import numpy as np

from ..util.dtype import dtype_range, dtype_limits
from .._shared import utils


__all__ = [
    'histogram',
    'cumulative_distribution',
    'equalize_hist',
    'rescale_intensity',
    'adjust_gamma',
    'adjust_log',
    'adjust_sigmoid',
]


DTYPE_RANGE = dtype_range.copy()
DTYPE_RANGE.update((d.__name__, limits) for d, limits in dtype_range.items())
DTYPE_RANGE.update(
    {
        'uint10': (0, 2**10 - 1),
        'uint12': (0, 2**12 - 1),
        'uint14': (0, 2**14 - 1),
        'bool': dtype_range[bool],
        'float': dtype_range[np.float64],
    }
)


def _offset_array(arr, low_boundary, high_boundary):
    """Offset the array to get the lowest value at 0 if negative."""
    if low_boundary < 0:
        offset = low_boundary
        dyn_range = high_boundary - low_boundary
        # get smallest dtype that can hold both minimum and offset maximum
        offset_dtype = np.promote_types(
            np.min_scalar_type(dyn_range), np.min_scalar_type(low_boundary)
        )
        if arr.dtype != offset_dtype:
            # prevent overflow errors when offsetting
            arr = arr.astype(offset_dtype)
        arr = arr - offset
    return arr


def _bincount_histogram_centers(image, source_range):
    """Compute bin centers for bincount-based histogram."""
    if source_range not in ['image', 'dtype']:
        raise ValueError(f'Incorrect value for `source_range` argument: {source_range}')
    if source_range == 'image':
        image_min = int(image.min().astype(np.int64))
        image_max = int(image.max().astype(np.int64))
    elif source_range == 'dtype':
        image_min, image_max = dtype_limits(image, clip_negative=False)
    bin_centers = np.arange(image_min, image_max + 1)
    return bin_centers


def _bincount_histogram(image, source_range, bin_centers=None):
    """
    Efficient histogram calculation for an image of integers.

    This function is significantly more efficient than np.histogram but
    works only on images of integers. It is based on np.bincount.

    Parameters
    ----------
    image : array
        Input image.
    source_range : string
        'image' determines the range from the input image.
        'dtype' determines the range from the expected range of the images
        of that data type.

    Returns
    -------
    hist : array
        The values of the histogram.
    bin_centers : array
        The values at the center of the bins.
    """
    if bin_centers is None:
        bin_centers = _bincount_histogram_centers(image, source_range)
    image_min, image_max = bin_centers[0], bin_centers[-1]
    image = _offset_array(image, image_min, image_max)
    hist = np.bincount(image.ravel(), minlength=image_max - min(image_min, 0) + 1)
    if source_range == 'image':
        idx = max(image_min, 0)
        hist = hist[idx:]
    return hist, bin_centers


def _get_outer_edges(image, hist_range):
    """Determine the outer bin edges to use for `numpy.histogram`.

    These are obtained from either the image or hist_range.

    Parameters
    ----------
    image : ndarray
        Image for which the histogram is to be computed.
    hist_range: 2-tuple of int or None
        Range of values covered by the histogram bins. If None, the minimum
        and maximum values of `image` are used.

    Returns
    -------
    first_edge, last_edge : int
        The range spanned by the histogram bins.

    Notes
    -----
    This function is adapted from ``np.lib.histograms._get_outer_edges``.
    """
    if hist_range is not None:
        first_edge, last_edge = hist_range
        if first_edge > last_edge:
            raise ValueError("max must be larger than min in hist_range parameter.")
        if not (np.isfinite(first_edge) and np.isfinite(last_edge)):
            raise ValueError(
                f'supplied hist_range of [{first_edge}, {last_edge}] is ' f'not finite'
            )
    elif image.size == 0:
        # handle empty arrays. Can't determine hist_range, so use 0-1.
        first_edge, last_edge = 0, 1
    else:
        first_edge, last_edge = image.min(), image.max()
        if not (np.isfinite(first_edge) and np.isfinite(last_edge)):
            raise ValueError(
                f'autodetected hist_range of [{first_edge}, {last_edge}] is '
                f'not finite'
            )

    # expand empty hist_range to avoid divide by zero
    if first_edge == last_edge:
        first_edge = first_edge - 0.5
        last_edge = last_edge + 0.5

    return first_edge, last_edge


def _get_bin_edges(image, nbins, hist_range):
    """Computes histogram bins for use with `numpy.histogram`.

