_penalty_quotient`.) * Let `quadratic_penalty_quotient = SQRT_E_DROP_TIME**2`. (The portion lost by offline validators after `D` cycles is about `D*D/2/quadratic_penalty_quotient`.)
* Let `time_since_finality = block.slot - last_finalized_slot`. * Let `time_since_finality = slot - last_finalized_slot`.
For every slot `s` in the range `last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`: * Let `total_balance_participating` be the total balance of validators that voted for the canonical beacon block at slot `s` (note: every attestation for a block in the slot span `s ... s + CYCLE_LENGTH - 1` counts as this)
* Let `total_balance_participating` be the total balance of validators that voted for the canonical beacon block at slot `s`. In the normal case every validator will be in one of the `CYCLE_LENGTH` slots following slot `s` and so can vote for a block at slot `s`.
* Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation. * Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation.
* If `time_since_finality <= 3 * CYCLE_LENGTH` adjust the balance of participating and non-participating validators as follows: * If `time_since_finality <= 3 * CYCLE_LENGTH` adjust the balance of participating and non-participating validators as follows:
* Participating validators gain `B // reward_quotient * (2 * total_balance_participating - total_balance) // total_balance`. (Note that this value may be negative.) * Participating validators gain `B // reward_quotient * (2 * total_balance_participating - total_balance) // total_balance`. (Note that this value may be negative.)
@ -950,13 +949,13 @@ In addition, validators with `status == PENALIZED` lose `B // reward_quotient +
#### Balance recalculations related to crosslink rewards #### Balance recalculations related to crosslink rewards
For every shard number `shard` for which a crosslink committee exists in the cycle prior to the most recent cycle (`last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`), let `V` be the corresponding validator set. Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation. For each `shard`, `V`: For every shard number `shard` for which a crosslink committee exists in the cycle prior to the most recent cycle (`s - CYCLE_LENGTH ... s - 1`), let `V` be the corresponding validator set. Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation. For each `shard`, `V`:
* Let `total_balance_of_v` be the total balance of `V`. * Let `total_balance_of_v` be the total balance of `V`.
* Let `winning_shard_hash` be the hash that the largest total deposits signed for the `shard` during the cycle. * Let `winning_shard_hash` be the hash that the largest total deposits signed for the `shard` during the cycle.
* Define a "participating validator" as a member of `V` that signed a crosslink of `winning_shard_hash`. * Define a "participating validator" as a member of `V` that signed a crosslink of `winning_shard_hash`.
* Let `total_balance_of_v_participating` be the total balance of the subset of `V` that participated. * Let `total_balance_of_v_participating` be the total balance of the subset of `V` that participated.
* Let `time_since_last_confirmation = block.slot - crosslinks[shard].slot`. * Let `time_since_last_confirmation = s - crosslinks[shard].slot`.
* Adjust balances as follows: * Adjust balances as follows:
* Participating validators gain `B // reward_quotient * (2 * total_balance_of_v_participating - total_balance_of_v) // total_balance_of_v`. * Participating validators gain `B // reward_quotient * (2 * total_balance_of_v_participating - total_balance_of_v) // total_balance_of_v`.
* Non-participating validators lose `B // reward_quotient`. * Non-participating validators lose `B // reward_quotient`.
@ -969,11 +968,39 @@ If `last_state_recalculation_slot % POW_HASH_VOTING_PERIOD == 0`, then:
* Set `state.candidate_hash_chain_tip = block.candidate_pow_hash_chain_tip` * Set `state.candidate_hash_chain_tip = block.candidate_pow_hash_chain_tip`
* Set `state.candidate_hash_chain_tip_votes = 0` * Set `state.candidate_hash_chain_tip_votes = 0`
### Validator set change #### Proposer reshuffling
A validator set change can happen after a state recalculation if all of the following criteria are satisfied: Run the following code:
```python
active_validator_indices = get_active_validator_indices(validators)
num_validators_to_reshuffle = len(active_validator_indices) // SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
for i in range(num_validators_to_reshuffle):
# Multiplying i to 2 to ensure we have different input to all the required hashes in the shuffling
# and none of the hashes used for entropy in this loop will be the same
vid = active_validator_indices[hash(state.randao_mix + bytes8(i * 2)) % len(active_validator_indices)]
new_shard = hash(state.randao_mix + bytes8(i * 2 + 1)) % SHARD_COUNT
shard_reassignment_record = ShardReassignmentRecord(
validator_index=vid,
shard=new_shard,
slot=s + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
)
state.persistent_committee_reassignments.append(shard_reassignment_record)
