auto &state = GetResultQuantState(op, res_index);
  if (state.params == params) {
    return false;
  }
  if (!state.IsEmpty()) {
    auto &rescale = GetResultRequantizeState(op, res_index);
    rescale.params = params;
    rescale.pos = RequantizeState::ON_INPUT;
    return false;
  }
  state.params = params;
  return true;
}

    RequantizeStates& rescales = GetOperandRequantizeStates(op, operand_index);
    for (RequantizeState& rescale : rescales) {
      if (rescale.params == quantized_type) {
        rescale.users.emplace_back(op, operand_index);
        return true;
      }
    }
    RequantizeState& rescale = rescales.emplace_back();
    rescale.pos = RequantizeState::ON_OUTPUT;
    rescale.params = quantized_type;

// ]
// func.func func_name_${key1}_fn (...) {
//   ...${key2}...
// }
// ```
// The above template with generate two functions by substituting `key1` and
// `key2` with given values.

module {
  // Rescales to the output scale and zero point.
  func.func private @internal_rescale_fn(%accumulation : tensor<*xi32>,
                         %input_scale : tensor<*xf32>, %input_zp : tensor<*xi32>,

		r := math.Sqrt(0.5 * imag(x))
		return complex(r, r)
	}
	a := real(x)
	b := imag(x)
	var scale float64
	// Rescale to avoid internal overflow or underflow.
	if math.Abs(a) > 4 || math.Abs(b) > 4 {
		a *= 0.25
		b *= 0.25
		scale = 2
	} else {
		a *= 1.8014398509481984e16 // 2**54
		b *= 1.8014398509481984e16
		scale = 7.450580596923828125e-9 // 2**-27
	}
	r := math.Hypot(a, b)
	var t float64
	if a > 0 {

      e.preventDefault();
    } else if (mode == TOUCHZOOM) {
      // Get two touches; new gap; rescale to ratio.
      const t1 = findTouch(e.touches, touchid);
      const t2 = findTouch(e.touches, touchid2);
      if (t1 == null || t2 == null) return;
      const gap = touchGap(t1, t2);
      rescale(initScale * gap / initGap, centerPoint);
      e.preventDefault();
    }
  }

			desiredReplicas = a.normalizeDesiredReplicasWithBehaviors(hpa, key, currentReplicas, desiredReplicas, minReplicas)
		}
		rescale = desiredReplicas != currentReplicas
	}

	if rescale {
		scale.Spec.Replicas = desiredReplicas
		_, err = a.scaleNamespacer.Scales(hpa.Namespace).Update(ctx, targetGR, scale, metav1.UpdateOptions{})
		if err != nil {

namespace mlir::quant::stablehlo {

// Checks whether an op is connected with a quantized composite function. If
// not, the same-scale op will not be quantized. This decision is based on the
// current assumption that the performance gain of the same-scale op itself
// could not beat the overhead of the quantize and dequantize routines need to
// be added around that op. When the assumption changes, this policy might

      } else {
        new_output_types.push_back(result.getType());
      }
    }

    // Remove this rescale op.
    rewriter.replaceOp(op, {pre_quantized});

    // Replace the output scale of the preceding op.
    rewriter.setInsertionPointAfter(def);
    OperationState new_state(def->getLoc(), def->getName().getStringRef(),
                             def->getOperands(), new_output_types,

      CHECK:        %[[rescale:.*]] = tfr.quant_rescale(%[[Sub]], %[[factor1]], %{{.*}}) : (!tfr.tensor, !tfr.tensor, i64) -> (!tfr.tensor)
      CHECK:        %[[attr:.*]] = tfr.constant i16 -> !tfr.attr
      CHECK:        %[[Cast:.*]] = tfr.call @tf__cast(%[[rescale]], %[[attr]], %{{.*}}) : (!tfr.tensor, !tfr.attr, i1) -> (!tfr.tensor)

  let assemblyFormat = [{
    `(` $act `,` $scale `,` $zp `)` attr-dict `:` functional-type(operands, results)
  }];
}

def TFR_TFRQuantRescaleOp : TFR_Op<"quant_rescale", [Pure]> {
  let description = [{
   The `quant_rescale` rescales the elements of the integer tensor by the
   floating-point rescale factor. This op needs to be legalized to the preferred
   operations of the backends.