pytorch/torch/quantization/observer.py

from __future__ import absolute_import, division, print_function, unicode_literals

import math
import warnings
from abc import ABCMeta, abstractmethod
from functools import partial

import torch
import torch.nn as nn
from torch._jit_internal import List, Optional

def _with_args(cls_or_self, **kwargs):
    r"""Wrapper that allows creation of class factories.

    This can be useful when there is a need to create classes with the same
    constructor arguments, but different instances.

    .. Example::

        >>> Foo.with_args = classmethod(_with_args)
        >>> foo_builder = Foo.with_args(a=3, b=4).with_args(answer=42)
        >>> foo_instance1 = foo_builder()
        >>> foo_instance2 = foo_builder()
        >>> id(foo_instance1) == id(foo_instance2)
        False
    """
    class _PartialWrapper(object):
        def __init__(self, p):
            self.p = p

        def __call__(self, *args, **keywords):
            return self.p(*args, **keywords)

        def __repr__(self):
            return self.p.__repr__()

        with_args = _with_args
    r = _PartialWrapper(partial(cls_or_self, **kwargs))
    return r


ABC = ABCMeta(str("ABC"), (object,), {})  # compatible with Python 2 *and* 3:


class ObserverBase(ABC, nn.Module):
    r"""Base observer Module.
    Any observer implementation should derive from this class.

    Concrete observers should follow the same API. In forward, they will update
    the statistics of the observed Tensor. And they should provide a
    `calculate_qparams` function that computes the quantization parameters given
    the collected statistics.

    Args:
        dtype: Quantized data type
    """
    def __init__(self, dtype):
        super(ObserverBase, self).__init__()
        self.dtype = dtype

    @abstractmethod
    def forward(self, x):
        pass

    @abstractmethod
    def calculate_qparams(self, **kwargs):
        pass

    # Returns all quantization parameters that's needed
    # for a quantize function call
    # For instance, per channel obsserver will return
    # scales, zero_points and axis
    @abstractmethod
    def get_qparams(self, **kwargs):
        pass

    with_args = classmethod(_with_args)


class _ObserverBase(ObserverBase):
    r"""Internal common base for all qint/quint8 observers.

    This base is for commonly used paramters used internally.
    Users should use `~torch.quantization.observer.ObserverBase` as a base class
    for custom observers.

    Args:
        dtype: Quantized data type.
        qscheme: Quantization scheme to be used.
        reduce_range: Reduces the range of the quantized data type by 1 bit.
                      This is sometimes required to avoid instruction overflow.

    .. warning::

        :attr:`dtype` can only take ``torch.qint8`` or ``torch.quint8``.

    .. warning::

        :attr:`qscheme` can only take one of the following options:

        - ``torch.per_tensor_affine``
        - ``torch.per_tensor_symmetric``
        - ``torch.per_channel_affine``
        - ``torch.per_channel_symmetric``
    """

    def __init__(self, dtype=torch.quint8, qscheme=torch.per_tensor_affine,
                 reduce_range=False):
        super(_ObserverBase, self).__init__(dtype=dtype)
        self.qscheme = qscheme
        self.reduce_range = reduce_range

        self.eps = torch.finfo(torch.float32).eps
        assert self.qscheme in (
            torch.per_tensor_affine,
            torch.per_tensor_symmetric,
            torch.per_channel_affine,
            torch.per_channel_symmetric,
        ), "Default Observer only works for per_tensor_affine, \
                per_tensor_symmetric, per_channel_affine and \
                per_channel_symmetric quantization scheme"
        assert self.dtype in (
            torch.qint8,
            torch.quint8,
        ), "Default Observer only works for qint8 and quint8 data type"

    def _calculate_per_channel_qparams(self, min_vals, max_vals):
        # type: (Tensor, Tensor) -> Tuple[Tensor, Tensor]
        r"""Calculates the per channel quantization parameters, given min and max
        value tensors.

