// element of 'x_data' (positively and negatively) by 'delta', and
    // updating the jacobian with the centered difference. When x_data is
    // complex-valued, we perturb its real and complex parts separately.
    for (int r = 0; r < x_size; ++r) {
      int unit_dimension = 0;
      for (X_T unit : BaseUnitsForType<X_T>::values()) {
        X_T x_delta = unit * X_T{delta};
        // Store current value of 'x' at 'r'.

			// Put a blank line between the current and new blocks, so that the end
			// of a file acts as a blank line.
			lastLine := lastBlock(doc).Pos().EndLine
			delta := lastLine + 2 - newdoc.Blocks[0].Pos().StartLine
			for _, b := range newdoc.Blocks {
				addLines(b, delta)
			}
		}
		// Append non-empty blocks to the result document.
		for _, b := range newdoc.Blocks {
			if _, ok := b.(*md.Empty); !ok {

  TF_EXPECT_OK(CompileWithComputation(function_to_hlo_args).status());

  Histogram histogram =
      compilation_time.Delta("graph_old_bridge_has_function_to_hlo");

  EXPECT_EQ(histogram.num(), 1);
  EXPECT_EQ(compilation_status.Delta("kOldBridgeNoMlirSuccess"), 1);
}

TEST_F(CompileTFGraphTest, SuccessfullyCompilesWithManualSharding) {
  // MLIR module from failing test.

// What remains is to choose e.
// Let m = 2^e/c + delta, 0 <= delta < 1
//   ⎣x * (2^e/c + delta) / 2^e⎦
//   ⎣x / c + x * delta / 2^e⎦
// We must have x * delta / 2^e < 1/c so that this
// additional term never rounds differently than ⎣x / c⎦ does.
// Rearranging,
//   2^e > x * delta * c
// x can be at most 2^n-1 and delta can be at most 1.
// So it is sufficient to have 2^e >= 2^n*c.

// DeltaDiscoveryStream is a server interface for Delta XDS.
type DeltaDiscoveryStream = discovery.AggregatedDiscoveryService_DeltaAggregatedResourcesServer

// DiscoveryClient is a client interface for XDS.
type DiscoveryClient = discovery.AggregatedDiscoveryService_StreamAggregatedResourcesClient

// DeltaDiscoveryClient is a client interface for Delta XDS.

  }

  private static Function<Integer, Integer> add(final int delta) {
    return new Function<Integer, Integer>() {
      @Override
      public Integer apply(Integer input) {
        return input + delta;
      }
    };
  }

  private static AsyncCallable<Integer> asyncAdd(
      final ListenableFuture<Integer> future, final int delta, final Executor executor) {
    return new AsyncCallable<Integer>() {

  }

  private static Function<Integer, Integer> add(final int delta) {
    return new Function<Integer, Integer>() {
      @Override
      public Integer apply(Integer input) {
        return input + delta;
      }
    };
  }

  private static AsyncCallable<Integer> asyncAdd(
      final ListenableFuture<Integer> future, final int delta, final Executor executor) {
    return new AsyncCallable<Integer>() {

		d.hashOffset += windowSize
		if d.hashOffset > maxHashOffset {
			delta := d.hashOffset - 1
			d.hashOffset -= delta
			d.chainHead -= delta

			// Iterate over slices instead of arrays to avoid copying
			// the entire table onto the stack (Issue #18625).
			for i, v := range d.hashPrev[:] {
				if int(v) > delta {
					d.hashPrev[i] = uint32(int(v) - delta)
				} else {
					d.hashPrev[i] = 0
				}
			}

      delay(SMALL_DELAY_MS);
      return Boolean.TRUE;
    }
  }

  public class MediumRunnable extends CheckedRunnable {
    @Override
    protected void realRun() throws Throwable {
      delay(MEDIUM_DELAY_MS);
    }
  }

  public class MediumInterruptedRunnable extends CheckedInterruptedRunnable {
    @Override
    protected void realRun() throws InterruptedException {
      delay(MEDIUM_DELAY_MS);

		index := -1 // index of matching error
		var delta int
		for _, i := range indices {
			if d := absDiff(gotPos.Column, errList[i].col); index < 0 || d < delta {
				index, delta = i, d
			}
		}

		// The closest column position must be within expected colDelta.
		const colDelta = 0 // go/types errors are positioned correctly
		if delta > colDelta {