[WIP] add receipt processing to phase 1 beacon chain

specs/core/1_beacon_chain_misc.md

@@ -50,6 +50,65 @@ def committee_to_compact_committee(state: BeaconState, committee: Sequence[Valid
     return CompactCommittee(pubkeys=pubkeys, compact_validators=compact_validators)
 ```
 
+#### `get_previous_power_of_2`
+
+```python
+def get_previous_power_of_2(x: int) -> int:
+    return x if x <= 2 else 2 * get_previous_power_of_2(x // 2)
+```
+
+
+#### `concat_generalized_indices`
+
+```python
+def concat_generalized_indices(*indices: Sequence[GeneralizedIndex]) -> GeneralizedIndex:
+    o = GeneralizedIndex(1)
+    for i in indices:
+        o = o * get_previous_power_of_2(i) + i
+    return o
+```
+
+#### `compute_historical_state_generalized_index`
+
+```python
+def compute_historical_state_generalized_index(frm: ShardSlot, to: ShardSlot) -> GeneralizedIndex:
+    o = GeneralizedIndex(1)
+    for i in range(63, -1, -1):
+          if (to-1) & 2**i > (frm-1) & 2**i:
+              to = to - ((to-1) % 2**i) - 1
+              o = concat_generalized_indices(o, get_generalized_index(ShardState, 'history_acc', i))
+    return o
+```
+
+#### `get_generalized_index_of_crosslink_header`
+
+```python
+def get_generalized_index_of_crosslink_header(index: int) -> GeneralizedIndex:
+    MAX_CROSSLINK_SIZE = SHARD_BLOCK_SIZE_LIMIT * SHARD_SLOTS_PER_BEACON_SLOT * SLOTS_PER_EPOCH * MAX_EPOCHS_PER_CROSSLINK
+    assert MAX_CROSSLINK_SIZE == get_previous_power_of_2(MAX_CROSSLINK_SIZE)
+    return GeneralizedIndex(MAX_CROSSLINK_SIZE // SHARD_HEADER_SIZE + index)
+```
+
+#### `process_shard_receipt`
+
+```python
+def process_shard_receipt(state: BeaconState, shard: Shard, proof: List[Hash, PLACEHOLDER], receipt: List[ShardReceiptDelta, PLACEHOLDER]):
+    receipt_slot = state.next_shard_receipt_period[shard] * SLOTS_PER_EPOCH * EPOCHS_PER_SHARD_PERIOD
+    first_slot_in_last_crosslink = state.current_crosslinks[shard].start_epoch * SLOTS_PER_EPOCH
+    gindex = concat_generalized_indices(
+        get_generalized_index_of_crosslink_header(0),
+        get_generalized_index(ShardBlockHeader, 'state_root')
+        compute_historical_state_generalized_index(receipt_slot, first_slot_in_last_crosslink)
+        get_generalized_index(ShardState, 'receipt_root')
+    )
+    assert verify_merkle_proof(
+        leaf=hash_tree_root(receipt),
+        proof=proof,
+        index=gindex,
+        root=state.current_crosslinks[shard].data_root
+    )
+```
+
 ## Changes
 
 ### Persistent committees
@@ -59,6 +118,7 @@ Add to the beacon state the following fields:
 * `previous_persistent_committee_root: Hash`
 * `current_persistent_committee_root: Hash`
 * `next_persistent_committee_root: Hash`
+* `next_shard_receipt_period: Vector[uint, SHARD_COUNT]`, values initialized to `PHASE_1_FORK_SLOT // SLOTS_PER_EPOCH // EPOCHS_PER_SHARD_PERIOD`
 
 Process the following function before `process_final_updates`: