text: """
  Quantilization functions and related stuff
  """
  from functools import partial
  
  import numpy as np
  
  from pandas._libs.lib import infer_dtype
  
  from pandas.core.dtypes.common import (
      _NS_DTYPE, ensure_int64, is_categorical_dtype, is_datetime64_dtype,
      is_datetime64tz_dtype, is_datetime_or_timedelta_dtype, is_integer,
      is_scalar, is_timedelta64_dtype)
  from pandas.core.dtypes.missing import isna
  
  from pandas import (
      Categorical, Index, Interval, IntervalIndex, Series, Timedelta, Timestamp,
      to_datetime, to_timedelta)
  import pandas.core.algorithms as algos
  import pandas.core.nanops as nanops
  
  
  def cut(x, bins, right=True, labels=None, retbins=False, precision=3,
          include_lowest=False, duplicates='raise'):
      """
      Bin values into discrete intervals.
  
      Use `cut` when you need to segment and sort data values into bins. This
      function is also useful for going from a continuous variable to a
      categorical variable. For example, `cut` could convert ages to groups of
      age ranges. Supports binning into an equal number of bins, or a
      pre-specified array of bins.
  
      Parameters
      ----------
      x : array-like
          The input array to be binned. Must be 1-dimensional.
      bins : int, sequence of scalars, or IntervalIndex
          The criteria to bin by.
  
          * int : Defines the number of equal-width bins in the range of `x`. The
            range of `x` is extended by .1% on each side to include the minimum
            and maximum values of `x`.
          * sequence of scalars : Defines the bin edges allowing for non-uniform
            width. No extension of the range of `x` is done.
          * IntervalIndex : Defines the exact bins to be used. Note that
            IntervalIndex for `bins` must be non-overlapping.
  
      right : bool, default True
          Indicates whether `bins` includes the rightmost edge or not. If
          ``right == True`` (the default), then the `bins` ``[1, 2, 3, 4]``
          indicate (1,2], (2,3], (3,4]. This argument is ignored when
          `bins` is an IntervalIndex.
      labels : array or bool, optional
          Specifies the labels for the returned bins. Must be the same length as
          the resulting bins. If False, returns only integer indicators of the
          bins. This affects the type of the output container (see below).
          This argument is ignored when `bins` is an IntervalIndex.
      retbins : bool, default False
          Whether to return the bins or not. Useful when bins is provided
          as a scalar.
      precision : int, default 3
          The precision at which to store and display the bins labels.
      include_lowest : bool, default False
          Whether the first interval should be left-inclusive or not.
      duplicates : {default 'raise', 'drop'}, optional
          If bin edges are not unique, raise ValueError or drop non-uniques.
  
          .. versionadded:: 0.23.0
  
      Returns
      -------
      out : Categorical, Series, or ndarray
          An array-like object representing the respective bin for each value
          of `x`. The type depends on the value of `labels`.
  
          * True (default) : returns a Series for Series `x` or a
            Categorical for all other inputs. The values stored within
            are Interval dtype.
  
          * sequence of scalars : returns a Series for Series `x` or a
            Categorical for all other inputs. The values stored within
            are whatever the type in the sequence is.
  
          * False : returns an ndarray of integers.
  
      bins : numpy.ndarray or IntervalIndex.
          The computed or specified bins. Only returned when `retbins=True`.
          For scalar or sequence `bins`, this is an ndarray with the computed
          bins. If set `duplicates=drop`, `bins` will drop non-unique bin. For
          an IntervalIndex `bins`, this is equal to `bins`.
  
      See Also
      --------
      qcut : Discretize variable into equal-sized buckets based on rank
          or based on sample quantiles.
      Categorical : Array type for storing data that come from a
          fixed set of values.
      Series : One-dimensional array with axis labels (including time series).
      IntervalIndex : Immutable Index implementing an ordered, sliceable set.
  
      Notes
      -----
      Any NA values will be NA in the result. Out of bounds values will be NA in
      the resulting Series or Categorical object.
  
