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Merge pull request #13 from ethereum/integer-sqrt 

add int_sqrt function
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Danny Ryan 2018-09-30 18:12:05 -05:00 committed by GitHub
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specs/casper_sharding_v2.1.md
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@ -282,7 +282,7 @@ Here's a diagram of what's going on:
![](http://vitalik.ca/files/ShuffleAndAssign.png?1)
We also define:
We also define two functions retrieving data from the state:
```python
def get_shards_and_committees_for_slot(crystallized_state, slot):
@ -298,6 +298,18 @@ def get_block_hash(active_state, curblock, slot):
`get_block_hash(*, *, h)` should always return the block in the chain at slot `h`, and `get_shards_and_committees_for_slot(*, h)` should not change unless the dynasty changes.
Finally, we abstractly define `int_sqrt(n)` for use in reward/penalty calculations as the largest integer `k` such that `k**2 <= n`. Here is one possible implementation, though clients are free to use their own including standard libraries if available and meet the specification.
```python
def int_sqrt(n):
k = n
while True:
newk = (k + (n // k)) // 2
if newk in (k, k+1):
return k
k = newk
```
### On startup
* Let `x = get_new_shuffling(bytes([0] * 32), validators, 1, 0)` and set `crystallized_state.shard_and_committee_for_slots` to `x + x`
@ -375,7 +387,7 @@ For all (`shard_id`, `shard_block_hash`) tuples, compute the total deposit size
Let `time_since_finality = block.slot_number - last_finalized_slot`, and 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:
* `total_deposits = sum([v.balance for i, v in enumerate(validators) if i in get_active_validator_indices(validators, current_dynasty)])` and `total_deposits_in_ETH = total_deposits // 10**18`
* `reward_quotient = BASE_REWARD_QUOTIENT * int(sqrt(total_deposits_in_ETH))` (1/this is the per-slot max interest rate)
* `reward_quotient = BASE_REWARD_QUOTIENT * int_sqrt(total_deposits_in_ETH)` (1/this is the per-slot max interest rate)
* `quadratic_penalty_quotient = (SQRT_E_DROP_TIME / SLOT_DURATION)**2` (after D slots, ~D<sup>2</sup>/2 divided by this is the portion lost by offline validators)
For each slot `S` in the range `last_state_recalc - CYCLE_LENGTH ... last_state_recalc - 1`: