text: """
  Generate Heirarchical Deterministic Wallets (HDWallet).
  
  Partially implements the BIP-0032, BIP-0043, and BIP-0044 specifications:
  BIP-0032: https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki
  BIP-0043: https://github.com/bitcoin/bips/blob/master/bip-0043.mediawiki
  BIP-0044: https://github.com/bitcoin/bips/blob/master/bip-0044.mediawiki
  
  Skips serialization and public key derivation as unnecssary for this library's purposes.
  
  Notes
  -----
  
  * Integers are modulo the order of the curve (referred to as n).
  * Addition (+) of two coordinate pair is defined as application of the EC group operation.
  * Concatenation (||) is the operation of appending one byte sequence onto another.
  
  
  Definitions
  -----------
  
  * point(p): returns the coordinate pair resulting from EC point multiplication
    (repeated application of the EC group operation) of the secp256k1 base point
    with the integer p.
  * ser_32(i): serialize a 32-bit unsigned integer i as a 4-byte sequence,
    most significant byte first.
  * ser_256(p): serializes the integer p as a 32-byte sequence, most significant byte first.
  * ser_P(P): serializes the coordinate pair P = (x,y) as a byte sequence using SEC1's compressed
    form: (0x02 or 0x03) || ser_256(x), where the header byte depends on the parity of the
    omitted y coordinate.
  * parse_256(p): interprets a 32-byte sequence as a 256-bit number, most significant byte first.
  
  """
  # Additional notes:
  # - This module currently only implements private parent key => private child key CKD function,
  #   as it is not necessary to the HD key derivation functions used in this library to implement
  #   the other functions yet (as this module is only used for derivation of private keys). That
  #   could change, but wasn't deemed necessary at the time this module was introduced.
  # - Unlike other libraries, this library does not use Bitcoin key serialization, because it is
  #   not intended to be ultimately used for Bitcoin key derivations. This presents a simplified
  #   API, and no expectation is given for `xpub/xpriv` key derivation.
  from typing import (
      Tuple,
      Type,
      Union,
  )
  
  from eth_utils import (
      ValidationError,
      to_int,
  )
  
  from ._utils import (
      SECP256K1_N,
      ec_point,
      hmac_sha512,
  )
  
  BASE_NODE_IDENTIFIERS = {"m", "M"}
  HARD_NODE_SUFFIXES = {"'", "H"}
  
  
  class Node(int):
      """
      A base node class.
      """
  
      TAG = ""  # No tag
      OFFSET = 0x0  # No offset
      index: int
  
      def __new__(cls, index):
          if 0 > index or index > 2**31:
              raise ValidationError(
                  f"{cls} cannot be initialized with value {index}"
              )
  
          # mypy/typeshed bug requires type ignore: https://github.com/python/typeshed/issues/2686
          obj = int.__new__(cls, index + cls.OFFSET)  # type: ignore
          obj.index = index
          return obj
  
      def __repr__(self):
          return f"{self.__class__.__name__}({self.index})"
  
      def __add__(self, other: int):
          return self.__class__(self.index + other)
  
      def serialize(self) -> bytes:
          return self.to_bytes(4, byteorder="big")
  
      def encode(self) -> str:
          return str(self.index) + self.TAG
  
      @staticmethod
      def decode(node: str) -> Union["SoftNode", "HardNode"]:
          if len(node) < 1:
              raise ValidationError("Cannot use empty string")
  
          node_class: Union[Type["SoftNode"], Type["HardNode"]]
          if node[-1] in HARD_NODE_SUFFIXES:
              node_class = HardNode
              node_index = node[:-1]
          else:
              node_class = SoftNode
              node_index = node
  
          try:
              node_value = int(node_index)
          except ValueError as err:
              raise ValidationError(f"'{node_index}' is not a valid node index.") from err
  
          return node_class(node_value)
  
  
  class SoftNode(Node):
      """
      Soft node (unhardened), where value = index .
      """
      TAG = ""  # No tag
      OFFSET = 0x0  # No offset
  
  
  class HardNode(Node):
      """
      Hard node, where value = index + BIP32_HARDENED_CONSTANT .
      """
      TAG = "H"  # "H" (or "'") means hard node (but use "H" for clarity)
      OFFSET = 0x80000000  # 2**31, BIP32 "Hardening constant"
  
  
  def derive_child_key(
      parent_key: bytes,
      parent_chain_code: bytes,
      node: Node,
  ) -> Tuple[bytes, bytes]:
      """
      Compute a derivitive key from the parent key.
  
