(RotateLeft64 x y) => (ROTRV x (NEGV <y.Type> y))

// unary ops
(Neg(64|32|16|8) ...) => (NEGV ...)
(Neg(32|64)F ...) => (NEG(F|D) ...)

(Com(64|32|16|8) x) => (NOR (MOVVconst [0]) x)

(Sqrt ...) => (SQRTD ...)
(Sqrt32 ...) => (SQRTF ...)

// boolean ops -- booleans are represented with 0=false, 1=true
(AndB ...) => (AND ...)
(OrB ...) => (OR ...)
(EqB x y) => (XOR (MOVVconst [1]) (XOR <typ.Bool> x y))

	res := new(statsResults)
	var sum, squaresum float64
	for _, s := range samples {
		sum += s
		squaresum += s * s
	}
	res.mean = sum / float64(len(samples))
	res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
	return res
}

func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
	t.Helper()
	actual := getStatsResults(samples)

		mean := totalFraction / float64(len(resourceToFractions))
		var sum float64
		for _, fraction := range resourceToFractions {
			sum = sum + (fraction-mean)*(fraction-mean)
		}
		std = math.Sqrt(sum / float64(len(resourceToFractions)))
	}

	// STD (standard deviation) is always a positive value. 1-deviation lets the score to be higher for node which has least deviation and

	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++ {

}

table DivOptions {
  fused_activation_function:ActivationFunctionType;
}

table TopKV2Options {
}

enum CombinerType : byte {
  SUM = 0,
  MEAN = 1,
  SQRTN = 2,
}

table EmbeddingLookupSparseOptions {
  combiner:CombinerType;
}

table GatherOptions {
  axis: int;
  // Parameters for Gather version 5 or above.
  batch_dims: int = 0;
}

    for (int exp : asList(-1022, -50, -1, 0, 1, 2, 3, 4, 100, 1022, 1023)) {
      for (RoundingMode mode : asList(HALF_EVEN, HALF_UP, HALF_DOWN)) {
        double x = Math.scalb(Math.sqrt(2) + 0.001, exp);
        double y = Math.scalb(Math.sqrt(2) - 0.001, exp);
        if (exp < 0) {
          assertEquals(exp + 1, DoubleMath.log2(x, mode));
          assertEquals(exp, DoubleMath.log2(y, mode));
        } else {

  func.return %2 : tensor<1x2xf32>

  // CHECK-DAG: %[[cst:.*]] = arith.constant dense<{{\[\[}}3.000000e+00, 4.000000e+00]]> : tensor<1x2xf32>
  // CHECK: %[[SQRT:[0-9].*]] = "tfl.sqrt"
  // CHECK: %[[RES:[0-9].*]] = tfl.add(%[[SQRT]], %[[cst]])
}

// CHECK-LABEL: fuseTileWithBinaryOp1
func.func @fuseTileWithBinaryOp1(%arg0: tensor<1x1xf32>, %arg1: tensor<1x128xf32>) -> tensor<1x128xf32> {

   *
   * @throws IllegalStateException if the dataset is empty
   */
  public double populationStandardDeviation() {
    return Math.sqrt(populationVariance());
  }

  /**
   * Returns the <a href="http://en.wikipedia.org/wiki/Variance#Sample_variance">unbiased sample

 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   if (value < 0) {
 *     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>to be replaced with the more compact
 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);

	z.neg = true // z cannot be zero if x is positive
	return z
}

// Sqrt sets z to ⌊√x⌋, the largest integer such that z² ≤ x, and returns z.
// It panics if x is negative.
func (z *Int) Sqrt(x *Int) *Int {
	if x.neg {
		panic("square root of negative number")
	}
	z.neg = false
	z.abs = z.abs.sqrt(x.abs)
	return z