content: # Author: Eric Larson
  # 2014
  
  """Tools for MLS generation"""
  
  import numpy as np
  
  from ._max_len_seq_inner import _max_len_seq_inner
  
  __all__ = ['max_len_seq']
  
  
  # These are definitions of linear shift register taps for use in max_len_seq()
  _mls_taps = {2: [1], 3: [2], 4: [3], 5: [3], 6: [5], 7: [6], 8: [7, 6, 1],
               9: [5], 10: [7], 11: [9], 12: [11, 10, 4], 13: [12, 11, 8],
               14: [13, 12, 2], 15: [14], 16: [15, 13, 4], 17: [14],
               18: [11], 19: [18, 17, 14], 20: [17], 21: [19], 22: [21],
               23: [18], 24: [23, 22, 17], 25: [22], 26: [25, 24, 20],
               27: [26, 25, 22], 28: [25], 29: [27], 30: [29, 28, 7],
               31: [28], 32: [31, 30, 10]}
  
  def max_len_seq(nbits, state=None, length=None, taps=None):
      """
      Maximum length sequence (MLS) generator.
  
      Parameters
      ----------
      nbits : int
          Number of bits to use. Length of the resulting sequence will
          be ``(2**nbits) - 1``. Note that generating long sequences
          (e.g., greater than ``nbits == 16``) can take a long time.
      state : array_like, optional
          If array, must be of length ``nbits``, and will be cast to binary
          (bool) representation. If None, a seed of ones will be used,
          producing a repeatable representation. If ``state`` is all
          zeros, an error is raised as this is invalid. Default: None.
      length : int, optional
          Number of samples to compute. If None, the entire length
          ``(2**nbits) - 1`` is computed.
      taps : array_like, optional
          Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence).
          If None, taps will be automatically selected (for up to
          ``nbits == 32``).
  
      Returns
      -------
      seq : array
          Resulting MLS sequence of 0's and 1's.
      state : array
          The final state of the shift register.
  
      Notes
      -----
      The algorithm for MLS generation is generically described in:
  
          https://en.wikipedia.org/wiki/Maximum_length_sequence
  
      The default values for taps are specifically taken from the first
      option listed for each value of ``nbits`` in:
  
          http://www.newwaveinstruments.com/resources/articles/
              m_sequence_linear_feedback_shift_register_lfsr.htm
  
      .. versionadded:: 0.15.0
  
      Examples
      --------
      MLS uses binary convention:
  
      >>> from scipy.signal import max_len_seq
      >>> max_len_seq(4)[0]
      array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8)
  
      MLS has a white spectrum (except for DC):
  
      >>> import matplotlib.pyplot as plt
      >>> from numpy.fft import fft, ifft, fftshift, fftfreq
      >>> seq = max_len_seq(6)[0]*2-1  # +1 and -1
      >>> spec = fft(seq)
      >>> N = len(seq)
      >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
      >>> plt.margins(0.1, 0.1)
      >>> plt.grid(True)
      >>> plt.show()
  
      Circular autocorrelation of MLS is an impulse:
  
      >>> acorrcirc = ifft(spec * np.conj(spec)).real
      >>> plt.figure()
      >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
      >>> plt.margins(0.1, 0.1)
      >>> plt.grid(True)
      >>> plt.show()
  
      Linear autocorrelation of MLS is approximately an impulse:
  
      >>> acorr = np.correlate(seq, seq, 'full')
      >>> plt.figure()
      >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
      >>> plt.margins(0.1, 0.1)
      >>> plt.grid(True)
      >>> plt.show()
  
      """
      if taps is None:
          if nbits not in _mls_taps:
              known_taps = np.array(list(_mls_taps.keys()))
              raise ValueError('nbits must be between %s and %s if taps is None'
                               % (known_taps.min(), known_taps.max()))
          taps = np.array(_mls_taps[nbits], np.intp)
      else:
          taps = np.unique(np.array(taps, np.intp))[::-1]
          if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1:
              raise ValueError('taps must be non-empty with values between '
                               'zero and nbits (inclusive)')
          taps = np.ascontiguousarray(taps)  # needed for Cython
      n_max = (2**nbits) - 1
      if length is None:
          length = n_max
      else:
          length = int(length)
          if length < 0:
              raise ValueError('length must be greater than or equal to 0')
      # We use int8 instead of bool here because numpy arrays of bools
      # don't seem to work nicely with Cython
      if state is None:
          state = np.ones(nbits, dtype=np.int8, order='c')
      else:
          # makes a copy if need be, ensuring it's 0's and 1's
          state = np.array(state, dtype=bool, order='c').astype(np.int8)
      if state.ndim != 1 or state.size != nbits:
          raise ValueError('state must be a 1-dimensional array of size nbits')
      if np.all(state == 0):
          raise ValueError('state must not be all zeros')
  
      seq = np.empty(length, dtype=np.int8, order='c')
      state = _max_len_seq_inner(taps, state, nbits, length, seq)
      return seq, state
  