memonger.py

## @package memonger
# Module caffe2.python.memonger





import networkx as nx
import collections
import time
import copy
from caffe2.python import workspace, core
from caffe2.proto import caffe2_pb2
import enum
import logging
import caffe2.python._import_c_extension as C

log = logging.getLogger("memonger")
log.setLevel(logging.INFO)
LiveRange = collections.namedtuple('LiveRange', ["defined", "used", "size"])


def share_grad_blobs(
    net,
    losses,
    param_grads,
    namescope,
    dont_share_blobs=None,
    share_activations=False,
    blob_shapes=None,
):
    '''
    Implements similar optimization as Torch's shareGradInput():
    for the gradients that are passed between layers, share blobs between
    operators when possible. This yields significant memory savings with
    deep networks.

    Returns an optimized protobuf (assign to net._net)
    '''
    def is_grad_blob(b):
        name = str(b)
        # Note: need to look at _{namescope} pattern as it matches
        # to handle the auto-split gradients
        return name.endswith("_grad") and (name.startswith(namescope) or
            name.startswith("_" + namescope)) and name not in param_grads

    def is_grad_op(op):
        # TODO: something smarter
        for b in list(op.input) + list(op.output):
            if is_grad_blob(b):
                return True
        return False

    log.warn("NOTE: Executing memonger to optimize gradient memory")

    # Collect ops that have something to do with gradients
    if namescope != "" and not namescope.endswith("/"):
        namescope += "/"

    netproto = copy.deepcopy(net.Proto())
    activations = []
    external_output = set(net.Proto().external_output)

    # Hacky way to get activations, think of a better way
    for op in net.Proto().op:
        for b in op.output:
            if b + "_w" in op.input and b not in external_output:
                activations.append(b)

    # Remove last activations, as they are usually accessed externally
    activations = set(activations[:-2])

    # Gradient ops
    grad_op_indices = []
    for idx, op in enumerate(netproto.op):
        if (is_grad_op(op)):
            grad_op_indices.append(idx)

    shared_blobs = set()
    for op in net.Proto().op:
        for b in list(op.input) + list(op.output):
            if is_grad_blob(b) or (share_activations and b in activations):
                shared_blobs.add(b)
    start_time = time.time()
    optim_str = C.memonger_compute_blob_recycling_for_dag(
        netproto.SerializeToString(),
        [str(s).encode('utf-8') for s in losses],
        grad_op_indices,
        set(str(s).encode('utf-8') for s in shared_blobs),
        namescope.encode('utf-8'),
        set() if dont_share_blobs is None else dont_share_blobs,
        {} if blob_shapes is None else blob_shapes
    )

    log.info("Memonger memory optimization took {} secs".format(
        time.time() - start_time),
    )

    optim = caffe2_pb2.NetDef()
    optim.ParseFromString(optim_str)
    assert verify_graph_equality(net.Proto(), optim), \
        "Memonger graph is not equal to original."
    assert verify_inplace_blobs(net.Proto(), optim), \
        "Inplace assignments differ in memonger net."
    return optim


def optimize_inference_for_dag(net, input_blobs, namescope=""):
    netproto = copy.deepcopy(net.Proto())
    external_input = set(net.Proto().external_input)
    external_output = set(net.Proto().external_output)

    def is_activation_blob(b):
        return b not in external_input and b not in external_output

    activation_blobs = set()
    seen_as_output = set()
    ops = list(net.Proto().op)
    op_indices = [index for index, op in enumerate(net.Proto().op)]

    # Sanity check: check that all external inputs are properly accounted
    # and that no gradient ops are included in 'net'
    for op in ops:
        for b in op.input:
            if is_activation_blob(b):
                activation_blobs.add(b)
                if b not in seen_as_output:
                    raise AssertionError("{} not in external input".format(b))
        for b in op.output:
            if is_activation_blob(b):
                activation_blobs.add(b)
        seen_as_output = seen_as_output.union(set(op.output))
        assert not op.is_gradient_op, \
            "You can only pass inference-only nets to optimize_inference_for_dag"
    start_time = time.time()
    optim_str = C.memonger_compute_blob_recycling_for_dag(
        netproto.SerializeToString(),
        [str(s).encode('utf-8') for s in input_blobs],
        op_indices,
        set(str(s).encode('utf-8') for s in activation_blobs),
        namescope.encode('utf-8'),
        set(),
        {}
    )

    log.info("Memonger memory optimization took {} secs".format(
        time.time() - start_time),
    )

    optim = caffe2_pb2.NetDef()
    optim.ParseFromString(optim_str)

    assert verify_graph_equality(net.Proto(), optim), \
        "Memonger graph is not equal to original."
    assert verify_inplace_blobs(net.Proto(), optim), \
        "Inplace assignments differ in memonger net."
    return optim


def estimate_memory_usage(protos, shapes, types, devicescope):
    import numpy as np
    '''
    Estimate memory usage of a model. This is an estimate because
    we assume a single threaded execution and miss some internal
    memory usage of operators. Only estimates the memory for a given
    device scope.

