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Avoid divisions by zero #1123

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May 30, 2019
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Avoid divisions by zero #1123

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cdfb886
Avoid divisions by zero
JustinDrake May 26, 2019
1c41654
Update 0_beacon-chain.md
JustinDrake May 29, 2019
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26 changes: 12 additions & 14 deletions specs/core/0_beacon-chain.md
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Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,7 @@
- [Initial values](#initial-values)
- [Time parameters](#time-parameters)
- [State list lengths](#state-list-lengths)
- [Reward and penalty quotients](#reward-and-penalty-quotients)
- [Rewards and penalties](#rewards-and-penalties)
- [Max operations per block](#max-operations-per-block)
- [Signature domains](#signature-domains)
- [Data structures](#data-structures)
Expand Down Expand Up @@ -103,7 +103,7 @@
- [Helper functions](#helper-functions-1)
- [Justification and finalization](#justification-and-finalization)
- [Crosslinks](#crosslinks)
- [Rewards and penalties](#rewards-and-penalties)
- [Rewards and penalties](#rewards-and-penalties-1)
- [Registry updates](#registry-updates)
- [Slashings](#slashings)
- [Final updates](#final-updates)
Expand Down Expand Up @@ -220,17 +220,17 @@ These configurations are updated for releases, but may be out of sync during `de
| `LATEST_ACTIVE_INDEX_ROOTS_LENGTH` | `2**13` (= 8,192) | epochs | ~36 days |
| `LATEST_SLASHED_EXIT_LENGTH` | `2**13` (= 8,192) | epochs | ~36 days |

### Reward and penalty quotients
### Rewards and penalties

| Name | Value |
| - | - |
| `BASE_REWARD_QUOTIENT` | `2**5` (= 32) |
| `BASE_REWARD_FACTOR` | `2**5` (= 32) |
| `WHISTLEBLOWING_REWARD_QUOTIENT` | `2**9` (= 512) |
| `PROPOSER_REWARD_QUOTIENT` | `2**3` (= 8) |
| `INACTIVITY_PENALTY_QUOTIENT` | `2**25` (= 33,554,432) |
| `MIN_SLASHING_PENALTY_QUOTIENT` | `2**5` (= 32) |

* **The `BASE_REWARD_QUOTIENT` is NOT final. Once all other protocol details are finalized, it will be adjusted to target a theoretical maximum total issuance of `2**21` ETH per year if `2**27` ETH is validating (and therefore `2**20` per year if `2**25` ETH is validating, etc.)**
* **The `BASE_REWARD_FACTOR` is NOT final. Once all other protocol details are finalized, it will be adjusted to target a theoretical maximum total issuance of `2**21` ETH per year if `2**27` ETH is validating (and therefore `2**20` per year if `2**25` ETH is validating, etc.)**
* The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**12 epochs` (~18 days) is the time it takes the inactivity penalty to reduce the balance of non-participating [validators](#dfn-validator) to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline [validators](#dfn-validator) after `n` epochs is about `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)` so after `INVERSE_SQRT_E_DROP_TIME` epochs it is roughly `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`.

### Max operations per block
Expand Down Expand Up @@ -963,9 +963,9 @@ def bytes_to_int(data: bytes) -> int:
```python
def get_total_balance(state: BeaconState, indices: List[ValidatorIndex]) -> Gwei:
"""
Return the combined effective balance of an array of ``validators``.
Return the combined effective balance of the ``indices``. (1 Gwei minimum to avoid divisions by zero.)
"""
return sum([state.validator_registry[index].effective_balance for index in indices])
return max(sum([state.validator_registry[index].effective_balance for index in indices]), 1)
```

### `get_domain`
Expand Down Expand Up @@ -1413,10 +1413,9 @@ def process_crosslinks(state: BeaconState) -> None:

```python
def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
adjusted_quotient = integer_squareroot(get_total_active_balance(state)) // BASE_REWARD_QUOTIENT
if adjusted_quotient == 0:
return 0
return state.validator_registry[index].effective_balance // adjusted_quotient // BASE_REWARDS_PER_EPOCH
total_balance = get_total_active_balance(state)
effective_balance = state.validator_registry[index].effective_balance
return effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance) // BASE_REWARDS_PER_EPOCH
```

```python
Expand Down Expand Up @@ -1531,10 +1530,9 @@ def process_registry_updates(state: BeaconState) -> None:
```python
def process_slashings(state: BeaconState) -> None:
current_epoch = get_current_epoch(state)
active_validator_indices = get_active_validator_indices(state, current_epoch)
total_balance = get_total_balance(state, active_validator_indices)
total_balance = get_total_active_balance(state)

# Compute `total_penalties`
# Compute slashed balances in the current epoch
total_at_start = state.latest_slashed_balances[(current_epoch + 1) % LATEST_SLASHED_EXIT_LENGTH]
total_at_end = state.latest_slashed_balances[current_epoch % LATEST_SLASHED_EXIT_LENGTH]
total_penalties = total_at_end - total_at_start
Expand Down