    Parameters
    ----------
    image : ndarray
        Image for which the histogram is to be computed.
    nbins : int
        The number of bins.
    hist_range: 2-tuple of int
        Range of values covered by the histogram bins.

    Returns
    -------
    bin_edges : ndarray
        The histogram bin edges.

    Notes
    -----
    This function is a simplified version of
    ``np.lib.histograms._get_bin_edges`` that only supports uniform bins.
    """
    first_edge, last_edge = _get_outer_edges(image, hist_range)
    # numpy/gh-10322 means that type resolution rules are dependent on array
    # shapes. To avoid this causing problems, we pick a type now and stick
    # with it throughout.
    bin_type = np.result_type(first_edge, last_edge, image)
    if np.issubdtype(bin_type, np.integer):
        bin_type = np.result_type(bin_type, float)

    # compute bin edges
    bin_edges = np.linspace(
        first_edge, last_edge, nbins + 1, endpoint=True, dtype=bin_type
    )
    return bin_edges


def _get_numpy_hist_range(image, source_range):
    if source_range == 'image':
        hist_range = None
    elif source_range == 'dtype':
        hist_range = dtype_limits(image, clip_negative=False)
    else:
        raise ValueError(f'Incorrect value for `source_range` argument: {source_range}')
    return hist_range


@utils.channel_as_last_axis(multichannel_output=False)
def histogram(
    image, nbins=256, source_range='image', normalize=False, *, channel_axis=None
):
    """Return histogram of image.

    Unlike `numpy.histogram`, this function returns the centers of bins and
    does not rebin integer arrays. For integer arrays, each integer value has
    its own bin, which improves speed and intensity-resolution.

    If `channel_axis` is not set, the histogram is computed on the flattened
    image. For color or multichannel images, set ``channel_axis`` to use a
    common binning for all channels. Alternatively, one may apply the function
    separately on each channel to obtain a histogram for each color channel
    with separate binning.

    Parameters
    ----------
    image : array
        Input image.
    nbins : int, optional
        Number of bins used to calculate histogram. This value is ignored for
        integer arrays.
    source_range : string, optional
        'image' (default) determines the range from the input image.
        'dtype' determines the range from the expected range of the images
        of that data type.
    normalize : bool, optional
        If True, normalize the histogram by the sum of its values.
    channel_axis : int or None, optional
        If None, the image is assumed to be a grayscale (single channel) image.
        Otherwise, this parameter indicates which axis of the array corresponds
        to channels.

    Returns
    -------
    hist : array
        The values of the histogram. When ``channel_axis`` is not None, hist
        will be a 2D array where the first axis corresponds to channels.
    bin_centers : array
        The values at the center of the bins.

    See Also
    --------
    cumulative_distribution

    Examples
    --------
    >>> from skimage import data, exposure, img_as_float
    >>> image = img_as_float(data.camera())
    >>> np.histogram(image, bins=2)
    (array([ 93585, 168559]), array([0. , 0.5, 1. ]))
    >>> exposure.histogram(image, nbins=2)
    (array([ 93585, 168559]), array([0.25, 0.75]))
    """
    sh = image.shape
    if len(sh) == 3 and sh[-1] < 4 and channel_axis is None:
        utils.warn(
            'This might be a color image. The histogram will be '
            'computed on the flattened image. You can instead '
            'apply this function to each color channel, or set '
            'channel_axis.'
        )

    if channel_axis is not None:
        channels = sh[-1]
        hist = []

        # compute bins based on the raveled array
        if np.issubdtype(image.dtype, np.integer):
            # here bins corresponds to the bin centers
            bins = _bincount_histogram_centers(image, source_range)
        else:
            # determine the bin edges for np.histogram
            hist_range = _get_numpy_hist_range(image, source_range)
            bins = _get_bin_edges(image, nbins, hist_range)

        for chan in range(channels):
            h, bc = _histogram(image[..., chan], bins, source_range, normalize)
            hist.append(h)
        # Convert to numpy arrays
        bin_centers = np.asarray(bc)
        hist = np.stack(hist, axis=0)
    else:
        hist, bin_centers = _histogram(image, nbins, source_range, normalize)

    return hist, bin_centers


def _histogram(image, bins, source_range, normalize):
    """