        Args:
            min_vals: Minimum values per channel
            max_vals: Maximum values per channel

        Returns:
            scales: Per channel scales tensor of shape (#channels,)
            zero_points: Per channel zero points tensor of shape (#channels,)
        """
        if min_vals.numel() == 0 or max_vals.numel() == 0:
            warnings.warn(
                "must run observer before calling calculate_qparams.\
                                    Returning default scale and zero point "
            )
            return torch.tensor([1.0]), torch.tensor([0])

        for i in range(len(min_vals)):
            assert (
                min_vals[i] <= max_vals[i]
            ), "min {} should be less than max {}".format(min_vals[i], max_vals[i])

        scales = torch.empty(min_vals.size(), dtype=torch.float32)
        zero_points = torch.empty(min_vals.size(), dtype=torch.int64)

        for i in range(len(scales)):
            qparam = self._calculate_qparams(
                min_vals[i], max_vals[i]
            )
            scales[i] = float(qparam[0])
            zero_points[i] = int(qparam[1])

        return scales, zero_points

    @torch.jit.export
    def _calculate_qparams(self, min_val, max_val):
        # type: (Tensor, Tensor) -> Tuple[Tensor, Tensor]
        r"""Calculates the per tensor quantization parameters, given the min/max.

        Args:
            min_val: Per tensor minimum value
            max_val: Per tensor maximum value

        Returns:
            scale: Scale as a tensor of shape (1,)
            zero_point: Zero point as a tensor of shape (1,)
        """

        if max_val.numel() == 0 or min_val.numel() == 0:
            warnings.warn("Must run observer before calling calculate_qparams.\
                           Returning default scale and zero point.")
            return torch.tensor([1.0]), torch.tensor([0])

        assert min_val <= max_val, "min {} should be less than max {}".format(
            min_val, max_val
        )

        if self.dtype == torch.qint8:
            if self.reduce_range:
                qmin, qmax = -64, 63
            else:
                qmin, qmax = -128, 127
        else:
            if self.reduce_range:
                qmin, qmax = 0, 127
            else:
                qmin, qmax = 0, 255

        max_val, min_val = float(max_val), float(min_val)
        min_val = min(0.0, min_val)
        max_val = max(0.0, max_val)
        if max_val == min_val:
            scale = 1.0
            zero_point = 0
        else:
            if self.qscheme == torch.per_tensor_symmetric or self.qscheme == torch.per_channel_symmetric:
                max_val = max(-min_val, max_val)
                scale = max_val / ((qmax - qmin) / 2)
                scale = max(scale, self.eps)
                zero_point = 0 if self.dtype == torch.qint8 else 128
            else:
                scale = (max_val - min_val) / float(qmax - qmin)
                scale = max(scale, self.eps)
                zero_point = qmin - round(min_val / scale)
                zero_point = max(qmin, zero_point)
                zero_point = min(qmax, zero_point)
                zero_point = int(zero_point)

        return torch.tensor([scale]), torch.tensor([zero_point])

    @torch.jit.export
    def get_qparams(self):
        r"""Get all quantization parameters needed for quantize call"""
        return self.calculate_qparams()

class MinMaxObserver(_ObserverBase):
    r"""Observer module for computing the quantization parameters based on the
    running min and max values.

    This observer uses the tensor min/max statistics to compute the quantization
    parameters. The module records the running minimum and maximum of incoming
    tensors, and uses this statistic to compute the quantization parameters.

    Args:
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit

    Given running min/max as :math:`x_\text{min}` and :math:`x_\text{max}`,
    scale :math:`s` and zero point :math:`z` are computed as:

    The running minimum/maximum :math:`x_\text{min/max}` is computed as:

    .. math::

        \begin{array}{ll}
        x_\text{min} &= \begin{cases}
            \min(X) & \text{if~}x_\text{min} = \text{None} \\
            \min\left(x_\text{min}, \min(X)\right) & \text{otherwise}
        \end{cases}\\
        x_\text{max} &= \begin{cases}
            \max(X) & \text{if~}x_\text{max} = \text{None} \\
            \max\left(x_\text{max}, \max(X)\right) & \text{otherwise}
        \end{cases}\\
        \end{array}

    where :math:`X` is the observed tensor.

