mindspore/mindspore/ops/_grad/grad_math_ops.py

# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================

"""Define the grad rules of math related operations."""

from functools import reduce
import numpy as np
from .. import functional as F
from .. import operations as P
from ..operations import _grad_ops as G
from ..composite.multitype_ops.zeros_like_impl import zeros_like
from ..functional import broadcast_gradient_args, reduced_shape, tuple_div
from .grad_base import bprop_getters
from ..primitive import constexpr
from ..composite.multitype_ops import _constexpr_utils as const_utils

shape_op = P.Shape()
reduce_sum = P.ReduceSum()
reshape = P.Reshape()
tile = P.Tile()


def binop_grad_common(x, y, dx, dy):
    """
    Common grad definition for binary operations.

    The function is usually used in backprop op to reduce additional dimensions created by broadcasting.
    """
    shape_of_x = shape_op(x)
    shape_of_y = shape_op(y)
    rx = broadcast_gradient_args(shape_of_x, shape_of_y)
    # if input shape is the same as dout shape, do not need to reduce
    reduce_dx = dx
    reduce_dy = dy
    if rx[0]:
        # if dx is scalar whose shape is (), do not need reduce
        if shape_op(dx):
            dx = reduce_sum(dx, rx[0])
        reduce_dx = reshape(dx, shape_of_x)
    if rx[1]:
        # if dy is scalar whose shape is (), do not need reduce
        if shape_op(dy):
            dy = reduce_sum(dy, rx[1])
        reduce_dy = reshape(dy, shape_of_y)
    return reduce_dx, reduce_dy


def _sum_grad(x, axis, dout):
    """Grad definition for `Sum` operation."""
    # input_shape = [2, 3] axis = [1]
    input_shape = shape_op(x)
    # output_shape_kept_dims = [2, 1]
    output_shape_kept_dims = reduced_shape(input_shape, axis)
    # tile_scaling = [1, 3]
    tile_scaling = tuple_div(input_shape, output_shape_kept_dims)
    grad = reshape(dout, output_shape_kept_dims)
    return tile(grad, tile_scaling)


def _min_or_max_grad(x, axis, out, dout):
    """Grad definition for `Min` and `Max` operations."""
    # input_shape = [2, 3] axis = [1]
    input_shape = shape_op(x)
    # output_shape_kept_dims = [2, 1]
    output_shape_kept_dims = reduced_shape(input_shape, axis)
    y = reshape(out, output_shape_kept_dims)
    grad = reshape(dout, output_shape_kept_dims)
    indicators = F.cast(F.equal(y, x), F.dtype(grad))
    min_num = F.cast(F.scalar_to_array(1e-24), F.dtype(grad))
    num_selected = reshape(reduce_sum(indicators, axis), output_shape_kept_dims) + min_num
    return indicators / num_selected * grad


def _argmin_or_argmax_grad(x, axis, keep_dims, op, out, dout):
    """ArgMinWiwhValue and ArgMaxWithValue grad."""
    expand = P.ExpandDims()
    x_shape = F.shape(x)
    x_dim = len(x_shape)
    x_axis = axis
    if x_axis < 0:
        x_axis = axis + x_dim
    onehot_axis = x_axis
    depth = x_shape[x_axis]
    if keep_dims:
        dout_expand = dout[1]
        out = op(x)
    else:
        dout_expand = expand(dout[1], onehot_axis)
    if onehot_axis >= len(shape_op(out[0])):
        onehot_axis = -1
    onehot = P.OneHot(onehot_axis)
    type_x = F.dtype(x)
    on_value = F.cast(F.scalar_to_array(1.0), type_x)
    off_value = F.cast(F.scalar_to_array(0.0), type_x)
    dx = dout_expand * onehot(out[0], depth, on_value, off_value)
    return dx


@bprop_getters.register(P.MatMul)
def bprop_matmul(self):
    """Grad definition for `MatMul` operation."""
    ta = self.transpose_a
    tb = self.transpose_b
    mul1 = P.MatMul(transpose_a=(ta and tb),
                    transpose_b=(ta or (not tb)))
    mul2 = P.MatMul(transpose_a=((not ta) or tb),
                    transpose_b=(ta and tb))

    def bprop(x, w, out, dout):
        if ta:
            dx = mul1(w, dout)
        else:
            dx = mul1(dout, w)
        if tb:
            dw = mul2(dout, x)
        else:
            dw = mul2(x, dout)
        return dx, dw

