Merge pull request #2190 from ethereum/update-ws-calc
Updated Weak Subjectivity Calculations
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Danny Ryan
GitHub
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fe52f377e6
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@ -8,13 +8,17 @@
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- [Introduction](#introduction)
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- [Prerequisites](#prerequisites)
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- [Custom Types](#custom-types)
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- [Constants](#constants)
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- [Configuration](#configuration)
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- [Weak Subjectivity Checkpoint](#weak-subjectivity-checkpoint)
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- [Weak Subjectivity Period](#weak-subjectivity-period)
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- [Calculating the Weak Subjectivity Period](#calculating-the-weak-subjectivity-period)
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- [`compute_weak_subjectivity_period`](#compute_weak_subjectivity_period)
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- [Weak Subjectivity Sync](#weak-subjectivity-sync)
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- [Weak Subjectivity Sync Procedure](#weak-subjectivity-sync-procedure)
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- [Checking for Stale Weak Subjectivity Checkpoint](#checking-for-stale-weak-subjectivity-checkpoint)
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- [`is_within_weak_subjectivity_period`](#is_within_weak_subjectivity_period)
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- [Distributing Weak Subjectivity Checkpoints](#distributing-weak-subjectivity-checkpoints)
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<!-- END doctoc generated TOC please keep comment here to allow auto update -->
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@ -34,10 +38,22 @@ For more information about weak subjectivity and why it is required, please refe
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This document uses data structures, constants, functions, and terminology from
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[Phase 0 -- The Beacon Chain](./beacon-chain.md) and [Phase 0 -- Beacon Chain Fork Choice](./fork-choice.md).
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## Custom Types
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| Name | SSZ Equivalent | Description |
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|---|---|---|
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| `Ether` | `uint64` | an amount in Ether |
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## Constants
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| Name | Value |
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|----------------|--------------|
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|---|---|
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| `ETH_TO_GWEI` | `uint64(10**9)` |
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## Configuration
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| Name | Value |
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|---|---|
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| `SAFETY_DECAY` | `uint64(10)` |
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## Weak Subjectivity Checkpoint
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@ -59,38 +75,64 @@ a safety margin of at least `1/3 - SAFETY_DECAY/100`.
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### Calculating the Weak Subjectivity Period
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*Note*: `compute_weak_subjectivity_period()` is planned to be updated when a more accurate calculation is made.
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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).
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*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).
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*Note*: The calculations here use `Ether` instead of `Gwei`, because the large magnitude of balances in `Gwei` can cause an overflow while computing using `uint64` arithmetic operations. Using `Ether` reduces the magnitude of the multiplicative factors by an order of `ETH_TO_GWEI` (`= 10**9`) and avoid the scope for overflows in `uint64`.
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#### `compute_weak_subjectivity_period`
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```python
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def compute_weak_subjectivity_period(state: BeaconState) -> uint64:
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weak_subjectivity_period = MIN_VALIDATOR_WITHDRAWABILITY_DELAY
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validator_count = len(get_active_validator_indices(state, get_current_epoch(state)))
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if validator_count >= MIN_PER_EPOCH_CHURN_LIMIT * CHURN_LIMIT_QUOTIENT:
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weak_subjectivity_period += SAFETY_DECAY * CHURN_LIMIT_QUOTIENT // (2 * 100)
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"""
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Returns the weak subjectivity period for the current ``state``.
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This computation takes into account the effect of:
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- validator set churn (bounded by ``get_validator_churn_limit()`` per epoch), and
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- validator balance top-ups (bounded by ``MAX_DEPOSITS * SLOTS_PER_EPOCH`` per epoch).