    Parameters
    ----------
    image : ndarray
        Image for which the histogram is to be computed.
    bins : int or ndarray
        The number of histogram bins. For images with integer dtype, an array
        containing the bin centers can also be provided. For images with
        floating point dtype, this can be an array of bin_edges for use by
        ``np.histogram``.
    source_range : string, optional
        'image' (default) determines the range from the input image.
        'dtype' determines the range from the expected range of the images
        of that data type.
    normalize : bool, optional
        If True, normalize the histogram by the sum of its values.
    """

    image = image.flatten()
    # For integer types, histogramming with bincount is more efficient.
    if np.issubdtype(image.dtype, np.integer):
        bin_centers = bins if isinstance(bins, np.ndarray) else None
        hist, bin_centers = _bincount_histogram(image, source_range, bin_centers)
    else:
        hist_range = _get_numpy_hist_range(image, source_range)
        hist, bin_edges = np.histogram(image, bins=bins, range=hist_range)
        bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.0

    if normalize:
        hist = hist / np.sum(hist)
    return hist, bin_centers


def cumulative_distribution(image, nbins=256):
    """Return cumulative distribution function (cdf) for the given image.

    Parameters
    ----------
    image : array
        Image array.
    nbins : int, optional
        Number of bins for image histogram.

    Returns
    -------
    img_cdf : array
        Values of cumulative distribution function.
    bin_centers : array
        Centers of bins.

    See Also
    --------
    histogram

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Cumulative_distribution_function

    Examples
    --------
    >>> from skimage import data, exposure, img_as_float
    >>> image = img_as_float(data.camera())
    >>> hi = exposure.histogram(image)
    >>> cdf = exposure.cumulative_distribution(image)
    >>> all(cdf[0] == np.cumsum(hi[0])/float(image.size))
    True
    """
    hist, bin_centers = histogram(image, nbins)
    img_cdf = hist.cumsum()
    img_cdf = img_cdf / float(img_cdf[-1])

    # cast img_cdf to single precision for float32 or float16 inputs
    cdf_dtype = utils._supported_float_type(image.dtype)
    img_cdf = img_cdf.astype(cdf_dtype, copy=False)

    return img_cdf, bin_centers


def equalize_hist(image, nbins=256, mask=None):
    """Return image after histogram equalization.

    Parameters
    ----------
    image : array
        Image array.
    nbins : int, optional
        Number of bins for image histogram. Note: this argument is
        ignored for integer images, for which each integer is its own
        bin.
    mask : ndarray of bools or 0s and 1s, optional
        Array of same shape as `image`. Only points at which mask == True
        are used for the equalization, which is applied to the whole image.

    Returns
    -------
    out : float array
        Image array after histogram equalization.

    Notes
    -----
    This function is adapted from [1]_ with the author's permission.

    References
    ----------
    .. [1] http://www.janeriksolem.net/histogram-equalization-with-python-and.html
    .. [2] https://en.wikipedia.org/wiki/Histogram_equalization

    """
    if mask is not None:
        mask = np.array(mask, dtype=bool)
        cdf, bin_centers = cumulative_distribution(image[mask], nbins)
    else:
        cdf, bin_centers = cumulative_distribution(image, nbins)
    out = np.interp(image.flat, bin_centers, cdf)
    out = out.reshape(image.shape)
    # Unfortunately, np.interp currently always promotes to float64, so we
    # have to cast back to single precision when float32 output is desired
    return out.astype(utils._supported_float_type(image.dtype), copy=False)


def intensity_range(image, range_values='image', clip_negative=False):
    """Return image intensity range (min, max) based on desired value type.

    Parameters
    ----------
    image : array
        Input image.
    range_values : str or 2-tuple, optional
        The image intensity range is configured by this parameter.
        The possible values for this parameter are enumerated below.

