"""

    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.

    """

    return old

    """

    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.

    """

    recent_blocks = chain.blocks[-255:]

    # TODO: This function has not been tested rigorously

    if len(recent_blocks) == 0:

        return []

    recent_block_hashes = []

    for block in recent_blocks:

        prev_block_hash = block.header.parent_hash

        recent_block_hashes.append(prev_block_hash)

    # We are computing the hash only for the most recent block and not for

    # the rest of the blocks as they have successors which have the hash of

    # the current block as parent hash.

    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))

    recent_block_hashes.append(most_recent_block_hash)

    return recent_block_hashes

    """

    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`.

    """

    validate_header(chain, block.header)

    validate_ommers(block.ommers, block.header, chain)

    block_env = vm.BlockEnvironment(

        chain_id=chain.chain_id,

        state=chain.state,

        block_gas_limit=block.header.gas_limit,

        block_hashes=get_last_256_block_hashes(chain),

        coinbase=block.header.coinbase,

        number=block.header.number,

        time=block.header.timestamp,

        difficulty=block.header.difficulty,

    )

    block_output = apply_body(

        block_env=block_env,

        transactions=block.transactions,

        ommers=block.ommers,

    )

    block_state_root = state_root(block_env.state)

    transactions_root = root(block_output.transactions_trie)

    receipt_root = root(block_output.receipts_trie)

    block_logs_bloom = logs_bloom(block_output.block_logs)

    if block_output.block_gas_used != block.header.gas_used:

        raise InvalidBlock(

            f"{block_output.block_gas_used} != {block.header.gas_used}"

        )

    if transactions_root != block.header.transactions_root:

        raise InvalidBlock

    if block_state_root != block.header.state_root:

        raise InvalidBlock

    if receipt_root != block.header.receipt_root:

        raise InvalidBlock

    if block_logs_bloom != block.header.bloom:

        raise InvalidBlock

    chain.blocks.append(block)

    if len(chain.blocks) > 255:

        # Real clients have to store more blocks to deal with reorgs, but the

        # protocol only requires the last 255

        chain.blocks = chain.blocks[-255:]

    """

    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.

    """

    if header.number < Uint(1):

        raise InvalidBlock

    parent_header_number = header.number - Uint(1)

    first_block_number = chain.blocks[0].header.number

    last_block_number = chain.blocks[-1].header.number

    if (

        parent_header_number < first_block_number

        or parent_header_number > last_block_number

    ):

        raise InvalidBlock

    parent_header = chain.blocks[

        parent_header_number - first_block_number

    ].header

    if header.gas_used > header.gas_limit:

        raise InvalidBlock

    parent_has_ommers = parent_header.ommers_hash != EMPTY_OMMER_HASH

    if header.timestamp <= parent_header.timestamp:

        raise InvalidBlock

    if header.number != parent_header.number + Uint(1):

        raise InvalidBlock

    if not check_gas_limit(header.gas_limit, parent_header.gas_limit):

        raise InvalidBlock

    if len(header.extra_data) > 32:

        raise InvalidBlock

    block_difficulty = calculate_block_difficulty(

        header.number,

        header.timestamp,

        parent_header.timestamp,

        parent_header.difficulty,

        parent_has_ommers,

    )

    if header.difficulty != block_difficulty:

        raise InvalidBlock

    block_parent_hash = keccak256(rlp.encode(parent_header))

    if header.parent_hash != block_parent_hash:

        raise InvalidBlock

    validate_proof_of_work(header)

    """

    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.

    """

    header_data_without_pow_artefacts = (

        header.parent_hash,

        header.ommers_hash,

        header.coinbase,

        header.state_root,

        header.transactions_root,

        header.receipt_root,

        header.bloom,

        header.difficulty,

        header.number,

        header.gas_limit,

        header.gas_used,

        header.timestamp,

        header.extra_data,

    )

    return keccak256(rlp.encode(header_data_without_pow_artefacts))

    """

    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.