      Examples
      --------
      Discretize into three equal-sized bins.
  
      >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]), 3)
      ... # doctest: +ELLIPSIS
      [(0.994, 3.0], (5.0, 7.0], (3.0, 5.0], (3.0, 5.0], (5.0, 7.0], ...
      Categories (3, interval[float64]): [(0.994, 3.0] < (3.0, 5.0] ...
  
      >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]), 3, retbins=True)
      ... # doctest: +ELLIPSIS
      ([(0.994, 3.0], (5.0, 7.0], (3.0, 5.0], (3.0, 5.0], (5.0, 7.0], ...
      Categories (3, interval[float64]): [(0.994, 3.0] < (3.0, 5.0] ...
      array([0.994, 3.   , 5.   , 7.   ]))
  
      Discovers the same bins, but assign them specific labels. Notice that
      the returned Categorical's categories are `labels` and is ordered.
  
      >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]),
      ...        3, labels=["bad", "medium", "good"])
      [bad, good, medium, medium, good, bad]
      Categories (3, object): [bad < medium < good]
  
      ``labels=False`` implies you just want the bins back.
  
      >>> pd.cut([0, 1, 1, 2], bins=4, labels=False)
      array([0, 1, 1, 3])
  
      Passing a Series as an input returns a Series with categorical dtype:
  
      >>> s = pd.Series(np.array([2, 4, 6, 8, 10]),
      ...               index=['a', 'b', 'c', 'd', 'e'])
      >>> pd.cut(s, 3)
      ... # doctest: +ELLIPSIS
      a    (1.992, 4.667]
      b    (1.992, 4.667]
      c    (4.667, 7.333]
      d     (7.333, 10.0]
      e     (7.333, 10.0]
      dtype: category
      Categories (3, interval[float64]): [(1.992, 4.667] < (4.667, ...
  
      Passing a Series as an input returns a Series with mapping value.
      It is used to map numerically to intervals based on bins.
  
      >>> s = pd.Series(np.array([2, 4, 6, 8, 10]),
      ...               index=['a', 'b', 'c', 'd', 'e'])
      >>> pd.cut(s, [0, 2, 4, 6, 8, 10], labels=False, retbins=True, right=False)
      ... # doctest: +ELLIPSIS
      (a    0.0
       b    1.0
       c    2.0
       d    3.0
       e    4.0
       dtype: float64, array([0, 2, 4, 6, 8]))
  
      Use `drop` optional when bins is not unique
  
      >>> pd.cut(s, [0, 2, 4, 6, 10, 10], labels=False, retbins=True,
      ...        right=False, duplicates='drop')
      ... # doctest: +ELLIPSIS
      (a    0.0
       b    1.0
       c    2.0
       d    3.0
       e    3.0
       dtype: float64, array([0, 2, 4, 6, 8]))
  
      Passing an IntervalIndex for `bins` results in those categories exactly.
      Notice that values not covered by the IntervalIndex are set to NaN. 0
      is to the left of the first bin (which is closed on the right), and 1.5
      falls between two bins.
  
      >>> bins = pd.IntervalIndex.from_tuples([(0, 1), (2, 3), (4, 5)])
      >>> pd.cut([0, 0.5, 1.5, 2.5, 4.5], bins)
      [NaN, (0, 1], NaN, (2, 3], (4, 5]]
      Categories (3, interval[int64]): [(0, 1] < (2, 3] < (4, 5]]
      """
      # NOTE: this binning code is changed a bit from histogram for var(x) == 0
  
      # for handling the cut for datetime and timedelta objects
      x_is_series, series_index, name, x = _preprocess_for_cut(x)
      x, dtype = _coerce_to_type(x)
  
      if not np.iterable(bins):
          if is_scalar(bins) and bins < 1:
              raise ValueError("`bins` should be a positive integer.")
  
