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package scodec.bits

import java.nio.{ ByteBuffer, ByteOrder }
import java.nio.charset.{ CharacterCodingException, Charset }
import java.security.{ AlgorithmParameters, GeneralSecurityException, Key, MessageDigest, SecureRandom }
import java.util.UUID
import java.util.zip.{ DataFormatException, Deflater }
import javax.crypto.Cipher

import ScalaVersionSpecific._

/**
 * Persistent vector of bits, stored as bytes.
 *
 * Bits are numbered left to right, starting at 0.
 *
 * @groupname collection Collection Like Methods
 * @groupprio collection 0
 *
 * @groupname bitwise Bitwise Operations
 * @groupprio bitwise 1
 *
 * @groupname conversions Conversions
 * @groupprio conversions 2
 *
 * @groupname crypto Cryptography
 * @groupprio crypto 3
 *
 * @define bitwiseOperationsReprDescription bit vector
 */
sealed abstract class BitVector extends BitwiseOperations[BitVector, Long] with Serializable {
  import BitVector._

  /**
   * Returns number of bits in this vector.
   *
   * @group collection
   */
  def size: Long

  /**
   * Alias for [[size]].
   * @group collection
   */
  final def length: Long = size

  /**
   * Returns true if this vector has no bits.
   *
   * @group collection
   */
  final def isEmpty: Boolean = sizeLessThan(1)

  /**
   * Returns true if this vector has a non-zero number of bits.
   *
   * @group collection
   */
  final def nonEmpty: Boolean = !isEmpty

  /**
   * Returns `true` if the size of this `BitVector` is greater than `n`. Unlike `size`, this
   * forces this `BitVector` from left to right, halting as soon as it has a definite answer.
   *
   * @group collection
   */
  final def sizeGreaterThan(n: Long): Boolean = n < 0 || !sizeLessThanOrEqual(n)

  /**
   * Returns `true` if the size of this `BitVector` is greater than or equal to `n`. Unlike `size`, this
   * forces this `BitVector` from left to right, halting as soon as it has a definite answer.
   *
   * @group collection
   */
  final def sizeGreaterThanOrEqual(n: Long): Boolean = n < 0 || !sizeLessThanOrEqual(n-1)

  /**
   * Returns `true` if the size of this `BitVector` is less than `n`. Unlike `size`, this
   * forces this `BitVector` from left to right, halting as soon as it has a definite answer.
   *
   * @group collection
   */
  def sizeLessThan(n: Long): Boolean

  /**
   * Returns `true` if the size of this `BitVector` is less than or equal to `n`. Unlike `size`, this
   * forces this `BitVector` from left to right, halting as soon as it has a definite answer.
   *
   * @group collection
   */
  final def sizeLessThanOrEqual(n: Long): Boolean =
    n == Long.MaxValue || sizeLessThan(n+1)

  /**
   * Returns the number of bits in this vector, or `None` if the size does not
   * fit into an `Int`.
   *
   * @group collection
   */
  final def intSize: Option[Int] = if (size <= Int.MaxValue) Some(size.toInt) else None

  /**
   * Returns true if the `n`th bit is high, false otherwise.
   *
   * @throws NoSuchElementException if `n >= size`
   *
   * @group collection
   */
  def get(n: Long): Boolean

  /**
   * Returns the `n`th byte, 0-indexed.
   *
   * @throws NoSuchElementException if `n >= bytes.size`
   *
   * @group collection
   */
  def getByte(n: Long): Byte

  /**
   * Alias for `get`.
   *
   * @group collection
   * @see get(Long)
   */
  final def apply(n: Long): Boolean = get(n)

  /**
   * Returns `Some(true)` if the `n`th bit is high, `Some(false)` if low, and `None` if `n >= size`.
   *
   * @group collection
   */
  final def lift(n: Long): Option[Boolean] =
    if (sizeGreaterThan(n)) Some(get(n))
    else None

  private[bits] def unchunk = this

  /**
   * Returns a new bit vector with the `n`th bit high if `high` is true or low if `high` is false.
   *
   * @group collection
   */
  def update(n: Long, high: Boolean): BitVector

  /**
   * Returns a vector with the specified bit inserted at the specified index.
   * @group collection
   */
  final def insert(idx: Long, b: Boolean): BitVector =
    (take(idx) :+ b) ++ drop(idx)

  /**
   * Returns a vector with the specified bit vector inserted at the specified index.
   * @group collection
   */
  final def splice(idx: Long, b: BitVector): BitVector =
    take(idx) ++ b ++ drop(idx)

  /**
   * Returns a vector with the specified bit vector replacing bits `[idx, idx + b.size]`.
   * @group collection
   */
  final def patch(idx: Long, b: BitVector): BitVector =
    take(idx) ++ b ++ drop(idx + b.size)

  /**
   * Returns a new bit vector with the `n`th bit high (and all other bits unmodified).
   *
   * @group collection
   */
  final def set(n: Long): BitVector = update(n, true)

  /**
   * Returns a new bit vector with the `n`th bit low (and all other bits unmodified).
   *
   * @group collection
   */
  final def clear(n: Long): BitVector = update(n, false)

  /**
   * Returns a new bit vector representing this vector's contents followed by the specified vector's contents.
   *
   * @group collection
   */
  def ++(b2: BitVector): BitVector =
    if (this.isEmpty) b2
    else Chunks(Append(this, b2))

  /**
   * Returns a new vector with the specified bit prepended.
   * @group collection
   */
  final def +:(b: Boolean): BitVector  = BitVector.bit(b) ++ this

  /**
   * Returns a new vector with the specified bit appended.
   * @group collection
   */
  final def :+(b: Boolean): BitVector = this ++ BitVector.bit(b)

  /**
   * Returns the depth of this tree. The result of `compact` has depth 0.
   */
  private[bits] def depth: Int = this match {
    case Append(l,r) => 1 + (l.depth max r.depth)
    case c: Chunks => 1 + c.chunks.depth
    case _ => 0
  }

  /**
   * Returns a vector of all bits in this vector except the first `n` bits.
   *
   * The resulting vector's size is `0 max (size - n)`.
   *
   * @group collection
   */
  def drop(n: Long): BitVector

  /**
   * Returns a vector of all bits in this vector except the last `n` bits.
   *
   * The resulting vector's size is `0 max (size - n)`.
   *
   * @group collection
   */
  final def dropRight(n: Long): BitVector =
    if (n <= 0) this
    else if (n >= size) BitVector.empty
    else take(size - n)

  /**
   * Returns a vector of the first `n` bits of this vector.
   *
   * The resulting vector's size is `n min size`.
   *
   * Note: if an `n`-bit vector is required, use the `acquire` method instead.
   *
   * @see acquire
   * @group collection
   */
  def take(n: Long): BitVector

  /**
   * Returns a vector of the last `n` bits of this vector.
   *
   * The resulting vector's size is `n min size`.
   *
   * @group collection
   */
  final def takeRight(n: Long): BitVector =
    if (n < 0) throw new IllegalArgumentException(s"takeRight($n)")
    else if (n >= size) this
    else this.drop(size-n)


  /**
   * Returns a pair of vectors that is equal to `(take(n), drop(n))`.
   * @group collection
   */
  final def splitAt(n: Long): (BitVector, BitVector) = (take(n), drop(n))

  /**
   * Returns a vector made up of the bits starting at index `from` up to index `until`,
   * not including the index `until`.
   *
   * @group collection
   */
  final def slice(from: Long, until: Long): BitVector =
    drop(from).take(until - (from max 0))

  /**
   * Returns a vector whose contents are the results of taking the first `n` bits of this vector.
   *
   * If this vector does not contain at least `n` bits, an error message is returned.
   *
   * @see take
   * @group collection
   */
  def acquire(n: Long): Either[String, BitVector] =
    if (sizeGreaterThanOrEqual(n)) Right(take(n))
    else Left(s"cannot acquire $n bits from a vector that contains $size bits")

  /**
   * Like `aquire`, but immediately consumes the `Either` via the pair of functions `err` and `f`.
   *
   * @see acquire
   * @group collection
   */
  final def acquireThen[R](n: Long)(err: String => R, f: BitVector => R): R =
    if (sizeGreaterThanOrEqual(n)) f(take(n))
    else err(s"cannot acquire $n bits from a vector that contains $size bits")

  /**
   * Consumes the first `n` bits of this vector and decodes them with the specified function,
   * resulting in a vector of the remaining bits and the decoded value. If this vector
   * does not have `n` bits or an error occurs while decoding, an error is returned instead.
   *
   * @group collection
   */
  final def consume[A](n: Long)(decode: BitVector => Either[String, A]): Either[String, (BitVector, A)] =
    for {
      toDecode <- acquire(n)
      decoded <- decode(toDecode)
    } yield (drop(n), decoded)

  /**
   * If this vector has at least `n` bits, returns `f(take(n),drop(n))`,
   * otherwise calls `err` with a meaningful error message. This function can be used
   * to avoid intermediate allocations of `Either` objects when using `acquire` or `consume`
   * directly.
   *
   * @see acquireThen
   * @group collection
   */
  final def consumeThen[R](n: Long)(err: String => R, f: (BitVector,BitVector) => R): R =
    if (sizeGreaterThanOrEqual(n)) f(take(n), drop(n)) // todo unsafeTake, unsafeDrop
    else err(s"cannot acquire $n bits from a vector that contains $size bits")

  /**
   * Returns true if this bit vector starts with the specified vector.
   * @group collection
   */
  final def startsWith(b: BitVector): Boolean =
    take(b.size) === b

  /**
   * Returns true if this bit vector ends with the specified vector.
   * @group collection
   */
  final def endsWith(b: BitVector): Boolean =
    takeRight(b.size) === b

  /**
   * Finds the first index of the specified bit pattern in this vector.
   * @return index of slice or -1 if not found
   * @group collection
   */
  final def indexOfSlice(slice: BitVector): Long = indexOfSlice(slice, 0)

  /**
   * Finds the first index after `from` of the specified bit pattern in this vector.
   * @return index of slice or -1 if not found
   * @group collection
   */
  final def indexOfSlice(slice: BitVector, from: Long): Long = {
    @annotation.tailrec
    def go(b: BitVector, idx: Long): Long = {
      if (b startsWith slice) idx
      else if (b.isEmpty) -1
      else go(b.tail, idx + 1)
    }
    go(drop(from), from)
  }

  /**
   * Determines if the specified slice is in this vector.
   * @group collection
   */
  final def containsSlice(slice: BitVector): Boolean = indexOfSlice(slice) >= 0

  // This was public before version 1.1.8 so it must stay here for bincompat
  // The public grouped method is adding via an extension method defined in the companion
  private[bits] final def grouped(n: Long): Stream[BitVector] =
    groupedIterator(n).toStream

  private final def groupedIterator(n: Long): Iterator[BitVector] =
    if (isEmpty) Iterator.empty
    else Iterator(take(n)) ++ drop(n).groupedIterator(n)

  /**
   * Returns the first bit of this vector or throws if vector is emtpy.
   * @group collection
   */
  final def head: Boolean = get(0)

  /**
   * Returns the first bit of this vector or `None` if vector is emtpy.
   * @group collection
   */
  final def headOption: Option[Boolean] = lift(0)

  /**
   * Returns a vector of all bits in this vector except the first bit.
   * @group collection
   */
  final def tail: BitVector = drop(1)

  /**
   * Returns a vector of all bits in this vector except the last bit.
   * @group collection
   */
  final def init: BitVector = dropRight(1)

  /**
   * Returns the last bit in this vector or throws if vector is empty.
   * @group collection
   */
  final def last: Boolean = apply(size - 1)

  /**
   * Returns the last bit in this vector or returns `None` if vector is empty.
   * @group collection
   */
  final def lastOption: Option[Boolean] = lift(size - 1)

  /**
   * Alias for `padRight`.
   *
   * @throws IllegalArgumentException if `n < size`
   * @group collection
   */
  final def padTo(n: Long): BitVector = padRight(n)

  /**
   * Returns an `n`-bit vector whose contents are 0 or more low bits followed by this vector's contents.
   *
   * @throws IllegalArgumentException if `n < size`
   * @group collection
   */
  final def padRight(n: Long): BitVector =
    if (n < size) throw new IllegalArgumentException(s"Trying to right-pad a vector of $size bits to only $n bits.")
    else this ++ BitVector.fill(n - size)(false)

  /**
   * Returns an `n`-bit vector whose contents are 0 or more low bits followed by this vector's contents.
   *
   * @throws IllegalArgumentException if `n < size`
   * @group collection
   */
  final def padLeft(n: Long): BitVector =
    if (n < size) throw new IllegalArgumentException(s"Trying to left-pad a vector of $size bits to only $n bits.")
    else BitVector.fill(n - size)(false) ++ this

  /**
   * Reverse the bits of this vector.
   *
   * @group collection
   */
  final def reverse: BitVector =
    // todo: this has a log time implementation, assuming a balanced tree
    BitVector(compact.underlying.reverse.map(reverseBitsInByte _)).drop(8 - validBitsInLastByte(size))

  /**
   * Returns a new vector of the same size with the byte order reversed.
   *
   * Note that `reverseByteOrder.reverseByteOrder == identity` only when `size` is evenly divisble by 8.
   * To invert `reverseByteOrder` for an arbitrary size, use `invertReverseByteOrder`.
   *
   * @group collection
   */
  final def reverseByteOrder: BitVector = {
    if (size % 8 == 0) toBytes(compact.underlying.reverse, size)
    else {
      val validFinalBits = validBitsInLastByte(size)
      val last = take(validFinalBits).compact
      val b = drop(validFinalBits).toByteVector.reverse
      val init = toBytes(b, size-last.size)
      init ++ last
    }
  }

  /**
   * Inverse of `reverseByteOrder`.
   *
   * @group collection
   */
  final def invertReverseByteOrder: BitVector = {
    if (size % 8 == 0) reverseByteOrder
    else {
      val validFinalBits = validBitsInLastByte(size)
      val (init, last) = splitAt(size - validFinalBits)
      last ++ init.bytes.reverse.bits
    }
  }

  /**
   * Returns a new vector of the same size with the bit order reversed.
   *
   * @group collection
   */
  final def reverseBitOrder: BitVector =
    BitVector(compact.underlying.map(reverseBitsInByte _)).drop(8 - validBitsInLastByte(size))

  /**
   * Returns the number of bits that are high.
   *
   * @group bitwise
   */
  final def populationCount: Long = {
    @annotation.tailrec
    def go(b: BitVector, acc: Long): Long = {
      if (b.isEmpty) acc
      else go(b.tail, if (b.head) acc + 1 else acc)
    }
    go(this, 0)
  }

  final def not: BitVector = mapBytes(_.not)
  final def and(other: BitVector): BitVector = zipBytesWith(other)(_ & _)
  final def or(other: BitVector): BitVector = zipBytesWith(other)(_ | _)
  final def xor(other: BitVector): BitVector = zipBytesWith(other)(_ ^ _)

  final def shiftLeft(n: Long): BitVector =
    if (n <= 0) this
    else if (n >= size) BitVector.low(size)
    else drop(n) ++ BitVector.low(n)

  final def shiftRight(n: Long, signExtension: Boolean): BitVector = {
    if (isEmpty || n <= 0) this
    else {
      val extensionHigh = signExtension && head
      if (n >= size) {
        if (extensionHigh) BitVector.high(size) else BitVector.low(size)
      } else {
        (if (extensionHigh) BitVector.high(n) else BitVector.low(n)) ++ dropRight(n)
      }
    }
  }

  final def rotateLeft(n: Long): BitVector =
    if (n <= 0) this
    else if (isEmpty) this
    else {
      val n0 = n % size
      if (n0 == 0) this
      else drop(n0) ++ take(n0)
    }

  final def rotateRight(n: Long): BitVector =
    if (n <= 0) this
    else if (isEmpty) this
    else {
      val n0 = n % size
      if (n0 == 0) this
      else takeRight(n0) ++ dropRight(n0)
    }

  /**
   * Return a `BitVector` with the same contents as `this`, but
   * based off a single `ByteVector`.
   *
   * This may involve copying data to a fresh `ByteVector`, but
   * has the advantage that lookups index directly into a single
   * `ByteVector` rather than traversing a logarithmic number of nodes
   * in this tree.
   *
   * Calling this method on an already compacted vector is a no-op.
   *
   * @group collection
   */
  final def compact: Bytes = {
    if (bytesNeededForBits(size) > Int.MaxValue)
      throw new IllegalArgumentException(s"cannot compact bit vector of size ${size.toDouble / 8 / 1e9} GB")

    // we collect up all the chunks, then merge them in O(n * log n)
    @annotation.tailrec
    def go(b: List[BitVector], acc: Vector[Bytes]): Vector[Bytes] = b match {
      case (s@Suspend(_)) :: rem => go(s.underlying :: rem, acc)
      case (b@Bytes(_,_)) :: rem => go(rem, acc :+ b)
      case Append(l,r)    :: rem => go(l :: r :: rem, acc)
      case (d: Drop)      :: rem => go(rem, acc :+ d.interpretDrop)
      case (c: Chunks)    :: rem => go(c.chunks.left :: c.chunks.right :: rem, acc)
      case _ => acc
    }

    this match {
      // common case, we have a single flat `Bytes`, in which case we compact and return it directly
      case bs@Bytes(b,n) =>
        val b2 = b.compact
        if (b2 eq b) bs
        else Bytes(b2,n)
      // other common case is a drop of a single flat `Bytes`
      case d: Drop =>
        val bs = d.interpretDrop
        val b2 = bs.underlying.compact
        if (b2 eq bs.underlying) bs
        else Bytes(b2, bs.size)
      // otherwise we fall back to general purpose algorithm
      case _ => reduceBalanced(go(List(this), Vector()))(_.size)(_ combine _) match {
        case Bytes(b,n) => Bytes(b.compact,n) // we compact the underlying ByteVector as well
      }
    }
  }

  /**
   * Produce a single flat `Bytes` by interpreting
   * any non-byte-aligned appends or drops. Unlike
   * `compact`, the underlying `ByteVector` is not
   * necessarily copied.
   *
   * @group collection
   */
  def align: Bytes

  /**
   * Return a `BitVector` with the same contents as `this`, but
   * based off a single flat `ByteVector`. This function is guaranteed
   * to copy all the bytes in this `BitVector`, unlike `compact`, which
   * may no-op if this `BitVector` already consists of a single `ByteVector`
   * chunk.
   *
   * @group collection
   */
  final def copy: Bytes = this match {
    case Bytes(b,n) => Bytes(b.copy, n)
    case _ => this.compact
  }

  /**
   * Forces any `Suspend` nodes in this `BitVector` and ensures the tree is balanced.
   *
   * @group collection
   */
  final def force: BitVector = {
    @annotation.tailrec
    def go(cont: Vector[BitVector]): BitVector = {
      if (cont.nonEmpty) { (cont.head, cont.tail) match { case (cur, cont) =>
        cur match {
          case b@Bytes(_,_) => cont.foldLeft[BitVector](b)(_ ++ _)
          case Append(l,r) => go(l +: r +: cont)
          case d@Drop(_, _) => cont.foldLeft[BitVector](d)(_ ++ _)
          case s@Suspend(_) => go(s.underlying +: cont)
          case b: Chunks => go(b.chunks +: cont)
        }
      }}
      else cont.foldLeft(BitVector.empty)(_ ++ _)
    }
    go(Vector(this))
  }

  /**
   * Return the sequence of bits in this vector. The returned
   * `IndexedSeq` is just a view; nothing is actually copied.
   *
   * @throws IllegalArgumentException if this vector's size exceeds Int.MaxValue
   * @see acquire
   * @see toIndexedSeq
   * @group conversions
   */
  final def toIndexedSeq: IndexedSeq[Boolean] = {
    intSize.map { n =>
      new IndexedSeq[Boolean] {
        def length = BitVector.this.size.toInt
        def apply(idx: Int): Boolean = BitVector.this.get(idx.toLong)
      }
    }.getOrElse {
      throw new IllegalArgumentException(s"BitVector too big for Seq: $size")
    }
  }

  /**
   * Converts the contents of this vector to a byte vector.
   *
   * If this vector's size does not divide evenly by 8, the last byte of the returned vector
   * will be zero-padded to the right.
   *
   * @group conversions
   */
  final def toByteVector: ByteVector =
    clearUnneededBits(size, compact.underlying)

  /**
   * Alias for [[toByteVector]].
   * @group conversions
   */
  final def bytes: ByteVector = toByteVector

  /**
   * Converts the contents of this vector to a byte array.
   *
   * If this vector's size does not divide evenly by 8, the last byte of the returned vector
   * will be zero-padded to the right.
   *
   * @group conversions
   */
  final def toByteArray: Array[Byte] = toByteVector.toArray

  /**
   * Converts the contents of this vector to a `java.nio.ByteBuffer`.
   *
   * The returned buffer is freshly allocated with limit set to the minimum number of bytes needed
   * to represent the contents of this vector, position set to zero, and remaining set to the limit.
   *
   * @see toByteVector
   * @group conversions
   */
  final def toByteBuffer: java.nio.ByteBuffer = toByteVector.toByteBuffer

  /**
   * Converts the contents of this bit vector to a binary string of `size` digits.
   *
   * @group conversions
   */
  final def toBin: String = toByteVector.toBin.take(size.toInt)

  /**
   * Converts the contents of this bit vector to a binary string of `size` digits.
   *
   * @group conversions
   */
  final def toBin(alphabet: Bases.BinaryAlphabet): String = toByteVector.toBin(alphabet).take(size.toInt)

  /**
   * Converts the contents of this bit vector to a hexadecimal string of `ceil(size / 4)` nibbles.
   *
   * The last nibble is right-padded with zeros if the size is not evenly divisible by 4.
   *
   * @group conversions
   */
  final def toHex: String = toHex(Bases.Alphabets.HexLowercase)

  /**
   * Converts the contents of this bit vector to a hexadecimal string of `ceil(size / 4)` nibbles.
   *
   * The last nibble is right-padded with zeros if the size is not evenly divisible by 4.
   *
   * @group conversions
   */
  final def toHex(alphabet: Bases.HexAlphabet): String = {
    val full = toByteVector.toHex(alphabet)
    size % 8 match {
      case 0 => full
      case n if n <= 4 => full.init
      case other => full
    }
  }

  /**
    * Converts the contents of this vector to a base 58 string.
    *
    * the order is assumed to be the same as (Bitcoin)[[https://en.bitcoin.it/wiki/Base58Check_encoding#Base58_symbol_chart]]
    *
    * @group conversions
    */
  final def toBase58: String = toBase58(Bases.Alphabets.Base58)

  /**
    * Converts the contents of this vector to a base 58 string using the specified alphabet.
    *
    * the order is assumed to be the same as (Bitcoin)[[https://en.bitcoin.it/wiki/Base58Check_encoding#Base58_symbol_chart]]
    *
    * @group conversions
    */
  final def toBase58(alphabet: Bases.Alphabet): String = toByteVector.toBase58(alphabet)

  /**
   * Converts the contents of this vector to a base 64 string.
   *
   * The last byte is right-padded with zeros if the size is not evenly divisible by 8.
   *
   * @group conversions
   */
  final def toBase64: String = toBase64(Bases.Alphabets.Base64)

  /**
   * Converts the contents of this vector to a base 64 string using the specified alphabet.
   *
   * The last byte is right-padded with zeros if the size is not evenly divisible by 8.
   *
   * @group conversions
   */
  final def toBase64(alphabet: Bases.Base64Alphabet): String = toByteVector.toBase64(alphabet)

  /**
   * Convert a slice of bits from this vector (`start` until `start+bits`) to a `Byte`.
   *
   * @param signed whether sign extension should be performed
   * @throws IllegalArgumentException if the slice refers to indices that are out of range
   * @group conversions
   */
  final def sliceToByte(start: Long, bits: Int, signed: Boolean = true): Byte = {
    if (start % 8 != 0) drop(start).sliceToByte(0, bits, signed)
    else if (isEmpty || bits == 0) 0.toByte
    else getByte(start, bits, signed)
  }

  private def getByte(start: Long, bits: Int, signed: Boolean): Byte = {
    require(sizeGreaterThanOrEqual(start + bits) && bits >= 0 && bits <= 8)
    var result = 0x0ff & getByte(start / 8)
    if (bits != 0) result = result >>> (8 - bits)
    // Sign extend if necessary
    if (signed && bits != 8 && ((1 << (bits - 1)) & result) != 0) {
      val toShift = 32 - bits
      result = (result << toShift) >> toShift
    }
    result.toByte
  }

  /**
   * Converts the contents of this vector to a byte.
   *
   * @param signed whether sign extension should be performed
   * @throws IllegalArgumentException if size is greater than 8
   * @group conversions
   */
  final def toByte(signed: Boolean = true): Byte = {
    require(sizeLessThanOrEqual(8))
    if (isEmpty) 0.toByte
    else getByte(0, size.toInt, signed)
  }

  /**
   * Convert a slice of bits from this vector (`start` until `start+bits`) to a `Short`.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if the slice refers to indices that are out of range
   * @group conversions
   */
  final def sliceToShort(start: Long, bits: Int,
                       signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Short = {
    if (start % 8 != 0) drop(start).sliceToShort(0, bits, signed, ordering)
    else if (ordering == ByteOrdering.LittleEndian) drop(start).invertReverseByteOrder.sliceToShort(0, bits, signed, ByteOrdering.BigEndian)
    else getBigEndianShort(start, bits, signed)
  }

  private def getBigEndianShort(start: Long, bits: Int, signed: Boolean): Short = {
    require(sizeGreaterThanOrEqual(start + bits) && bits >= 0 && bits <= 16)
    val mod = bits % 8
    var result = 0
    val bytesNeeded = bytesNeededForBits(bits.toLong)
    val base = start / 8
    @annotation.tailrec
    def go(i: Int): Unit =
      if (i < bytesNeeded) {
        result = (result << 8) | (0x0ff & this.getByte(base + i))
        go(i + 1)
      }
    go(0)
    if (mod != 0) result = result >>> (8 - mod)
    // Sign extend if necessary
    if (signed && bits != 16 && ((1 << (bits - 1)) & result) != 0) {
      val toShift = 32 - bits
      result = (result << toShift) >> toShift
    }
    result.toShort
  }

  /**
   * Converts the contents of this vector to a short.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if size is greater than 16
   * @group conversions
   */
  final def toShort(signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Short = {
    require(sizeLessThanOrEqual(16))
    if (ordering == ByteOrdering.LittleEndian) invertReverseByteOrder.toShort(signed, ByteOrdering.BigEndian)
    else getBigEndianShort(0, size.toInt, signed)
  }

  /**
   * Convert a slice of bits from this vector (`start` until `start+bits`) to an `Int`.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if the slice refers to indices that are out of range
   * @group conversions
   */
  final def sliceToInt(start: Long, bits: Int,
                       signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Int = {
    if (start % 8 != 0) drop(start).sliceToInt(0, bits, signed, ordering)
    else if (ordering == ByteOrdering.LittleEndian) drop(start).invertReverseByteOrder.sliceToInt(0, bits, signed, ByteOrdering.BigEndian)
    else getBigEndianInt(start, bits, signed)
  }

  private def getBigEndianInt(start: Long, bits: Int, signed: Boolean): Int = {
    require(sizeGreaterThanOrEqual(start + bits) && bits >= 0 && bits <= 32)
    val mod = bits % 8
    var result = 0
    val bytesNeeded = bytesNeededForBits(bits.toLong)
    val base = start / 8
    @annotation.tailrec
    def go(i: Int): Unit =
      if (i < bytesNeeded) {
        result = (result << 8) | (0x0ff & this.getByte(base + i))
        go(i + 1)
      }
    go(0)
    if (mod != 0) result = result >>> (8 - mod)
    // Sign extend if necessary
    if (signed && bits != 32 && ((1 << (bits - 1)) & result) != 0) {
      val toShift = 32 - bits
      result = (result << toShift) >> toShift
    }
    result
  }

  /**
   * Converts the contents of this vector to an int.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if size is greater than 32
   * @group conversions
   */
  final def toInt(signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Int = {
    require(sizeLessThanOrEqual(32))
    this match {
      case bytes: Bytes =>
        size.toInt match {
          case 32 if signed =>
            bytes.underlying.toByteBuffer.order(ordering.toJava).getInt

          case 16 =>
            val sh = bytes.underlying.toByteBuffer.order(ordering.toJava).getShort
            if (signed) sh.toInt else sh & 0x0ffff

          case 8 =>
            val b = bytes.underlying.toByteBuffer.get
            if (signed) b.toInt else b & 0x0ff

          case bits =>
            if (ordering == ByteOrdering.LittleEndian) invertReverseByteOrder.toInt(signed, ByteOrdering.BigEndian)
            else getBigEndianInt(0, bits, signed)
        }
      case _ =>
        if (ordering == ByteOrdering.LittleEndian) invertReverseByteOrder.toInt(signed, ByteOrdering.BigEndian)
        else getBigEndianInt(0, size.toInt, signed)
    }
  }