    The scale :math:`s` and zero point :math:`z` are then computed as:

    .. math::

        \begin{aligned}
            \text{if Symmetric:}&\\
            &s = 2 \max(|x_\text{min}|, x_\text{max}) /
                \left( Q_\text{max} - Q_\text{min} \right) \\
            &z = \begin{cases}
                0 & \text{if dtype is qint8} \\
                128 & \text{otherwise}
            \end{cases}\\
            \text{Otherwise:}&\\
                &s = \left( x_\text{max} - x_\text{min}  \right ) /
                    \left( Q_\text{max} - Q_\text{min} \right ) \\
                &z = Q_\text{min} - \text{round}(x_\text{min} / s)
        \end{aligned}

    where :math:`Q_\text{min}` and :math:`Q_\text{max}` are the minimum and
    maximum of the quantized data type.

    .. warning:: Only works with ``torch.per_tensor_symmetric`` quantization scheme

    .. warning:: :attr:`dtype` can only take ``torch.qint8`` or ``torch.quint8``.

    .. note:: If the running minimum equals to the running maximum, the scale
              and zero_point are set to 1.0 and 0.
    """

    def __init__(self, dtype=torch.quint8, qscheme=torch.per_tensor_affine,
                 reduce_range=False):
        # For x86 quantized kernels, we need to ensure that the vpmaddubsw
        # instruction does not overflow. We allow for a reduce_range argument to
        # observers that reduces the quantized range to (0,127) or (-64, 63).
        # For more details see aten/src/ATen/native/quantized/cpu/qconv.cpp
        # This is not an optimal choice for non x86 backends as it loses a bit
        # of precision for activations.

        super(MinMaxObserver, self).__init__(dtype=dtype,
                                             qscheme=qscheme,
                                             reduce_range=reduce_range)
        self.register_buffer('min_val', torch.tensor([]))
        self.register_buffer('max_val', torch.tensor([]))
        if self.qscheme == torch.per_tensor_symmetric and \
           self.reduce_range and \
           self.dtype == torch.quint8:
            raise NotImplementedError("Cannot reduce range for symmetric \
                                       quantization for quint8")

    def forward(self, x_orig):
        r"""Records the running minimum and maximum of ``x``."""
        x = x_orig.detach()  # avoid keeping autograd tape
        min_val = self.min_val
        max_val = self.max_val
        if min_val.numel() == 0 or max_val.numel() == 0:
            min_val = torch.min(x)
            max_val = torch.max(x)
        else:
            min_val = torch.min(torch.min(x), min_val)
            max_val = torch.max(torch.max(x), max_val)
        self.min_val = min_val
        self.max_val = max_val
        return x_orig

    @torch.jit.export
    def calculate_qparams(self):
        r"""Calculates the quantization parameters."""
        return self._calculate_qparams(self.min_val, self.max_val)

    @torch.jit.export
    def extra_repr(self):
        return "min_val={}, max_val={}".format(self.min_val, self.max_val)

    def _save_to_state_dict(self, destination, prefix, keep_vars):
        super(MinMaxObserver, self)._save_to_state_dict(destination, prefix, keep_vars)
        destination[prefix + 'min_val'] = self.min_val
        destination[prefix + 'max_val'] = self.max_val

    def _load_from_state_dict(self, state_dict, prefix, local_metadata, strict,
                              missing_keys, unexpected_keys, error_msgs):

        local_state = ['min_val', 'max_val']
        for name in local_state:
            key = prefix + name
            if key in state_dict:
                val = state_dict[key]
                setattr(self, name, val)
            elif strict:
                missing_keys.append(key)
        super(MinMaxObserver, self)._load_from_state_dict(state_dict, prefix, local_metadata, strict,
                                                          missing_keys, unexpected_keys, error_msgs)


class MovingAverageMinMaxObserver(MinMaxObserver):
    r"""Observer module for computing the quantization parameters based on the
    moving average of the min and max values.

    This observer computes the quantization parameters based on the moving
    averages of minimums and maximums of the incoming tensors. The module
    records the average minimum and maximum of incoming tensors, and uses this
    statistic to compute the quantization parameters.