          try:  # for array-like
              sz = x.size
          except AttributeError:
              x = np.asarray(x)
              sz = x.size
  
          if sz == 0:
              raise ValueError('Cannot cut empty array')
  
          rng = (nanops.nanmin(x), nanops.nanmax(x))
          mn, mx = [mi + 0.0 for mi in rng]
  
          if np.isinf(mn) or np.isinf(mx):
              # GH 24314
              raise ValueError('cannot specify integer `bins` when input data '
                               'contains infinity')
          elif mn == mx:  # adjust end points before binning
              mn -= .001 * abs(mn) if mn != 0 else .001
              mx += .001 * abs(mx) if mx != 0 else .001
              bins = np.linspace(mn, mx, bins + 1, endpoint=True)
          else:  # adjust end points after binning
              bins = np.linspace(mn, mx, bins + 1, endpoint=True)
              adj = (mx - mn) * 0.001  # 0.1% of the range
              if right:
                  bins[0] -= adj
              else:
                  bins[-1] += adj
  
      elif isinstance(bins, IntervalIndex):
          if bins.is_overlapping:
              raise ValueError('Overlapping IntervalIndex is not accepted.')
  
      else:
          if is_datetime64tz_dtype(bins):
              bins = np.asarray(bins, dtype=_NS_DTYPE)
          else:
              bins = np.asarray(bins)
          bins = _convert_bin_to_numeric_type(bins, dtype)
  
          # GH 26045: cast to float64 to avoid an overflow
          if (np.diff(bins.astype('float64')) < 0).any():
              raise ValueError('bins must increase monotonically.')
  
      fac, bins = _bins_to_cuts(x, bins, right=right, labels=labels,
                                precision=precision,
                                include_lowest=include_lowest,
                                dtype=dtype,
                                duplicates=duplicates)
  
      return _postprocess_for_cut(fac, bins, retbins, x_is_series,
                                  series_index, name, dtype)
  
  
  def qcut(x, q, labels=None, retbins=False, precision=3, duplicates='raise'):
      """
      Quantile-based discretization function. Discretize variable into
      equal-sized buckets based on rank or based on sample quantiles. For example
      1000 values for 10 quantiles would produce a Categorical object indicating
      quantile membership for each data point.
  
      Parameters
      ----------
      x : 1d ndarray or Series
      q : integer or array of quantiles
          Number of quantiles. 10 for deciles, 4 for quartiles, etc. Alternately
          array of quantiles, e.g. [0, .25, .5, .75, 1.] for quartiles
      labels : array or boolean, default None
          Used as labels for the resulting bins. Must be of the same length as
          the resulting bins. If False, return only integer indicators of the
          bins.
      retbins : bool, optional
          Whether to return the (bins, labels) or not. Can be useful if bins
          is given as a scalar.
      precision : int, optional
          The precision at which to store and display the bins labels
      duplicates : {default 'raise', 'drop'}, optional
          If bin edges are not unique, raise ValueError or drop non-uniques.
  
          .. versionadded:: 0.20.0
  
      Returns
      -------
      out : Categorical or Series or array of integers if labels is False
          The return type (Categorical or Series) depends on the input: a Series
          of type category if input is a Series else Categorical. Bins are
          represented as categories when categorical data is returned.
      bins : ndarray of floats
          Returned only if `retbins` is True.
  
      Notes
      -----
      Out of bounds values will be NA in the resulting Categorical object
  
      Examples
      --------
      >>> pd.qcut(range(5), 4)
      ... # doctest: +ELLIPSIS
      [(-0.001, 1.0], (-0.001, 1.0], (1.0, 2.0], (2.0, 3.0], (3.0, 4.0]]
      Categories (4, interval[float64]): [(-0.001, 1.0] < (1.0, 2.0] ...
  
