ethereum.forks.muir_glacier.forkethereum.forks.berlin.fork

Ethereum Specification.

.. contents:: Table of Contents :backlinks: none :local:

Introduction

Entry point for the Ethereum specification.

BLOCK_REWARD

69
BLOCK_REWARD = U256(2 * 10**18)

MINIMUM_DIFFICULTY

70
MINIMUM_DIFFICULTY = Uint(131072)

MAX_OMMER_DEPTH

71
MAX_OMMER_DEPTH = Uint(6)

BOMB_DELAY_BLOCKS

72
BOMB_DELAY_BLOCKS = 9000000

EMPTY_OMMER_HASH

73
EMPTY_OMMER_HASH = keccak256(rlp.encode([]))

BlockChain

History and current state of the block chain.

76
@final
77
@dataclass
class BlockChain:

blocks

83
    blocks: List[Block]

state

84
    state: State

chain_id

85
    chain_id: U64

apply_fork

Transforms the state from the previous hard fork (old) into the block chain object for this hard fork and returns it.

When forks need to implement an irregular state transition, this function is used to handle the irregularity. See the :ref:DAO Fork <dao-fork> for an example.

Parameters

old : Previous block chain object.

Returns

new : BlockChain Upgraded block chain object for this hard fork.

def apply_fork(old: BlockChain) -> BlockChain:
89
    <snip>
108
    return old

get_last_256_block_hashes

Obtain the list of hashes of the previous 256 blocks in order of increasing block number.

This function will return less hashes for the first 256 blocks.

The BLOCKHASH opcode needs to access the latest hashes on the chain, therefore this function retrieves them.

Parameters

chain : History and current state.

Returns

recent_block_hashes : List[Hash32] Hashes of the recent 256 blocks in order of increasing block number.

def get_last_256_block_hashes(chain: BlockChain) -> List[Hash32]:
112
    <snip>
132
    recent_blocks = chain.blocks[-255:]
133
    # TODO: This function has not been tested rigorously
134
    if len(recent_blocks) == 0:
135
        return []
136
137
    recent_block_hashes = []
138
139
    for block in recent_blocks:
140
        prev_block_hash = block.header.parent_hash
141
        recent_block_hashes.append(prev_block_hash)
142
143
    # We are computing the hash only for the most recent block and not for
144
    # the rest of the blocks as they have successors which have the hash of
145
    # the current block as parent hash.
146
    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))
147
    recent_block_hashes.append(most_recent_block_hash)
148
149
    return recent_block_hashes

state_transition

Attempts to apply a block to an existing block chain.

All parts of the block's contents need to be verified before being added to the chain. Blocks are verified by ensuring that the contents of the block make logical sense with the contents of the parent block. The information in the block's header must also match the corresponding information in the block.

To implement Ethereum, in theory clients are only required to store the most recent 255 blocks of the chain since as far as execution is concerned, only those blocks are accessed. Practically, however, clients should store more blocks to handle reorgs.

Parameters

chain : History and current state. block : Block to apply to chain.

def state_transition(chain: BlockChain, ​​block: Block) -> None:
153
    <snip>
175
    validate_header(chain, block.header)
176
    validate_ommers(block.ommers, block.header, chain)
177
178
    block_state = BlockState(pre_state=chain.state)
179
180
    block_env = vm.BlockEnvironment(
181
        chain_id=chain.chain_id,
182
        state=block_state,
183
        block_gas_limit=block.header.gas_limit,
184
        block_hashes=get_last_256_block_hashes(chain),
185
        coinbase=block.header.coinbase,
186
        number=block.header.number,
187
        time=block.header.timestamp,
188
        difficulty=block.header.difficulty,
189
    )
190
191
    block_output = apply_body(
192
        block_env=block_env,
193
        transactions=block.transactions,
194
        ommers=block.ommers,
195
    )
196
    block_diff = extract_block_diff(block_state)
197
    block_state_root, _ = chain.state.compute_state_root_and_trie_changes(
198
        block_diff.account_changes,
199
        block_diff.storage_changes,
200
        block_diff.storage_clears,
201
    )
202
    transactions_root = root(block_output.transactions_trie)
203
    receipt_root = root(block_output.receipts_trie)
204
    block_logs_bloom = logs_bloom(block_output.block_logs)
205
206
    if block_output.block_gas_used != block.header.gas_used:
207
        raise InvalidBlock(
208
            f"{block_output.block_gas_used} != {block.header.gas_used}"
209
        )
210
    if transactions_root != block.header.transactions_root:
211
        raise InvalidBlock
212
    if block_state_root != block.header.state_root:
213
        raise InvalidBlock
214
    if receipt_root != block.header.receipt_root:
215
        raise InvalidBlock
216
    if block_logs_bloom != block.header.bloom:
217
        raise InvalidBlock
218
219
    apply_changes_to_state(chain.state, block_diff)
220
    chain.blocks.append(block)
221
    if len(chain.blocks) > 255:
222
        # Real clients have to store more blocks to deal with reorgs, but the
223
        # protocol only requires the last 255
224
        chain.blocks = chain.blocks[-255:]

