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Aditya Asgaonkar 2021-01-27 15:16:15 -08:00
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specs/phase0/weak-subjectivity.md
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@ -14,8 +14,6 @@
- [Weak Subjectivity Checkpoint](#weak-subjectivity-checkpoint)
- [Weak Subjectivity Period](#weak-subjectivity-period)
- [Calculating the Weak Subjectivity Period](#calculating-the-weak-subjectivity-period)
- [`get_active_validator_count`](#get_active_validator_count)
- [`compute_avg_active_validator_balance`](#compute_avg_active_validator_balance)
- [`compute_weak_subjectivity_period`](#compute_weak_subjectivity_period)
- [Weak Subjectivity Sync](#weak-subjectivity-sync)
- [Weak Subjectivity Sync Procedure](#weak-subjectivity-sync-procedure)
@ -77,44 +75,33 @@ a safety margin of at least `1/3 - SAFETY_DECAY/100`.
### Calculating the Weak Subjectivity Period
A detailed analysis of the calculation of the weak subjectivity period is made in [this report](https://github.com/runtimeverification/beacon-chain-verification/blob/master/weak-subjectivity/weak-subjectivity-analysis.pdf). The expressions in the report use fractions, whereas we only use uint64 arithmetic in eth2.0-specs. The expressions have been simplified to avoid computing fractions, and more details can be found [here](https://www.overleaf.com/read/wgjzjdjpvpsd).
A detailed analysis of the calculation of the weak subjectivity period is made in [this report](https://github.com/runtimeverification/beacon-chain-verification/blob/master/weak-subjectivity/weak-subjectivity-analysis.pdf).
#### `get_active_validator_count`
*Note*: The expressions in the report use fractions, whereas eth2.0-specs uses only `uint64` arithmetic. The expressions have been simplified to avoid computing fractions, and more details can be found [here](https://www.overleaf.com/read/wgjzjdjpvpsd).
```python
def get_active_validator_count(state: BeaconState) -> uint64:
active_validator_count = len(get_active_validator_indices(state, get_current_epoch(state)))
return active_validator_count
```
#### `compute_avg_active_validator_balance`
```python
def compute_avg_active_validator_balance(state: BeaconState) -> Ether:
total_active_balance = get_total_active_balance(state)
active_validator_count = get_active_validator_count(state)
avg_active_validator_balance_gwei = total_active_balance // active_validator_count
avg_active_validator_balance_eth = avg_active_validator_balance_gwei // ETH_TO_GWEI
return avg_active_validator_balance_eth
```
*Note*: The calculations here use `Ether` instead of `Gwei`, because the large magitude of balances in `Gwei` can cause an overflow while computing using `uint64` arithmetic operations. Using `Ether` reduces the magintude of the multiplicative factors by an order of `ETH_TO_GWEI` (`= 10**9`) and avoid the scope for overflows in `uint64`.
#### `compute_weak_subjectivity_period`
```python
def compute_weak_subjectivity_period(state: BeaconState) -> uint64:
"""
Returns the weak subjectivity period for the current ``state``.
This computation takes into account the effect of:
- validator set churn (bounded by ``get_validator_churn_limit()`` per epoch), and
- validator balance top-ups (bounded by ``MAX_DEPOSITS * SLOTS_PER_EPOCH`` per epoch).
A detailed calculation can be found at:
https://github.com/runtimeverification/beacon-chain-verification/blob/master/weak-subjectivity/weak-subjectivity-analysis.pdf
"""
ws_period = MIN_VALIDATOR_WITHDRAWABILITY_DELAY
N = get_active_validator_count(state)
t = compute_avg_active_validator_balance(state)
T = MAX_EFFECTIVE_BALANCE // 10**9
N = len(get_active_validator_indices(state, get_current_epoch(state)))
t = get_total_active_balance(state) // N // ETH_TO_GWEI
T = MAX_EFFECTIVE_BALANCE // ETH_TO_GWEI
delta = get_validator_churn_limit(state)
Delta = MAX_DEPOSITS * SLOTS_PER_EPOCH
D = SAFETY_DECAY
case = (
T * (200 + 3 * D) < t * (200 + 12 * D)
)
if case == 1:
if T * (200 + 3 * D) < t * (200 + 12 * D):
arg1 = (
N * (t * (200 + 12 * D) - T * (200 + 3 * D)) // (600 * delta * (2 * t + T))
)
@ -130,28 +117,22 @@ def compute_weak_subjectivity_period(state: BeaconState) -> uint64:
return ws_period
```
A brief reference for what these values look like in practice:
A brief reference for what these values look like in practice ([reference script](https://gist.github.com/adiasg/3aceab409b36aa9a9d9156c1baa3c248)):
| Safety Decay | Validator Count | Average Active Validator Balance | Weak Subjectivity Period |
| Safety Decay | Avg. Val. Balance (ETH) | Val. Count | Weak Sub. Period (Epochs) |
| ---- | ---- | ---- | ---- |
| 10 | 8192 | 28 | 318 |
| 10 | 8192 | 32 | 358 |
| 10 | 16384 | 28 | 380 |
| 10 | 16384 | 32 | 460 |
| 10 | 32768 | 28 | 504 |
| 10 | 32768 | 32 | 665 |
| 20 | 8192 | 28 | 411 |
| 20 | 8192 | 32 | 460 |
| 20 | 16384 | 28 | 566 |
| 20 | 16384 | 32 | 665 |
| 20 | 32768 | 28 | 876 |
| 20 | 32768 | 32 | 1075 |
| 33 | 8192 | 28 | 532 |
| 33 | 8192 | 32 | 593 |
| 33 | 16384 | 28 | 808 |
| 33 | 16384 | 32 | 931 |
| 33 | 32768 | 28 | 1360 |
| 33 | 32768 | 32 | 1607 |
| 10 | 28 | 32768 | 504 |
| 10 | 28 | 65536 | 752 |
| 10 | 28 | 131072 | 1248 |
| 10 | 28 | 262144 | 2241 |
| 10 | 28 | 524288 | 2241 |
| 10 | 28 | 1048576 | 2241 |
| 10 | 32 | 32768 | 665 |
| 10 | 32 | 65536 | 1075 |
| 10 | 32 | 131072 | 1894 |
| 10 | 32 | 262144 | 3532 |
| 10 | 32 | 524288 | 3532 |
| 10 | 32 | 1048576 | 3532 |
## Weak Subjectivity Sync