public:
  explicit SqrtGradientFunction(AbstractTensorHandle* sqrt) : sqrt_(sqrt) {
    sqrt->Ref();
  }
  Status Compute(AbstractContext* ctx,
                 absl::Span<AbstractTensorHandle* const> grad_outputs,
                 absl::Span<AbstractTensorHandle*> grad_inputs) override {
    std::string name = "Sqrt_Grad";
    TF_RETURN_IF_ERROR(SqrtGrad(ctx, sqrt_.get(), grad_outputs[0],

      BigInteger plusHalfSquared = result.pow(2).add(result).shiftLeft(2).add(ONE);
      BigInteger x4 = x.shiftLeft(2);
      // sqrt(x) <= result + 0.5, so 4 * x <= (result + 0.5)^2 * 4
      // (result + 0.5)^2 * 4 = (result^2 + result)*4 + 1
      assertTrue(x4.compareTo(plusHalfSquared) <= 0);
      BigInteger minusHalfSquared = result.pow(2).subtract(result).shiftLeft(2).add(ONE);

// This decomposition is only correct inside XLA as it ignores use_locking
// attribute.
// alpha <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)
// m_t <- beta1 * m_{t-1} + (1 - beta1) * g_t
// v_t <- beta2 * v_{t-1} + (1 - beta2) * g_t * g_t
// variable <- variable - alpha * m_t / (sqrt(v_t) + epsilon)
def DecomposeResourceApplyAdamNonNesterov :
  Pattern<
    (TF_ResourceApplyAdamOp:$src_op

        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */
  @GwtIncompatible // TODO
  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);

        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */
  @GwtIncompatible // TODO
  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);

// 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_

    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(

	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.
//

	}

	// 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.

	var c float64
	// find c such that Prob(mean-c*stddev < x < mean+c*stddev)^N > .9999
	for c = 0.0; math.Pow(math.Erf(c/math.Sqrt(2)), float64(N)) < .9999; c += .1 {
	}
	c *= 11.0 // allowed slack: 40% to 60% - we don't need to be perfectly random
	mean := .5 * REP
	stddev := .5 * math.Sqrt(REP)
	low := int(mean - c*stddev)
	high := int(mean + c*stddev)
	for i := 0; i < n; i++ {
		for j := 0; j < hashSize; j++ {