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A detailed calculation can be found at:
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https://github.com/runtimeverification/beacon-chain-verification/blob/master/weak-subjectivity/weak-subjectivity-analysis.pdf
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"""
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ws_period = MIN_VALIDATOR_WITHDRAWABILITY_DELAY
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N = len(get_active_validator_indices(state, get_current_epoch(state)))
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t = get_total_active_balance(state) // N // ETH_TO_GWEI
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T = MAX_EFFECTIVE_BALANCE // ETH_TO_GWEI
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delta = get_validator_churn_limit(state)
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Delta = MAX_DEPOSITS * SLOTS_PER_EPOCH
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D = SAFETY_DECAY
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if T * (200 + 3 * D) < t * (200 + 12 * D):
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epochs_for_validator_set_churn = (
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N * (t * (200 + 12 * D) - T * (200 + 3 * D)) // (600 * delta * (2 * t + T))
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)
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epochs_for_balance_top_ups = (
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N * (200 + 3 * D) // (600 * Delta)
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)
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ws_period += max(epochs_for_validator_set_churn, epochs_for_balance_top_ups)
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else:
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weak_subjectivity_period += SAFETY_DECAY * validator_count // (2 * 100 * MIN_PER_EPOCH_CHURN_LIMIT)
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return weak_subjectivity_period
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ws_period += (
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3 * N * D * t // (200 * Delta * (T - t))
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)
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return ws_period
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```
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*Details about the calculation*:
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- `100` appears in the denominator to get the actual percentage ratio from `SAFETY_DECAY`
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- For more information about other terms in this equation, refer to
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[Weak Subjectivity in Eth2.0](https://notes.ethereum.org/@adiasg/weak-subjectvity-eth2)
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A brief reference for what these values look like in practice ([reference script](https://gist.github.com/adiasg/3aceab409b36aa9a9d9156c1baa3c248)):
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A brief reference for what these values look like in practice:
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| `validator_count` | `weak_subjectivity_period` |
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| ---- | ---- |
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| 1024 | 268 |
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| 2048 | 281 |
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| 4096 | 307 |
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| 8192 | 358 |
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| 16384 | 460 |
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| 32768 | 665 |
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| 65536 | 1075 |
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| 131072 | 1894 |
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| 262144 | 3532 |
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| 524288 | 3532 |
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| Safety Decay | Avg. Val. Balance (ETH) | Val. Count | Weak Sub. Period (Epochs) |
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| ---- | ---- | ---- | ---- |
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| 10 | 28 | 32768 | 504 |
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| 10 | 28 | 65536 | 752 |
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| 10 | 28 | 131072 | 1248 |
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| 10 | 28 | 262144 | 2241 |
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| 10 | 28 | 524288 | 2241 |
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| 10 | 28 | 1048576 | 2241 |
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| 10 | 32 | 32768 | 665 |
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| 10 | 32 | 65536 | 1075 |
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| 10 | 32 | 131072 | 1894 |
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| 10 | 32 | 262144 | 3532 |
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| 10 | 32 | 524288 | 3532 |
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| 10 | 32 | 1048576 | 3532 |
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## Weak Subjectivity Sync
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@ -101,10 +143,13 @@ Clients should allow users to input a Weak Subjectivity Checkpoint at startup, a
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1. Input a Weak Subjectivity Checkpoint as a CLI parameter in `block_root:epoch_number` format,
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where `block_root` (an "0x" prefixed 32-byte hex string) and `epoch_number` (an integer) represent a valid `Checkpoint`.
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Example of the format:
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```
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0x8584188b86a9296932785cc2827b925f9deebacce6d72ad8d53171fa046b43d9:9544
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```
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2. - *IF* `epoch_number > store.finalized_checkpoint.epoch`,
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2. Check the weak subjectivity requirements:
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- *IF* `epoch_number > store.finalized_checkpoint.epoch`,
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then *ASSERT* during block sync that block with root `block_root` is in the sync path at epoch `epoch_number`.
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Emit descriptive critical error if this assert fails, then exit client process.
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- *IF* `epoch_number <= store.finalized_checkpoint.epoch`,
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@ -112,11 +157,14 @@ Clients should allow users to input a Weak Subjectivity Checkpoint at startup, a
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Emit descriptive critical error if this assert fails, then exit client process.
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### Checking for Stale Weak Subjectivity Checkpoint
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Clients may choose to validate that the input Weak Subjectivity Checkpoint is not stale at the time of startup.
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To support this mechanism, the client needs to take the state at the Weak Subjectivity Checkpoint as
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a CLI parameter input (or fetch the state associated with the input Weak Subjectivity Checkpoint from some source).
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The check can be implemented in the following way:
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#### `is_within_weak_subjectivity_period`
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```python
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def is_within_weak_subjectivity_period(store: Store, ws_state: BeaconState, ws_checkpoint: Checkpoint) -> bool:
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# Clients may choose to validate the input state against the input Weak Subjectivity Checkpoint
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@ -130,4 +178,5 @@ def is_within_weak_subjectivity_period(store: Store, ws_state: BeaconState, ws_c
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```
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## Distributing Weak Subjectivity Checkpoints
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This section will be updated soon.
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