*/
      sqrt0 = sqrtApproxWithDoubles(x.shiftRight(shift)).shiftLeft(shift >> 1);
    }
    BigInteger sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    if (sqrt0.equals(sqrt1)) {
      return sqrt0;
    }
    do {
      sqrt0 = sqrt1;
      sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    } while (sqrt1.compareTo(sqrt0) < 0);
    return sqrt0;
  }

  @GwtIncompatible // TODO

       */
      sqrt0 = sqrtApproxWithDoubles(x.shiftRight(shift)).shiftLeft(shift >> 1);
    }
    BigInteger sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    if (sqrt0.equals(sqrt1)) {
      return sqrt0;
    }
    do {
      sqrt0 = sqrt1;
      sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    } while (sqrt1.compareTo(sqrt0) < 0);
    return sqrt0;
  }

  @GwtIncompatible // TODO

 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],

		{name: "NEGF", argLength: 1, reg: fp11, asm: "NEGF"},   // -arg0, float32
		{name: "NEGD", argLength: 1, reg: fp11, asm: "NEGD"},   // -arg0, float64
		{name: "SQRTD", argLength: 1, reg: fp11, asm: "SQRTD"}, // sqrt(arg0), float64
		{name: "SQRTF", argLength: 1, reg: fp11, asm: "SQRTF"}, // sqrt(arg0), float32

		{name: "MASKEQZ", argLength: 2, reg: gp21, asm: "MASKEQZ"}, // returns 0 if arg1 == 0, otherwise returns arg0

    assertThat(INTEGER_MANY_VALUES_STATS_ITERABLE.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT));
    assertThat(LONG_MANY_VALUES_STATS_ITERATOR.populationStandardDeviation())

        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));
    assertThat(longManyValuesAccumulatorByAddAllVarargs.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));

      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);

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

  /* Relies on the correctness of sqrt(int, FLOOR). */
  @GwtIncompatible // sqrt
  public void testSqrtExactMatchesFloorOrThrows() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {
      int floor = IntMath.sqrt(x, FLOOR);

// 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);