validate_header

Verifies a block header.

In order to consider a block's header valid, the logic for the quantities in the header should match the logic for the block itself. For example the header timestamp should be greater than the block's parent timestamp because the block was created after the parent block. Additionally, the block's number should be directly following the parent block's number since it is the next block in the sequence.

Parameters

chain : History and current state. header : Header to check for correctness.

def validate_header(chain: BlockChain, ​​header: Header) -> None:
228
    <snip>
246
    if header.number < Uint(1):
247
        raise InvalidBlock
248
    parent_header_number = header.number - Uint(1)
249
    first_block_number = chain.blocks[0].header.number
250
    last_block_number = chain.blocks[-1].header.number
251
252
    if (
253
        parent_header_number < first_block_number
254
        or parent_header_number > last_block_number
255
    ):
256
        raise InvalidBlock
257
258
    parent_header = chain.blocks[
259
        parent_header_number - first_block_number
260
    ].header
261
262
    if header.gas_used > header.gas_limit:
263
        raise InvalidBlock
264
265
    parent_has_ommers = parent_header.ommers_hash != EMPTY_OMMER_HASH
266
    if header.timestamp <= parent_header.timestamp:
267
        raise InvalidBlock
268
    if header.number != parent_header.number + Uint(1):
269
        raise InvalidBlock
270
    if not check_gas_limit(header.gas_limit, parent_header.gas_limit):
271
        raise InvalidBlock
272
    if len(header.extra_data) > 32:
273
        raise InvalidBlock
274
275
    block_difficulty = calculate_block_difficulty(
276
        header.number,
277
        header.timestamp,
278
        parent_header.timestamp,
279
        parent_header.difficulty,
280
        parent_has_ommers,
281
    )
282
    if header.difficulty != block_difficulty:
283
        raise InvalidBlock
284
285
    block_parent_hash = keccak256(rlp.encode(parent_header))
286
    if header.parent_hash != block_parent_hash:
287
        raise InvalidBlock
288
289
    validate_proof_of_work(header)

generate_header_hash_for_pow

Generate rlp hash of the header which is to be used for Proof-of-Work verification.

In other words, the PoW artefacts mix_digest and nonce are ignored while calculating this hash.

A particular PoW is valid for a single hash, that hash is computed by this function. The nonce and mix_digest are omitted from this hash because they are being changed by miners in their search for a sufficient proof-of-work.

Parameters

header : The header object for which the hash is to be generated.

Returns

hash : Hash32 The PoW valid rlp hash of the passed in header.

def generate_header_hash_for_pow(header: Header) -> Hash32:
293
    <snip>
316
    header_data_without_pow_artefacts = (
317
        header.parent_hash,
318
        header.ommers_hash,
319
        header.coinbase,
320
        header.state_root,
321
        header.transactions_root,
322
        header.receipt_root,
323
        header.bloom,
324
        header.difficulty,
325
        header.number,
326
        header.gas_limit,
327
        header.gas_used,
328
        header.timestamp,
329
        header.extra_data,
330
    )
331
332
    return keccak256(rlp.encode(header_data_without_pow_artefacts))

validate_proof_of_work

Validates the Proof of Work constraints.

In order to verify that a miner's proof-of-work is valid for a block, a mix-digest and result are calculated using the hashimoto_light hash function. The mix digest is a hash of the header and the nonce that is passed through and it confirms whether or not proof-of-work was done on the correct block. The result is the actual hash value of the block.