    Also, currently it does not handle correctly if blob sizes vary
    during execution, as it uses only the final blob size.

    Returns (total, highwater, by op type) memory allocation in bytes.
    '''
    sizeofs = {
        caffe2_pb2.TensorProto.DOUBLE: 8,
        caffe2_pb2.TensorProto.FLOAT: 4,
        caffe2_pb2.TensorProto.FLOAT16: 2,
        caffe2_pb2.TensorProto.INT32: 4,
        caffe2_pb2.TensorProto.INT8: 1,
        caffe2_pb2.TensorProto.UINT8: 1,
        caffe2_pb2.TensorProto.UINT16: 2,
        caffe2_pb2.TensorProto.INT16: 2,
        caffe2_pb2.TensorProto.BOOL: 1,
        caffe2_pb2.TensorProto.INT64: 8,
    }

    def split_net(proto):
        ops = [op for op in proto.op if
               op.device_option == devicescope or op.type in {"Free", "Alias"}]
        del proto.op[:]
        proto.op.extend(ops)
        return proto

    def num_bytes(blob):
        if blob not in shapes or blob not in types:
            log.warning("Unknown blob encountered: {}".format(blob))
            return 0
        sizeof = sizeofs[types[blob]]
        return sizeof * np.prod(shapes[blob])

    protos = [split_net(proto) for proto in protos]
    allocs_by_ops = collections.defaultdict(lambda: 0)

    # Evaluate
    current_allocated = 0
    max_allocated = 0
    total_allocated = 0
    allocated = set()
    for proto in protos:
        for op in proto.op:
            if op.type == "Free" or op.type == "Alias":
                for o in op.output:
                    if o in allocated:
                        current_allocated -= num_bytes(o)
                        allocated.remove(o)
            else:
                for output in op.output:
                    if output not in allocated:
                        nbytes = num_bytes(output)
                        total_allocated += nbytes
                        current_allocated += nbytes
                        max_allocated = max(max_allocated, current_allocated)
                        allocated.add(output)
                        allocs_by_ops[op.type] += nbytes

    return (total_allocated, max_allocated, allocs_by_ops)


def release_blobs_when_used(netproto, dont_free_blobs, selector_fun=None):
    '''
    Insert Free-ops after a blob has been used the last time, so that its
    memory can be reclaimed. Use this only with efficient caching memory
    managers (such as CUB, --caffe2_cuda_memory_pool=cub).

    Blobs used with Alias op won't be freed.

    @dont_free_blobs:  is a set of blobs that should not be freed
    @selector_fun:     optional lambda that return True if blob name
                       can be released. Use for easy special filtering, like
                       excluding blobs with "loss" in the name.

    Returns a new protobuffer. To use with a model, use:
        model.net._net = memonger.release_blobs_when_used(..)
    '''
    input_blobs = set()
    can_release = set()
    alias_blobs = set()
    netproto = copy.deepcopy(netproto)

    for op in netproto.op:
        if op.type == 'Alias':
            alias_blobs.add(op.input[0])
            continue
        for inp in op.input:
            input_blobs.add(inp)
        for outp in op.output:
            if outp not in input_blobs:
                if selector_fun is None or selector_fun(outp):
                    can_release.add(outp)

    # Remove such blobs that are not input at all and external outputs
    can_release = can_release - set(netproto.external_output)
    can_release = can_release.intersection(input_blobs)
    can_release = can_release - dont_free_blobs
    can_release = can_release - alias_blobs

    ops = list(netproto.op)