    return bprop


@bprop_getters.register(P.BatchMatMul)
def bprop_batchmatmul(self):
    """Grad definition for `BatchMatMul` operation."""
    ta = self.transpose_a
    tb = self.transpose_b
    mul1 = P.BatchMatMul(transpose_a=(ta and tb),
                         transpose_b=(ta or (not tb)))
    mul2 = P.BatchMatMul(transpose_a=((not ta) or tb),
                         transpose_b=(ta and tb))

    def bprop(x, w, out, dout):
        if ta:
            dx = mul1(w, dout)
        else:
            dx = mul1(dout, w)
        if tb:
            dw = mul2(dout, x)
        else:
            dw = mul2(x, dout)
        return dx, dw

    return bprop


@bprop_getters.register(P.TensorAdd)
def get_bprop_tensor_add(self):
    """Grad definition for `TensorAdd` operation."""

    def bprop(x, y, out, dout):
        return binop_grad_common(x, y, dout, dout)

    return bprop


@bprop_getters.register(P.Neg)
def get_bprop_neg(self):
    """Grad definition for `Neg` operation."""
    neg_grad = P.Neg()

    def bprop(x, out, dout):
        dx = neg_grad(dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.Sub)
def get_bprop_sub(self):
    """Grad definition for `Sub` operation."""
    neg_func = P.Neg()

    def bprop(x, y, out, dout):
        return binop_grad_common(x, y, dout, neg_func(dout))

    return bprop


@bprop_getters.register(P.Mul)
def get_bprop_mul(self):
    """Grad definition for `Mul` operation."""
    mul_func = P.Mul()

    def bprop(x, y, out, dout):
        bc_dx = mul_func(y, dout)
        bc_dy = mul_func(x, dout)
        return binop_grad_common(x, y, bc_dx, bc_dy)

    return bprop


@bprop_getters.register(P.RealDiv)
def get_bprop_real_div(self):
    """Grad definition for `RealDiv` operation."""
    div_op = P.RealDiv()
    neg = P.Neg()
    mul_op = P.Mul()

    def bprop(x, y, out, dout):
        bc_x = div_op(dout, y)
        bc_y = neg(mul_op(bc_x, out))
        return binop_grad_common(x, y, bc_x, bc_y)

    return bprop


@bprop_getters.register(P.Div)
def get_bprop_div(self):
    """Grad definition for `Div` operation."""
    div_op = P.Div()
    neg = P.Neg()
    mul_op = P.Mul()

    def bprop(x, y, out, dout):
        bc_x = div_op(dout, y)
        bc_y = neg(mul_op(bc_x, out))
        return binop_grad_common(x, y, bc_x, bc_y)

    return bprop


@bprop_getters.register(P.DivNoNan)
def get_bprop_div_no_nan(self):
    """Grad definition for `DivNoNan` operation."""
    div_no_nan_op = P.DivNoNan()
    neg = P.Neg()
    mul_op = P.Mul()

    def bprop(x, y, out, dout):
        bc_x = div_no_nan_op(dout, y)
        bc_y = neg(mul_op(bc_x, out))
        return binop_grad_common(x, y, bc_x, bc_y)

    return bprop


@bprop_getters.register(P.Floor)
def get_bprop_floor(self):
    """Grad definition for `floor` operation."""
    fill_ = P.Fill()
    shape_ = P.Shape()
    dtype_ = P.DType()

    def bprop(x, out, dout):
        bc_x = fill_(dtype_(x), shape_(x), 0.)
        return (bc_x,)

    return bprop


@bprop_getters.register(P.FloorDiv)
def get_bprop_floordiv(self):
    """Grad definition for `FloorDiv` operation."""
    div_op = P.FloorDiv()
    neg = P.Neg()
    mul_op = P.Mul()

    def bprop(x, y, out, dout):
        bc_x = div_op(dout, y)
        bc_y = neg(mul_op(bc_x, out))
        return binop_grad_common(x, y, bc_x, bc_y)

    return bprop


@bprop_getters.register(P.FloorMod)
def get_bprop_floormod(self):
    """Grad definition for `FloorMod` operation."""

