tools/autograd/gen_autograd_functions.py

# Generates C++ autograd functions for the derivatives of ATen operations
#
# This writes two files:
#  Functions.h/cpp: subclasses of autograd::Node
#  python_functions.h/cpp: Python bindings for the above classes
#
from typing import Dict, List, Sequence, Tuple

from torchgen.api.autograd import (
    Derivative,
    DifferentiabilityInfo,
    SavedAttribute,
    uses_retain_variables,
    uses_single_grad,
)
from torchgen.api.types import (
    ArrayRefCType,
    BaseCType,
    Binding,
    boolT,
    doubleT,
    intArrayRefT,
    iTensorListRefT,
    ListCType,
    longT,
    MutRefCType,
    OptionalCType,
    optionalIntArrayRefT,
    optionalSymIntArrayRefT,
    scalarT,
    stringT,
    symIntArrayRefT,
    SymIntT,
    TENSOR_LIST_LIKE_CTYPES,
    tensorListT,
    tensorT,
)
from torchgen.code_template import CodeTemplate
from torchgen.model import Argument, FunctionSchema
from torchgen.utils import FileManager

from .gen_inplace_or_view_type import VIEW_FUNCTIONS

FUNCTION_DECLARATION = CodeTemplate(
    """\
struct TORCH_API ${op} : public ${superclass} {
  using ${superclass}::${superclass};
  variable_list apply(variable_list&& grads) override;
  std::string name() const override { return "${op}"; }
  void release_variables() override {
    ${thread_lock}
    ${release_variables}
  }
  ${will_release_variables}
  ${saved_variables}
  ${saved_list_sizes}
};
"""
)

WILL_RELEASE_VARIABLES = CodeTemplate(
    """\
bool retain_variables = true;
void will_release_variables() override {
  retain_variables = false;
}
"""
)

FUNCTION_DEFINITION = CodeTemplate(
    """\
variable_list ${op}::apply(variable_list&& grads) {
  ${thread_lock}
  ${asserts}
  IndexRangeGenerator gen;
  ${compute_index_ranges}
  variable_list grad_inputs(gen.size());
  ${body}
  return grad_inputs;
}
"""
)

GRAD_INPUT_MASK = CodeTemplate(
    """\
  auto grad_input_mask = std::array<bool, ${n}>{
    ${masks}
  };\
"""
)

DERIVATIVE_SINGLE = CodeTemplate(
    """\
if (task_should_compute_output({ ${name}_ix })) {
  auto grad_result = ${derivative};
  copy_range(grad_inputs, ${name}_ix, grad_result);
}
"""
)

DERIVATIVE_MULTI_COPY_RANGE = CodeTemplate(
    """\
  if (task_should_compute_output({ ${name}_ix })) {
    copy_range(grad_inputs, ${name}_ix, std::get<${i}>(grad_result));
  }
"""
)

DERIVATIVE_MULTI = CodeTemplate(
    """\
if (task_should_compute_output({ ${idx_ranges} })) {
  ${grad_input_mask}
  auto grad_result = ${derivative};
  ${copy_ranges}
}
"""
)

# Generates python bindings
#
# This generates the definitions for:
#   (1) The PyTypeObject for each backward grad_fn subclassing Node
#   (2) The entry for PyTypeObject's tp_getset slot (an array of PyGetSetDef structs)
#       We generate one PyGetSetDef struct for each of grad_fn's saved inputs and outputs
#       Each PyGetSetDef has a function ptr to a getter, also defined here (3).
#   (3) Getters for each of grad_fn's saved inputs and outputs.
#
PY_FUNCTION_DEFINITION = CodeTemplate(
    """\
static PyTypeObject ${op}Class;
addClass<${op}>(${op}Class, "${op}", ${op}_properties);
"""
)

PY_FUNCTION_PROPS_AND_GETTERS = CodeTemplate(
    """\
${all_getter_definitions}

static struct PyGetSetDef ${op}_properties[] = {
  THP_FUNCTION_DEFAULT_PROPERTIES,
  ${all_getsetdef_structs}
  {nullptr} /* sentinel */
};

"""
)

PY_GETSETDEF_STRUCT = CodeTemplate(
    """\
{(char*)"_saved_${name}", (getter)THP${op}_${name}_getter, nullptr, nullptr, nullptr}"""
)

PY_RAW_GETSETDEF_STRUCT = CodeTemplate(
    """\
{(char*)"_raw_saved_${name}", (getter)THP${op}_${name}_raw_getter, nullptr, nullptr, nullptr}"""
)

