def _SubGrad(op, grad):
    x = op.inputs[0]
    y = op.inputs[1]
    sx = array_ops.shape(x)
    sy = array_ops.shape(y)
    rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
    return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx), array_ops.reshape(-math_ops.reduce_sum(grad, ry), sy))

def _BetaincGrad(op, grad):
  """Returns gradient of betainc(a, b, x) with respect to x."""
  # TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
  a, b, x = op.inputs

  # two cases: x is a scalar and a/b are same-shaped tensors, or vice
  # versa; so its sufficient to check against shape(a).
  sa = array_ops.shape(a)
  sx = array_ops.shape(x)
  # pylint: disable=protected-access
  _, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
  # pylint: enable=protected-access

  # Perform operations in log space before summing, because terms
  # can grow large.
  log_beta = (
      gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b) -
      gen_math_ops.lgamma(a + b))
  partial_x = math_ops.exp((b - 1) * math_ops.log(1 - x) +
                           (a - 1) * math_ops.log(x) - log_beta)

  # TODO(b/36815900): Mark None return values as NotImplemented
  return (
      None,  # da
      None,  # db
      array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))

def _reduce_and_reshape_grad(g, t):
  """Returns the gradient, sum-reduced and reshaped to `t`'s shape."""
  shape = array_ops.shape(t)
  g_shape = array_ops.shape(g)
  # pylint: disable=protected-access
  bcast_dims, _ = gen_array_ops._broadcast_gradient_args(shape, g_shape)
  # pylint: enable=protected-access
  return array_ops.reshape(math_ops.reduce_sum(g, bcast_dims), shape)

def _DivGrad(op, grad):
  x = op.inputs[0]
  y = op.inputs[1]
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)  # pylint: disable=protected-access
  return (array_ops.reshape(math_ops.reduce_sum(grad / y, rx), sx),
          array_ops.reshape(math_ops.reduce_sum(grad *
                                         (-x / math_ops.square(y)), ry), sy))

def _ComplexGrad(op, grad):
  """Returns the real and imaginary components of 'grad', respectively."""
  x = op.inputs[0]
  y = op.inputs[1]
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  return (array_ops.reshape(math_ops.reduce_sum(math_ops.real(grad), rx), sx),
          array_ops.reshape(math_ops.reduce_sum(math_ops.imag(grad), ry), sy))

def _PowGrad(op, grad):
    """Returns grad * (y*x^(y-1), z*log(x))."""
    x = op.inputs[0]
    y = op.inputs[1]
    z = op.outputs[0]
    sx = array_ops.shape(x)
    sy = array_ops.shape(y)
    rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
    gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
    gy = array_ops.reshape(math_ops.reduce_sum(grad * z * math_ops.log(x), ry), sy)
    return gx, gy

def _MulGrad(op, grad):
  """The gradient of scalar multiplication."""
  x = op.inputs[0]
  y = op.inputs[1]
  assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  x = math_ops.conj(x)
  y = math_ops.conj(y)
  return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
          array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))

def _PowGrad(op, grad):
    """Returns grad * (y*x^(y-1), z*log(x))."""
    x = op.inputs[0]
    y = op.inputs[1]
    z = op.outputs[0]
    sx = array_ops.shape(x)
    sy = array_ops.shape(y)
    rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
    gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
    # Avoid false singularity at x = 0
    log_x = math_ops.select(x > 0, math_ops.log(x), array_ops.zeros_like(x))
    gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
    return gx, gy

def _PolygammaGrad(op, grad):
    """Returns gradient of psi(n, x) with respect to n and x."""
    # TODO(tillahoffmann): Add derivative with respect to n
    n = op.inputs[0]
    x = op.inputs[1]
    # Broadcast gradients
    sn = array_ops.shape(n)
    sx = array_ops.shape(x)
    unused_rn, rx = gen_array_ops._broadcast_gradient_args(sn, sx)
    # Evaluate gradient
    with ops.control_dependencies([grad.op]):
        partial_x = math_ops.polygamma(n + 1, x)
        return (None, array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))

def _ZetaGrad(op, grad):
    """Returns gradient of zeta(x, q) with respect to x and q."""
    # TODO(tillahoffmann): Add derivative with respect to x
    x = op.inputs[0]
    q = op.inputs[1]
    # Broadcast gradients
    sx = array_ops.shape(x)
    sq = array_ops.shape(q)
    unused_rx, rq = gen_array_ops._broadcast_gradient_args(sx, sq)
    # Evaluate gradient
    with ops.control_dependencies([grad.op]):
        partial_q = -x * math_ops.zeta(x + 1, q)
        return (None, array_ops.reshape(math_ops.reduce_sum(partial_q * grad, rq), sq))

def _IgammaGrad(op, grad):
    """Returns gradient of igamma(a, x) with respect to a and x."""
    # TODO(ebrevdo): Perhaps add the derivative w.r.t. a
    a = op.inputs[0]
    x = op.inputs[1]
    sa = array_ops.shape(a)
    sx = array_ops.shape(x)
    unused_ra, rx = gen_array_ops._broadcast_gradient_args(sa, sx)