    """

    header_hash = generate_header_hash_for_pow(header)

    # TODO: Memoize this somewhere and read from that data instead of

    # calculating cache for every block validation.

    cache = generate_cache(header.number)

    mix_digest, result = hashimoto_light(

        header_hash, header.nonce, cache, dataset_size(header.number)

    )

    if mix_digest != header.mix_digest:

        raise InvalidBlock

    limit = Uint(U256.MAX_VALUE) + Uint(1)

    if Uint.from_be_bytes(result) > (limit // header.difficulty):

        raise InvalidBlock

    """

    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.

    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.

    """

    gas_available = block_env.block_gas_limit - block_output.block_gas_used

    if tx.gas > gas_available:

        raise GasUsedExceedsLimitError("gas used exceeds limit")

    sender_address = recover_sender(block_env.chain_id, tx)

    sender_account = get_account(block_env.state, sender_address)

    max_gas_fee = tx.gas * tx.gas_price

    if sender_account.nonce > Uint(tx.nonce):

        raise NonceMismatchError("nonce too low")

    elif sender_account.nonce < Uint(tx.nonce):

        raise NonceMismatchError("nonce too high")

    if Uint(sender_account.balance) < max_gas_fee + Uint(tx.value):

        raise InsufficientBalanceError("insufficient sender balance")

    if sender_account.code:

        raise InvalidSenderError("not EOA")

    return sender_address

    """

    Make the receipt for a transaction that was executed.

    Parameters

    ----------

    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.

    """

    receipt = Receipt(

        succeeded=error is None,

        cumulative_gas_used=cumulative_gas_used,

        bloom=logs_bloom(logs),

        logs=logs,

    )

    return receipt

    """

    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.

    """

    block_output = vm.BlockOutput()

    for i, tx in enumerate(transactions):

        process_transaction(block_env, block_output, tx, Uint(i))

    pay_rewards(block_env.state, block_env.number, block_env.coinbase, ommers)

    return block_output

    """

    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.

    """

    block_hash = keccak256(rlp.encode(block_header))

    if keccak256(rlp.encode(ommers)) != block_header.ommers_hash:

        raise InvalidBlock

    if len(ommers) == 0:

        # Nothing to validate

        return

    # Check that each ommer satisfies the constraints of a header

    for ommer in ommers:

        if Uint(1) > ommer.number or ommer.number >= block_header.number:

            raise InvalidBlock

        validate_header(chain, ommer)

    if len(ommers) > 2:

        raise InvalidBlock

    ommers_hashes = [keccak256(rlp.encode(ommer)) for ommer in ommers]

    if len(ommers_hashes) != len(set(ommers_hashes)):

        raise InvalidBlock

    recent_canonical_blocks = chain.blocks[-(MAX_OMMER_DEPTH + Uint(1)) :]

    recent_canonical_block_hashes = {

        keccak256(rlp.encode(block.header))

        for block in recent_canonical_blocks

    }

    recent_ommers_hashes: Set[Hash32] = set()

    for block in recent_canonical_blocks:

        recent_ommers_hashes = recent_ommers_hashes.union(

            {keccak256(rlp.encode(ommer)) for ommer in block.ommers}

        )

    for ommer_index, ommer in enumerate(ommers):

        ommer_hash = ommers_hashes[ommer_index]

        if ommer_hash == block_hash:

            raise InvalidBlock

        if ommer_hash in recent_canonical_block_hashes:

            raise InvalidBlock

        if ommer_hash in recent_ommers_hashes:

            raise InvalidBlock

        # Ommer age with respect to the current block. For example, an age of

        # 1 indicates that the ommer is a sibling of previous block.

        ommer_age = block_header.number - ommer.number

        if Uint(1) > ommer_age or ommer_age > MAX_OMMER_DEPTH:

            raise InvalidBlock

        if ommer.parent_hash not in recent_canonical_block_hashes:

            raise InvalidBlock

        if ommer.parent_hash == block_header.parent_hash:

            raise InvalidBlock

    """

    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

    ----------

    state :

        Current account state.

    block_number :

        Position of the block within the chain.

    coinbase :

        Address of account which receives block reward and transaction fees.

    ommers :

        List of ommers mentioned in the current block.