    # .. then find last use of each can-release blob, and insert a Free op
    for j in reversed(range(0, len(netproto.op))):
        op = netproto.op[j]
        for inp in op.input:
            if inp in can_release:
                can_release.remove(inp)
                ops.insert(j + 1, core.CreateOperator("Free", [inp], [inp]))

    del netproto.op[:]
    netproto.op.extend(ops)
    return netproto


def _find_source_nodes(g):
    ''' Return nodes without predecessors '''
    ret = []
    for cn in g:
        cur_pred = list(g.predecessors(cn))
        if not cur_pred:
            ret.append(cn)
    return ret


def _find_target_nodes(g):
    ''' Return nodes without successors '''
    ret = []
    for cn in g:
        cur_succ = list(g.successors(cn))
        if not cur_succ:
            ret.append(cn)
    return ret


def _add_single_target_ifneeded(g):
    targets = _find_target_nodes(g)
    assert len(targets) >= 1
    if len(targets) == 1:
        return g
    ret = copy.deepcopy(g)

    def _next_available_idx(g):
        ret = -1
        for cn in g:
            if cn > ret:
                ret = cn
        ret += 1
        return ret

    target_node_idx = _next_available_idx(g)
    ret.add_node(target_node_idx)
    for cn in targets:
        ret.add_edge(cn, target_node_idx)

    return ret


def _get_path(pred_list, dist_list):
    ''' Get the path from nx.bellman_ford()'s output '''

    # distances are negative
    assert all(dist_list[x] <= 0 for x in dist_list)
    # node with longest distance to source is the target
    target = min(dist_list, key=lambda x: dist_list[x])

    ret = []
    cur = target

    while cur is not None:
        ret.append(cur)
        # Hack to get networkx 2.0 happy: it uses list in pred.
        # TODO(tulloch): are there cases with multiple predecessors?
        try:
            cur = pred_list[cur][0] if pred_list[cur] else None
        except TypeError:
            cur = pred_list[cur]

    return list(reversed(ret))


def _get_longest_paths(g, source_nodes):
    ''' Get the longest path for nodes in 'source_nodes'
        Find with bellman_ford() by setting weight = -1
    '''

    ng = copy.deepcopy(g)
    for u, v in ng.edges():
        ng[u][v]["weight"] = -1

    ret = {}
    for cn in source_nodes:
        pred, dist = nx.bellman_ford_predecessor_and_distance(ng, cn, weight="weight")
        path = _get_path(pred, dist)
        assert path[0] == cn
        assert len(path) - 1 == -dist[path[-1]]
        ret[cn] = path

    return ret


def _build_tree(paths):
    ''' Build a tree for given paths based on common elements.
        Last elements of all paths are the same, which is the root of the tree.
    '''
    assert all(cp[-1] == paths[0][-1] for cp in paths)
    g = nx.DiGraph()
    node_set = {y for x in paths for y in x}
    g.add_nodes_from(node_set)
    for cp in paths:
        for ce in zip(cp[0:-1], cp[1:]):
            g.add_edge(ce[1], ce[0])

    root = paths[0][-1]
    _compute_tree_height(g, root)

    return (g, root)


def _compute_tree_height(g, root):
    ''' Compute the heights of the tree for all nodes
        Height of leaves are 0
    '''
    def _get_height(root):
        children = list(g.successors(root))
        height = 0
        if children:
            child_heights = [_get_height(x) for x in children]
            height = max(child_heights) + 1
        g.nodes[root]["height"] = height
        return height

    _get_height(root)


def _sort_tree_leaves(g, root):
    ''' For each node, sort its child nodes based on the height of the nodes.
        Return the leaf nodes of the tree after sorting.
    '''
    def _get_height(root):
        return g.nodes[root]["height"]

    def _get_sorted_leaves(root):
        children = list(g.successors(root))
        if not children:
            return [root]
        child_heights = [_get_height(x) for x in children]
        order = sorted(range(len(children)), key=lambda x: child_heights[x])
        ret = []
        for co in order:
            cr = children[co]
            ret += _get_sorted_leaves(cr)

        return ret

    return _get_sorted_leaves(root)


def topological_sort_traversal_longest_path(g):
    ''' The graph 'g' may contain several source nodes (nodes without incoming
        edge), which could be in any order and still be a valid
        topological sorting result. We would like to arrange these source nodes
        so that the average live spans of the computed blobs are shorter.
        The idea is to sort the source nodes based on the length of their path to
        the target node so that the one with longer path is used first.
        This is done by:
        - Add a single target node if there are multiple target nodes in 'g'.
        - Find the longest path between each source and the target node.
        - Convert the longest paths to a tree with the target node being the root
          and source nodes being the leaves.
        - Sort the nodes of the tree based on the height of the tree.
    '''
    gt = _add_single_target_ifneeded(g)
    source_nodes = _find_source_nodes(gt)
    lpaths = _get_longest_paths(gt, source_nodes)
    tree, root = _build_tree(list(lpaths.values()))
    sorted_sources = _sort_tree_leaves(tree, root)
    assert(sorted(sorted_sources) == sorted(source_nodes))