    Args:
        averaging_constant: Averaging constant for min/max.
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit

    The moving average min/max is computed as follows

    .. math::

        \begin{array}{ll}
                x_\text{min} = \begin{cases}
                    \min(X) & \text{if~}x_\text{min} = \text{None} \\
                    (1 - c) x_\text{min} + c \min(X) & \text{otherwise}
                \end{cases}\\
                x_\text{max} = \begin{cases}
                    \max(X) & \text{if~}x_\text{max} = \text{None} \\
                    (1 - c) x_\text{max} + c \max(X) & \text{otherwise}
                \end{cases}\\
        \end{array}

    where :math:`x_\text{min/max}` is the running average min/max, :math:`X` is
    is the incoming tensor, and :math:`c` is the ``averaging_constant``.

    The scale and zero point are then computed as in
    :class:`~torch.quantization.observer.MinMaxObserver`.

    .. note:: Only works with ``torch.per_tensor_affine`` quantization shceme.

    .. note:: If the running minimum equals to the running maximum, the scale
              and zero_point are set to 1.0 and 0.
    """
    def __init__(self, averaging_constant=0.01, dtype=torch.quint8,
                 qscheme=torch.per_tensor_affine, reduce_range=False):
        self.averaging_constant = averaging_constant
        super(MovingAverageMinMaxObserver, self).__init__(dtype=dtype,
                                                          qscheme=qscheme,
                                                          reduce_range=reduce_range)

    def forward(self, x_orig):
        x = x_orig.detach()  # avoid keeping autograd tape
        min_val = self.min_val
        max_val = self.max_val
        if min_val.numel() == 0 or max_val.numel() == 0:
            min_val = torch.min(x)
            max_val = torch.max(x)
        else:
            min_val = min_val + self.averaging_constant * (torch.min(x) - min_val)
            max_val = max_val + self.averaging_constant * (torch.max(x) - max_val)
        self.min_val = min_val
        self.max_val = max_val
        return x_orig


class PerChannelMinMaxObserver(_ObserverBase):
    r"""Observer module for computing the quantization parameters based on the
    running per channel min and max values.

    This observer uses the tensor min/max statistics to compute the per channel
    quantization parameters. The module records the running minimum and maximum
    of incoming tensors, and uses this statistic to compute the quantization
    parameters.

    Args:
        ch_axis: Channel axis
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit

    The quantization parameters are computed the same way as in
    :class:`~torch.quantization.observer.MinMaxObserver`, with the difference
    that the running min/max values are stored per channel.
    Scales and zero points are thus computed per channel as well.

    .. note:: If the running minimum equals to the running maximum, the scales
              and zero_points are set to 1.0 and 0.
    """

    def __init__(self, ch_axis=0, dtype=torch.quint8,
                 qscheme=torch.per_channel_affine, reduce_range=False):
        super(PerChannelMinMaxObserver, self).__init__(dtype=dtype,
                                                       qscheme=qscheme,
                                                       reduce_range=reduce_range)
        self.ch_axis = ch_axis
        self.register_buffer('min_vals', torch.tensor([]))
        self.register_buffer('max_vals', torch.tensor([]))
        if (
            self.qscheme == torch.per_channel_symmetric
            and self.reduce_range
            and self.dtype == torch.quint8
        ):
            raise NotImplementedError(
                "Cannot reduce range for symmetric quantization for quint8"
            )

    def forward(self, x_orig):
        return self._forward(x_orig)

    @torch.jit.ignore
    def _forward(self, x_orig):
        x = x_orig.detach()  # avoid keeping autograd tape
        min_vals = self.min_vals
        max_vals = self.max_vals
        x_dim = x.size()

        new_axis_list = list(range(len(x_dim)))
        new_axis_list[self.ch_axis] = 0
        new_axis_list[0] = self.ch_axis
        y = x.permute(tuple(new_axis_list))
        y = torch.flatten(y, start_dim=1)
        if min_vals.numel() == 0 or max_vals.numel() == 0:
            min_vals = torch.min(y, 1)[0]
            max_vals = torch.max(y, 1)[0]
        else:
            min_vals = torch.min(torch.min(y, 1)[0], min_vals)
            max_vals = torch.max(torch.max(y, 1)[0], max_vals)
        self.min_vals = min_vals
        self.max_vals = max_vals
        return x_orig

    @torch.jit.export
    def calculate_qparams(self):
        return self._calculate_per_channel_qparams(self.min_vals, self.max_vals)