# Getter templates
GETTER_DEFINITION = CodeTemplate(
    """\
PyObject* THP${op}_${name}_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  auto prop = static_cast<${op}*>(self->cdata.get())->${name};
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_SAVEDVAR = CodeTemplate(
    """\
PyObject* THP${op}_${name}_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  const auto& prop = static_cast<${op}*>(self->cdata.get())->${name}_;
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_RAW_SAVEDVAR = CodeTemplate(
    """\
PyObject* THP${op}_${name}_raw_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  const auto& prop = static_cast<${op}*>(self->cdata.get())->${name}_;
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_VEC_SAVEDVAR = CodeTemplate(
    """\
PyObject* THP${op}_${name}_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  const auto *node = static_cast<${op}*>(self->cdata.get());
  const auto& prop = node->${name}_;
  if (node->${name}_released_) {
    PyErr_SetString(PyExc_RuntimeError, ERR_BACKWARD_TWICE);
    return nullptr;
  }
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_RAW_VEC_SAVEDVAR = CodeTemplate(
    """\
PyObject* THP${op}_${name}_raw_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  const auto *node = static_cast<${op}*>(self->cdata.get());
  const auto& prop = node->${name}_;
  if (node->${name}_released_) {
    PyErr_SetString(PyExc_RuntimeError, ERR_BACKWARD_TWICE);
    return nullptr;
  }
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_OPT = CodeTemplate(
    """\
PyObject* THP${op}_${name}_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  auto opt_prop = static_cast<${op}*>(self->cdata.get())->${name};
  if (!opt_prop.has_value()) {
    Py_RETURN_NONE;
  }
  auto prop = opt_prop.value();
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

GETTER_DEFINITION_OPT_ARRAYREF = CodeTemplate(
    """\
PyObject* THP${op}_${name}_getter(THPCppFunction *self, void *_unused) {
  HANDLE_TH_ERRORS
  auto opt_prop = static_cast<${op}*>(self->cdata.get())->${name};
  if (!opt_prop.list.has_value()) {
    Py_RETURN_NONE;
  }
  auto prop = opt_prop.list.value();
  ${body}
  END_HANDLE_TH_ERRORS
}
"""
)

# Getter body
GETTER_BODY_SAVEDVAR = """\
return THPVariable_Wrap(prop.unpack(self->cdata));
"""

GETTER_BODY_RAW_SAVEDVAR = """\
pybind11::object obj = pybind11::cast(prop, pybind11::return_value_policy::reference);
return obj.release().ptr();
"""

GETTER_BODY_VEC_SAVEDVAR = """\
PyObject* tup = PyTuple_New((Py_ssize_t) prop.size());
for (auto i: c10::irange(prop.size())) {
  PyTuple_SetItem(tup, (Py_ssize_t) i, THPVariable_Wrap(prop[i].unpack(self->cdata)));
}
return tup;
"""

GETTER_BODY_RAW_VEC_SAVEDVAR = """\
PyObject* tup = PyTuple_New((Py_ssize_t) prop.size());
for (auto i : c10::irange(prop.size())) {
  pybind11::object obj = pybind11::cast(prop[i], pybind11::return_value_policy::reference);
  PyTuple_SetItem(tup, (Py_ssize_t) i, obj.release().ptr());
}
return tup;
"""

GETTER_BODY_ARRAYREF_LONG = """\
PyObject* tup = PyTuple_New((Py_ssize_t) prop.size());
for (auto i : c10::irange(prop.size())) {
  PyTuple_SetItem(tup, (Py_ssize_t) i, PyLong_FromUnsignedLong((uint64_t) prop[i]));
}
return tup;
"""

GETTER_BODY_ARRAYREF_SYMINT = """\
PyObject* tup = PyTuple_New((Py_ssize_t) prop.size());
for (auto i : c10::irange(prop.size())) {
    auto si = prop[i];
    if (si.is_symbolic()) {
      auto py_symint = py::cast(si.toSymIntNodeImpl()).release().ptr();
      PyTuple_SetItem(tup, (Py_ssize_t) i, py_symint);
    } else {
       PyTuple_SetItem(tup, (Py_ssize_t) i, PyLong_FromUnsignedLong(si.as_int_unchecked()));
    }
}
return tup;
"""

