Update casper_sharding_v2.1.md
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@ -298,15 +298,18 @@ def get_block_hash(active_state, curblock, slot):
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`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.
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Finally, we abstractly define `integer_sqrt` for use in reward/penalty calculations:
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Finally, we abstractly define `integer_sqrt(x)` for use in reward/penalty calculations as the largest integer `n` such that `n**2 <= x`. Here is one possible implementation, though clients are free to use their own including standard libraries if available.
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```python
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def integer_sqrt(n):
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return max(n in Z: n**2 <= x)
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x = n
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y = (x + 1) // 2
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while y < x:
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x = y
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y = (x + n // x) // 2
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return x
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```
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We leave `integer_sqrt` implementation details to each particular language/framework.
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### On startup
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* Let `x = get_new_shuffling(bytes([0] * 32), validators, 1, 0)` and set `crystallized_state.shard_and_committee_for_slots` to `x + x`
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