    @torch.jit.export
    def get_qparams(self):
        scales, zero_points = self.calculate_qparams()
        return scales, zero_points, self.ch_axis

    def extra_repr(self):
        return "min_val={}, max_val={}".format(self.min_vals, self.max_vals)

    def _save_to_state_dict(self, destination, prefix, keep_vars):
        super(PerChannelMinMaxObserver, self)._save_to_state_dict(destination, prefix, keep_vars)
        destination[prefix + 'min_vals'] = self.min_vals
        destination[prefix + 'max_vals'] = self.max_vals

    def _load_from_state_dict(self, state_dict, prefix, local_metadata, strict,
                              missing_keys, unexpected_keys, error_msgs):
        local_state = ['min_vals', 'max_vals']
        for name in local_state:
            key = prefix + name
            if key in state_dict:
                val = state_dict[key]
                setattr(self, name, val)
            elif strict:
                missing_keys.append(key)
        super(PerChannelMinMaxObserver, self)._load_from_state_dict(state_dict, prefix, local_metadata, strict,
                                                                    missing_keys, unexpected_keys, error_msgs)

class MovingAveragePerChannelMinMaxObserver(PerChannelMinMaxObserver):
    r"""Observer module for computing the quantization parameters based on the
    running per channel min and max values.

    This observer uses the tensor min/max statistics to compute the per channel
    quantization parameters. The module records the running minimum and maximum
    of incoming tensors, and uses this statistic to compute the quantization
    parameters.

    Args:
        averaging_constant: Averaging constant for min/max.
        ch_axis: Channel axis
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit

    The quantization parameters are computed the same way as in
    :class:`~torch.quantization.observer.MovingAverageMinMaxObserver`, with the
    difference that the running min/max values are stored per channel.
    Scales and zero points are thus computed per channel as well.

    .. note:: If the running minimum equals to the running maximum, the scales
              and zero_points are set to 1.0 and 0.
    """

    def __init__(self, averaging_constant=0.01, ch_axis=0, dtype=torch.quint8,
                 qscheme=torch.per_channel_affine, reduce_range=False):
        super(MovingAveragePerChannelMinMaxObserver, self).__init__(
            ch_axis=ch_axis, dtype=dtype, qscheme=qscheme,
            reduce_range=reduce_range)
        self.averaging_constant = averaging_constant

    def forward(self, x_orig):
        x = x_orig.detach()  # avoid keeping autograd tape
        min_vals = self.min_vals
        max_vals = self.max_vals
        x_dim = x.size()

        new_axis_list = list(range(len(x_dim)))
        new_axis_list[self.ch_axis] = 0
        new_axis_list[0] = self.ch_axis
        y = x.permute(tuple(new_axis_list))
        y = torch.flatten(y, start_dim=1)
        if min_vals.numel() == 0 or max_vals.numel() == 0:
            min_vals = torch.min(y, 1)[0]
            max_vals = torch.max(y, 1)[0]
        else:
            min_vals = min_vals + self.averaging_constant * (torch.min(y, 1)[0] - min_vals)
            max_vals = max_vals + self.averaging_constant * (torch.max(y, 1)[0] - max_vals)
        self.min_vals = min_vals
        self.max_vals = max_vals
        return x_orig

class HistogramObserver(_ObserverBase):
    r"""
    The module records the running histogram of tensor values along with
    min/max values. ``calculate_qparams`` will calculate scale and zero_point.

    Args:
        bins: Number of bins to use for the histogram
        upsample_rate: Factor by which the histograms are upsampled, this is
                       used to interpolate histograms with varying ranges across observations
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit

    The scale and zero point are computed as follows:

    1. Create the histogram of the incoming inputs.
        The histogram is computed continuously, and the ranges per bin change
        with every new tensor observed.
    2. Search the distribution in the histogram for optimal min/max values.
        The search for the min/max values ensures the minimization of the
        quantization error with respect to the floating point model.
    3. Compute the scale and zero point the same way as in the
        :class:`~torch.quantization.MinMaxObserver`
    """

    def __init__(self, bins=2048, upsample_rate=128, dtype=torch.quint8,
                 qscheme=torch.per_tensor_affine, reduce_range=False):
        # bins: The number of bins used for histogram calculation.
        super(HistogramObserver, self).__init__(dtype=dtype,
                                                qscheme=qscheme,
                                                reduce_range=reduce_range)
        self.bins = bins
        self.register_buffer('histogram', torch.zeros(self.bins))
        self.register_buffer('min_val', torch.tensor([]))
        self.register_buffer('max_val', torch.tensor([]))
        self.dst_nbins = 2 ** torch.iinfo(self.dtype).bits
        self.upsample_rate = upsample_rate

    @torch.jit.ignore
    def _non_linear_param_search(self):
        r"""Non-linear parameter search.

        An approximation for L2 error minimization for selecting min/max.
        By selecting new min/max, we filter out outliers in input distribution.
        This follows the implementation of NormMinimization::NonlinearQuantizationParamsSearch in
        caffe2/quantization/server/norm_minimization.cc
        """
        def _get_norm(delta_begin, delta_end, density, norm_type):
            r"""
            Compute the norm of the values uniformaly distributed between
            delta_begin and delta_end.

            norm = density * (integral_{begin, end} x^2)
                 = density * (end^3 - begin^3) / 3
            """
            assert norm_type == "L2", "Only L2 norms are currently supported"
            norm = 0.0
            if norm_type == "L2":
                norm = (
                    delta_end * delta_end * delta_end
                    - delta_begin * delta_begin * delta_begin
                ) / 3
            return density * norm

        def _compute_quantization_error(next_start_bin, next_end_bin, norm_type):
            r"""
            Compute the quantization error if we use start_bin to end_bin as the
            min and max to do the quantization.
            """
            bin_width = (self.max_val.item() - self.min_val.item()) / self.bins

            norm = 0.0
            dst_bin_width = bin_width * (next_end_bin - next_start_bin + 1) / self.dst_nbins
            if dst_bin_width == 0.0:
                return 0.0
            for src_bin in range(self.bins):
                # distances from the beginning of first dst_bin to the beginning and
                # end of src_bin
                src_bin_begin = (src_bin - next_start_bin) * bin_width
                src_bin_end = src_bin_begin + bin_width

                # which dst_bins the beginning and end of src_bin belong to?
                dst_bin_of_begin = min(
                    self.dst_nbins - 1, max(0.0, math.floor(src_bin_begin / dst_bin_width))
                )
                dst_bin_of_end = min(
                    self.dst_nbins - 1, max(0.0, math.floor(src_bin_end / dst_bin_width))
                )
                dst_bin_of_begin_center = (
                    dst_bin_of_begin * dst_bin_width + dst_bin_width / 2
                )

                density = self.histogram[src_bin] / bin_width
                if dst_bin_of_begin == dst_bin_of_end:
                    # if src_bin is entirely within 1 dst_bin
                    delta_begin = src_bin_begin - dst_bin_of_begin_center
                    delta_end = src_bin_end - dst_bin_of_begin_center
                    norm = norm + _get_norm(delta_begin, delta_end, density, norm_type)
                else:
                    delta_begin = src_bin_begin - dst_bin_of_begin_center
                    delta_end = dst_bin_width / 2
                    norm = norm + _get_norm(delta_begin, delta_end, density, norm_type)

                    norm = norm + (dst_bin_of_end - dst_bin_of_begin - 1) * _get_norm(
                        -dst_bin_width / 2, dst_bin_width / 2, density, norm_type
                    )

                    dst_bin_of_end_center = (
                        dst_bin_of_end * dst_bin_width + dst_bin_width / 2
                    )

                    delta_begin = -dst_bin_width / 2
                    delta_end = src_bin_end - dst_bin_of_end_center
                    norm = norm + _get_norm(delta_begin, delta_end, density, norm_type)
            return norm

        assert self.histogram.size()[0] == self.bins, "bins mistmatch"
        bin_width = (self.max_val - self.min_val) / self.bins

        # cumulative sum
        total = sum(self.histogram)
        cSum = torch.cumsum(self.histogram, dim=0)

        stepsize = 1e-5  # granularity
        alpha = 0.0  # lower bound
        beta = 1.0  # upper bound
        start_bin = 0
        end_bin = self.bins - 1
        norm_min = float("inf")

        while alpha < beta:
            # Find the next step
            next_alpha = alpha + stepsize
            next_beta = beta - stepsize