GETTER_BODY_ARRAYREF_DOUBLE = """\
PyObject* tup = PyTuple_New((Py_ssize_t) prop.size());
for (auto i : c10::irange(prop.size())) {
  PyTuple_SetItem(tup, (Py_ssize_t) i, PyFloat_FromDouble((double) prop[i]));
}
return tup;
"""

GETTER_BODY_INT64_T = """\
return PyLong_FromUnsignedLong((int64_t) prop);
"""

GETTER_BODY_SYMINT = """\
return prop.is_symbolic() ? py::cast(prop.toSymIntNodeImpl()).release().ptr() : PyLong_FromUnsignedLong(prop.as_int_unchecked());
"""

GETTER_BODY_DOUBLE = """\
return PyFloat_FromDouble((double) prop);
"""

GETTER_BODY_BOOL = """\
if (prop) {
  Py_RETURN_TRUE;
} else {
  Py_RETURN_FALSE;
}
"""

GETTER_BODY_STRING = """\
return PyUnicode_FromStringAndSize(prop.data(), prop.size());
"""

GETTER_BODY_SCALAR = """\
if (prop.isComplex()) {
  auto cprop = prop.to<c10::complex<double>>();
  return PyComplex_FromDoubles(cprop.real(), cprop.imag());
} else if (prop.isFloatingPoint()) {
  return PyFloat_FromDouble(prop.to<double>());
} else if (prop.isIntegral(/*includeBool=*/false)) {
  return PyLong_FromLong(prop.to<int64_t>());
} else if (prop.isBoolean()) {
  if (prop.to<bool>()) {
    Py_RETURN_TRUE;
  } else {
    Py_RETURN_FALSE;
  }
} else {
  PyErr_SetString(PyExc_RuntimeError, "Unknown scalar type");
  return nullptr;
}
"""

MISC_GETTER_DEFS = {
    OptionalCType(BaseCType(longT)): (GETTER_DEFINITION_OPT, GETTER_BODY_INT64_T),
    OptionalCType(BaseCType(SymIntT)): (GETTER_DEFINITION_OPT, GETTER_BODY_SYMINT),
    BaseCType(doubleT): (GETTER_DEFINITION, GETTER_BODY_DOUBLE),
    OptionalCType(BaseCType(doubleT)): (GETTER_DEFINITION_OPT, GETTER_BODY_DOUBLE),
    BaseCType(boolT): (GETTER_DEFINITION, GETTER_BODY_BOOL),
    BaseCType(scalarT): (GETTER_DEFINITION, GETTER_BODY_SCALAR),
    OptionalCType(BaseCType(scalarT)): (GETTER_DEFINITION_OPT, GETTER_BODY_SCALAR),
}

# These functions have backwards which cannot be traced, and so must have
# their backward functions traced opaquely.
# VIEW_FUNCTIONS are not traceable because they use as_strided, which
# has an untraceable backwards, see
# https://github.com/pytorch/pytorch/issues/4250
# TODO: This is probably not exhaustive, but it's a start
UNTRACEABLE_FUNCTIONS = VIEW_FUNCTIONS


def get_infos_with_derivatives_list(
    differentiability_infos: Dict[FunctionSchema, Dict[str, DifferentiabilityInfo]]
) -> List[DifferentiabilityInfo]:

    diff_info_list = [
        info
        for diffinfo_dict in differentiability_infos.values()
        for info in diffinfo_dict.values()
    ]

    return list(filter(lambda info: info.args_with_derivatives, diff_info_list))


def gen_autograd_functions_lib(
    out: str,
    differentiability_infos: Dict[FunctionSchema, Dict[str, DifferentiabilityInfo]],
    template_path: str,
) -> None:
    """Functions.h and Functions.cpp body

    These contain the auto-generated subclasses of torch::autograd::Node
    for each every differentiable torch function.
    """

    # get a 1D list of diffinfos, we do not need them to be per FunctionSchema/DispatchKey here
    # infos with the diff dispatchkeys but the same name will still be in the same shard.
    infos = get_infos_with_derivatives_list(differentiability_infos)
    declarations = list(map(lambda f: process_function(f, FUNCTION_DECLARATION), infos))
    definitions = list(map(lambda f: process_function(f, FUNCTION_DEFINITION), infos))

    file_basename = "Functions"
    fm = FileManager(install_dir=out, template_dir=template_path, dry_run=False)
    for suffix in [".h", ".cpp"]:
        fname = file_basename + suffix
        fm.write_with_template(
            fname,
            fname,
            lambda: {
                "generated_comment": "@"
                + f"generated from {fm.template_dir_for_comments()}/"
                + fname,
                "autograd_function_declarations": declarations,
                "autograd_function_definitions": definitions,
            },
        )