Parameters

header : Header of interest.

def validate_proof_of_work(header: Header) -> None:
336
    <snip>
351
    header_hash = generate_header_hash_for_pow(header)
352
    # TODO: Memoize this somewhere and read from that data instead of
353
    # calculating cache for every block validation.
354
    cache = generate_cache(header.number)
355
    mix_digest, result = hashimoto_light(
356
        header_hash, header.nonce, cache, dataset_size(header.number)
357
    )
358
    if mix_digest != header.mix_digest:
359
        raise InvalidBlock
360
361
    limit = Uint(U256.MAX_VALUE) + Uint(1)
362
    if Uint.from_be_bytes(result) > (limit // header.difficulty):
363
        raise InvalidBlock

check_transaction

Check if the transaction is includable in the block.

Parameters

block_env : The block scoped environment. block_output : The block output for the current block. tx : The transaction. tx_state : The transaction state tracker.

Returns

sender_address : The sender of the transaction.

Raises

GasUsedExceedsLimitError : If the gas used by the transaction exceeds the block's gas limit. NonceMismatchError : If the nonce of the transaction is not equal to the sender's nonce. InsufficientBalanceError : If the sender's balance is not enough to pay for the transaction. InvalidSenderError : If the transaction is from an address that does not exist anymore.

def check_transaction(block_env: ethereum.forks.muir_glacier.vm.BlockEnvironmentethereum.forks.berlin.vm.BlockEnvironment, ​​block_output: ethereum.forks.muir_glacier.vm.BlockOutputethereum.forks.berlin.vm.BlockOutput, ​​tx: Transaction, ​​tx_state: TransactionState) -> Address:
372
    <snip>
403
    gas_available = block_env.block_gas_limit - block_output.block_gas_used
404
    if tx.gas > gas_available:
405
        raise GasUsedExceedsLimitError("gas used exceeds limit")
406
    sender_address = recover_sender(block_env.chain_id, tx)
407
    sender_account = get_account(tx_state, sender_address)
408
409
    max_gas_fee = tx.gas * tx.gas_price
410
411
    if sender_account.nonce > Uint(tx.nonce):
412
        raise NonceMismatchError("nonce too low")
413
    elif sender_account.nonce < Uint(tx.nonce):
414
        raise NonceMismatchError("nonce too high")
415
    if Uint(sender_account.balance) < max_gas_fee + Uint(tx.value):
416
        raise InsufficientBalanceError("insufficient sender balance")
417
    if sender_account.code_hash != EMPTY_CODE_HASH:
418
        raise InvalidSenderError("not EOA")
419
420
    return sender_address

make_receipt

Make the receipt for a transaction that was executed.

Parameters

tx : The executed transaction. error : Error in the top level frame of the transaction, if any. cumulative_gas_used : The total gas used so far in the block after the transaction was executed. logs : The logs produced by the transaction.

Returns

receipt : The receipt for the transaction.

def make_receipt(tx: Transaction, ​​error: Optional[EthereumException], ​​cumulative_gas_used: Uint, ​​logs: Tuple[Log, ...]) -> ReceiptBytes | Receipt:
429
    <snip>
450
    receipt = Receipt(
451
        succeeded=error is None,
452
        cumulative_gas_used=cumulative_gas_used,
453
        bloom=logs_bloom(logs),
454
        logs=logs,
455
    )
456
451
    return receipt
457
    return encode_receipt(tx, receipt)

apply_body

Executes a block.

Many of the contents of a block are stored in data structures called tries. There is a transactions trie which is similar to a ledger of the transactions stored in the current block. There is also a receipts trie which stores the results of executing a transaction, like the post state and gas used. This function creates and executes the block that is to be added to the chain.

Parameters

block_env : The block scoped environment. transactions : Transactions included in the block. ommers : Headers of ancestor blocks which are not direct parents (formerly uncles.)

Returns

block_output : The block output for the current block.

def apply_body(block_env: ethereum.forks.muir_glacier.vm.BlockEnvironmentethereum.forks.berlin.vm.BlockEnvironment, ​​transactions: Tuple[TransactionLegacyTransaction | Bytes, ...], ​​ommers: Tuple[Header, ...]) -> ethereum.forks.muir_glacier.vm.BlockOutputethereum.forks.berlin.vm.BlockOutput:
465
    <snip>
491
    block_output = vm.BlockOutput()
492
487
    for i, tx in enumerate(transactions):
493
    for i, tx in enumerate(map(decode_transaction, transactions)):
494
        process_transaction(block_env, block_output, tx, Uint(i))
495
496
    pay_rewards(block_env, ommers)
497
498
    return block_output

validate_ommers

Validates the ommers mentioned in the block.