            # find the left and right bins between the quantile bounds
            l = start_bin
            r = end_bin
            while l < end_bin and cSum[l] < next_alpha * total:
                l = l + 1
            while r > start_bin and cSum[r] > next_beta * total:
                r = r - 1

            # decide the next move
            next_start_bin = start_bin
            next_end_bin = end_bin
            if (l - start_bin) > (end_bin - r):
                # move the start bin
                next_start_bin = l
                alpha = next_alpha
            else:
                # move the end bin
                next_end_bin = r
                beta = next_beta

            if next_start_bin == start_bin and next_end_bin == end_bin:
                continue

            # calculate the quantization error using next_start_bin and next_end_bin
            norm = _compute_quantization_error(next_start_bin, next_end_bin, "L2")

            if norm > norm_min:
                break
            norm_min = norm
            start_bin = next_start_bin
            end_bin = next_end_bin

        new_min = self.min_val + bin_width * start_bin
        new_max = self.min_val + bin_width * (end_bin + 1)
        return new_min, new_max

    @torch.jit.ignore
    def _adjust_min_max(self, combined_min, combined_max, upsample_rate):
        # type: (Tensor, Tensor, int) -> Tuple[Tensor, Tensor, int, int]
        # We ensure that:
        # (combined_max - combined_min)/(downsample_rate*Nbins) = (max - min)/(upsample_rate*Nbins)
        # This allows us to have a common grid of resolution s, where we can align
        # the input histogram
        # start_idx maps min_val to the histogram bin index.

        hist_bin_width = (self.max_val - self.min_val) / (self.bins * upsample_rate)
        downsample_rate = torch.ceil((combined_max - combined_min) / (self.bins * hist_bin_width)).to(torch.int).item()
        e = downsample_rate * (self.bins * hist_bin_width) - (combined_max - combined_min)
        combined_max = combined_max + e / 2
        combined_min = combined_min - e / 2
        start_idx = torch.round((self.min_val - combined_min) / hist_bin_width).to(torch.int).item()
        return combined_min, combined_max, downsample_rate, start_idx

    @torch.jit.ignore
    def _combine_histograms(self, orig_hist, new_hist, upsample_rate, downsample_rate, start_idx, Nbins):
        # type: (Tensor, Tensor, int, int, int, int) -> Tensor
        # First up-sample the histogram with new data by a factor of L
        # This creates an approximate probability density thats piecwise constant
        upsampled_histogram = new_hist.repeat_interleave(upsample_rate)
        # Now insert the upsampled histogram into the output
        # histogram, which is initialized with zeros.
        # The offset at which the histogram is introduced is determined
        # by the start index as the output histogram can cover a wider range
        histogram_with_output_range = torch.zeros((Nbins * downsample_rate))
        histogram_with_output_range[start_idx:Nbins * upsample_rate + start_idx] = upsampled_histogram
        # Compute integral histogram, double precision is needed to ensure
        # that there are no overflows
        integral_histogram = torch.cumsum(histogram_with_output_range, 0,
                                          dtype=torch.double)[downsample_rate - 1 :: downsample_rate]
        # Finally perform interpolation
        shifted_integral_histogram = torch.zeros((Nbins))
        shifted_integral_histogram[1:Nbins] = integral_histogram[0:-1]
        interpolated_histogram = (integral_histogram - shifted_integral_histogram) / upsample_rate
        orig_hist = orig_hist + interpolated_histogram.to(torch.float)
        return orig_hist