        'image'
            Return image min/max as the range.
        'dtype'
            Return min/max of the image's dtype as the range.
        dtype-name
            Return intensity range based on desired `dtype`. Must be valid key
            in `DTYPE_RANGE`. Note: `image` is ignored for this range type.
        2-tuple
            Return `range_values` as min/max intensities. Note that there's no
            reason to use this function if you just want to specify the
            intensity range explicitly. This option is included for functions
            that use `intensity_range` to support all desired range types.

    clip_negative : bool, optional
        If True, clip the negative range (i.e. return 0 for min intensity)
        even if the image dtype allows negative values.
    """
    if range_values == 'dtype':
        range_values = image.dtype.type

    if range_values == 'image':
        i_min = np.min(image)
        i_max = np.max(image)
    elif range_values in DTYPE_RANGE:
        i_min, i_max = DTYPE_RANGE[range_values]
        if clip_negative:
            i_min = 0
    else:
        i_min, i_max = range_values
    return i_min, i_max


def _output_dtype(dtype_or_range, image_dtype):
    """Determine the output dtype for rescale_intensity.

    The dtype is determined according to the following rules:
    - if ``dtype_or_range`` is a dtype, that is the output dtype.
    - if ``dtype_or_range`` is a dtype string, that is the dtype used, unless
      it is not a NumPy data type (e.g. 'uint12' for 12-bit unsigned integers),
      in which case the data type that can contain it will be used
      (e.g. uint16 in this case).
    - if ``dtype_or_range`` is a pair of values, the output data type will be
      ``_supported_float_type(image_dtype)``. This preserves float32 output for
      float32 inputs.

    Parameters
    ----------
    dtype_or_range : type, string, or 2-tuple of int/float
        The desired range for the output, expressed as either a NumPy dtype or
        as a (min, max) pair of numbers.
    image_dtype : np.dtype
        The input image dtype.

    Returns
    -------
    out_dtype : type
        The data type appropriate for the desired output.
    """
    if type(dtype_or_range) in [list, tuple, np.ndarray]:
        # pair of values: always return float.
        return utils._supported_float_type(image_dtype)
    if type(dtype_or_range) == type:
        # already a type: return it
        return dtype_or_range
    if dtype_or_range in DTYPE_RANGE:
        # string key in DTYPE_RANGE dictionary
        try:
            # if it's a canonical numpy dtype, convert
            return np.dtype(dtype_or_range).type
        except TypeError:  # uint10, uint12, uint14
            # otherwise, return uint16
            return np.uint16
    else:
        raise ValueError(
            'Incorrect value for out_range, should be a valid image data '
            f'type or a pair of values, got {dtype_or_range}.'
        )


def rescale_intensity(image, in_range='image', out_range='dtype'):
    """Return image after stretching or shrinking its intensity levels.

    The desired intensity range of the input and output, `in_range` and
    `out_range` respectively, are used to stretch or shrink the intensity range
    of the input image. See examples below.

    Parameters
    ----------
    image : array
        Image array.
    in_range, out_range : str or 2-tuple, optional
        Min and max intensity values of input and output image.
        The possible values for this parameter are enumerated below.

        'image'
            Use image min/max as the intensity range.
        'dtype'
            Use min/max of the image's dtype as the intensity range.
        dtype-name
            Use intensity range based on desired `dtype`. Must be valid key
            in `DTYPE_RANGE`.
        2-tuple
            Use `range_values` as explicit min/max intensities.

    Returns
    -------
    out : array
        Image array after rescaling its intensity. This image is the same dtype
        as the input image.

    Notes
    -----
    .. versionchanged:: 0.17
        The dtype of the output array has changed to match the input dtype, or
        float if the output range is specified by a pair of values.

    See Also
    --------
    equalize_hist

    Examples
    --------
    By default, the min/max intensities of the input image are stretched to
    the limits allowed by the image's dtype, since `in_range` defaults to
    'image' and `out_range` defaults to 'dtype':

    >>> image = np.array([51, 102, 153], dtype=np.uint8)
    >>> rescale_intensity(image)
    array([  0, 127, 255], dtype=uint8)

    It's easy to accidentally convert an image dtype from uint8 to float:

    >>> 1.0 * image
    array([ 51., 102., 153.])