  /**
   * Convert a slice of bits from this vector (`start` until `start+bits`) to a `Long`.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if the slice refers to indices that are out of range
   * @group conversions
   */
  final def sliceToLong(start: Long, bits: Int,
                        signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Long = {
    if (start % 8 != 0) drop(start).sliceToLong(0, bits, signed, ordering)
    else if (ordering == ByteOrdering.LittleEndian) drop(start).invertReverseByteOrder.sliceToLong(0, bits, signed, ByteOrdering.BigEndian)
    else getBigEndianLong(start, bits, signed)
  }

  private def getBigEndianLong(start: Long, bits: Int, signed: Boolean): Long = {
    require(sizeGreaterThanOrEqual(start + bits) && bits >= 0 && bits <= 64)
    val mod = bits % 8
    var result = 0L
    val bytesNeeded = bytesNeededForBits(bits.toLong)
    val base = start / 8
    @annotation.tailrec
    def go(i: Int): Unit =
      if (i < bytesNeeded) {
        result = (result << 8) | (0x0ffL & this.getByte(base + i))
        go(i + 1)
      }
    go(0)
    if (mod != 0) result = result >>> (8 - mod)
    // Sign extend if necessary
    if (signed && bits != 64 && ((1 << (bits - 1)) & result) != 0) {
      val toShift = 64 - bits
      result = (result << toShift) >> toShift
    }
    result
  }

  /**
   * Converts the contents of this vector to a long.
   *
   * @param signed whether sign extension should be performed
   * @param ordering order bytes should be processed in
   * @throws IllegalArgumentException if size is greater than 64
   * @group conversions
   */
  final def toLong(signed: Boolean = true, ordering: ByteOrdering = ByteOrdering.BigEndian): Long = {
    require(sizeLessThanOrEqual(64))
    this match {
      case bytes: Bytes =>
        size.toInt match {
          case 64 if signed =>
            bytes.underlying.toByteBuffer.order(ordering.toJava).getLong

          case 32 =>
            val i = bytes.underlying.toByteBuffer.order(ordering.toJava).getInt
            if (signed) i.toLong else i & 0x0ffffffffL

          case 16 =>
            val sh = bytes.underlying.toByteBuffer.order(ordering.toJava).getShort
            if (signed) sh.toLong else sh & 0x0ffffL

          case 8 =>
            val b = bytes.underlying.toByteBuffer.get
            if (signed) b.toLong else b & 0x0ffL

          case bits =>
            if (ordering == ByteOrdering.LittleEndian) invertReverseByteOrder.toLong(signed, ByteOrdering.BigEndian)
            else getBigEndianLong(0, bits, signed)
        }

      case _ =>
        if (ordering == ByteOrdering.LittleEndian) invertReverseByteOrder.toLong(signed, ByteOrdering.BigEndian)
        else getBigEndianLong(0, size.toInt, signed)
    }
  }

  /**
    * Converts the contents of this bit vector to a UUID.
    *
    * @throws IllegalArgumentException if size is not exactly 128.
    * @group conversions
    */
  final def toUUID: UUID = {
    // Sanity check
    if (size != 128) {
      throw new IllegalArgumentException(s"Cannot convert BitVector of size $size to UUID; must be 128 bits")
    }
    // Convert
    val byteBuffer = toByteBuffer
    val mostSignificant = byteBuffer.getLong
    val leastSignificant = byteBuffer.getLong
    new UUID(mostSignificant, leastSignificant)
  }

  /**
   * Decodes this vector as a string using the implicitly available charset.
   * @group conversions
   */
  final def decodeString(implicit charset: Charset): Either[CharacterCodingException, String] =
    bytes.decodeString(charset)

  /**
   * Decodes this vector as a string using the UTF-8 charset.
   * @group conversions
   */
  final def decodeUtf8: Either[CharacterCodingException, String] =
    bytes.decodeUtf8

  /**
   * Decodes this vector as a string using the US-ASCII charset.
   * @group conversions
   */
  final def decodeAscii: Either[CharacterCodingException, String] =
    bytes.decodeAscii

  /**
   * Compresses this vector using ZLIB.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param level compression level, 0-9, with 0 disabling compression and 9 being highest level of compression -- see `java.util.zip.Deflater` for details
   * @param strategy compression strategy -- see `java.util.zip.Deflater` for details
   * @param nowrap if true, ZLIB header and checksum will not be used
   * @param chunkSize buffer size, in bytes, to use when compressing
   * @group conversions
   */
  final def deflate(level: Int = Deflater.DEFAULT_COMPRESSION, strategy: Int = Deflater.DEFAULT_STRATEGY, nowrap: Boolean = false, chunkSize: Int = 4096): BitVector =
    bytes.deflate(level, strategy, nowrap, chunkSize).bits

  /**
   * Decompresses this vector using ZLIB.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param chunkSize buffer size, in bytes, to use when compressing
   * @group conversions
   */
  final def inflate(chunkSize: Int = 4096): Either[DataFormatException, BitVector] =
    bytes.inflate(chunkSize).map(_.bits)

  /**
   * Computes a digest of this bit vector.
   *
   * Exceptions thrown from the underlying JCA API are propagated.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param algorithm digest algorithm to use
   * @group crypto
   */
  final def digest(algorithm: String): BitVector = digest(MessageDigest.getInstance(algorithm))

  /**
   * Computes a digest of this bit vector.
   *
   * Exceptions thrown from the underlying JCA API are propagated.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param digest digest to use
   * @group crypto
   */
  final def digest(digest: MessageDigest): BitVector = BitVector(bytes.digest(digest))

  /**
   * Encrypts this bit vector using the specified cipher and key.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param ci cipher to use for encryption
   * @param key key to encrypt with
   * @param aparams optional algorithm paramaters used for encryption (e.g., initialization vector)
   * @param sr secure random
   * @group crypto
   */
  final def encrypt(ci: Cipher, key: Key, aparams: Option[AlgorithmParameters] = None)(implicit sr: SecureRandom): Either[GeneralSecurityException, BitVector] =
    cipher(ci, key, Cipher.ENCRYPT_MODE, aparams)(sr)

  /**
   * Decrypts this bit vector using the specified cipher and key.
   *
   * The last byte is zero padded if the size is not evenly divisible by 8.
   *
   * @param ci cipher to use for decryption
   * @param key key to decrypt with
   * @param aparams optional algorithm paramaters used for decryption (e.g., initialization vector)
   * @param sr secure random
   * @group crypto
   */
  final def decrypt(ci: Cipher, key: Key, aparams: Option[AlgorithmParameters] = None)(implicit sr: SecureRandom): Either[GeneralSecurityException, BitVector] =
    cipher(ci, key, Cipher.DECRYPT_MODE, aparams)(sr)

  /**
   * Returns true if the specified `BitVector` has the same contents as this vector.
   * @group collection
   */
  final def ===(other: BitVector): Boolean = {
    val chunkSize = 8L * 1024 * 64
    @annotation.tailrec
    def go(x: BitVector, y: BitVector): Boolean = {
      if (x.isEmpty) y.isEmpty
      else {
        val chunkX = x.take(chunkSize)
        val chunkY = y.take(chunkSize)
        chunkX.size == chunkY.size &&
        chunkX.toByteVector === chunkY.toByteVector &&
        go(x.drop(chunkSize), y.drop(chunkSize))
      }
    }
    go(this, other)
  }

  /**
   * Returns true if the specified value is a `BitVector` with the same contents as this vector.
   * @see [[BitVector.===]]
   * @group collection
   */
  override final def equals(other: Any): Boolean = other match {
    case o: BitVector => this === o
    case _ => false
  }

  /**
   * Calculates the hash code of this vector. The result is cached.
   * @group collection
   */
  override final lazy val hashCode = {
    // todo: this could be recomputed more efficiently using the tree structure
    // given an associative hash function
    import util.hashing.MurmurHash3._
    val chunkSize = 8L * 1024 * 64
    @annotation.tailrec
    def go(bits: BitVector, h: Int, iter: Int): Int = {
      if (bits.isEmpty) finalizeHash(h, iter)
      else go(bits.drop(chunkSize), mix(h, bytesHash(bits.take(chunkSize).toByteArray)), iter + 1)
    }
    go(this, stringHash("BitVector"), 1)
  }

  /**
   * Display the size and bytes of this `BitVector`.
   * For bit vectors beyond a certain size, only a hash of the
   * contents are shown.
   * @group collection
   */
  override final def toString =
    if (isEmpty) "BitVector(empty)"
    else if (sizeLessThan(513)) s"BitVector($size bits, 0x${toHex})"
    else s"BitVector($size bits, #${hashCode})"

  // impl details

  final protected def checkBounds(n: Long): Unit =
    if (!sizeGreaterThan(n)) outOfBounds(n)

  final protected def outOfBounds(n: Long): Nothing =
    throw new NoSuchElementException(s"invalid index: $n of $size")

  final protected def mapBytes(f: ByteVector => ByteVector): BitVector = this match {
    case Bytes(bs, n) => toBytes(f(bs), n)
    case Append(l,r) => Append(l.mapBytes(f), r.mapBytes(f))
    case Drop(b,n) => Drop(b.mapBytes(f).compact, n)
    case s@Suspend(_) => Suspend(() => s.underlying.mapBytes(f))
    case c: Chunks => Chunks(Append(c.chunks.left.mapBytes(f), c.chunks.right.mapBytes(f)))
  }

  private[bits] def cipher(ci: Cipher, key: Key, opmode: Int, aparams: Option[AlgorithmParameters] = None)(implicit sr: SecureRandom): Either[GeneralSecurityException, BitVector] =
    bytes.cipher(ci, key, opmode, aparams)(sr).map { _.bits }

