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
@dataclass
class BlockChain:

blocks

82
    blocks: List[Block]

state

83
    state: State

chain_id

84
    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:
88
    <snip>
107
    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]:
111
    <snip>
131
    recent_blocks = chain.blocks[-255:]
132
    # TODO: This function has not been tested rigorously
133
    if len(recent_blocks) == 0:
134
        return []
135
136
    recent_block_hashes = []
137
138
    for block in recent_blocks:
139
        prev_block_hash = block.header.parent_hash
140
        recent_block_hashes.append(prev_block_hash)
141
142
    # We are computing the hash only for the most recent block and not for
143
    # the rest of the blocks as they have successors which have the hash of
144
    # the current block as parent hash.
145
    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))
146
    recent_block_hashes.append(most_recent_block_hash)
147
148
    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:
152
    <snip>
174
    validate_header(chain, block.header)
175
    validate_ommers(block.ommers, block.header, chain)
176
177
    block_state = BlockState(pre_state=chain.state)
178
179
    block_env = vm.BlockEnvironment(
180
        chain_id=chain.chain_id,
181
        state=block_state,
182
        block_gas_limit=block.header.gas_limit,
183
        block_hashes=get_last_256_block_hashes(chain),
184
        coinbase=block.header.coinbase,
185
        number=block.header.number,
186
        time=block.header.timestamp,
187
        difficulty=block.header.difficulty,
188
    )
189
190
    block_output = apply_body(
191
        block_env=block_env,
192
        transactions=block.transactions,
193
        ommers=block.ommers,
194
    )
195
    block_diff = extract_block_diff(block_state)
196
    block_state_root, _ = chain.state.compute_state_root_and_trie_changes(
197
        block_diff.account_changes,
198
        block_diff.storage_changes,
199
        block_diff.storage_clears,
200
    )
201
    transactions_root = root(block_output.transactions_trie)
202
    receipt_root = root(block_output.receipts_trie)
203
    block_logs_bloom = logs_bloom(block_output.block_logs)
204
205
    if block_output.block_gas_used != block.header.gas_used:
206
        raise InvalidBlock(
207
            f"{block_output.block_gas_used} != {block.header.gas_used}"
208
        )
209
    if transactions_root != block.header.transactions_root:
210
        raise InvalidBlock
211
    if block_state_root != block.header.state_root:
212
        raise InvalidBlock
213
    if receipt_root != block.header.receipt_root:
214
        raise InvalidBlock
215
    if block_logs_bloom != block.header.bloom:
216
        raise InvalidBlock
217
218
    apply_changes_to_state(chain.state, block_diff)
219
    chain.blocks.append(block)
220
    if len(chain.blocks) > 255:
221
        # Real clients have to store more blocks to deal with reorgs, but the
222
        # protocol only requires the last 255
223
        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:
227
    <snip>
245
    if header.number < Uint(1):
246
        raise InvalidBlock
247
    parent_header_number = header.number - Uint(1)
248
    first_block_number = chain.blocks[0].header.number
249
    last_block_number = chain.blocks[-1].header.number
250
251
    if (
252
        parent_header_number < first_block_number
253
        or parent_header_number > last_block_number
254
    ):
255
        raise InvalidBlock
256
257
    parent_header = chain.blocks[
258
        parent_header_number - first_block_number
259
    ].header
260
261
    if header.gas_used > header.gas_limit:
262
        raise InvalidBlock
263
264
    parent_has_ommers = parent_header.ommers_hash != EMPTY_OMMER_HASH
265
    if header.timestamp <= parent_header.timestamp:
266
        raise InvalidBlock
267
    if header.number != parent_header.number + Uint(1):
268
        raise InvalidBlock
269
    if not check_gas_limit(header.gas_limit, parent_header.gas_limit):
270
        raise InvalidBlock
271
    if len(header.extra_data) > 32:
272
        raise InvalidBlock
273
274
    block_difficulty = calculate_block_difficulty(
275
        header.number,
276
        header.timestamp,
277
        parent_header.timestamp,
278
        parent_header.difficulty,
279
        parent_has_ommers,
280
    )
281
    if header.difficulty != block_difficulty:
282
        raise InvalidBlock
283
284
    block_parent_hash = keccak256(rlp.encode(parent_header))
285
    if header.parent_hash != block_parent_hash:
286
        raise InvalidBlock
287
288
    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:
292
    <snip>
315
    header_data_without_pow_artefacts = (
316
        header.parent_hash,
