* usually have much noticeable impact. A value of one permits only one thread to modify the cache
   * at a time, but since read operations and cache loading computations can proceed concurrently,
   * this still yields higher concurrency than full synchronization.
   *
   * <p>Defaults to 4. <b>Note:</b>The default may change in the future. If you care about this

	//         == n * (n-1) * ... * (n-k+1) / 1 * (1+1) * ... * k
	//
	// Using the multiplicative formula produces smaller values
	// at each step, requiring fewer allocations and computations:
	//
	// z = 1
	// for i := 0; i < k; i = i+1 {
	//     z *= n-i
	//     z /= i+1
	// }
	//
	// finally to avoid computing i+1 twice per loop:
	//
	// z = 1
	// i := 0

}

void init() {
        SansTypeface = loadfont();
}

// issue 5242
// Cgo incorrectly computed the alignment of structs
// with no Go accessible fields as 0, and then panicked on
// modulo-by-zero computations.

// issue 50987
// disable arm64 GCC warnings
#cgo CFLAGS: -Wno-psabi -Wno-unknown-warning-option

typedef struct {
} foo;

typedef struct {
	int x : 1;
} bar;

//
// then pulling `f` out of the cluster may reduce the number of compilations and
// will never increase the number of compilations.
//
// We may reduce the number of compilations if f is many to one.  For instance
// if f(x,y) = x-y then x=3,y=1 and x=4,y=2 will generate two different
// compilations if f is in the cluster but only one compilation if f is outside
// the cluster.
//

  %1 = "tf.ReadVariableOp"(%0) : (tensor<!tf_type.resource<tensor<i32>>>) -> tensor<i32>
  // CHECK:      [[COMPUTATION:%.+]] = "tf_device.cluster_func"([[INPUT]])
  %2 = "tf_device.cluster_func"(%1) {func = @computation, use_spmd_for_xla_partitioning = true} : (tensor<i32>) -> tensor<i32>
  // CHECK:      [[OUTPUT:%.+]]:2 = "tf.TPUPartitionedOutputV2"([[COMPUTATION]])
  // CHECK-SAME: _XlaSharding = ""
  // CHECK-SAME: partition_dims = []

  return true;
}

namespace {

// Compiles the XLA computation into executable code.
Status CompileXla(xla::CompileOnlyClient* client,
                  const xla::XlaComputation& computation,
                  const xla::cpu::CpuAotCompilationOptions& aot_opts,
                  CompileResult* compile_result) {
  // Retrieves arg and result layouts from the computation.
  // TODO(toddw): Should we let the user choose the major/minor ordering?

  xla::Tuple(&builder, tuple_values);

  TF_ASSERT_OK_AND_ASSIGN(XlaComputation computation, builder.Build());
  EXPECT_EQ(computation.proto().computations_size(), 2);

  TF_ASSERT_OK(CreateMlirModule());
  TF_ASSERT_OK_AND_ASSIGN(TupleOp root_tuple,
                          ImportXlaComputationIntoModule(computation));
  EXPECT_TRUE(root_tuple);

  int num_func_ops = 0;

//
// References:
//
// Baillie and Wagstaff, "Lucas Pseudoprimes", Mathematics of Computation 35(152),
// October 1980, pp. 1391-1417, especially page 1401.
// https://www.ams.org/journals/mcom/1980-35-152/S0025-5718-1980-0583518-6/S0025-5718-1980-0583518-6.pdf
//
// Grantham, "Frobenius Pseudoprimes", Mathematics of Computation 70(234),
// March 2000, pp. 873-891.

namespace foo {
namespace bar {

// MyClass represents a computation previously specified in a
// TensorFlow graph, now compiled into executable code. This extends the generic
// XlaCompiledCpuFunction class with statically type-safe arg and result
// methods. Usage example:
//
//   MyClass computation;
//   // ...set args using computation.argN methods
//   CHECK(computation.Run());
//   // ...inspect results using computation.resultN methods

  }

  if (output_to_input_alias.empty()) return absl::OkStatus();

  xla::HloModuleProto* module_proto =
      compilation_result->computation->mutable_proto();
  absl::StatusOr<xla::ProgramShape> program_shape_or_status =
      compilation_result->computation->GetProgramShape();
  TF_RET_CHECK(program_shape_or_status.ok());

  xla::ProgramShape& program_shape = program_shape_or_status.value();