size := len(x.limbs)
	xLimbs := x.limbs[:size]
	yLimbs := y.limbs[:size]

	var c uint
	for i := 0; i < size; i++ {
		_, c = bits.Sub(xLimbs[i], yLimbs[i], c)
	}
	// If there was a carry, then subtracting y underflowed, so
	// x is not greater than or equal to y.
	return not(choice(c))
}

// assign sets x <- y if on == 1, and does nothing otherwise.
//
// Both operands must have the same announced length.

	// irreducible polynomial so the result has to be reduced. The
	// irreducible polynomial is 1+x+x^2+x^7+x^128. We can subtract that to
	// eliminate the term at x^128 which also means subtracting the other
	// four terms. In characteristic 2 fields, subtraction == addition ==
	// XOR.
	if msbSet {
		double.low ^= 0xe100000000000000
	}

	return
}

var gcmReductionTable = []uint16{

	// utilization, because the GC might be executing continuously and thrashing,
	// yet the CPU utilization with respect to GOMAXPROCS will be quite low, so
	// the limiter fails to turn on. By subtracting idle time, we're removing time that
	// we know the application was idle giving a more accurate picture of whether
	// the GC is thrashing.
	//

	d -= daysPer400Years * n

	// Cut off 100-year cycles.
	// The last cycle has one extra leap year, so on the last day
	// of that year, day / daysPer100Years will be 4 instead of 3.
	// Cut it back down to 3 by subtracting n>>2.
	n = d / daysPer100Years
	n -= n >> 2
	y += 100 * n
	d -= daysPer100Years * n

	// Cut off 4-year cycles.
	// The last cycle has a missing leap year, which does not

    static final Comparator<Entry<?>> INSTANCE = new DecreasingCount();

    @Override
    public int compare(Entry<?> entry1, Entry<?> entry2) {
      return entry2.getCount() - entry1.getCount(); // subtracting two nonnegative integers
    }
  }

  /**
   * An {@link AbstractMultiset} with additional default implementations, some of them linear-time

			t.Errorf("Expected %v, actual %v", testValue, v2.String())
		}
	}
}

// TestQuantitySubZeroPreservesSuffix verifies that a suffix is preserved
// independent of the order of operations when subtracting a zero and non-zero val
func TestQuantitySubZeroPreservesSuffix(t *testing.T) {
	testValues := []string{"100m", "1Gi"}
	zero := MustParse("0")
	for _, testValue := range testValues {
		value := MustParse(testValue)

    // numerical stability, subtract each batch with their max element so that
    // the maximum input value is zero. It can be shown that softmax computed
    // after adding or subtracting all inputs in a batch using a common value
    // gives mathematically equivalent result.
    auto max_logits =
        rewriter.create<TF::MaxOp>(loc, logits, reduce_dim,

	return (x + to - 1) &^ (to - 1)
}

// splitImm24uScaled splits an immediate into a scaled 12 bit unsigned lo value
// and an unscaled shifted 12 bit unsigned hi value. These are typically used
// by adding or subtracting the hi value and using the lo value as the offset
// for a load or store.
func splitImm24uScaled(v int32, shift int) (int32, int32, error) {
	if v < 0 {

      // the gradient. Note that we save one `PadOp` and some unnecessary kernel
      // computations, compared to the `xla::AvgPoolGrad` implementation, by
      // subtracting the original exterior padding before `ReduceWindowOp`
      // instead of trimming the result of `ReduceWindowOp` (the final result is
      // the same because all strides are 1).
      low_padding[dim] =

  TF_DerivedOperandTypeAttr T = TF_DerivedOperandTypeAttr<3>;
}

def TF_ResourceApplyGradientDescentOp : TF_Op<"ResourceApplyGradientDescent", []> {
  let summary = "Update '*var' by subtracting 'alpha' * 'delta' from it.";

  let arguments = (ins
    Arg<TF_ResourceTensor, [{Should be from a Variable().}], [TF_VariableRead, TF_VariableWrite]>:$var,