  /**
   * Pretty print this `BitVector`.
   */
  private[bits] def internalPretty(prefix: String): String = this match {
    case Append(l,r) => prefix + "append\n" +
                        l.internalPretty(prefix + "  ") + "\n" +
                        r.internalPretty(prefix + "  ")
    case Bytes(b, n) => prefix + s"bits $n\n" + b.pretty("  " + prefix)
    case Drop(u, n) => prefix + s"drop ${n}\n" +
                       u.internalPretty(prefix + "  ")
    case s@Suspend(_) => prefix + "suspend\n" + s.underlying.internalPretty(prefix + "  ")
    case c: Chunks => prefix + "chunks\n" +
                      c.chunks.left.internalPretty("  ") + "\n" +
                      c.chunks.right.internalPretty("  ")
  }

  private def zipBytesWith(other: BitVector)(op: (Byte, Byte) => Int): BitVector = {
    // todo: this has a much more efficient recursive algorithm -
    // only need to compact close to leaves of the tree
    toBytes(this.compact.underlying.zipWithI(other.compact.underlying)(op), this.size min other.size)
  }

  protected final def writeReplace(): AnyRef = new SerializationProxy(toByteArray, size)
}

/**
 * Companion for [[BitVector]].
 *
 * @groupname constants Constants
 * @groupprio constants 0
 *
 * @groupname constructors Constructors
 * @groupprio constructors 1
 *
 * @groupname numeric Numeric Conversions
 * @groupprio numeric 2
 *
 * @groupname base Base Conversions
 * @groupprio base 3
 */
object BitVector {

  /**
   * Empty bit vector.
   * @group constants
   */
  val empty: BitVector = toBytes(ByteVector.empty, 0)

  /**
   * 1-bit vector with only bit set low.
   * @group constants
   */
  val zero: BitVector = toBytes(ByteVector(0), 1)

  /**
   * 1-bit vector with only bit set high.
   * @group constants
   */
  val one: BitVector = toBytes(ByteVector(0xff), 1)

  /**
   * 8-bit vector with all bits set low.
   * @group constants
   */
  val lowByte: BitVector = toBytes(ByteVector.low(1), 8)

  /**
   * 8-bit vector with all bits set high.
   * @group constants
   */
  val highByte: BitVector = toBytes(ByteVector.high(1), 8)

  /**
   * 1-bit vector with only bit set to specified value.
   * @group constructors
   */
  def bit(high: Boolean): BitVector = if (high) one else zero

  /**
   * n-bit vector with bit at index `i` set to value of boolean at index `i` in specified iterable.
   * @group constructors
   */
  def bits(b: Iterable[Boolean]): BitVector =
    b.iterator.zipWithIndex.foldLeft(low(b.size.toLong))((acc,b) =>
      acc.update(b._2.toLong, b._1)
    )

  /**
   * n-bit vector with all bits set high.
   * @group constructors
   */
  def high(n: Long): BitVector = fill(n)(true)

  /**
   * n-bit vector with all bits set low.
   * @group constructors
   */
  def low(n: Long): BitVector = fill(n)(false)

  /**
   * Constructs a `BitVector` from a `ByteVector`.
   * This method has runtime O(1).
   * @group constructors
   */
  def apply(bs: ByteVector): BitVector = toBytes(bs, bs.size.toLong * 8)

  /**
   * Constructs a `BitVector` from a `ByteBuffer`. The given `ByteBuffer` is
   * is copied to ensure the resulting `BitVector` is immutable.
   * If this is not desired, use `BitVector.view`.
   * @group constructors
   */
  def apply(buffer: ByteBuffer): BitVector = apply(ByteVector(buffer))

  /**
   * Constructs a `BitVector` from an `Array[Byte]`. The given `Array[Byte]` is
   * is copied to ensure the resulting `BitVector` is immutable.
   * If this is not desired, use `BitVector.view`.
   * @group constructors
   */
  def apply(bs: Array[Byte]): BitVector = toBytes(ByteVector(bs), bs.size.toLong * 8)

  /**
   * Constructs a `BitVector` from a collection of bytes.
   * @group constructors
   */
  def apply(bs: IterableOnce[Byte]): BitVector = apply(ByteVector(bs))

  /**
   * Constructs a `BitVector` from a list of literal bytes. Only the least significant
   * byte is used of each integral value.
   * @group constructors
   */
  def apply[A: Integral](bytes: A*): BitVector = apply(ByteVector(bytes: _*))

  /**
   * Constructs a `BitVector` from a `ByteBuffer` using the buffer limit * 8 as the size.
   * Unlike `apply`, this does not make a copy of the input buffer, so callers should take care
   * not to modify the contents of the buffer passed to this function.
   * @group constructors
   */
  def view(buffer: ByteBuffer): BitVector = toBytes(ByteVector.view(buffer), buffer.limit().toLong * 8)

  /**
   * Constructs a `BitVector` from the first `sizeInBits` of the `ByteBuffer`.
   * Unlike `apply`, this does not make a copy of the input buffer, so callers should take care
   * not to modify the contents of the buffer passed to this function.
   * @group constructors
   */
  def view(buffer: ByteBuffer, sizeInBits: Long): BitVector = {
    toBytes(ByteVector.view(buffer), sizeInBits)
  }

  /**
   * Constructs a `BitVector` from an `Array[Byte]`. Unlike `apply`, this
   * does not make a copy of the input array, so callers should take care
   * not to modify the contents of the array passed to this function.
   * @group constructors
   */
  def view(bs: Array[Byte]): BitVector = view(bs, bs.size.toLong * 8)

  /**
   * Constructs a `BitVector` from an `Array[Byte]`. Unlike `apply`, this
   * does not make a copy of the input array, so callers should take care
   * not to modify the contents of the array passed to this function.
   * @group constructors
   */
  def view(bs: Array[Byte], sizeInBits: Long): BitVector = toBytes(ByteVector.view(bs), sizeInBits)

  /**
   * Constructs an `n`-bit `BitVector` where each bit is set to the specified value.
   * @group constructors
   */
  def fill(n: Long)(high: Boolean): BitVector = {
    val needed = bytesNeededForBits(n)
    val bs = ByteVector.fill(needed)(if (high) -1 else 0)
    toBytes(bs, n)
  }

  /**
   * Constructs a bit vector with the 2's complement encoding of the specified byte.
   * @param s value to encode
   * @param size size of vector (<= 8)
   * @group numeric
   */
  def fromByte(b: Byte, size: Int = 8): BitVector = {
    require(size <= 8)
    (BitVector(b) << (8L - size)).take(size.toLong)
  }

  /**
   * Constructs a bit vector with the 2's complement encoding of the specified value.
   * @param s value to encode
   * @param size size of vector (<= 16)
   * @param ordering byte ordering of vector
   * @group numeric
   */
  def fromShort(s: Short, size: Int = 16, ordering: ByteOrdering = ByteOrdering.BigEndian): BitVector = {
    require(size <= 16)
    val buffer = ByteBuffer.allocate(2).order(ByteOrder.BIG_ENDIAN).putShort(s)
    buffer.flip()
    val relevantBits = (BitVector.view(buffer) << (16L - size)).take(size.toLong)
    if (ordering == ByteOrdering.BigEndian) relevantBits else relevantBits.reverseByteOrder
  }

  /**
   * Constructs a bit vector with the 2's complement encoding of the specified value.
   * @param i value to encode
   * @param size size of vector (<= 32)
   * @param ordering byte ordering of vector
   * @group numeric
   */
  def fromInt(i: Int, size: Int = 32, ordering: ByteOrdering = ByteOrdering.BigEndian): BitVector = {
    require(size <= 32)
    val buffer = ByteBuffer.allocate(4).order(ByteOrder.BIG_ENDIAN).putInt(i)
    buffer.flip()
    val relevantBits = (BitVector.view(buffer) << (32L - size)).take(size.toLong)
    if (ordering == ByteOrdering.BigEndian) relevantBits else relevantBits.reverseByteOrder
  }

  /**
   * Constructs a bit vector with the 2's complement encoding of the specified value.
   * @param i value to encode
   * @param size size of vector (<= 64)
   * @param ordering byte ordering of vector
   * @group numeric
   */
  def fromLong(l: Long, size: Int = 64, ordering: ByteOrdering = ByteOrdering.BigEndian): BitVector = {
    require(size <= 64)
    val buffer = ByteBuffer.allocate(8).order(ByteOrder.BIG_ENDIAN).putLong(l)
    buffer.flip()
    val relevantBits = (BitVector.view(buffer) << (64L - size)).take(size.toLong)
    if (ordering == ByteOrdering.BigEndian) relevantBits else relevantBits.reverseByteOrder
  }

  /**
    * Constructs a bit vector containing the binary representation of the specified UUID.
    * The bits are in MSB-to-LSB order.
    *
    * @param u value to encode
    * @group conversions
    */
  final def fromUUID(u: UUID): BitVector = {
    val buf = ByteBuffer.allocate(16)
    buf.putLong(u.getMostSignificantBits)
    buf.putLong(u.getLeastSignificantBits)
    // Go via Array[Byte] to avoid hanging on to intermediate ByteBuffer via AtByteBuffer.
    view(buf.array())
  }

  /**
   * Constructs a `BitVector` from a binary string or returns an error message if the string is not valid binary.
   *
   * The string may start with a `0b` and it may contain whitespace or underscore characters.
   * @group base
   */
  def fromBinDescriptive(str: String, alphabet: Bases.BinaryAlphabet = Bases.Alphabets.Binary): Either[String, BitVector] =
    ByteVector.fromBinInternal(str, alphabet).map { case (bytes, size) =>
      val toDrop = size match {
        case 0 => 0
        case n if n % 8 == 0 => 0
        case n => 8 - (n % 8)
      }
      bytes.toBitVector.drop(toDrop.toLong)
    }

  /**
   * Constructs a `BitVector` from a binary string or returns `None` if the string is not valid binary.
   *
   * The string may start with a `0b` and it may contain whitespace or underscore characters.
   * @group base
   */
  def fromBin(str: String, alphabet: Bases.BinaryAlphabet = Bases.Alphabets.Binary): Option[BitVector] = fromBinDescriptive(str, alphabet).toOption