    # Perform operations in log space before summing, because Gamma(a)
    # and Gamma'(a) can grow large.
    partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x) - math_ops.lgamma(a))
    return (None, array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))

def _MulGrad(op, grad):
  x = op.inputs[0]
  y = op.inputs[1]
  assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  if x.dtype.base_dtype == dtypes.complex64:
    return (array_ops.reshape(math_ops.reduce_sum(grad * math_ops.conj(y), rx), sx),
            array_ops.reshape(math_ops.reduce_sum(math_ops.conj(x) * grad, ry), sy))
  else:
    return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
            array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))

def _DivGrad(op, grad):
  """The gradient for the Div operator."""
  x = op.inputs[0]
  y = op.inputs[1]
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  # pylint: disable=protected-access
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  # pylint: enable=protected-access
  x = math_ops.conj(x)
  y = math_ops.conj(y)
  return (array_ops.reshape(math_ops.reduce_sum(math_ops.div(grad, y), rx), sx),
          array_ops.reshape(math_ops.reduce_sum(
              grad * math_ops.div(-x, math_ops.square(y)), ry), sy))

def _SubGrad(op, grad):
  """Gradient for Sub."""
  x = op.inputs[0]
  y = op.inputs[1]
  if (isinstance(grad, ops.Tensor) and
      _ShapesFullySpecifiedAndEqual(x, y, grad)):
    return grad, -grad
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  # pylint: disable=protected-access
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  # pylint: enable=protected-access
  return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx),
          array_ops.reshape(-math_ops.reduce_sum(grad, ry), sy))

def _FloorModGrad(op, grad):
  """Returns grad * (1, -floor(x/y))."""
  x = math_ops.conj(op.inputs[0])
  y = math_ops.conj(op.inputs[1])

  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  # pylint: disable=protected-access
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  # pylint: enable=protected-access
  floor_xy = math_ops.floor_div(x, y)
  gx = array_ops.reshape(math_ops.reduce_sum(grad, rx), sx)
  gy = array_ops.reshape(
      math_ops.reduce_sum(grad * math_ops.negative(floor_xy), ry), sy)
  return gx, gy

def _SquaredDifferenceGrad(op, grad):
  """Returns the gradient for (x-y)^2."""
  x = op.inputs[0]
  y = op.inputs[1]
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  # pylint: disable=protected-access
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  # pylint: enable=protected-access
  with ops.control_dependencies([grad]):
    # The parens ensure that if grad is IndexedSlices, it'll get multiplied by
    # Tensor (not a number like 2.0) which causes it to convert to Tensor.
    x_grad = math_ops.scalar_mul(2.0, grad) * (x - y)
  return (array_ops.reshape(math_ops.reduce_sum(x_grad, rx), sx),
          -array_ops.reshape(math_ops.reduce_sum(x_grad, ry), sy))

def _MaximumMinimumGrad(op, grad, selector_op):
  """Factor out the code for the gradient of Maximum or Minimum."""
  x = op.inputs[0]
  y = op.inputs[1]
  gdtype = grad.dtype
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  gradshape = array_ops.shape(grad)
  zeros = array_ops.zeros(gradshape, gdtype)
  xmask = selector_op(x, y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  xgrad = array_ops.where(xmask, grad, zeros)
  ygrad = array_ops.where(xmask, zeros, grad)
  gx = array_ops.reshape(math_ops.reduce_sum(xgrad, rx), sx)
  gy = array_ops.reshape(math_ops.reduce_sum(ygrad, ry), sy)
  return (gx, gy)

def _IgammaGrad(op, grad):
  """Returns gradient of igamma(a, x) with respect to x."""
  # TODO(ebrevdo): Perhaps add the derivative w.r.t. a
  a = op.inputs[0]
  x = op.inputs[1]
  sa = array_ops.shape(a)
  sx = array_ops.shape(x)
  # pylint: disable=protected-access
  unused_ra, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
  # pylint: enable=protected-access

  # Perform operations in log space before summing, because Gamma(a)
  # and Gamma'(a) can grow large.
  partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x) - math_ops.lgamma(a))
  # TODO(b/36815900): Mark None return values as NotImplemented
  return (None, array_ops.reshape(
      math_ops.reduce_sum(partial_x * grad, rx), sx))

def _MulGrad(op, grad):
  """The gradient of scalar multiplication."""
  x = op.inputs[0]
  y = op.inputs[1]
  # pylint: disable=protected-access
  if (isinstance(grad, ops.Tensor) and
      _ShapesFullySpecifiedAndEqual(x, y, grad) and
      grad.dtype in (dtypes.int32, dtypes.float32)):
    return gen_math_ops._mul(grad, y), gen_math_ops._mul(grad, x)
  assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
  sx = array_ops.shape(x)
  sy = array_ops.shape(y)
  rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
  # pylint: enable=protected-access
  x = math_ops.conj(x)
  y = math_ops.conj(y)
  return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
          array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))

def _PowGrad(op, grad):
    """Returns grad * (y*x^(y-1), z*log(x))."""
    x = op.inputs[0]
    y = op.inputs[1]
    z = op.outputs[0]
    sx = array_ops.shape(x)
    sy = array_ops.shape(y)
    rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
    gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
    # Avoid false singularity at x = 0
    if x.dtype.is_complex:
        # real(x) < 0 is fine for the complex case
        log_x = math_ops.select(math_ops.not_equal(x, 0), math_ops.log(x), array_ops.zeros_like(x))
    else:
        # There's no sensible real value to return if x < 0, so return 0
        log_x = math_ops.select(x > 0, math_ops.log(x), array_ops.zeros_like(x))
    gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
    return gx, gy