// MODEL-DEBUG: %[[f_sqrt1:.*]] = "tfl.sqrt"(%[[f_conv]]
// MODEL-DEBUG: %[[q_sqrt1:.*]] = "tfl.sqrt"(%[[dq0]]
// MODEL-DEBUG: %[[q1:.*]] = "tfl.quantize"(%[[q_sqrt1]])
// MODEL-DEBUG: %[[dq1:.*]] = "tfl.dequantize"(%[[q1]])
// MODEL-DEBUG: %[[f_sqrt2:.*]] = "tfl.sqrt"(%[[f_sqrt1]])
// MODEL-DEBUG-NOT: debug_
// MODEL-DEBUG-SAME: (tensor<?x1x1x3xf32>)
// MODEL-DEBUG: %[[q_sqrt2:.*]] = "tfl.sqrt"(%[[dq1]]
// MODEL-DEBUG-NOT: debug_

// a slash between ImportPath and # in the anchored forms.
// For example, here are some baseURL values and URLs they can generate:
//
//	"/pkg/" → "/pkg/math/#Sqrt"
//	"/pkg"  → "/pkg/math#Sqrt"
//	"/"     → "/math/#Sqrt"
//	""      → "/math#Sqrt"
func (l *DocLink) DefaultURL(baseURL string) string {
	if l.ImportPath != "" {
		slash := ""
		if strings.HasSuffix(baseURL, "/") {
			slash = "/"
		} else {

    if (!fp_type) {
      return failure();
    }

    // result = (x - mean) * scale / sqrt(variance + epsilon) + offset
    // Let multiplier = scale / sqrt(variance + epsilon), to compute
    // (x - mean) * scale / sqrt(variance + epsilon) + offset,
    // is then to compute (x * multiplier) + (offset - mean * multiplier).

    auto epsilon = materializeEpsilon(

// operations. Specifically, performs the following calculation:
//
//   (x - mean) * scale / sqrt(variance + epsilon) + offset
//
// Let multiplier = scale / sqrt(variance + epsilon),
// to compute
//   (x - mean) * scale / sqrt(variance + epsilon) + offset,
// is then to compute
//   (x * multiplier) + (offset - mean * multiplier).
//

    // CHECK: [[LR_MULTIPLY:%.*]] = "tf.Mul"([[LR]], [[GRAD]]) : (tensor<f32>, tensor<f32>) -> tensor<f32>
    // CHECK: [[SQRT:%.*]] = "tf.Sqrt"([[NEW_ACC]]) : (tensor<*xf32>) -> tensor<*xf32>
    // CHECK: [[DIVISOR:%.*]] = "tf.AddV2"([[SQRT]], [[EPSILON]]) : (tensor<*xf32>, tensor<f32>) -> tensor<*xf32>

	t0.Square(&t0)            // 2^251 - 2
	t0.Square(&t0)            // 2^252 - 4
	return v.Multiply(&t0, x) // 2^252 - 3 -> x^(2^252-3)
}

// sqrtM1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion.
var sqrtM1 = &Element{1718705420411056, 234908883556509,
	2233514472574048, 2117202627021982, 765476049583133}

// SqrtRatio sets r to the non-negative square root of the ratio of u and v.
//

	{VNEG_EQ_F64, []int{1, 0}, "VNEG", "NEGD"},
	{VABS_EQ_F32, []int{1, 0}, "VABS", "ABSF"},
	{VABS_EQ_F64, []int{1, 0}, "VABS", "ABSD"},
	{VSQRT_EQ_F32, []int{1, 0}, "VSQRT", "SQRTF"},
	{VSQRT_EQ_F64, []int{1, 0}, "VSQRT", "SQRTD"},
	{VCMP_EQ_F32, []int{1, 0}, "VCMP", "CMPF"},
	{VCMP_EQ_F64, []int{1, 0}, "VCMP", "CMPD"},
	{VCMP_E_EQ_F32, []int{1, 0}, "VCMP.E", "CMPF"},
	{VCMP_E_EQ_F64, []int{1, 0}, "VCMP.E", "CMPD"},

  // 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>

	}

	// Expect a uniform distribution of byte values, which lie in [0, 255].
	var (
		mean       = 255.0 / 2
		stddev     = 256.0 / math.Sqrt(12.0)
		errorScale = stddev / math.Sqrt(float64(n))
	)

	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}

	// Cast bytes as floats to use the common distribution-validity checks.

                const std::vector<Output>& grad_inputs,
                std::vector<Output>* grad_outputs) {
  // y = asin(x)
  // dy/dx = 1 / sqrt(1 - x^2)
  auto x2 = Square(scope, op.input(0));
  auto one = Cast(scope, Const(scope, 1.0), op.input(0).type());
  auto dydx = Reciprocal(scope, Sqrt(scope, Sub(scope, one, x2)));
  // grad(x) = grad(y) * conj(dy/dx)
  auto dx = Mul(scope, grad_inputs[0], ConjugateHelper(scope, dydx));