An ommer block is a block that wasn't canonically added to the blockchain because it wasn't validated as fast as the canonical block but was mined at the same time.

To be considered valid, the ommers must adhere to the rules defined in the Ethereum protocol. The maximum amount of ommers is 2 per block and there cannot be duplicate ommers in a block. Many of the other ommer constraints are listed in the in-line comments of this function.

Parameters

ommers : List of ommers mentioned in the current block. block_header: The header of current block. chain : History and current state.

def validate_ommers(ommers: Tuple[Header, ...], ​​block_header: Header, ​​chain: BlockChain) -> None:
504
    <snip>
526
    block_hash = keccak256(rlp.encode(block_header))
527
    if keccak256(rlp.encode(ommers)) != block_header.ommers_hash:
528
        raise InvalidBlock
529
530
    if len(ommers) == 0:
531
        # Nothing to validate
532
        return
533
534
    # Check that each ommer satisfies the constraints of a header
535
    for ommer in ommers:
536
        if Uint(1) > ommer.number or ommer.number >= block_header.number:
537
            raise InvalidBlock
538
        validate_header(chain, ommer)
539
    if len(ommers) > 2:
540
        raise InvalidBlock
541
542
    ommers_hashes = [keccak256(rlp.encode(ommer)) for ommer in ommers]
543
    if len(ommers_hashes) != len(set(ommers_hashes)):
544
        raise InvalidBlock
545
546
    recent_canonical_blocks = chain.blocks[-(MAX_OMMER_DEPTH + Uint(1)) :]
547
    recent_canonical_block_hashes = {
548
        keccak256(rlp.encode(block.header))
549
        for block in recent_canonical_blocks
550
    }
551
    recent_ommers_hashes: Set[Hash32] = set()
552
    for block in recent_canonical_blocks:
553
        recent_ommers_hashes = recent_ommers_hashes.union(
554
            {keccak256(rlp.encode(ommer)) for ommer in block.ommers}
555
        )
556
557
    for ommer_index, ommer in enumerate(ommers):
558
        ommer_hash = ommers_hashes[ommer_index]
559
        if ommer_hash == block_hash:
560
            raise InvalidBlock
561
        if ommer_hash in recent_canonical_block_hashes:
562
            raise InvalidBlock
563
        if ommer_hash in recent_ommers_hashes:
564
            raise InvalidBlock
565
566
        # Ommer age with respect to the current block. For example, an age of
567
        # 1 indicates that the ommer is a sibling of previous block.
568
        ommer_age = block_header.number - ommer.number
569
        if Uint(1) > ommer_age or ommer_age > MAX_OMMER_DEPTH:
570
            raise InvalidBlock
571
        if ommer.parent_hash not in recent_canonical_block_hashes:
572
            raise InvalidBlock
573
        if ommer.parent_hash == block_header.parent_hash:
574
            raise InvalidBlock

pay_rewards

Pay rewards to the block miner as well as the ommers miners.

The miner of the canonical block is rewarded with the predetermined block reward, BLOCK_REWARD, plus a variable award based off of the number of ommer blocks that were mined around the same time, and included in the canonical block's header. An ommer block is a block that wasn't added to the canonical blockchain because it wasn't validated as fast as the accepted block but was mined at the same time. Although not all blocks that are mined are added to the canonical chain, miners are still paid a reward for their efforts. This reward is called an ommer reward and is calculated based on the number associated with the ommer block that they mined.

Parameters

block_env : The block scoped environment. ommers : List of ommers mentioned in the current block.

def pay_rewards(block_env: ethereum.forks.muir_glacier.vm.BlockEnvironmentethereum.forks.berlin.vm.BlockEnvironment, ​​ommers: Tuple[Header, ...]) -> None:
581
    <snip>
603
    rewards_state = TransactionState(parent=block_env.state)
604
    ommer_count = U256(len(ommers))
605
    miner_reward = BLOCK_REWARD + (ommer_count * (BLOCK_REWARD // U256(32)))
606
    create_ether(rewards_state, block_env.coinbase, miner_reward)
607
608
    for ommer in ommers:
609
        # Ommer age with respect to the current block.
610
        ommer_age = U256(block_env.number - ommer.number)
611
        ommer_miner_reward = ((U256(8) - ommer_age) * BLOCK_REWARD) // U256(8)
612
        create_ether(rewards_state, ommer.coinbase, ommer_miner_reward)
613
614
    incorporate_tx_into_block(rewards_state)

process_transaction

Execute a transaction against the provided environment.