      >>> pd.qcut(range(5), 3, labels=["good", "medium", "bad"])
      ... # doctest: +SKIP
      [good, good, medium, bad, bad]
      Categories (3, object): [good < medium < bad]
  
      >>> pd.qcut(range(5), 4, labels=False)
      array([0, 0, 1, 2, 3])
      """
      x_is_series, series_index, name, x = _preprocess_for_cut(x)
  
      x, dtype = _coerce_to_type(x)
  
      if is_integer(q):
          quantiles = np.linspace(0, 1, q + 1)
      else:
          quantiles = q
      bins = algos.quantile(x, quantiles)
      fac, bins = _bins_to_cuts(x, bins, labels=labels,
                                precision=precision, include_lowest=True,
                                dtype=dtype, duplicates=duplicates)
  
      return _postprocess_for_cut(fac, bins, retbins, x_is_series,
                                  series_index, name, dtype)
  
  
  def _bins_to_cuts(x, bins, right=True, labels=None,
                    precision=3, include_lowest=False,
                    dtype=None, duplicates='raise'):
  
      if duplicates not in ['raise', 'drop']:
          raise ValueError("invalid value for 'duplicates' parameter, "
                           "valid options are: raise, drop")
  
      if isinstance(bins, IntervalIndex):
          # we have a fast-path here
          ids = bins.get_indexer(x)
          result = algos.take_nd(bins, ids)
          result = Categorical(result, categories=bins, ordered=True)
          return result, bins
  
      unique_bins = algos.unique(bins)
      if len(unique_bins) < len(bins) and len(bins) != 2:
          if duplicates == 'raise':
              raise ValueError("Bin edges must be unique: {bins!r}.\nYou "
                               "can drop duplicate edges by setting "
                               "the 'duplicates' kwarg".format(bins=bins))
          else:
              bins = unique_bins
  
      side = 'left' if right else 'right'
      ids = ensure_int64(bins.searchsorted(x, side=side))
  
      if include_lowest:
          ids[x == bins[0]] = 1
  
      na_mask = isna(x) | (ids == len(bins)) | (ids == 0)
      has_nas = na_mask.any()
  
      if labels is not False:
          if labels is None:
              labels = _format_labels(bins, precision, right=right,
                                      include_lowest=include_lowest,
                                      dtype=dtype)
          else:
              if len(labels) != len(bins) - 1:
                  raise ValueError('Bin labels must be one fewer than '
                                   'the number of bin edges')
          if not is_categorical_dtype(labels):
              labels = Categorical(labels, categories=labels, ordered=True)
  
          np.putmask(ids, na_mask, 0)
          result = algos.take_nd(labels, ids - 1)
  
      else:
          result = ids - 1
          if has_nas:
              result = result.astype(np.float64)
              np.putmask(result, na_mask, np.nan)
  
      return result, bins
  
  
  def _coerce_to_type(x):
      """
      if the passed data is of datetime/timedelta type,
      this method converts it to numeric so that cut method can
      handle it
      """
      dtype = None
  
      if is_datetime64tz_dtype(x):
          dtype = x.dtype
      elif is_datetime64_dtype(x):
          x = to_datetime(x)
          dtype = np.dtype('datetime64[ns]')
      elif is_timedelta64_dtype(x):
          x = to_timedelta(x)
          dtype = np.dtype('timedelta64[ns]')
  
      if dtype is not None:
          # GH 19768: force NaT to NaN during integer conversion
          x = np.where(x.notna(), x.view(np.int64), np.nan)
  
      return x, dtype
  
  
  def _convert_bin_to_numeric_type(bins, dtype):
      """
      if the passed bin is of datetime/timedelta type,
      this method converts it to integer
  
      Parameters
      ----------
      bins : list-like of bins
      dtype : dtype of data
  