  /**
   * Constructs a `BitVector` from a binary string or throws an IllegalArgumentException if the string is not valid binary.
   *
   * The string may start with a `0b` and it may contain whitespace or underscore characters.
   *
   * @throws IllegalArgumentException if the string is not valid hexadecimal
   * @group base
   */
  def fromValidBin(str: String, alphabet: Bases.BinaryAlphabet = Bases.Alphabets.Binary): BitVector =
    fromBinDescriptive(str, alphabet).fold(msg => throw new IllegalArgumentException(msg), identity)

  /**
   * Constructs a `BitVector` from a hexadecimal string or returns an error message if the string is not valid hexadecimal.
   *
   * The string may start with a `0x` and it may contain whitespace or underscore characters.
   * @group base
   */
  def fromHexDescriptive(str: String, alphabet: Bases.HexAlphabet = Bases.Alphabets.HexLowercase): Either[String, BitVector] =
    ByteVector.fromHexInternal(str, alphabet).map { case (bytes, count) =>
      val toDrop = if (count % 2 == 0) 0 else 4
      bytes.toBitVector.drop(toDrop.toLong)
    }

  /**
   * Constructs a `BitVector` from a hexadecimal string or returns `None` if the string is not valid hexadecimal.
   *
   * The string may start with a `0x` and it may contain whitespace or underscore characters.
   * @group base
   */
  def fromHex(str: String, alphabet: Bases.HexAlphabet = Bases.Alphabets.HexLowercase): Option[BitVector] = fromHexDescriptive(str, alphabet).toOption

  /**
   * Constructs a `BitVector` from a hexadecimal string or throws an IllegalArgumentException if the string is not valid hexadecimal.
   *
   * The string may start with a `0x` and it may contain whitespace or underscore characters.
   *
   * @throws IllegalArgumentException if the string is not valid hexadecimal
   * @group base
   */
  def fromValidHex(str: String, alphabet: Bases.HexAlphabet = Bases.Alphabets.HexLowercase): BitVector =
    fromHexDescriptive(str, alphabet).fold(msg => throw new IllegalArgumentException(msg), identity)

  /**
    * Constructs a `BitVector` from a base 58 string or returns an error message if the string is not valid base 58.
    * Details pertaining to base 58 decoding can be found in the comment for ByteVector.fromBase58Descriptive.
    * The string may contain whitespace characters which are ignored.
    * @group base
    */
  def fromBase58Descriptive(str: String, alphabet: Bases.Alphabet = Bases.Alphabets.Base58): Either[String, BitVector] =
    ByteVector.fromBase58Descriptive(str, alphabet).map { _.toBitVector }

  /**
    * Constructs a `BitVector` from a base 58 string or returns `None` if the string is not valid base 58.
    * Details pertaining to base 58 decoding can be found in the comment for ByteVector.fromBase58Descriptive.
    * The string may contain whitespace characters which are ignored.
    * @group base
    */
  def fromBase58(str: String,alphabet: Bases.Alphabet = Bases.Alphabets.Base58): Option[BitVector] = fromBase58Descriptive(str, alphabet).toOption

  /**
    * Constructs a `BitVector` from a base 58 string or throws an IllegalArgumentException if the string is not valid base 58.
    * Details pertaining to base 58 decoding can be found in the comment for ByteVector.fromBase58Descriptive.
    * The string may contain whitespace characters which are ignored.
    *
    * @throws IllegalArgumentException if the string is not valid base 58
    * @group base
    */
  def fromValidBase58(str: String, alphabet: Bases.Alphabet = Bases.Alphabets.Base58): BitVector =
    fromBase58Descriptive(str, alphabet).fold(msg => throw new IllegalArgumentException(msg), identity)

  /**
   * Constructs a `BitVector` from a base 64 string or returns an error message if the string is not valid base 64.
   * Details pertaining to base 64 decoding can be found in the comment for ByteVector.fromBase64Descriptive.
   * The string may contain whitespace characters which are ignored.
   * @group base
   */
  def fromBase64Descriptive(str: String, alphabet: Bases.Base64Alphabet = Bases.Alphabets.Base64): Either[String, BitVector] =
    ByteVector.fromBase64Descriptive(str, alphabet).map { _.toBitVector }

  /**
   * Constructs a `BitVector` from a base 64 string or returns `None` if the string is not valid base 64.
   * Details pertaining to base 64 decoding can be found in the comment for ByteVector.fromBase64Descriptive.
   * The string may contain whitespace characters which are ignored.
   * @group base
   */
  def fromBase64(str: String, alphabet: Bases.Base64Alphabet = Bases.Alphabets.Base64): Option[BitVector] = fromBase64Descriptive(str, alphabet).toOption

  /**
   * Constructs a `BitVector` from a base 64 string or throws an IllegalArgumentException if the string is not valid base 64.
   * Details pertaining to base 64 decoding can be found in the comment for ByteVector.fromBase64Descriptive.
   * The string may contain whitespace characters which are ignored.
   *
   * @throws IllegalArgumentException if the string is not valid base 64
   * @group base
   */
  def fromValidBase64(str: String, alphabet: Bases.Base64Alphabet = Bases.Alphabets.Base64): BitVector =
    fromBase64Descriptive(str, alphabet).fold(msg => throw new IllegalArgumentException(msg), identity)

  /**
   * Encodes the specified string to a `BitVector` using the implicitly available `Charset`.
   *
   * @group constructors
   */
  def encodeString(str: String)(implicit charset: Charset): Either[CharacterCodingException, BitVector] =
    ByteVector.encodeString(str)(charset).map { _.bits }

  /**
   * Encodes the specified string to a `BitVector` using the UTF-8 charset.
   *
   * @group constructors
   */
  def encodeUtf8(str: String): Either[CharacterCodingException, BitVector] =
    ByteVector.encodeUtf8(str).map { _.bits }

  /**
   * Encodes the specified string to a `BitVector` using the US-ASCII charset.
   *
   * @group constructors
   */
  def encodeAscii(str: String): Either[CharacterCodingException, BitVector] =
    ByteVector.encodeAscii(str).map { _.bits }

  /**
   * Concatenates all the given `BitVector`s into a single instance.
   *
   * @group constructors
   */
  def concat(bvs: IterableOnce[BitVector]): BitVector = bvs.foldLeft(BitVector.empty)(_ ++ _)

  /**
   * Create a lazy `BitVector` by repeatedly extracting chunks from `S`.
   * The returned `BitVector` will have the structure of a fully lazy
   * right-associated cons list. Thus, `get`, `take`, and `drop` will
   * be efficient when operating on the head of the list, but accessing
   * later indices (for `takeRight`, say, or `get(size-1)` will require
   * forcing the stream up to that point.
   *
   * Use `force` if you wish to convert the result to an in-memory strict
   * `BitVector` backed by a balanced tree.
   *
   * @group constructors
   */
  def unfold[S](s: S)(f: S => Option[(BitVector, S)]): BitVector =
    Suspend { () => f(s).map { case (h,t) => Append(h, unfold(t)(f)) }
                        .getOrElse { BitVector.empty } }

  /**
   * Produce a lazy `BitVector` from the given `InputStream`, using `chunkSizeInBytes`
   * to control the number of bytes read in each chunk (defaulting to 16MB).
   * This simply calls [[scodec.bits.BitVector.unfold]] with a function to extract a series
   * of flat byte arrays from the `InputStream`.
   *
   * This function does not handle closing the `InputStream` and has all the usual
   * drawbacks of lazy I/O - `I/O` exceptions may be raised unexpectedly in pure code as
   * chunks are forced, and it must memoize the results to prevent the underlying side
   * effects from being observed. Streaming applications should take care to ensure
   * that the head of the stream is not left on the stack, as this will cause the entire
   * stream to be retained in memory.
   *
   * @param chunkSizeInBytes the number of bytes to read in each chunk
   * @group constructors
   */
  def fromInputStream(in: java.io.InputStream, chunkSizeInBytes: Int = 1024 * 1000 * 16): BitVector =
    unfold(in) { in =>
      val buf = new Array[Byte](chunkSizeInBytes)
      val nRead = in.read(buf)
      if (nRead == chunkSizeInBytes) Some((BitVector(buf), in))
      else if (nRead == -1) None
      else Some((BitVector(buf.take(nRead): Array[Byte]), in))
    }

  /**
   * Produce a lazy `BitVector` from the given `ReadableByteChannel`, using `chunkSizeInBytes`
   * to control the number of bytes read in each chunk (defaulting to 16MB). This function
   * does lazy I/O, see [[scodec.bits.BitVector.fromInputStream]] for caveats. The `direct`
   * parameter, if `true`, allows for (but does not enforce) using a 'direct' `java.nio.ByteBuffer`
   * for each chunk, which means the buffer and corresponding `BitVector` chunk may be backed by a
   * 'view' rather than an in-memory array. This may be more efficient for some workloads. See
   * `java.nio.ByteBuffer` for more information.
   *
   * @param chunkSizeInBytes the number of bytes to read in each chunk
   * @param direct true if we should attempt to use a 'direct' `java.nio.ByteBuffer` for reads
   * @group constructors
   */
  def fromChannel(in: java.nio.channels.ReadableByteChannel, chunkSizeInBytes: Int = 1024 * 1000 * 16,
                  direct: Boolean = false): BitVector =
    unfold(in) { in =>
      val buf = if (direct) java.nio.ByteBuffer.allocateDirect(chunkSizeInBytes)
                else        java.nio.ByteBuffer.allocate(chunkSizeInBytes)
      val nRead = in.read(buf)
      buf.flip
      if (nRead != -1) Some((BitVector.view(buf, nRead.toLong*8), in))
      else None
    }