This function processes the actions needed to execute a transaction. It decrements the sender's account balance after calculating the gas fee and refunds them the proper amount after execution. Calling contracts, deploying code, and incrementing nonces are all examples of actions that happen within this function or from a call made within this function.

Accounts that are marked for deletion are processed and destroyed after execution.

Parameters

block_env : Environment for the Ethereum Virtual Machine. block_output : The block output for the current block. tx : Transaction to execute. index: Index of the transaction in the block.

def process_transaction(block_env: ethereum.forks.muir_glacier.vm.BlockEnvironmentethereum.forks.berlin.vm.BlockEnvironment, ​​block_output: ethereum.forks.muir_glacier.vm.BlockOutputethereum.forks.berlin.vm.BlockOutput, ​​tx: Transaction, ​​index: Uint) -> None:
623
    <snip>
647
    tx_state = TransactionState(parent=block_env.state)
648
643
    trie_set(block_output.transactions_trie, rlp.encode(Uint(index)), tx)
649
    trie_set(
650
        block_output.transactions_trie,
651
        rlp.encode(index),
652
        encode_transaction(tx),
653
    )
654
655
    intrinsic_gas = validate_transaction(tx)
656
657
    sender = check_transaction(
658
        block_env=block_env,
659
        block_output=block_output,
660
        tx=tx,
661
        tx_state=tx_state,
662
    )
663
664
    sender_account = get_account(tx_state, sender)
665
666
    gas = tx.gas - intrinsic_gas
667
    increment_nonce(tx_state, sender)
668
669
    gas_fee = tx.gas * tx.gas_price
670
    sender_balance_after_gas_fee = Uint(sender_account.balance) - gas_fee
671
    set_account_balance(tx_state, sender, U256(sender_balance_after_gas_fee))
672
673
    access_list_addresses = set()
674
    access_list_storage_keys = set()
675
    if isinstance(tx, AccessListTransaction):
676
        for access in tx.access_list:
677
            access_list_addresses.add(access.account)
678
            for slot in access.slots:
679
                access_list_storage_keys.add((access.account, slot))
680
681
    tx_env = vm.TransactionEnvironment(
682
        origin=sender,
683
        gas_price=tx.gas_price,
684
        gas=gas,
685
        access_list_addresses=access_list_addresses,
686
        access_list_storage_keys=access_list_storage_keys,
687
        state=tx_state,
688
        index_in_block=index,
668
        tx_hash=get_transaction_hash(tx),
689
        tx_hash=get_transaction_hash(encode_transaction(tx)),
690
    )
691
692
    message = prepare_message(block_env, tx_env, tx)
693
694
    tx_output = process_message_call(message)
695
696
    tx_gas_used_before_refund = tx.gas - tx_output.gas_left
697
    tx_gas_refund = min(
698
        tx_gas_used_before_refund // Uint(2), Uint(tx_output.refund_counter)
699
    )
700
    tx_gas_used_after_refund = tx_gas_used_before_refund - tx_gas_refund
701
    tx_gas_left = tx.gas - tx_gas_used_after_refund
702
    gas_refund_amount = tx_gas_left * tx.gas_price
703
704
    transaction_fee = tx_gas_used_after_refund * tx.gas_price
705
706
    # refund gas
707
    create_ether(tx_state, sender, U256(gas_refund_amount))
708
709
    # transfer miner fees
710
    coinbase_balance_after_mining_fee = get_account(
711
        tx_state, block_env.coinbase
712
    ).balance + U256(transaction_fee)
713
    if coinbase_balance_after_mining_fee != 0:
714
        set_account_balance(
715
            tx_state,
716
            block_env.coinbase,
717
            coinbase_balance_after_mining_fee,
718
        )
719
    elif account_exists_and_is_empty(tx_state, block_env.coinbase):
720
        destroy_account(tx_state, block_env.coinbase)
721
722
    for address in tx_output.accounts_to_delete:
723
        destroy_account(tx_state, address)
724
725
    destroy_touched_empty_accounts(tx_state, tx_output.touched_accounts)
726
727
    block_output.block_gas_used += tx_gas_used_after_refund
728
729
    receipt = make_receipt(
709
        tx_output.error, block_output.block_gas_used, tx_output.logs
730
        tx, tx_output.error, block_output.block_gas_used, tx_output.logs
731
    )
732
733
    receipt_key = rlp.encode(Uint(index))
734
    block_output.receipt_keys += (receipt_key,)
735
736
    trie_set(
737
        block_output.receipts_trie,
738
        receipt_key,
739
        receipt,
740
    )
741
742
    block_output.block_logs += tx_output.logs
743
744
    incorporate_tx_into_block(tx_state)