def gen_autograd_functions_python(
    out: str,
    differentiability_infos: Dict[FunctionSchema, Dict[str, DifferentiabilityInfo]],
    template_path: str,
) -> None:

    fm = FileManager(install_dir=out, template_dir=template_path, dry_run=False)
    num_shards = 5
    fm.write(
        "python_functions.h",
        lambda: {
            "generated_comment": "@"
            + f"generated from {fm.template_dir_for_comments()}/python_functions.h",
            "shard_forward_declare": [
                f"void initialize_autogenerated_functions_{i}();"
                for i in range(num_shards)
            ],
            "shard_call": [
                f"initialize_autogenerated_functions_{i}();" for i in range(num_shards)
            ],
        },
    )

    # get a 1D list of diffinfos, we do not need them to be per FunctionSchema/DispatchKey here
    # infos with the diff dispatchkeys but the same name will still be in the same shard.
    infos = get_infos_with_derivatives_list(differentiability_infos)
    fm.write_sharded(
        "python_functions.cpp",
        infos,
        key_fn=lambda info: info.name,
        base_env={
            "generated_comment": "@"
            + f"generated from {fm.template_dir_for_comments()}/python_functions.cpp",
        },
        env_callable=lambda info: {
            "py_function_initializers": [
                process_function(info, PY_FUNCTION_DEFINITION)
            ],
            "py_function_props_and_getters": [
                process_function(info, PY_FUNCTION_PROPS_AND_GETTERS)
            ],
        },
        num_shards=num_shards,
        sharded_keys={"py_function_initializers", "py_function_props_and_getters"},
    )


def process_function(info: DifferentiabilityInfo, template: CodeTemplate) -> str:
    saved_variables: List[str] = []
    release_variables: List[str] = []
    saved_list_sizes: List[str] = []
    unpack: List[str] = []
    asserts: List[str] = []
    compute_index_ranges: List[str] = []
    getter_definitions: List[str] = []
    py_getsetdef_structs: List[str] = []

    for arg in info.args_with_derivatives:
        if arg.type in TENSOR_LIST_LIKE_CTYPES:
            size = f"{arg.name}_size_"
            saved_list_sizes.append(f"size_t {arg.name}_size_;")
        else:
            size = "1"
        compute_index_ranges.append(f"auto {arg.name}_ix = gen.range({size});")

    def save_var(var: SavedAttribute, is_output: bool) -> None:
        name = var.nctype.name
        type = var.nctype.type
        should_append_getsetdef = True
        should_append_raw_getsetdef = False