  /**
   * Produce a lazy `BitVector` from the given `FileChannel`, using `chunkSizeInBytes`
   * to control the number of bytes read in each chunk (defaulting to 16MB). Unlike
   * [[scodec.bits.BitVector.fromChannel]], this memory-maps chunks in, rather than copying
   * them explicitly.
   *
   * Behavior is unspecified if this function is used concurrently with the underlying
   * file being written.
   *
   * @param chunkSizeInBytes the number of bytes to read in each chunk
   * @group constructors
   */
  def fromMmap(in: java.nio.channels.FileChannel, chunkSizeInBytes: Int = 1024 * 1000 * 16): BitVector =
    unfold(in -> 0L) { case (in,pos) =>
      if (pos == in.size) None
      else {
        require (pos < in.size)
        val bytesToRead = (in.size - pos) min chunkSizeInBytes.toLong
        val buf = in.map(java.nio.channels.FileChannel.MapMode.READ_ONLY, pos, bytesToRead)
        require(buf.limit() == bytesToRead)
        Some((BitVector.view(buf), (in -> (pos + bytesToRead))))
      }
    }

  /** Smart constructor for `Bytes`. */
  private[scodec] def toBytes(bs: ByteVector, sizeInBits: Long): Bytes = {
    val needed = bytesNeededForBits(sizeInBits)
    require(needed <= bs.size)
    val b = if (bs.size > needed) bs.take(needed) else bs
    Bytes(b, sizeInBits)
  }

  private[scodec] case class Bytes(val underlying: ByteVector, val size: Long) extends BitVector {
    private def invalidBits = 8 - validBitsInLastByte(size)
    def align = this
    def sizeLessThan(n: Long) = size < n
    def take(n: Long): Bytes = toBytes(underlying, math.max(0L, math.min(size,n)))
    def drop(n: Long): BitVector = {
      if (n >= size) BitVector.empty
      else if (n <= 0) this
      else if (n % 8 == 0) Bytes(underlying.drop(n / 8), size - n)
      else Drop(this, n)
    }
    def get(n: Long): Boolean = {
      checkBounds(n)
      getBit(underlying(n / 8), (n % 8).toInt)
    }
    def getByte(n: Long): Byte = {
      if (n < underlying.size-1)
        underlying(n)
      else { // last byte may have some garbage bits, clear these out
        val valid = 8 - invalidBits
        (underlying(n) & topNBits(valid.toInt)).toByte
      }
    }

    def update(n: Long, high: Boolean): BitVector = {
      checkBounds(n)
      val b2 = underlying.update(
        n / 8,
        underlying.lift(n / 8).map(setBit(_, (n % 8).toInt, high)).getOrElse {
          outOfBounds(n)
        }
      )
      Bytes(b2, size)
    }
    def combine(other: Bytes): Bytes = {
      val invalidBits = this.invalidBits
      val otherBytes = other.underlying
      if (isEmpty) {
        other
      } else if (otherBytes.isEmpty) {
        this
      } else if (invalidBits == 0) {
        toBytes(underlying ++ otherBytes, size + other.size)
      } else {
        val bytesCleared = clearUnneededBits(size, underlying) // this is key
        val hi = bytesCleared(bytesCleared.size - 1)
        val lo = (((otherBytes.head & topNBits(invalidBits.toInt)) & 0x000000ff) >>> validBitsInLastByte(size).toInt).toByte
        val updatedOurBytes = bytesCleared.update(bytesCleared.size - 1, (hi | lo).toByte)
        val updatedOtherBytes = other.drop(invalidBits).toByteVector
        toBytes(updatedOurBytes ++ updatedOtherBytes, size + other.size)
      }
    }
  }

  private[scodec] case class Drop(underlying: Bytes, m: Long) extends BitVector {
    def size = math.max(0, underlying.size - m)
    def sizeLessThan(n: Long) = size < n
    def align = interpretDrop

    def drop(n: Long): BitVector =
      if (n >= size) BitVector.empty
      else if (n <= 0) this
      else { val nm = n+m
             val d = Drop(underlying, nm)
             if (nm > 32768 && nm % 8 == 0) d.interpretDrop // occasionally
             else d
           }
    def take(n: Long): BitVector =
      if (n >= size) this
      else if (n <= 0) BitVector.empty
      else underlying.take(m + n).drop(m)

    def get(n: Long): Boolean =
      underlying.get(m + n)
    def getByte(n: Long): Byte =
      this.drop(n*8).take(8).align.getByte(0)
    def update(n: Long, high: Boolean): BitVector =
      Drop(underlying.update(m + n, high).compact, m)

    def interpretDrop: Bytes = {
      val low = m max 0
      val newSize = size
      if (newSize == 0) BitVector.empty.align
      else {
        val lowByte = low / 8
        val shiftedByWholeBytes: ByteVector =
          underlying.underlying.slice(lowByte, lowByte + bytesNeededForBits(newSize) + 1)
        val bitsToShiftEachByte = (low % 8).toInt
        val newBytes = {
          if (bitsToShiftEachByte == 0) shiftedByWholeBytes
          else {
            (shiftedByWholeBytes zipWithI (shiftedByWholeBytes.drop(1) :+ (0: Byte))) { case (a, b) =>
              val hi = (a << bitsToShiftEachByte)
              val low = (((b & topNBits(bitsToShiftEachByte)) & 0x000000ff) >>> (8 - bitsToShiftEachByte))
              hi | low
            }
          }
        }
        toBytes(if (newSize <= (newBytes.size - 1) * 8) newBytes.dropRight(1) else newBytes, newSize)
      }
    }
  }
  private[scodec] case class Append(left: BitVector,
                                    right: BitVector) extends BitVector {

    def get(n: Long): Boolean =
      if (n < left.size) left.get(n)
      else right.get(n - left.size)
    def getByte(n: Long): Byte =
      if (n < left.size/8) left.getByte(n)
      else if (left.size%8 == 0 && n > left.size/8) right.getByte(n - left.size/8)
      else drop(n*8).take(8).align.getByte(0) // fall back to inefficient impl (todo: improve this)
    def update(n: Long, high: Boolean): BitVector =
      if (n < left.size) Append(left.update(n, high), right)
      else Append(left, right.update(n - left.size, high))
    def align = left.align combine right.align

    @volatile var knownSize: Long = right match {
      case s: Suspend => -1L
      case _ => { // eagerly compute the size if we're strict
        val sz = left.size + right.size
        sz
      }
    }
    var sizeLowerBound = left.size

    def size = {
      if (knownSize != -1L) knownSize
      else { // faster to just allow recomputation if there's contention
        @annotation.tailrec
        def go(rem: List[BitVector], acc: Long): Long = rem match {
          case Nil => acc
          case Append(x, y) :: t => go(x :: y :: t, acc)
          case Chunks(Append(x, y)) :: t => go(x :: y :: t, acc)
          case (s: Suspend) :: t => go(s.underlying :: t, acc)
          case h :: t => go(t, acc + h.size)
        }
        val sz = go(List(left, right), 0)
        knownSize = sz
        sz
      }
    }

    def take(n: Long) = {
      // NB: not worth early termination in event that sizeLessThanOrEqual(n) is true -
      // this case is rare, and requires traversing same BitVector twice, once to compute
      // sizeLessThan, then again to implement the `take`
      val npos = math.max(0L, n)
      if (npos == 0) BitVector.empty
      else if (npos <= left.size) left.take(npos)
      else {
        @annotation.tailrec
        def go(accL: BitVector, cur: BitVector, n: Long): BitVector = cur match {
          case Append(left, right) => if (n <= left.size) accL ++ left.take(n)
                                      else go(accL ++ left, right, n - left.size)
          case s: Suspend => go(accL, s.underlying, n)
          case _ => accL ++ cur.take(n)
        }
        go(left, right, npos - left.size)
      }
    }

    def drop(n: Long) = {
      val npos = math.max(0L, n)
      if (npos == 0) this
      else {
        @annotation.tailrec
        def go(cur: BitVector, n: Long): BitVector = cur match {
          case Append(left, right) => if (n >= left.size) go(right, n - left.size)
                                      else Append(left.drop(n), right)
          case s: Suspend => go(s.underlying, n)
          case _ => cur.drop(n)
        }
        if (npos >= left.size) go(right, npos - left.size)
        else Append(left.drop(npos), right)
      }
    }

    def sizeLessThan(n: Long) = {
      if (knownSize != -1L) knownSize < n
      else if (sizeLowerBound >= n) false
      else {
        @annotation.tailrec
        def go(cur: BitVector, n: Long, seen: Long): Boolean = cur match {
          case Append(l,r) => if (l.size >= n) { sizeLowerBound = math.max(seen + l.size, sizeLowerBound); false }
                              else go(r, n - l.size, seen + l.size)
          case s: Suspend => go(s.underlying, n, seen)
          case _ => {
            sizeLowerBound = math.max(seen, sizeLowerBound)
            cur.size < n
          }
        }
        go(this, n, 0)
      }
    }
  }
  private[scodec] case class Suspend(thunk: () => BitVector) extends BitVector {
    lazy val underlying = thunk()
    def sizeLessThan(n: Long) = underlying.sizeLessThan(n)
    def get(n: Long): Boolean = underlying.get(n)
    def take(n: Long) = underlying.take(n)
    def drop(n: Long) = underlying.drop(n)
    def getByte(n: Long): Byte = underlying.getByte(n)
    def update(n: Long, high: Boolean): BitVector = underlying.update(n, high)
    def size = underlying.size
    def align = underlying.align
  }

  /**
   * A vector of chunks of exponentially decreasing size. Supports
   * amortized constant time `++` and logarithmic time for all other
   * operations.
   */
  private[scodec] case class Chunks(chunks: Append) extends BitVector {

    override def unchunk = Append(chunks.left, chunks.right.unchunk)
    def align = chunks.align

    def take(n: Long) = chunks.take(n)
    def drop(n: Long) = chunks.drop(n)

    override def ++(b: BitVector): BitVector =
      if (b.isEmpty) this
      else if (this.isEmpty) b
      else {
        @annotation.tailrec
        def go(chunks: Append, last: BitVector): BitVector = {
          val lastN = last.size
          if (lastN >= chunks.size || lastN*2 <= chunks.right.size)
            Chunks(Append(chunks, last))
          else chunks.left match {
            case left: Append =>
              val rN = chunks.right.size
              val aligned = (lastN % 8) + (rN % 8) == 0
              if (rN <= 256 && aligned)
                go(left, chunks.right.align combine last.align)
              else
                go(left, Append(chunks.right, last))
            case _ => Chunks(Append(chunks, last))
          }
        }
        go(chunks, b.unchunk)
      }

    def size = chunks.size
    def sizeLessThan(n: Long) = chunks.sizeLessThan(n)

    def update(n: Long, high: Boolean): BitVector =
      chunks.update(n, high)

    def get(n: Long): Boolean = chunks.get(n)
    def getByte(n: Long): Byte = chunks.getByte(n)
  }