    Use `rescale_intensity` to rescale to the proper range for float dtypes:

    >>> image_float = 1.0 * image
    >>> rescale_intensity(image_float)
    array([0. , 0.5, 1. ])

    To maintain the low contrast of the original, use the `in_range` parameter:

    >>> rescale_intensity(image_float, in_range=(0, 255))
    array([0.2, 0.4, 0.6])

    If the min/max value of `in_range` is more/less than the min/max image
    intensity, then the intensity levels are clipped:

    >>> rescale_intensity(image_float, in_range=(0, 102))
    array([0.5, 1. , 1. ])

    If you have an image with signed integers but want to rescale the image to
    just the positive range, use the `out_range` parameter. In that case, the
    output dtype will be float:

    >>> image = np.array([-10, 0, 10], dtype=np.int8)
    >>> rescale_intensity(image, out_range=(0, 127))
    array([  0. ,  63.5, 127. ])

    To get the desired range with a specific dtype, use ``.astype()``:

    >>> rescale_intensity(image, out_range=(0, 127)).astype(np.int8)
    array([  0,  63, 127], dtype=int8)

    If the input image is constant, the output will be clipped directly to the
    output range:
    >>> image = np.array([130, 130, 130], dtype=np.int32)
    >>> rescale_intensity(image, out_range=(0, 127)).astype(np.int32)
    array([127, 127, 127], dtype=int32)
    """
    if out_range in ['dtype', 'image']:
        out_dtype = _output_dtype(image.dtype.type, image.dtype)
    else:
        out_dtype = _output_dtype(out_range, image.dtype)

    imin, imax = map(float, intensity_range(image, in_range))
    omin, omax = map(
        float, intensity_range(image, out_range, clip_negative=(imin >= 0))
    )

    if np.any(np.isnan([imin, imax, omin, omax])):
        utils.warn(
            "One or more intensity levels are NaN. Rescaling will broadcast "
            "NaN to the full image. Provide intensity levels yourself to "
            "avoid this. E.g. with np.nanmin(image), np.nanmax(image).",
            stacklevel=2,
        )

    image = np.clip(image, imin, imax)

    if imin != imax:
        image = (image - imin) / (imax - imin)
        return (image * (omax - omin) + omin).astype(out_dtype)
    else:
        return np.clip(image, omin, omax).astype(out_dtype)


def _assert_non_negative(image):
    if np.any(image < 0):
        raise ValueError(
            'Image Correction methods work correctly only on '
            'images with non-negative values. Use '
            'skimage.exposure.rescale_intensity.'
        )


def _adjust_gamma_u8(image, gamma, gain):
    """LUT based implementation of gamma adjustment."""
    lut = 255 * gain * (np.linspace(0, 1, 256) ** gamma)
    lut = np.minimum(np.rint(lut), 255).astype('uint8')
    return lut[image]


def adjust_gamma(image, gamma=1, gain=1):
    """Performs Gamma Correction on the input image.

    Also known as Power Law Transform.
    This function transforms the input image pixelwise according to the
    equation ``O = I**gamma`` after scaling each pixel to the range 0 to 1.

    Parameters
    ----------
    image : ndarray
        Input image.
    gamma : float, optional
        Non negative real number. Default value is 1.
    gain : float, optional
        The constant multiplier. Default value is 1.

    Returns
    -------
    out : ndarray
        Gamma corrected output image.

    See Also
    --------
    adjust_log

    Notes
    -----
    For gamma greater than 1, the histogram will shift towards left and
    the output image will be darker than the input image.

    For gamma less than 1, the histogram will shift towards right and
    the output image will be brighter than the input image.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Gamma_correction

    Examples
    --------
    >>> from skimage import data, exposure, img_as_float
    >>> image = img_as_float(data.moon())
    >>> gamma_corrected = exposure.adjust_gamma(image, 2)
    >>> # Output is darker for gamma > 1
    >>> image.mean() > gamma_corrected.mean()
    True
    """
    if gamma < 0:
        raise ValueError("Gamma should be a non-negative real number.")

    dtype = image.dtype.type

    if dtype is np.uint8:
        out = _adjust_gamma_u8(image, gamma, gain)
    else:
        _assert_non_negative(image)

        scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])

        out = (((image / scale) ** gamma) * scale * gain).astype(dtype)

    return out


def adjust_log(image, gain=1, inv=False):
    """Performs Logarithmic correction on the input image.