317
        header.ommers_hash,
318
        header.coinbase,
319
        header.state_root,
320
        header.transactions_root,
321
        header.receipt_root,
322
        header.bloom,
323
        header.difficulty,
324
        header.number,
325
        header.gas_limit,
326
        header.gas_used,
327
        header.timestamp,
328
        header.extra_data,
329
    )
330
331
    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:
335
    <snip>
350
    header_hash = generate_header_hash_for_pow(header)
351
    # TODO: Memoize this somewhere and read from that data instead of
352
    # calculating cache for every block validation.
353
    cache = generate_cache(header.number)
354
    mix_digest, result = hashimoto_light(
355
        header_hash, header.nonce, cache, dataset_size(header.number)
356
    )
357
    if mix_digest != header.mix_digest:
358
        raise InvalidBlock
359
360
    limit = Uint(U256.MAX_VALUE) + Uint(1)
361
    if Uint.from_be_bytes(result) > (limit // header.difficulty):
362
        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:
371
    <snip>
402
    gas_available = block_env.block_gas_limit - block_output.block_gas_used
403
    if tx.gas > gas_available:
404
        raise GasUsedExceedsLimitError("gas used exceeds limit")
405
    sender_address = recover_sender(block_env.chain_id, tx)
406
    sender_account = get_account(tx_state, sender_address)
407
408
    max_gas_fee = tx.gas * tx.gas_price
409
410
    if sender_account.nonce > Uint(tx.nonce):
411
        raise NonceMismatchError("nonce too low")
412
    elif sender_account.nonce < Uint(tx.nonce):
413
        raise NonceMismatchError("nonce too high")
414
    if Uint(sender_account.balance) < max_gas_fee + Uint(tx.value):
415
        raise InsufficientBalanceError("insufficient sender balance")
416
    if sender_account.code_hash != EMPTY_CODE_HASH:
417
        raise InvalidSenderError("not EOA")
418
419
    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:
428
    <snip>
449
    receipt = Receipt(
450
        succeeded=error is None,
451
        cumulative_gas_used=cumulative_gas_used,
452
        bloom=logs_bloom(logs),
453
        logs=logs,
454
    )
455
450
    return receipt
456
    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:
464
    <snip>
490
    block_output = vm.BlockOutput()
491
486
    for i, tx in enumerate(transactions):
492
    for i, tx in enumerate(map(decode_transaction, transactions)):
493
        process_transaction(block_env, block_output, tx, Uint(i))
494
495
    pay_rewards(block_env, ommers)
496
497
    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:
503
    <snip>
525
    block_hash = keccak256(rlp.encode(block_header))
526
    if keccak256(rlp.encode(ommers)) != block_header.ommers_hash:
527
        raise InvalidBlock
528
529
    if len(ommers) == 0:
530
        # Nothing to validate
531
        return
532
533
    # Check that each ommer satisfies the constraints of a header
534
    for ommer in ommers:
535
        if Uint(1) > ommer.number or ommer.number >= block_header.number:
536
            raise InvalidBlock
537
        validate_header(chain, ommer)
538
    if len(ommers) > 2:
539
        raise InvalidBlock
540
541
    ommers_hashes = [keccak256(rlp.encode(ommer)) for ommer in ommers]
542
    if len(ommers_hashes) != len(set(ommers_hashes)):
543
        raise InvalidBlock
544
545
    recent_canonical_blocks = chain.blocks[-(MAX_OMMER_DEPTH + Uint(1)) :]
546
    recent_canonical_block_hashes = {
547
        keccak256(rlp.encode(block.header))
548
        for block in recent_canonical_blocks
549
    }
550
    recent_ommers_hashes: Set[Hash32] = set()
551
    for block in recent_canonical_blocks:
552
        recent_ommers_hashes = recent_ommers_hashes.union(
553
            {keccak256(rlp.encode(ommer)) for ommer in block.ommers}
554
        )
555
556
    for ommer_index, ommer in enumerate(ommers):
557
        ommer_hash = ommers_hashes[ommer_index]
558
        if ommer_hash == block_hash:
559
            raise InvalidBlock
560
        if ommer_hash in recent_canonical_block_hashes:
561
            raise InvalidBlock
562
        if ommer_hash in recent_ommers_hashes:
563
            raise InvalidBlock
564
565
        # Ommer age with respect to the current block. For example, an age of
566
        # 1 indicates that the ommer is a sibling of previous block.
567
        ommer_age = block_header.number - ommer.number
568
        if Uint(1) > ommer_age or ommer_age > MAX_OMMER_DEPTH:
569
            raise InvalidBlock
570
        if ommer.parent_hash not in recent_canonical_block_hashes:
571
            raise InvalidBlock
572
        if ommer.parent_hash == block_header.parent_hash:
573
            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:
580
    <snip>