  /** Concatenate `vs` to produce a single `BitVector`. */
  def concat(vs: Vector[BitVector]): BitVector =
    // quite snappy with new algorithm!
    vs.foldLeft(BitVector.empty)(_ ++ _)

  // bit twiddling operations

  private def getBit(byte: Byte, n: Int): Boolean =
    ((0x00000080 >> n) & byte) != 0

  private def setBit(byte: Byte, n: Int, high: Boolean): Byte = {
    if (high) (0x00000080 >> n) | byte
    else (~(0x00000080 >> n)) & byte
  }.toByte

  private def validBitsInLastByte(size: Long): Long = {
    val mod = size % 8
    (if (mod == 0) 8 else mod)
  }

  /** Gets a byte mask with the top `n` bits enabled. */
  private def topNBits(n: Int): Byte =
    (-1 << (8 - n)).toByte

  private def bytesNeededForBits(size: Long): Long =
    (size + 7) / 8

  /** Returns the bitwise reversal of the provided byte. */
  def reverseBitsInByte(b: Byte): Byte =
    bitReversalTable(b & 0xff)

  private val bitReversalTable: Array[Byte] = Array(
    0x00.toByte, 0x80.toByte, 0x40.toByte, 0xC0.toByte, 0x20.toByte, 0xA0.toByte, 0x60.toByte, 0xE0.toByte,
    0x10.toByte, 0x90.toByte, 0x50.toByte, 0xD0.toByte, 0x30.toByte, 0xB0.toByte, 0x70.toByte, 0xF0.toByte,
    0x08.toByte, 0x88.toByte, 0x48.toByte, 0xC8.toByte, 0x28.toByte, 0xA8.toByte, 0x68.toByte, 0xE8.toByte,
    0x18.toByte, 0x98.toByte, 0x58.toByte, 0xD8.toByte, 0x38.toByte, 0xB8.toByte, 0x78.toByte, 0xF8.toByte,
    0x04.toByte, 0x84.toByte, 0x44.toByte, 0xC4.toByte, 0x24.toByte, 0xA4.toByte, 0x64.toByte, 0xE4.toByte,
    0x14.toByte, 0x94.toByte, 0x54.toByte, 0xD4.toByte, 0x34.toByte, 0xB4.toByte, 0x74.toByte, 0xF4.toByte,
    0x0C.toByte, 0x8C.toByte, 0x4C.toByte, 0xCC.toByte, 0x2C.toByte, 0xAC.toByte, 0x6C.toByte, 0xEC.toByte,
    0x1C.toByte, 0x9C.toByte, 0x5C.toByte, 0xDC.toByte, 0x3C.toByte, 0xBC.toByte, 0x7C.toByte, 0xFC.toByte,
    0x02.toByte, 0x82.toByte, 0x42.toByte, 0xC2.toByte, 0x22.toByte, 0xA2.toByte, 0x62.toByte, 0xE2.toByte,
    0x12.toByte, 0x92.toByte, 0x52.toByte, 0xD2.toByte, 0x32.toByte, 0xB2.toByte, 0x72.toByte, 0xF2.toByte,
    0x0A.toByte, 0x8A.toByte, 0x4A.toByte, 0xCA.toByte, 0x2A.toByte, 0xAA.toByte, 0x6A.toByte, 0xEA.toByte,
    0x1A.toByte, 0x9A.toByte, 0x5A.toByte, 0xDA.toByte, 0x3A.toByte, 0xBA.toByte, 0x7A.toByte, 0xFA.toByte,
    0x06.toByte, 0x86.toByte, 0x46.toByte, 0xC6.toByte, 0x26.toByte, 0xA6.toByte, 0x66.toByte, 0xE6.toByte,
    0x16.toByte, 0x96.toByte, 0x56.toByte, 0xD6.toByte, 0x36.toByte, 0xB6.toByte, 0x76.toByte, 0xF6.toByte,
    0x0E.toByte, 0x8E.toByte, 0x4E.toByte, 0xCE.toByte, 0x2E.toByte, 0xAE.toByte, 0x6E.toByte, 0xEE.toByte,
    0x1E.toByte, 0x9E.toByte, 0x5E.toByte, 0xDE.toByte, 0x3E.toByte, 0xBE.toByte, 0x7E.toByte, 0xFE.toByte,
    0x01.toByte, 0x81.toByte, 0x41.toByte, 0xC1.toByte, 0x21.toByte, 0xA1.toByte, 0x61.toByte, 0xE1.toByte,
    0x11.toByte, 0x91.toByte, 0x51.toByte, 0xD1.toByte, 0x31.toByte, 0xB1.toByte, 0x71.toByte, 0xF1.toByte,
    0x09.toByte, 0x89.toByte, 0x49.toByte, 0xC9.toByte, 0x29.toByte, 0xA9.toByte, 0x69.toByte, 0xE9.toByte,
    0x19.toByte, 0x99.toByte, 0x59.toByte, 0xD9.toByte, 0x39.toByte, 0xB9.toByte, 0x79.toByte, 0xF9.toByte,
    0x05.toByte, 0x85.toByte, 0x45.toByte, 0xC5.toByte, 0x25.toByte, 0xA5.toByte, 0x65.toByte, 0xE5.toByte,
    0x15.toByte, 0x95.toByte, 0x55.toByte, 0xD5.toByte, 0x35.toByte, 0xB5.toByte, 0x75.toByte, 0xF5.toByte,
    0x0D.toByte, 0x8D.toByte, 0x4D.toByte, 0xCD.toByte, 0x2D.toByte, 0xAD.toByte, 0x6D.toByte, 0xED.toByte,
    0x1D.toByte, 0x9D.toByte, 0x5D.toByte, 0xDD.toByte, 0x3D.toByte, 0xBD.toByte, 0x7D.toByte, 0xFD.toByte,
    0x03.toByte, 0x83.toByte, 0x43.toByte, 0xC3.toByte, 0x23.toByte, 0xA3.toByte, 0x63.toByte, 0xE3.toByte,
    0x13.toByte, 0x93.toByte, 0x53.toByte, 0xD3.toByte, 0x33.toByte, 0xB3.toByte, 0x73.toByte, 0xF3.toByte,
    0x0B.toByte, 0x8B.toByte, 0x4B.toByte, 0xCB.toByte, 0x2B.toByte, 0xAB.toByte, 0x6B.toByte, 0xEB.toByte,
    0x1B.toByte, 0x9B.toByte, 0x5B.toByte, 0xDB.toByte, 0x3B.toByte, 0xBB.toByte, 0x7B.toByte, 0xFB.toByte,
    0x07.toByte, 0x87.toByte, 0x47.toByte, 0xC7.toByte, 0x27.toByte, 0xA7.toByte, 0x67.toByte, 0xE7.toByte,
    0x17.toByte, 0x97.toByte, 0x57.toByte, 0xD7.toByte, 0x37.toByte, 0xB7.toByte, 0x77.toByte, 0xF7.toByte,
    0x0F.toByte, 0x8F.toByte, 0x4F.toByte, 0xCF.toByte, 0x2F.toByte, 0xAF.toByte, 0x6F.toByte, 0xEF.toByte,
    0x1F.toByte, 0x9F.toByte, 0x5F.toByte, 0xDF.toByte, 0x3F.toByte, 0xBF.toByte, 0x7F.toByte, 0xFF.toByte
  )

  /** Clears (sets to 0) any bits in the last byte that are not used for storing `size` bits. */
  private def clearUnneededBits(size: Long, bytes: ByteVector): ByteVector = {
    val valid = validBitsInLastByte(size).toInt
    if (bytes.nonEmpty && valid < 8) {
      val idx = bytes.size - 1
      val last = bytes(idx)
      bytes.update(idx, (last & topNBits(valid)).toByte)
    } else {
      bytes
    }
  }

  /**
   * Do a 'balanced' reduction of `v`. Provided `f` is associative, this
   * returns the same result as `v.reduceLeft(f)`, but uses a balanced
   * tree of concatenations, which is more efficient for operations that
   * must copy both `A` values to combine them in `f`.
   *
   * Implementation uses a stack that combines the top two elements of the
   * stack using `f` if the top element is more than half the size of the
   * element below it.
   */
  private[bits] def reduceBalanced[A](v: Iterable[A])(size: A => Long)(
                                      f: (A,A) => A): A = {
    @annotation.tailrec
    def fixup(stack: List[(A,Long)]): List[(A,Long)] = stack match {
      // h actually appeared first in `v`, followed by `h2`, preserve this order
      case (h2,n) :: (h,m) :: t if n > m/2 =>
        fixup { (f(h, h2), m+n) :: t }
      case _ => stack
    }
    v.foldLeft(List[(A,Long)]())((stack,a) => fixup((a -> size(a)) :: stack))
     .reverse.map(_._1)
     .reduceLeft(f)
  }

  @SerialVersionUID(1L)
  private class SerializationProxy(private val bytes: Array[Byte], private val size: Long) extends Serializable {
    def readResolve: AnyRef = BitVector.view(bytes, size)
  }

  implicit class GroupedOp(val self: BitVector) extends AnyVal {
    /**
     * Converts this vector in to a sequence of `n`-bit vectors.
     * @group collection
     */
    final def grouped(n: Long): Iterator[BitVector] = self.groupedIterator(n)
  }

}




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