while len(state.persistent_committee_reassignments) > 0 and state.persistent_committee_reassignments[0].slot <= s:
rec = state.persistent_committee_reassignments.pop(0)
for committee in state.persistent_committees:
if rec.validator_index in committee:
committee.pop(
committee.index(rec.validator_index)
)
state.persistent_committees[rec.shard].append(rec.validator_index)
```
#### Validator set change
A validator set change can happen if all of the following criteria are satisfied:
* `block.slot - state.validator_set_change_slot >= MIN_VALIDATOR_SET_CHANGE_INTERVAL`
* `last_finalized_slot > state.validator_set_change_slot` * `last_finalized_slot > state.validator_set_change_slot`
* For every shard number `shard` in `shard_and_committee_for_slots`, `crosslinks[shard].slot > state.validator_set_change_slot` * For every shard number `shard` in `shard_and_committee_for_slots`, `crosslinks[shard].slot > state.validator_set_change_slot`
@ -1040,13 +1067,13 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
# STUB: withdraw to shard chain # STUB: withdraw to shard chain
``` ```
* Set `state.validator_set_change_slot = state.last_state_recalculation_slot` * Set `state.validator_set_change_slot = s`
* Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]` * Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]`
* Let `next_start_shard = (shard_and_committee_for_slots[-1][-1].shard + 1) % SHARD_COUNT` * Let `next_start_shard = (shard_and_committee_for_slots[-1][-1].shard + 1) % SHARD_COUNT`
* Set `shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, next_start_shard)` * Set `shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, next_start_shard)`
* Set `state.next_shuffling_seed = state.randao_mix` * Set `state.next_shuffling_seed = state.randao_mix`
### If a validator set change does NOT happen #### If a validator set change does NOT happen
* Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]` * Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]`
* Let `time_since_finality = block.slot - state.validator_set_change_slot` * Let `time_since_finality = block.slot - state.validator_set_change_slot`
@ -1055,47 +1082,11 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
#### Finally... #### Finally...
* Remove all attestation records older than slot `state.last_state_recalculation_slot` * Remove all attestation records older than slot `s`
* Empty the `state.pending_specials` list
* For any validator with index `v` with balance less than `MIN_ONLINE_DEPOSIT_SIZE` and status `ACTIVE`, run `exit_validator(v, state, penalize=False, current_slot=block.slot)` * For any validator with index `v` with balance less than `MIN_ONLINE_DEPOSIT_SIZE` and status `ACTIVE`, run `exit_validator(v, state, penalize=False, current_slot=block.slot)`
* Set `state.recent_block_hashes = state.recent_block_hashes[CYCLE_LENGTH:]` * Set `state.recent_block_hashes = state.recent_block_hashes[CYCLE_LENGTH:]`
* Set `state.last_state_recalculation_slot += CYCLE_LENGTH` * Set `state.last_state_recalculation_slot += CYCLE_LENGTH`
For any validator that was added or removed from the active validator list during this state recalculation:
* If the validator was removed, remove their index from the `persistent_committees` and remove any `ShardReassignmentRecord`s containing their index from `persistent_committee_reassignments`.
* If the validator was added with index `validator_index`:
* let `assigned_shard = hash(state.randao_mix + bytes8(validator_index)) % SHARD_COUNT`
* let `reassignment_record = ShardReassignmentRecord(validator_index=validator_index, shard=assigned_shard, slot=block.slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD)`
* Append `reassignment_record` to the end of `persistent_committee_reassignments`
Now run the following code to reshuffle a few proposers:
```python
active_validator_indices = get_active_validator_indices(validators)
num_validators_to_reshuffle = len(active_validator_indices) // SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
for i in range(num_validators_to_reshuffle):
# Multiplying i to 2 to ensure we have different input to all the required hashes in the shuffling
# and none of the hashes used for entropy in this loop will be the same
vid = active_validator_indices[hash(state.randao_mix + bytes8(i * 2)) % len(active_validator_indices)]
new_shard = hash(state.randao_mix + bytes8(i * 2 + 1)) % SHARD_COUNT
shard_reassignment_record = ShardReassignmentRecord(
validator_index=vid,
shard=new_shard,
slot=block.slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
)
state.persistent_committee_reassignments.append(shard_reassignment_record)
while len(state.persistent_committee_reassignments) > 0 and state.persistent_committee_reassignments[0].slot <= block.slot:
rec = state.persistent_committee_reassignments.pop(0)
for committee in state.persistent_committees:
if rec.validator_index in committee:
committee.pop(
committee.index(rec.validator_index)
)
state.persistent_committees[rec.shard].append(rec.validator_index)
```
### TODO ### TODO
Note: This spec is ~65% complete. Note: This spec is ~65% complete.