    """

    ommer_count = U256(len(ommers))

    miner_reward = BLOCK_REWARD + (ommer_count * (BLOCK_REWARD // U256(32)))

    create_ether(state, coinbase, miner_reward)

    for ommer in ommers:

        # Ommer age with respect to the current block.

        ommer_age = U256(block_number - ommer.number)

        ommer_miner_reward = ((U256(8) - ommer_age) * BLOCK_REWARD) // U256(8)

        create_ether(state, ommer.coinbase, ommer_miner_reward)

    """

    Execute a transaction against the provided environment.

    This function processes the actions needed to execute a transaction.

    It decrements the sender's account 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.

    """

    trie_set(block_output.transactions_trie, rlp.encode(Uint(index)), tx)

    intrinsic_gas = validate_transaction(tx)

    sender = check_transaction(

        block_env=block_env,

        block_output=block_output,

        tx=tx,

    )

    sender_account = get_account(block_env.state, sender)

    gas = tx.gas - intrinsic_gas

    increment_nonce(block_env.state, sender)

    gas_fee = tx.gas * tx.gas_price

    sender_balance_after_gas_fee = Uint(sender_account.balance) - gas_fee

    set_account_balance(

        block_env.state, sender, U256(sender_balance_after_gas_fee)

    )

    tx_env = vm.TransactionEnvironment(

        origin=sender,

        gas_price=tx.gas_price,

        gas=gas,

        index_in_block=index,

        tx_hash=get_transaction_hash(tx),

        traces=[],

    )

    message = prepare_message(block_env, tx_env, tx)

    tx_output = process_message_call(message)

    tx_gas_used_before_refund = tx.gas - tx_output.gas_left

    tx_gas_refund = min(

        tx_gas_used_before_refund // Uint(2), Uint(tx_output.refund_counter)

    )

    tx_gas_used_after_refund = tx_gas_used_before_refund - tx_gas_refund

    tx_gas_left = tx.gas - tx_gas_used_after_refund

    gas_refund_amount = tx_gas_left * tx.gas_price

    transaction_fee = tx_gas_used_after_refund * tx.gas_price

    # refund gas

    sender_balance_after_refund = get_account(

        block_env.state, sender

    ).balance + U256(gas_refund_amount)

    set_account_balance(block_env.state, sender, sender_balance_after_refund)

    # transfer miner fees

    coinbase_balance_after_mining_fee = get_account(

        block_env.state, block_env.coinbase

    ).balance + U256(transaction_fee)

    if coinbase_balance_after_mining_fee != 0:

        set_account_balance(

            block_env.state,

            block_env.coinbase,

            coinbase_balance_after_mining_fee,

        )

    elif account_exists_and_is_empty(block_env.state, block_env.coinbase):

        destroy_account(block_env.state, block_env.coinbase)

    for address in tx_output.accounts_to_delete:

        destroy_account(block_env.state, address)

    destroy_touched_empty_accounts(block_env.state, tx_output.touched_accounts)

    block_output.block_gas_used += tx_gas_used_after_refund

    receipt = make_receipt(

        tx_output.error, block_output.block_gas_used, tx_output.logs

    )

    receipt_key = rlp.encode(Uint(index))

    block_output.receipt_keys += (receipt_key,)

    trie_set(

        block_output.receipts_trie,

        receipt_key,

        receipt,

    )

    block_output.block_logs += tx_output.logs

    """

    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

    ``GAS_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 ``GAS_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.

    """

    max_adjustment_delta = parent_gas_limit // GAS_LIMIT_ADJUSTMENT_FACTOR

    if gas_limit >= parent_gas_limit + max_adjustment_delta:

        return False

    if gas_limit <= parent_gas_limit - max_adjustment_delta:

        return False

    if gas_limit < GAS_LIMIT_MINIMUM:

        return False

    return True

    """

    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 ``GENESIS_DIFFICULTY``.

    Parameters