    def bprop(x, y, out, dout):
        bc_x = dout
        bc_y = -dout * (x // y)
        return binop_grad_common(x, y, bc_x, bc_y)

    return bprop


@bprop_getters.register(P.Square)
def get_bprop_square(self):
    """Grad definition for `Square` operation."""
    mul_func = P.Mul()
    fill_func = P.Fill()
    dtype = P.DType()

    def bprop(x, out, dout):
        temp = mul_func(dout, x)
        dx = mul_func(fill_func(dtype(temp), shape_op(x), 2.0), temp)
        return (dx,)

    return bprop


@bprop_getters.register(P.Sqrt)
def get_bprop_sqrt(self):
    """Grad definition for `Sqrt` operation."""
    mul_func = P.Mul()
    fill_func = P.Fill()
    div_op = P.RealDiv()
    sqrt = P.Sqrt()
    dtype = P.DType()

    def bprop(x, out, dout):
        temp = div_op(fill_func(dtype(x), shape_op(x), 0.5), sqrt(x))
        dx = mul_func(dout, temp)
        return (dx,)

    return bprop


@bprop_getters.register(P.Rsqrt)
def get_bprop_rsqrt(self):
    """Grad definition for `Rsqrt` operation."""

    def bprop(x, out, dout):
        grad = F.fill(F.dtype(x), F.shape(x), -0.5) / (F.sqrt(x) * x)
        dx = dout * grad
        return (dx,)

    return bprop


@bprop_getters.register(P.Reciprocal)
def get_bprop_reciprocal(self):
    """Grad definition for `Reciprocal` operation."""
    neg = P.Neg()
    mul = P.Mul()
    square = P.Square()
    reciprocal = P.Reciprocal()

    def bprop(x, out, dout):
        g = neg(reciprocal(square(x)))
        dx = mul(dout, g)
        return (dx,)

    return bprop


@bprop_getters.register(P.Log)
def get_bprop_log(self):
    """Grad definition for `Log` operation."""
    reciprocal = P.Reciprocal()

    def bprop(x, out, dout):
        g = reciprocal(x)
        dx = g * dout
        return dx, 0

    return bprop


@bprop_getters.register(P.Log1p)
def get_bprop_log1p(self):
    """Grad definition for `Log1p` operation."""
    reciprocal = P.Reciprocal()

    def bprop(x, out, dout):
        x_1p = x + 1
        g = reciprocal(x_1p)
        dx = g * dout
        return dx, 0

    return bprop


@bprop_getters.register(P.Erf)
def get_bprop_erf(self):
    """Grad definition for `Erf` operation."""
    exp = P.Exp()
    square = P.Square()
    sqrt = P.Sqrt()
    cast = P.Cast()
    dtype = P.DType()

    def bprop(x, out, dout):
        half_root_pi = cast(2 / sqrt(F.scalar_to_tensor(np.pi)), dtype(x))
        x_square = square(x)
        dx = dout * half_root_pi * exp(-x_square)
        return (dx,)

    return bprop


@bprop_getters.register(P.Erfc)
def get_bprop_erfc(self):
    """Grad definition for `Erfc` operation."""
    exp = P.Exp()
    square = P.Square()
    sqrt = P.Sqrt()
    cast = P.Cast()
    dtype = P.DType()

    def bprop(x, out, dout):
        half_root_pi = cast(2 / sqrt(F.scalar_to_tensor(np.pi)), dtype(x))
        x_square = square(x)
        dx = dout * (-half_root_pi * exp(-x_square))
        return (dx,)
    return bprop


@bprop_getters.register(P.Pow)
def get_bprop_pow(self):
    """Grad definition for `Pow` operation."""
    pow_op = P.Pow()
    ln = P.Log()

    def bprop(x, power, out, dout):
        bc_dx = power * pow_op(x, power - 1.0) * dout
        bc_dpower = out * ln(x) * dout
        return binop_grad_common(x, power, bc_dx, bc_dpower)

    return bprop


@bprop_getters.register(P.Exp)
def get_bprop_exp(self):
    """Grad definition for `Exp` operation."""
    exp_ = P.Exp()

    def bprop(x, out, dout):
        g = exp_(x)
        dx = g * dout
        return (dx,)

    return bprop


@bprop_getters.register(P.Expm1)
def get_bprop_expm1(self):
    """Grad definition for `Expm1` operation."""
    exp_ = P.Exp()

    def bprop(x, out, dout):
        g = exp_(x)
        dx = g * dout
        return (dx,)

    return bprop


@bprop_getters.register(P.Minimum)
def get_bprop_minimum(self):
    """Grad definition for `Minimum` operation."""
    input_grad = G.MinimumGrad()

    def bprop(x, y, out, dout):
        dx, dy = input_grad(x, y, dout)
        return dx, dy

    return bprop


@bprop_getters.register(P.Maximum)
def get_bprop_maximum(self):
    """Grad definition for `Maximum` operation."""
    input_grad = G.MaximumGrad()

    def bprop(x, y, out, dout):
        dx, dy = input_grad(x, y, dout)
        return dx, dy

    return bprop


@bprop_getters.register(P.ReduceSum)
def get_bprop_reducesum(self):
    """Grad definition for `ReduceSum` operation."""

