// CHECK-DAG: %[[EPS_BCAST:.+]] = mhlo.constant dense<1.001000e-05> : tensor<256xf32>
  // CHECK-DAG: %[[VARIANCE_EPS:.+]] = mhlo.add %[[VARIANCE]], %[[EPS_BCAST]] : tensor<256xf32>
  // CHECK-DAG: %[[STDDEV:.+]] = mhlo.sqrt %[[VARIANCE_EPS]] : tensor<256xf32>
  // CHECK-DAG: %[[STDDEV_BCAST:.+]] = "mhlo.broadcast_in_dim"(%[[STDDEV]]) <{broadcast_dimensions = dense<1> : tensor<1xi64>}> : (tensor<256xf32>) -> tensor<4x256xf32>

//   ******@****.***

// Complex natural logarithm
//
// DESCRIPTION:
//
// Returns complex logarithm to the base e (2.718...) of
// the complex argument z.
//
// If
//       z = x + iy, r = sqrt( x**2 + y**2 ),
// then
//       w = log(r) + i arctan(y/x).
//
// The arctangent ranges from -PI to +PI.
//
// ACCURACY:
//
//                      Relative error:

// ComplexAbs is a helper type that defines an Abs method for
// complex types.
type ComplexAbs[T Complex] T

func (a ComplexAbs[T]) Abs() ComplexAbs[T] {
	r := float64(real(a))
	i := float64(imag(a))
	d := math.Sqrt(r * r + i * i)
	return ComplexAbs[T](complex(d, 0))
}

func OrderedAbsDifference[T OrderedNumeric](a, b T) T {
	return T(AbsDifference(OrderedAbs[T](a), OrderedAbs[T](b)))
}

// // complex types.
// type complexAbs[T Complex] T
//
// func (a complexAbs[T]) Abs() complexAbs[T] {
// 	r := float64(real(a))
// 	i := float64(imag(a))
// 	d := math.Sqrt(r*r + i*i)
// 	return complexAbs[T](complex(d, 0))
// }
//
// // OrderedAbsDifference returns the absolute value of the difference
// // between a and b, where a and b are of an ordered type.

// ComplexAbs is a helper type that defines an Abs method for
// complex types.
type ComplexAbs[T Complex] T

func (a ComplexAbs[T]) Abs() ComplexAbs[T] {
	r := float64(real(a))
	i := float64(imag(a))
	d := math.Sqrt(r * r + i * i)
	return ComplexAbs[T](complex(d, 0))
}

func OrderedAbsDifference[T OrderedNumeric](a, b T) T {
	return T(AbsDifference(OrderedAbs[T](a), OrderedAbs[T](b)))
}

// // complex types.
// type ComplexAbs[T Complex] T
// 
// func (a ComplexAbs[T]) Abs() ComplexAbs[T] {
// 	r := float64(real(a))
// 	i := float64(imag(a))
// 	d := math.Sqrt(r * r + i * i)
// 	return ComplexAbs[T](complex(d, 0))
// }
// 
// func OrderedAbsDifference[T OrderedNumeric](a, b T) T {
// 	return T(AbsDifference(OrderedAbs[T](a), OrderedAbs[T](b)))
// }
// 

	switch {
	case math.IsNaN(x) || math.IsInf(x, 1):
		return x
	case x < 0:
		return math.NaN()
	case x == 0:
		return math.Inf(-1)
	}

	// reduce
	f1, ki := math.Frexp(x)
	if f1 < math.Sqrt2/2 {
		f1 *= 2
		ki--
	}
	f := f1 - 1
	k := float64(ki)

	// compute
	s := float64(f / (2 + f))
	s2 := float64(s * s)
	s4 := float64(s2 * s2)

	}
	return
}

func ComplexAbs[T Complex](a T) T {
	// TODO use direct conversion instead of realimag once #50937 is fixed
	r, i := realimag(a)
	// r := float64(real(a))
	// i := float64(imag(a))
	d := math.Sqrt(r*r + i*i)
	return T(complex(d, 0))
}

// OrderedAbsDifference returns the absolute value of the difference
// between a and b, where a and b are of an ordered type.
func OrderedAbsDifference[T OrderedNumeric](a, b T) T {

  // y = a * x
  auto y = MatMul(root.WithOpName("y"), a, x);
  // y2 = y.^2
  auto y2 = Square(root, y);
  // y2_sum = sum(y2)
  auto y2_sum = Sum(root, y2, 0);
  // y_norm = sqrt(y2_sum)
  auto y_norm = Sqrt(root, y2_sum);
  // y_normalized = y ./ y_norm
  auto y_normalized = Div(root.WithOpName("y_normalized"), y, y_norm);
  Tensor out;
  test::GetTensor(root, y_normalized, &out);

}

func (a complexAbs[T]) Abs() T {
	// TODO use direct conversion instead of realimag once #50937 is fixed
	r, i := realimag(a.Value_)
	// r := float64(real(a.Value))
	// i := float64(imag(a.Value))
	d := math.Sqrt(r*r + i*i)
	return T(complex(d, 0))
}

func (a complexAbs[T]) Value() T {
	return a.Value_
}

// OrderedAbsDifference returns the absolute value of the difference