        if (
            type == BaseCType(tensorT)
            or type == OptionalCType(BaseCType(tensorT))
            or type == MutRefCType(OptionalCType(BaseCType(tensorT)))
            or (type == BaseCType(scalarT) and is_output)
        ):
            saved_variables.append(f"SavedVariable {name}_;")
            release_variables.append(f"{name}_.reset_data();")
            ptr = "shared_from_this()" if is_output else ""
            unpack.append(f"auto {name} = {name}_.unpack({ptr});")
            getter_definitions.append(
                GETTER_DEFINITION_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_SAVEDVAR
                )
            )
            getter_definitions.append(
                GETTER_DEFINITION_RAW_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_RAW_SAVEDVAR
                )
            )
            should_append_raw_getsetdef = True
        elif type == BaseCType(tensorListT) or type == BaseCType(iTensorListRefT):
            saved_variables.append(f"std::vector<SavedVariable> {name}_;")
            saved_variables.append(f"bool {name}_released_ = false;")
            # Just clear() is sufficient, we don't need to loop and clear each variable.
            # Because the SavedVariable owns a tensor and a grad_fn, removing the SavedVariable makes them go away as well.
            release_variables.append(f"{name}_.clear();")
            release_variables.append(f"{name}_released_ = true;")
            unpack.append(f"auto {name} = unpack_list({name}_);")
            asserts.append(f"TORCH_CHECK(!{name}_released_, ERR_BACKWARD_TWICE);")
            getter_definitions.append(
                GETTER_DEFINITION_VEC_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_VEC_SAVEDVAR
                )
            )
            getter_definitions.append(
                GETTER_DEFINITION_RAW_VEC_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_RAW_VEC_SAVEDVAR
                )
            )
            should_append_raw_getsetdef = True
        elif type == ListCType(OptionalCType(BaseCType(tensorT))):
            saved_variables.append(f"std::vector<SavedVariable> {name}_;")
            saved_variables.append(f"bool {name}_released_ = false;")
            # Just clear() is sufficient, we don't need to loop and clear each variable.
            # Because the SavedVariable owns a tensor and a grad_fn, removing the SavedVariable makes them go away as well.
            release_variables.append(f"{name}_.clear();")
            release_variables.append(f"{name}_released_ = true;")
            unpack.append(f"auto {name} = unpack_opt_list({name}_);")
            asserts.append(f"TORCH_CHECK(!{name}_released_, ERR_BACKWARD_TWICE);")
            getter_definitions.append(
                GETTER_DEFINITION_VEC_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_VEC_SAVEDVAR
                )
            )
            getter_definitions.append(
                GETTER_DEFINITION_RAW_VEC_SAVEDVAR.substitute(
                    op=info.op, name=name, body=GETTER_BODY_RAW_VEC_SAVEDVAR
                )
            )
            should_append_raw_getsetdef = True
        elif type == BaseCType(intArrayRefT):
            saved_variables.append(f"std::vector<int64_t> {name};")
            getter_definitions.append(
                GETTER_DEFINITION.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_LONG
                )
            )
        elif type == BaseCType(symIntArrayRefT):
            saved_variables.append(f"std::vector<c10::SymInt> {name};")
            getter_definitions.append(
                GETTER_DEFINITION.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_SYMINT
                )
            )
        elif type == BaseCType(optionalIntArrayRefT):
            saved_variables.append(f"c10::OptionalArray<int64_t> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT_ARRAYREF.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_LONG
                )
            )
        elif type == BaseCType(optionalSymIntArrayRefT):
            saved_variables.append(f"c10::OptionalArray<c10::SymInt> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT_ARRAYREF.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_SYMINT
                )
            )
        elif type == OptionalCType(BaseCType(intArrayRefT)):
            saved_variables.append(f"c10::OptionalArray<int64_t> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT_ARRAYREF.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_LONG
                )
            )
        elif type == OptionalCType(BaseCType(symIntArrayRefT)):
            saved_variables.append(f"c10::OptionalArray<c10::SymInt> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT_ARRAYREF.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_SYMINT
                )
            )
        elif type == OptionalCType(ArrayRefCType(BaseCType(doubleT))):
            saved_variables.append(f"c10::OptionalArray<double> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT_ARRAYREF.substitute(
                    op=info.op, name=name, body=GETTER_BODY_ARRAYREF_DOUBLE
                )
            )
        elif type == BaseCType(longT):
            saved_variables.append(f"{type.cpp_type()} {name} = 0;")
            getter_definitions.append(
                GETTER_DEFINITION.substitute(
                    op=info.op, name=name, body=GETTER_BODY_INT64_T
                )
            )
        elif type == BaseCType(SymIntT):
            saved_variables.append(f"c10::SymInt {name};")
            getter_definitions.append(
                GETTER_DEFINITION.substitute(
                    op=info.op, name=name, body=GETTER_BODY_SYMINT
                )
            )
        elif type == BaseCType(stringT):
            saved_variables.append(f"std::string {name};")
            getter_definitions.append(
                GETTER_DEFINITION.substitute(
                    op=info.op, name=name, body=GETTER_BODY_STRING
                )
            )
        elif type == OptionalCType(BaseCType(stringT)):
            saved_variables.append(f"c10::optional<std::string> {name};")
            getter_definitions.append(
                GETTER_DEFINITION_OPT.substitute(
                    op=info.op, name=name, body=GETTER_BODY_STRING
                )
            )
        else:
            # Check for indicators that you're putting a non-owning reference
            # into the saved variable field.  If this is spuriously firing,
            # edit this field.  Otherwise, you probably need to add a case
            # above.
            assert (
                "ref" not in type.cpp_type().lower()
                and "view" not in type.cpp_type().lower()
                and "*" not in type.cpp_type()
                and "&" not in type.cpp_type()
            ), f"{type.cpp_type()} looks like it contains a non-owning reference"
            saved_variables.append(f"{type.cpp_type()} {name};")

            if type in MISC_GETTER_DEFS:
                getter_def, body = MISC_GETTER_DEFS[type]
                getter_definitions.append(
                    getter_def.substitute(op=info.op, name=name, body=body)
                )
            else:
                # Types we don't expose python bindings to yet:
                #   TypeAndSize, at::ScalarType, TensorOptions, TensorGeometry,
                #   std::vector<std::vector<int64_t>>, std::vector<at::ScalarType>
                should_append_getsetdef = False

        if should_append_getsetdef:
            py_getsetdef_structs.append(
                PY_GETSETDEF_STRUCT.substitute(op=info.op, name=name)
            )
        if should_append_raw_getsetdef:
            py_getsetdef_structs.append(
                PY_RAW_GETSETDEF_STRUCT.substitute(op=info.op, name=name)
            )

    for var in info.all_saved_inputs:
        save_var(var, is_output=False)
    for var in info.all_saved_outputs:
        save_var(var, is_output=True)