    def bprop(x, axis, out, dout):
        dx = _sum_grad(x, axis, dout)
        return dx, zeros_like(axis)

    return bprop


@bprop_getters.register(P.CumSum)
def get_bprop_cumsum(self):
    """Grad definition for `CumSum` operation."""
    cumsum = P.CumSum(exclusive=self.exclusive, reverse=not self.reverse)

    def bprop(x, axis, out, dout):
        return cumsum(dout, axis), zeros_like(axis)

    return bprop


@constexpr
def _split_shape_index(input_shape, axis):
    """Calculate reduce_prod grad transpose indices and perm shape."""
    rank = len(input_shape)
    if isinstance(axis, int):
        axis = tuple([axis])
    reduction_indices = tuple([(i + rank) % rank for i in axis])
    other_indices = tuple(set(range(rank)) - set(reduction_indices))
    reduced_num = reduce(lambda x, y: x * y, [1] + [input_shape[i] for i in reduction_indices])
    other_num = reduce(lambda x, y: x * y, [1] + [input_shape[i] for i in other_indices])
    perm = reduction_indices + other_indices
    return tuple([reduced_num, other_num]), perm


@constexpr
def _invert_permutation(perm):
    """Calculate invert permutation."""
    out = [0] * len(perm)
    for i, value in enumerate(perm):
        out[value] = i
    return tuple(out)


@bprop_getters.register(P.ReduceProd)
def get_bprop_reduceprod(self):
    """Grad definition for `ReduceProd` operation."""
    transpose = P.Transpose()
    left_cumprod = P.CumProd(exclusive=True)
    right_cumprod = P.CumProd(exclusive=True, reverse=True)

    def bprop(x, axis, out, dout):
        """Grad definition for `Product` operation."""
        # Expand dout to full input shape
        input_shape = shape_op(x)
        output_shape_kept_dims = reduced_shape(input_shape, axis)
        dout = reshape(dout, output_shape_kept_dims)
        tile_scaling = tuple_div(input_shape, output_shape_kept_dims)
        grad = tile(dout, tile_scaling)

        # Pack all reduced dimensions into a single one, so we can perform the cumprod ops.
        pack_shape, perm = _split_shape_index(input_shape, axis)
        permuted = transpose(x, perm)
        permuted_shape = shape_op(permuted)
        reshaped = reshape(permuted, pack_shape)

        # Calculate product, leaving out the current entry
        left = left_cumprod(reshaped, 0)
        right = right_cumprod(reshaped, 0)
        y = reshape(left * right, permuted_shape)

        # Invert the transpose and reshape operations.
        # Make sure to set the statically known shape information through a reshape.
        out = transpose(y, _invert_permutation(perm)) * grad
        dx = reshape(out, input_shape)
        return dx, zeros_like(axis)

    return bprop


@bprop_getters.register(P.CumProd)
def get_bprop_cumprod(self):
    """Grad definition for `CumProd` operation."""
    cumprod = P.CumProd(exclusive=self.exclusive, reverse=self.reverse)
    cumsum = P.CumSum(exclusive=self.exclusive, reverse=not self.reverse)

    def bprop(x, axis, out, dout):
        """Grad definition for `Product` operation."""
        # This will fails when x contains 0
        prod = cumprod(x, axis)
        out = cumsum(prod * dout, axis)
        return out / x, zeros_like(axis)

    return bprop


@bprop_getters.register(P.ReduceAll)
def get_bprop_reduceall(self):
    """Grad definition for `ReduceAll` operation."""

    def bprop(x, axis, out, dout):
        return zeros_like(x), zeros_like(axis)

    return bprop


@bprop_getters.register(P.ReduceMax)
def get_bprop_reducemax(self):
    """Grad definition for `Max` operation."""

    def bprop(x, axis, out, dout):
        dx = _min_or_max_grad(x, axis, out, dout)
        return (dx, zeros_like(axis))

    return bprop


@bprop_getters.register(P.ArgMaxWithValue)
def get_bprop_argmaxwithvalue(self):
    """Grad definition for `ArgMaxWithValue` operation."""
    axis = self.axis
    keep_dims = self.keep_dims
    op = P.ArgMaxWithValue(axis)

    def bprop(x, out, dout):
        dx = _argmin_or_argmax_grad(x, axis, keep_dims, op, out, dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.ReduceMin)
def get_bprop_reducemin(self):
    """Grad definition for `ReduceMin` operation."""