602
    rewards_state = TransactionState(parent=block_env.state)
603
    ommer_count = U256(len(ommers))
604
    miner_reward = BLOCK_REWARD + (ommer_count * (BLOCK_REWARD // U256(32)))
605
    create_ether(rewards_state, block_env.coinbase, miner_reward)
606
607
    for ommer in ommers:
608
        # Ommer age with respect to the current block.
609
        ommer_age = U256(block_env.number - ommer.number)
610
        ommer_miner_reward = ((U256(8) - ommer_age) * BLOCK_REWARD) // U256(8)
611
        create_ether(rewards_state, ommer.coinbase, ommer_miner_reward)
612
613
    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:
622
    <snip>
646
    tx_state = TransactionState(parent=block_env.state)
647
642
    trie_set(block_output.transactions_trie, rlp.encode(Uint(index)), tx)
648
    trie_set(
649
        block_output.transactions_trie,
650
        rlp.encode(index),
651
        encode_transaction(tx),
652
    )
653
654
    intrinsic_gas = validate_transaction(tx)
655
656
    sender = check_transaction(
657
        block_env=block_env,
658
        block_output=block_output,
659
        tx=tx,
660
        tx_state=tx_state,
661
    )
662
663
    sender_account = get_account(tx_state, sender)
664
665
    gas = tx.gas - intrinsic_gas
666
    increment_nonce(tx_state, sender)
667
668
    gas_fee = tx.gas * tx.gas_price
669
    sender_balance_after_gas_fee = Uint(sender_account.balance) - gas_fee
670
    set_account_balance(tx_state, sender, U256(sender_balance_after_gas_fee))
671
672
    access_list_addresses = set()
673
    access_list_storage_keys = set()
674
    if isinstance(tx, AccessListTransaction):
675
        for access in tx.access_list:
676
            access_list_addresses.add(access.account)
677
            for slot in access.slots:
678
                access_list_storage_keys.add((access.account, slot))
679
680
    tx_env = vm.TransactionEnvironment(
681
        origin=sender,
682
        gas_price=tx.gas_price,
683
        gas=gas,
684
        access_list_addresses=access_list_addresses,
685
        access_list_storage_keys=access_list_storage_keys,
686
        state=tx_state,
687
        index_in_block=index,
667
        tx_hash=get_transaction_hash(tx),
688
        tx_hash=get_transaction_hash(encode_transaction(tx)),
689
    )
690
691
    message = prepare_message(block_env, tx_env, tx)
692
693
    tx_output = process_message_call(message)
694
695
    tx_gas_used_before_refund = tx.gas - tx_output.gas_left
696
    tx_gas_refund = min(
697
        tx_gas_used_before_refund // Uint(2), Uint(tx_output.refund_counter)
698
    )
699
    tx_gas_used_after_refund = tx_gas_used_before_refund - tx_gas_refund
700
    tx_gas_left = tx.gas - tx_gas_used_after_refund
701
    gas_refund_amount = tx_gas_left * tx.gas_price
702
703
    transaction_fee = tx_gas_used_after_refund * tx.gas_price
704
705
    # refund gas
706
    sender_balance_after_refund = get_account(tx_state, sender).balance + U256(
707
        gas_refund_amount
708
    )
709
    set_account_balance(tx_state, sender, sender_balance_after_refund)
710
711
    # transfer miner fees
712
    coinbase_balance_after_mining_fee = get_account(
713
        tx_state, block_env.coinbase
714
    ).balance + U256(transaction_fee)
715
    if coinbase_balance_after_mining_fee != 0:
716
        set_account_balance(
717
            tx_state,
718
            block_env.coinbase,
719
            coinbase_balance_after_mining_fee,
720
        )
721
    elif account_exists_and_is_empty(tx_state, block_env.coinbase):
722
        destroy_account(tx_state, block_env.coinbase)
723
724
    for address in tx_output.accounts_to_delete:
725
        destroy_account(tx_state, address)
726
727
    destroy_touched_empty_accounts(tx_state, tx_output.touched_accounts)
728
729
    block_output.block_gas_used += tx_gas_used_after_refund
730
731
    receipt = make_receipt(
711
        tx_output.error, block_output.block_gas_used, tx_output.logs
732
        tx, tx_output.error, block_output.block_gas_used, tx_output.logs
733
    )
734
735
    receipt_key = rlp.encode(Uint(index))
736
    block_output.receipt_keys += (receipt_key,)
737
738
    trie_set(
739
        block_output.receipts_trie,
740
        receipt_key,
741
        receipt,
742
    )
743
744
    block_output.block_logs += tx_output.logs
745
746
    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:
750
    <snip>
778
    max_adjustment_delta = parent_gas_limit // GasCosts.LIMIT_ADJUSTMENT_FACTOR
779
    if gas_limit >= parent_gas_limit + max_adjustment_delta:
780
        return False
781
    if gas_limit <= parent_gas_limit - max_adjustment_delta:
782
        return False
783
    if gas_limit < GasCosts.LIMIT_MINIMUM:
784
        return False
785
786
    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)))