    # lock the mutex when we release variables and in Node::apply to protect thread safety
    # see Note [Thread Safety on Autograd Node]
    if len(release_variables) > 0:
        thread_lock = "std::lock_guard<std::mutex> lock(mutex_);"
    else:
        thread_lock = ""

    if uses_retain_variables(info):
        will_release_variables = WILL_RELEASE_VARIABLES.substitute()
    else:
        will_release_variables = ""

    body: List[str] = []

    if uses_single_grad(info):
        body.append("const auto& grad = grads[0];")
    else:
        # Generate aliases for gradients named for returned values.
        body.extend(
            f"const auto& {name} = grads[{info.available_named_gradients.index(name)}];"
            for name in info.used_named_gradients
        )

    def emit_derivative(
        derivative: Derivative,
        args_with_derivatives: Sequence[Binding],
    ) -> Tuple[bool, str]:
        formula = derivative.formula
        var_names = derivative.var_names
        if len(var_names) == 1:
            checks_any_grad_defined = False
            if "not_implemented" not in formula:
                matching_args = [
                    arg for arg in args_with_derivatives if arg.name == var_names[0]
                ]
                if len(matching_args) == 1:
                    # We can add undefined grad support if the input variable is a Tensor
                    arg = matching_args[0]
                    if isinstance(arg.argument, Argument) and str(
                        arg.argument.type
                    ) in ("Tensor", "Tensor?"):
                        formula = "any_grad_defined ? (" + formula + ") : Tensor()"
                        checks_any_grad_defined = True
            return (
                checks_any_grad_defined,
                DERIVATIVE_SINGLE.substitute(name=var_names[0], derivative=formula),
            )
        else:
            if "grad_input_mask" in formula:
                masks = [
                    f"task_should_compute_output({{ {n}_ix }})," for n in var_names
                ]
                grad_input_mask = GRAD_INPUT_MASK.substitute(
                    masks=masks, n=len(var_names)
                )
            else:
                grad_input_mask = ""
            idx_ranges = ", ".join(f"{n}_ix" for n in var_names)
            copy_ranges: List[str] = []
            for i, n in enumerate(var_names):
                copy_ranges.append(DERIVATIVE_MULTI_COPY_RANGE.substitute(name=n, i=i))
            return False, DERIVATIVE_MULTI.substitute(
                idx_ranges=idx_ranges,
                copy_ranges=copy_ranges,
                derivative=formula,
                grad_input_mask=grad_input_mask,
            )

    body.extend(unpack)
    need_any_grad_defined_var = False
    for derivative in info.derivatives:
        checks_any_grad_defined, derivative_text = emit_derivative(
            derivative, info.args_with_derivatives
        )
        body.append(derivative_text)
        need_any_grad_defined_var |= checks_any_grad_defined
    # Since single-output derivative formulas need to check if grads are
    # defined, only perform the check once, before all the formulas
    if need_any_grad_defined_var:
        body.insert(
            -len(info.derivatives),
            "bool any_grad_defined = any_variable_defined(grads);",
        )

    if info.name in UNTRACEABLE_FUNCTIONS:
        superclass = "Node"
    else:
        superclass = "TraceableFunction"

    all_getsetdef_structs = (
        ",\n".join(py_getsetdef_structs) + "," if len(py_getsetdef_structs) != 0 else ""
    )
    all_getter_definitions = "\n".join(getter_definitions)

    return template.substitute(
        op=info.op,
        compute_index_ranges=compute_index_ranges,
        saved_variables=saved_variables,
        release_variables=release_variables,
        saved_list_sizes=saved_list_sizes,
        asserts=asserts,
        thread_lock=thread_lock,
        will_release_variables=will_release_variables,
        body=body,
        superclass=superclass,
        all_getter_definitions=all_getter_definitions,
        all_getsetdef_structs=all_getsetdef_structs,
    )