    def bprop(x, axis, out, dout):
        dx = _min_or_max_grad(x, axis, out, dout)
        return (dx, zeros_like(axis))

    return bprop


@bprop_getters.register(P.ArgMinWithValue)
def get_bprop_argminwithvalue(self):
    """Generate bprop for ArgMinWithValue"""
    axis = self.axis
    keep_dims = self.keep_dims
    op = P.ArgMinWithValue(axis)

    def bprop(x, out, dout):
        dx = _argmin_or_argmax_grad(x, axis, keep_dims, op, out, dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.ReduceMean)
def get_bprop_reduce_mean(self):
    """Grad definition for `ReduceMean` operation."""
    div_op = P.RealDiv()
    cast = P.Cast()
    dtype = P.DType()

    def bprop(x, axis, out, dout):
        grad = _sum_grad(x, axis, dout)
        div_shape = F.shape_mul(shape_op(x)) / F.shape_mul(shape_op(out))
        dx = div_op(grad, cast(F.scalar_to_array(div_shape), dtype(grad)))
        return dx, zeros_like(axis)

    return bprop


@bprop_getters.register(P.Equal)
def get_bprop_equal(self):
    """Grad definition for `Equal` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.NotEqual)
def get_bprop_not_equal(self):
    """Grad definition for `NotEqual` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.Greater)
def get_bprop_greater(self):
    """Grad definition for `Greater` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.GreaterEqual)
def get_bprop_greater_equal(self):
    """Grad definition for `GreaterEqual` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.Less)
def get_bprop_less(self):
    """Grad definition for `Less` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.LessEqual)
def get_bprop_less_equal(self):
    """Grad definition for `LessEqual` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.LogicalNot)
def get_bprop_logical_not(self):
    """Grad definition for `LogicalNot` operation."""

    def bprop(x, out, dout):
        return (zeros_like(x),)

    return bprop


@bprop_getters.register(P.LogicalAnd)
def get_bprop_logical_and(self):
    """Grad definition for `LogicalAnd` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.LogicalOr)
def get_bprop_logical_or(self):
    """Grad definition for `LogicalOr` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.NPUAllocFloatStatus)
def get_bprop_npu_alloc_float_status(self):
    """Grad definition for `NPUAllocFloatStatus` operation."""

    def bprop(out, dout):
        return ()

    return bprop


@bprop_getters.register(P.NPUGetFloatStatus)
def get_bprop_npu_get_float_status(self):
    """Grad definition for `NPUGetFloatStatus` operation."""

    def bprop(x, out, dout):
        return (zeros_like(x),)

    return bprop


@bprop_getters.register(P.NPUClearFloatStatus)
def get_bprop_npu_clear_float_status(self):
    """Grad definition for `NPUClearFloatStatus` operation."""

    def bprop(x, out, dout):
        return (zeros_like(x),)

    return bprop


@bprop_getters.register(P.AssignAdd)
def get_bprop_assign_add(self):
    """Grad definition for `AssignAdd` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.AssignSub)
def get_bprop_assign_sub(self):
    """Grad definition for `AssignSub` operation."""

    def bprop(x, y, out, dout):
        return zeros_like(x), zeros_like(y)

    return bprop


@bprop_getters.register(P.Sin)
def get_bprop_sin(self):
    """Grad definition for `Sin` operation."""
    cos = P.Cos()

    def bprop(x, out, dout):
        dx = dout * cos(x)
        return (dx,)

    return bprop


@bprop_getters.register(P.Asin)
def get_bprop_asin(self):
    """Grad definition for `Asin` operation."""
    input_grad = G.AsinGrad()

    def bprop(x, out, dout):
        dx = input_grad(x, dout)
        return (dx,)
    return bprop


@bprop_getters.register(P.Asinh)
def get_bprop_asinh(self):
    """Grad definition for `Asinh` operation."""
    input_grad = G.AsinhGrad()

    def bprop(x, out, dout):
        dx = input_grad(out, dout)
        return (dx,)
    return bprop