check_gas_limit

Validates the gas limit for a block.

The bounds of the gas limit, max_adjustment_delta, is set as the quotient of the parent block's gas limit and the LIMIT_ADJUSTMENT_FACTOR. Therefore, if the gas limit that is passed through as a parameter is greater than or equal to the sum of the parent's gas and the adjustment delta then the limit for gas is too high and fails this function's check. Similarly, if the limit is less than or equal to the difference of the parent's gas and the adjustment delta or the predefined LIMIT_MINIMUM then this function's check fails because the gas limit doesn't allow for a sufficient or reasonable amount of gas to be used on a block.

Parameters

gas_limit : Gas limit to validate.

parent_gas_limit : Gas limit of the parent block.

Returns

check : bool True if gas limit constraints are satisfied, False otherwise.

def check_gas_limit(gas_limit: Uint, ​​parent_gas_limit: Uint) -> bool:
748
    <snip>
776
    max_adjustment_delta = parent_gas_limit // GasCosts.LIMIT_ADJUSTMENT_FACTOR
777
    if gas_limit >= parent_gas_limit + max_adjustment_delta:
778
        return False
779
    if gas_limit <= parent_gas_limit - max_adjustment_delta:
780
        return False
781
    if gas_limit < GasCosts.LIMIT_MINIMUM:
782
        return False
783
784
    return True

calculate_block_difficulty

Computes difficulty of a block using its header and parent header.

The difficulty is determined by the time the block was created after its parent. The offset is calculated using the parent block's difficulty, parent_difficulty, and the timestamp between blocks. This offset is then added to the parent difficulty and is stored as the difficulty variable. If the time between the block and its parent is too short, the offset will result in a positive number thus making the sum of parent_difficulty and offset to be a greater value in order to avoid mass forking. But, if the time is long enough, then the offset results in a negative value making the block less difficult than its parent.

The base standard for a block's difficulty is the predefined value set for the genesis block since it has no parent. So, a block can't be less difficult than the genesis block, therefore each block's difficulty is set to the maximum value between the calculated difficulty and the MINIMUM_DIFFICULTY.

Parameters

block_number : Block number of the block. block_timestamp : Timestamp of the block. parent_timestamp : Timestamp of the parent block. parent_difficulty : difficulty of the parent block. parent_has_ommers: does the parent have ommers.

Returns

difficulty : ethereum.base_types.Uint Computed difficulty for a block.

def calculate_block_difficulty(block_number: Uint, ​​block_timestamp: U256, ​​parent_timestamp: U256, ​​parent_difficulty: Uint, ​​parent_has_ommers: bool) -> Uint:
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    <snip>
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    offset = (
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        int(parent_difficulty)
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        // 2048
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        * max(
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            (2 if parent_has_ommers else 1)
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            - int(block_timestamp - parent_timestamp) // 9,
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            -99,
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        )
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    )
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    difficulty = int(parent_difficulty) + offset
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    # Historical Note: The difficulty bomb was not present in Ethereum at the
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    # start of Frontier, but was added shortly after launch. However since the
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    # bomb has no effect prior to block 200000 we pretend it existed from
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    # genesis.
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    # See https://github.com/ethereum/go-ethereum/pull/1588
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    num_bomb_periods = ((int(block_number) - BOMB_DELAY_BLOCKS) // 100000) - 2
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    if num_bomb_periods >= 0:
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        difficulty += 2**num_bomb_periods
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    # Some clients raise the difficulty to `MINIMUM_DIFFICULTY` prior to adding
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    # the bomb. This bug does not matter because the difficulty is always much
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    # greater than `MINIMUM_DIFFICULTY` on Mainnet.
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    return Uint(max(difficulty, int(MINIMUM_DIFFICULTY)))