    def forward(self, x_orig):
        # type: (Tensor) -> Tensor
        x = x_orig.detach()
        min_val = self.min_val
        max_val = self.max_val
        if min_val.numel() == 0 or max_val.numel() == 0:
            min_val = torch.min(x)
            max_val = torch.max(x)
            self.min_val = min_val
            self.max_val = max_val
            self.histogram = torch.histc(x, self.bins, min=min_val, max=max_val)
        else:
            new_min = torch.min(x)
            new_max = torch.max(x)
            combined_min = torch.min(new_min, min_val)
            combined_max = torch.max(new_max, max_val)
            # combine the existing histogram and new histogram into 1 histogram
            # We do this by first upsampling the histogram to a dense grid
            # and then downsampling the histogram efficiently
            combined_min, combined_max, downsample_rate, start_idx = \
                self._adjust_min_max(combined_min, combined_max, self.upsample_rate)
            combined_histogram = torch.histc(x, self.bins, min=combined_min, max=combined_max)
            if combined_min == min_val and combined_max == max_val:
                combined_histogram += self.histogram
            else:
                combined_histogram = self._combine_histograms(
                    combined_histogram,
                    self.histogram,
                    self.upsample_rate,
                    downsample_rate,
                    start_idx,
                    self.bins)

            self.histogram = combined_histogram
            self.min_val = combined_min
            self.max_val = combined_max
        return x

    @torch.jit.export
    def calculate_qparams(self):
        if self.min_val.numel() == 0 or self.max_val.numel() == 0:
            warnings.warn(
                "must run observer before calling calculate_qparams.\
                                    Returning default scale and zero point "
            )
            return torch.tensor([1.0]), torch.tensor([0])
        assert self.bins == len(self.histogram), (
            "The number of bins in histogram should be equal to the number of bins "
            "supplied while making this observer"
        )

        new_min, new_max = self._non_linear_param_search()

        return self._calculate_qparams(new_min, new_max)

    def _save_to_state_dict(self, destination, prefix, keep_vars):
        super(HistogramObserver, self)._save_to_state_dict(destination, prefix, keep_vars)
        destination[prefix + 'min_val'] = self.min_val
        destination[prefix + 'max_val'] = self.max_val

    def _load_from_state_dict(self, state_dict, prefix, local_metadata, strict,
                              missing_keys, unexpected_keys, error_msgs):

        local_state = ['min_val', 'max_val']
        for name in local_state:
            key = prefix + name
            if key in state_dict:
                val = state_dict[key]
                setattr(self, name, val)
            elif strict:
                missing_keys.append(key)
        super(HistogramObserver, self)._load_from_state_dict(state_dict, prefix, local_metadata, strict,
                                                             missing_keys, unexpected_keys, error_msgs)

class RecordingObserver(_ObserverBase):
    r"""
    The module is mainly for debug and records the tensor values during runtime.

    Args:
        dtype: Quantized data type
        qscheme: Quantization scheme to be used
        reduce_range: Reduces the range of the quantized data type by 1 bit
    """
    __annotations__ = {"tensor_val": List[Optional[torch.Tensor]]}

    def __init__(self, **kwargs):
        super(RecordingObserver, self).__init__(**kwargs)
        self.tensor_val = []

    def forward(self, x):
        self.tensor_val.append(x.clone())
        return x

    @torch.jit.export
    def calculate_qparams(self):
        raise Exception("calculate_qparams should not be called for RecordingObserver")

    @torch.jit.export
    def get_tensor_value(self):
        return self.tensor_val


class NoopObserver(ObserverBase):
    r"""
    Observer that doesn't do anything and just passes its configuration to the
    quantized module's ``.from_float()``.

    Primarily used for quantization to float16 which doesn't require determining
    ranges.

    Args:
        dtype: Quantized data type
    """
    def __init__(self, dtype=torch.float16):
        if dtype != torch.float16:
            raise ValueError("Only float16 quantization can be used without calibration process")
        super(NoopObserver, self).__init__(dtype=dtype)

    def forward(self, x):
        return x

    def calculate_qparams(self):
        raise Exception("calculate_qparams should not be called for NoopObserver")

    def get_qparams(self):
        return self.calculate_qparams()


# Restrict activations to be in the range (0,127)
default_observer = MinMaxObserver.with_args(reduce_range=True)
default_debug_observer = RecordingObserver
default_weight_observer = MinMaxObserver.with_args(dtype=torch.qint8, qscheme=torch.per_tensor_symmetric)
default_histogram_observer = HistogramObserver.with_args(reduce_range=True)
default_per_channel_weight_observer = PerChannelMinMaxObserver.with_args(dtype=torch.qint8, qscheme=torch.per_channel_symmetric)