@bprop_getters.register(P.Sinh)
def get_bprop_sinh(self):
    """Grad definition for `Sinh` operation."""
    cosh = P.Cosh()

    def bprop(x, out, dout):
        dx = cosh(x) * dout
        return (dx,)

    return bprop


@bprop_getters.register(P.Cos)
def get_bprop_cos(self):
    """Grad definition for `Cos` operation."""
    sin = P.Sin()
    neg = P.Neg()

    def bprop(x, out, dout):
        dx = dout * neg(sin(x))
        return (dx,)

    return bprop


@bprop_getters.register(P.ACos)
def get_bprop_acos(self):
    """Grad definition for `ACos` operation."""
    input_grad = G.ACosGrad()

    def bprop(x, out, dout):
        dx = input_grad(x, dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.Acosh)
def get_bprop_acosh(self):
    """Grad definition for `Acosh` operation."""
    input_grad = G.AcoshGrad()

    def bprop(x, out, dout):
        dx = input_grad(out, dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.Cosh)
def get_bprop_cosh(self):
    """Grad definition for `Cosh` operation."""
    sinh = P.Sinh()

    def bprop(x, out, dout):
        dx = sinh(x) * dout
        return (dx,)

    return bprop


@bprop_getters.register(P.Abs)
def get_bprop_abs(self):
    """Grad definition for `Abs` operation."""
    abs_grad = G.AbsGrad()

    def bprop(x, out, dout):
        dx = abs_grad(x, dout)
        return (dx,)

    return bprop


@bprop_getters.register(P.ScalarCast)
def get_bprop_scalar_cast(self):
    """Generate bprop for ScalarCast"""

    def bprop(x, t, out, dout):
        return F.scalar_cast(dout, F.typeof(x)), zeros_like(t)

    return bprop


@bprop_getters.register(P.AddN)
def get_bprop_scalar_addn(self):
    """Generate bprop for AddN"""

    def bprop(x, out, dout):
        dx = ()
        for _ in range(len(x)):
            dx = dx + (dout,)
        return dx

    return bprop


@bprop_getters.register(P.Sign)
def get_bprop_sign(self):
    """Generate bprop for Sign"""

    def bprop(x, out, dout):
        return (zeros_like(x),)

    return bprop


@bprop_getters.register(P.Round)
def get_bprop_round(self):
    """Generate bprop for Round"""

    def bprop(x, out, dout):
        return (zeros_like(x),)

    return bprop


@bprop_getters.register(P.Atan2)
def get_bprop_atan2(self):
    """Generate bprop for Atan2"""

    square = P.Square()

    def bprop(x, y, out, dout):
        tmp = dout / (square(x) + square(y))
        bc_dx = tmp * y
        bc_dy = tmp * (-x)
        return binop_grad_common(x, y, bc_dx, bc_dy)

    return bprop


@bprop_getters.register(P.BesselI0e)
def get_bprop_bessel_i0e(self):
    """Generate bprop for BesselI0e"""
    sign = P.Sign()
    bessel_i1e = P.BesselI1e()

    def bprop(x, out, dout):
        dx = dout * (bessel_i1e(x) - sign(x) * out)
        return (dx,)
    return bprop


@bprop_getters.register(P.Atan)
def get_bprop_atan(self):
    """Grad definition for `Atan` operation."""
    input_grad = G.AtanGrad()

    def bprop(x, out, dout):
        dx = input_grad(x, dout)
        return (dx,)
    return bprop


@bprop_getters.register(P.BesselI1e)
def get_bprop_bessel_i1e(self):
    """Generate bprop for BesselI1e"""

    sign = P.Sign()
    bessel_i0e = P.BesselI0e()
    less = P.Less()
    select = P.Select()
    reciprocal = P.Reciprocal()
    cast = P.Cast()
    dtype = P.DType()

    def bprop(x, out, dout):
        zeros = zeros_like(x)
        np_eps = const_utils.get_np_eps(dtype(x))
        eps = cast(np_eps, dtype(x))
        x_is_valid = less(eps, x)
        x_safe = select(x_is_valid, x, eps + zeros)
        tmp = bessel_i0e(x_safe) - out * (sign(x) + reciprocal(x_safe))
        dx = select(x_is_valid, tmp, 0.5 + zeros)
        return (dx,)
    return bprop


@bprop_getters.register(P.Atanh)
def get_bprop_atanh(self):
    """Grad definition for `Atanh` operation."""
    power = P.Pow()
    div = P.Div()

    def bprop(x, out, dout):
        tmp = 1 - power(x, 2)
        dx = div(1, tmp) * dout
        return (dx,)
    return bprop