    This function transforms the input image pixelwise according to the
    equation ``O = gain*log(1 + I)`` after scaling each pixel to the range
    0 to 1. For inverse logarithmic correction, the equation is
    ``O = gain*(2**I - 1)``.

    Parameters
    ----------
    image : ndarray
        Input image.
    gain : float, optional
        The constant multiplier. Default value is 1.
    inv : float, optional
        If True, it performs inverse logarithmic correction,
        else correction will be logarithmic. Defaults to False.

    Returns
    -------
    out : ndarray
        Logarithm corrected output image.

    See Also
    --------
    adjust_gamma

    References
    ----------
    .. [1] http://www.ece.ucsb.edu/Faculty/Manjunath/courses/ece178W03/EnhancePart1.pdf

    """
    _assert_non_negative(image)
    dtype = image.dtype.type
    scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])

    if inv:
        out = (2 ** (image / scale) - 1) * scale * gain
        return dtype(out)

    out = np.log2(1 + image / scale) * scale * gain
    return out.astype(dtype)


def adjust_sigmoid(image, cutoff=0.5, gain=10, inv=False):
    """Performs Sigmoid Correction on the input image.

    Also known as Contrast Adjustment.
    This function transforms the input image pixelwise according to the
    equation ``O = 1/(1 + exp*(gain*(cutoff - I)))`` after scaling each pixel
    to the range 0 to 1.

    Parameters
    ----------
    image : ndarray
        Input image.
    cutoff : float, optional
        Cutoff of the sigmoid function that shifts the characteristic curve
        in horizontal direction. Default value is 0.5.
    gain : float, optional
        The constant multiplier in exponential's power of sigmoid function.
        Default value is 10.
    inv : bool, optional
        If True, returns the negative sigmoid correction. Defaults to False.

    Returns
    -------
    out : ndarray
        Sigmoid corrected output image.

    See Also
    --------
    adjust_gamma

    References
    ----------
    .. [1] Gustav J. Braun, "Image Lightness Rescaling Using Sigmoidal Contrast
           Enhancement Functions",
           http://markfairchild.org/PDFs/PAP07.pdf

    """
    _assert_non_negative(image)
    dtype = image.dtype.type
    scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])

    if inv:
        out = (1 - 1 / (1 + np.exp(gain * (cutoff - image / scale)))) * scale
        return dtype(out)

    out = (1 / (1 + np.exp(gain * (cutoff - image / scale)))) * scale
    return out.astype(dtype)


def is_low_contrast(
    image,
    fraction_threshold=0.05,
    lower_percentile=1,
    upper_percentile=99,
    method='linear',
):
    """Determine if an image is low contrast.

    Parameters
    ----------
    image : array-like
        The image under test.
    fraction_threshold : float, optional
        The low contrast fraction threshold. An image is considered low-
        contrast when its range of brightness spans less than this
        fraction of its data type's full range. [1]_
    lower_percentile : float, optional
        Disregard values below this percentile when computing image contrast.
    upper_percentile : float, optional
        Disregard values above this percentile when computing image contrast.
    method : str, optional
        The contrast determination method.  Right now the only available
        option is "linear".

    Returns
    -------
    out : bool
        True when the image is determined to be low contrast.

    Notes
    -----
    For boolean images, this function returns False only if all values are
    the same (the method, threshold, and percentile arguments are ignored).

    References
    ----------
    .. [1] https://scikit-image.org/docs/dev/user_guide/data_types.html

    Examples
    --------
    >>> image = np.linspace(0, 0.04, 100)
    >>> is_low_contrast(image)
    True
    >>> image[-1] = 1
    >>> is_low_contrast(image)
    True
    >>> is_low_contrast(image, upper_percentile=100)
    False
    """
    image = np.asanyarray(image)

    if image.dtype == bool:
        return not ((image.max() == 1) and (image.min() == 0))

    if image.ndim == 3:
        from ..color import rgb2gray, rgba2rgb  # avoid circular import

        if image.shape[2] == 4:
            image = rgba2rgb(image)
        if image.shape[2] == 3:
            image = rgb2gray(image)

    dlimits = dtype_limits(image, clip_negative=False)
    limits = np.percentile(image, [lower_percentile, upper_percentile])
    ratio = (limits[1] - limits[0]) / (dlimits[1] - dlimits[0])

    return ratio < fraction_threshold