    if nx.__version__ < '2.0':
        ret = nx.topological_sort(g, sorted_sources)
    else:
        # Manually making a sorted descendent list
        dependency_order = list(sorted_sources)
        seen_nodes = set(sorted_sources)
        for s in sorted_sources:
            desc = nx.descendants(g, s)
            for d in desc:
                if d not in seen_nodes:
                    seen_nodes.add(d)
                    dependency_order.append(d)
        sort_key = dict((v, len(dependency_order) - i) for i, v in enumerate(dependency_order))
        ret = nx.algorithms.dag.lexicographical_topological_sort(
            g, key=lambda x: sort_key[x])
        ret = list(ret)
    assert(len(ret) == len(g.nodes))
    return ret


def topological_sort_traversal(g):
    return list(nx.topological_sort(g))


def compute_ranges(linearized_ops, blob_sizes=None):
    if not blob_sizes:
        log.warning('Provide blob sizes to get more accurate assignments.')

    blobs = collections.defaultdict(
        lambda: LiveRange(defined=None, used=None, size=None))
    for i, op in enumerate(linearized_ops):
        for blob in op.input:
            used = blobs[blob].used
            if used is None:
                used = i
            else:
                used = max(used, i)
            blobs[blob] = blobs[blob]._replace(used=used)
            blob_size = blob_sizes[blob] if blob_sizes else None
            assert not blob_sizes or blob_size is not None
            blobs[blob] = blobs[blob]._replace(size=blob_size)
        for blob in op.output:
            defined = blobs[blob].defined
            if defined is None:
                defined = i
            else:
                defined = min(defined, i)
            blobs[blob] = blobs[blob]._replace(defined=defined)
            blob_size = blob_sizes[blob] if blob_sizes else None
            assert not blob_sizes or blob_size is not None
            blobs[blob] = blobs[blob]._replace(size=blob_size)

    return blobs


def is_compatible(candidate_range, assignment, static_blobs):
    (name, range_) = assignment[-1]
    if name in static_blobs:
        return False
    if candidate_range.defined is None or range_.defined is None \
      or range_.used is None:
        return False
    return candidate_range.defined > range_.used


def compute_blob_assignments(assignments):
    blob_assignments = {}
    for assignment in assignments:
        if len(assignment) == 1:
            continue
        last_blob, _ = assignment[-1]
        for (blob, _) in assignment:
            blob_assignments[blob] = last_blob
    return blob_assignments


def _get_max_size(assignment):
    if not assignment:
        return 0
    ret = max([x[1].size for x in assignment])
    ret = 0 if ret is None else ret
    return ret


def get_memory_usage(assignments):
    ret = 0
    for cur in assignments:
        ret += _get_max_size(cur)
    return ret


def compute_assignments_greedy(ranges_sorted, init_assignments=None):
    assignments = init_assignments or []
    visited = {y[0] for x in assignments for y in x}

    for (name, range_) in ranges_sorted:
        if name in visited:
            continue
        assigned = False
        best_assignment = 0
        min_dist = float("inf")
        candidate_size = range_.size or 0
        for idx, assignment in enumerate(assignments):
            if is_compatible(range_, assignment, []):
                assigned = True
                dist = abs(_get_max_size(assignment) - candidate_size)
                if dist < min_dist:
                    min_dist = dist
                    best_assignment = idx
        if assigned:
            assignment = assignments[best_assignment]
            assignment.append((name, range_))
        else:
            assignments.append([(name, range_)])
    return assignments


def _get_count(assignments):
    ''' Return number of blobs in assignments '''
    if assignments:
        return sum([len(x) for x in assignments])
    return 0


def compute_assignments_dp(ranges_sorted, init_assignment, counter=None):
    ''' Compute assignment for blobs in 'ranges_sorted' on top of 'init_assignment'
        using dynamic programming + recursion.

        ranges_sorted: blobs sorted by 'used'
        init_assignment: assignment to start with, blobs in 'ranges_sorted' should
                         not be used in 'init_assignment'

        Using f(b, k, init) to represent the best assignment for blobs b[0:k]
        given initial assignment 'init', we have
            f(b, k, init) = f(b, j, init) +
                            find_best(b[j:k], f(b, j, init))
        where j is the index of the last best assignment that is independent of
        blob b[k - 1] (b[k - 1] is compatible with all assignments in
        f(b, j, init)), and find_best(b1, init1) gives the best assignment
        for blobs in 'b1' based on the initial assignment 'init1', and blobs
        b1[0:-1] should be incompatible with b1[-1]. f(b, len(b), []) gives
        the best assignment for blobs 'b'.