      Raises
      ------
      ValueError if bins are not of a compat dtype to dtype
      """
      bins_dtype = infer_dtype(bins, skipna=False)
      if is_timedelta64_dtype(dtype):
          if bins_dtype in ['timedelta', 'timedelta64']:
              bins = to_timedelta(bins).view(np.int64)
          else:
              raise ValueError("bins must be of timedelta64 dtype")
      elif is_datetime64_dtype(dtype) or is_datetime64tz_dtype(dtype):
          if bins_dtype in ['datetime', 'datetime64']:
              bins = to_datetime(bins).view(np.int64)
          else:
              raise ValueError("bins must be of datetime64 dtype")
  
      return bins
  
  
  def _convert_bin_to_datelike_type(bins, dtype):
      """
      Convert bins to a DatetimeIndex or TimedeltaIndex if the original dtype is
      datelike
  
      Parameters
      ----------
      bins : list-like of bins
      dtype : dtype of data
  
      Returns
      -------
      bins : Array-like of bins, DatetimeIndex or TimedeltaIndex if dtype is
             datelike
      """
      if is_datetime64tz_dtype(dtype):
          bins = to_datetime(bins.astype(np.int64),
                             utc=True).tz_convert(dtype.tz)
      elif is_datetime_or_timedelta_dtype(dtype):
          bins = Index(bins.astype(np.int64), dtype=dtype)
      return bins
  
  
  def _format_labels(bins, precision, right=True,
                     include_lowest=False, dtype=None):
      """ based on the dtype, return our labels """
  
      closed = 'right' if right else 'left'
  
      if is_datetime64tz_dtype(dtype):
          formatter = partial(Timestamp, tz=dtype.tz)
          adjust = lambda x: x - Timedelta('1ns')
      elif is_datetime64_dtype(dtype):
          formatter = Timestamp
          adjust = lambda x: x - Timedelta('1ns')
      elif is_timedelta64_dtype(dtype):
          formatter = Timedelta
          adjust = lambda x: x - Timedelta('1ns')
      else:
          precision = _infer_precision(precision, bins)
          formatter = lambda x: _round_frac(x, precision)
          adjust = lambda x: x - 10 ** (-precision)
  
      breaks = [formatter(b) for b in bins]
      labels = IntervalIndex.from_breaks(breaks, closed=closed)
  
      if right and include_lowest:
          # we will adjust the left hand side by precision to
          # account that we are all right closed
          v = adjust(labels[0].left)
  
          i = IntervalIndex([Interval(v, labels[0].right, closed='right')])
          labels = i.append(labels[1:])
  
      return labels
  
  
  def _preprocess_for_cut(x):
      """
      handles preprocessing for cut where we convert passed
      input to array, strip the index information and store it
      separately
      """
      x_is_series = isinstance(x, Series)
      series_index = None
      name = None
  
      if x_is_series:
          series_index = x.index
          name = x.name
  
      # Check that the passed array is a Pandas or Numpy object
      # We don't want to strip away a Pandas data-type here (e.g. datetimetz)
      ndim = getattr(x, 'ndim', None)
      if ndim is None:
          x = np.asarray(x)
      if x.ndim != 1:
          raise ValueError("Input array must be 1 dimensional")
  
      return x_is_series, series_index, name, x
  
  
  def _postprocess_for_cut(fac, bins, retbins, x_is_series,
                           series_index, name, dtype):
      """
      handles post processing for the cut method where
      we combine the index information if the originally passed
      datatype was a series
      """
      if x_is_series:
          fac = Series(fac, index=series_index, name=name)
  
      if not retbins:
          return fac
  
      bins = _convert_bin_to_datelike_type(bins, dtype)
  
      return fac, bins
  
  
  def _round_frac(x, precision):
      """
      Round the fractional part of the given number
      """
      if not np.isfinite(x) or x == 0:
          return x
      else:
          frac, whole = np.modf(x)
          if whole == 0:
              digits = -int(np.floor(np.log10(abs(frac)))) - 1 + precision
          else:
              digits = precision
          return np.around(x, digits)
  
  
  def _infer_precision(base_precision, bins):
      """Infer an appropriate precision for _round_frac
      """
      for precision in range(base_precision, 20):
          levels = [_round_frac(b, precision) for b in bins]
          if algos.unique(levels).size == bins.size:
              return precision
      return base_precision  # default
  