      From BIP32:
  
      The function CKDpriv((k_par, c_par), i) → (k_i, c_i) computes a child extended
      private key from the parent extended private key:
  
      1. Check whether the child is a hardened key (i ≥ 2**31). If the child is a hardened key,
         let I = HMAC-SHA512(Key = c_par, Data = 0x00 || ser_256(k_par) || ser_32(i)).
         (Note: The 0x00 pads the private key to make it 33 bytes long.)
         If it is not a hardened key, then
         let I = HMAC-SHA512(Key = c_par, Data = ser_P(point(k_par)) || ser_32(i)).
      2. Split I into two 32-byte sequences, I_L and I_R.
      3. The returned child key k_i is parse_256(I_L) + k_par (mod n).
      4. The returned chain code c_i is I_R.
      5. In case parse_256(I_L) ≥ n or k_i = 0, the resulting key is invalid,
         and one should proceed with the next value for i.
         (Note: this has probability lower than 1 in 2**127.)
  
      """
      assert len(parent_chain_code) == 32
      if isinstance(node, HardNode):
          # NOTE Empty byte is added to align to SoftNode case
          assert len(parent_key) == 32  # Should be guaranteed here in return statment
          child = hmac_sha512(parent_chain_code, b"\x00" + parent_key + node.serialize())
  
      elif isinstance(node, SoftNode):
          assert len(ec_point(parent_key)) == 33  # Should be guaranteed by Account class
          child = hmac_sha512(parent_chain_code, ec_point(parent_key) + node.serialize())
  
      else:
          raise ValidationError(f"Cannot process: {node}")
  
      assert len(child) == 64
  
      if to_int(child[:32]) >= SECP256K1_N:
          # Invalid key, compute using next node (< 2**-127 probability)
          return derive_child_key(parent_key, parent_chain_code, node + 1)
  
      child_key = (to_int(child[:32]) + to_int(parent_key)) % SECP256K1_N
      if child_key == 0:
          # Invalid key, compute using next node (< 2**-127 probability)
          return derive_child_key(parent_key, parent_chain_code, node + 1)
  
      child_key_bytes = child_key.to_bytes(32, byteorder="big")
      child_chain_code = child[32:]
      return child_key_bytes, child_chain_code
  
  
  class HDPath:
      def __init__(self, path: str):
          """
          Create a new Hierarchical Deterministic path by decoding the given path.
  
          Initializes an hd account generator using the
          given path string (from BIP-0032). The path is decoded into nodes of the
          derivation key tree, which define a pathway from a given master seed to
          the child key that is used for a given purpose. Please also reference BIP-
          0043 (which definites the first level as the "purpose" field of an HD path)
          and BIP-0044 (which defines a commonly-used, 5-level scheme for BIP32 paths)
          for examples of how this object may be used. Please note however that this
          object makes no such assumptions of the use of BIP43 or BIP44, or later BIPs.
          :param path             : BIP32-compatible derivation path
          :type path              : str as "m/idx_0/.../idx_n" or "m/idx_0/.../idx_n"
                                    where idx_* is either an integer value (soft node)
                                    or an integer value followed by either the "'" char
                                    or the "H" char (hardened node)
          """
          if len(path) < 1:
              raise ValidationError("Cannot parse path from empty string.")
  
          nodes = path.split('/')  # Should at least make 1 entry in resulting list
          if nodes[0] not in BASE_NODE_IDENTIFIERS:
              raise ValidationError(f'Path is not valid: "{path}". Must start with "m"')
  
          decoded_path = []
          for idx, node in enumerate(nodes[1:]):  # We don't need the root node 'm'
              try:
                  decoded_path.append(Node.decode(node))
              except ValidationError as err:
                  raise ValidationError(
                      f'Path "{path}" is not valid. Issue with node "{node}": {err}'
                  ) from err
  
          self._path = decoded_path
  
      def __repr__(self) -> str:
          return f'{self.__class__.__name__}(path="{self.encode()}")'
  
      def encode(self) -> str:
          """
          Encodes this class to a string (reversing the decoding in the constructor).
          """
          encoded_path = ('m',) + tuple(node.encode() for node in self._path)
          return '/'.join(encoded_path)
  
      def derive(self, seed: bytes) -> bytes:
          """
          Perform the BIP32 Heirarchical Derivation recursive loop with the given Path.
  
          Note that the key and chain_code are initialized with the master seed, and that
          the key that is returned is the child key at the end of derivation process (and
          the chain code is discarded)
          """
          master_node = hmac_sha512(b"Bitcoin seed", seed)
          key = master_node[:32]
          chain_code = master_node[32:]
          for node in self._path:
              key, chain_code = derive_child_key(key, chain_code, node)
          return key
  