        For find_best(b, init), since b[0:-1] are not compatible with b[-1], we
        could reduce it to a smaller problem to find best assignment for b[0:-1]
        as
            find_best(b, init) = min {
                f(b[0:-1], len(b) - 1, init - x) + [x, b[-1]] for x in init, or
                f(b[0:-1], len(b) - 1, init) + [b[-1]]
            }
        where min{} gives the assignment with minimum memory usage.
    '''

    def _get_compatible_prev(candidate_range, best_assignments, cur_idx):
        ''' Find closest position k of best_assignments that is independent of
            candidate_range that candiate_range is compatible with all assignments
            in best_assignments[k].
            Return -1 if not found.
        '''
        def is_compatible_all(candidate_range, assignments):
            ''' return true if compatible for all assignments in assignments '''
            return all([is_compatible(candidate_range[1], x, []) for x in assignments])

        ii = cur_idx - 1
        while ii >= 0:
            cba = best_assignments[ii]
            if is_compatible_all(candidate_range, cba):
                return ii
            ii -= 1
        return -1

    def _find_best(ranges, init_assignment, prev_best_assignment, counter):
        ''' Find the best assignment for blobs 'ranges' given an initialized
            assignment 'init_assignment'.

            Blobs in ranges[0:-1] should be incompatible with blob range[-1].
            'prev_best_assignment': best assignment for blobs in ranges[:-1]

            By assigning ranges[-1] to each assignment k in 'init_assignment' or
            in a new assignment, the problem becomes a smaller problem to find
            the best assignment for ranges[0:-1] given the initial assignment
            init_assigment[0:k, (k+1):-1].
        '''
        # Blob to check
        find_range = ranges[-1]
        # Blobs in ranges[0:-1] are incompatible with ranges[-1] so that we can
        # reduce it to a smaller problem.
        assert all(not is_compatible(x[1], [find_range], []) for x in ranges[0:-1])

        sz = len(init_assignment)
        best_candidates = []
        # Try to assign 'find_range' to each assignment in init_assignment
        for ii in range(sz):
            if not is_compatible(find_range[1], init_assignment[ii], []):
                continue
            cur_best = copy.deepcopy(init_assignment)
            cur_best[ii].append(find_range)
            if len(ranges) > 1:
                cur_best_tmp = [x for i, x in enumerate(cur_best) if i != ii]
                # reduce to a smaller dp problem
                cur_best_tmp = compute_assignments_dp(
                    ranges[:-1], cur_best_tmp, counter)
                cur_best = cur_best_tmp + [cur_best[ii]]
            best_candidates.append(cur_best)
        # Try to put 'find_range' in a new assignment
        best_candidates.append(prev_best_assignment + [[find_range]])

        ret = min(best_candidates, key=lambda x: get_memory_usage(x))
        return ret

    if not counter:
        counter = [0]
    counter[0] += 1

    if counter and counter[0] % 5000 == 0:
        rs = [ranges_sorted[0][1].defined, ranges_sorted[-1][1].used]
        log.info('Finding assignments {} ({} -> {})...'.format(
            counter[0], rs[0], rs[1]))

    init_assignment = init_assignment or []
    # best_assignments[k]: best assignments for first k blobs ranges_sorted[0:(k+1)]
    best_assignments = []
    # Find best assignment for blobs ranges_sorted[0:ii]
    for ii, cur_range in enumerate(ranges_sorted):
        # closest best_assignment that is independent of ranges_sorted[ii]
        prev_idx = _get_compatible_prev(cur_range, best_assignments, ii)
        prev_best = copy.deepcopy(init_assignment) if prev_idx < 0 else \
                    copy.deepcopy(best_assignments[prev_idx])
        # Need to find best assignment for blobs in 'ranges_part'
        ranges_part = ranges_sorted[(prev_idx + 1):(ii + 1)]
        cur_best = _find_best(
            ranges_part, prev_best,
            best_assignments[-1] if best_assignments else init_assignment,
            counter)
        assert _get_count(cur_best) == _get_count(prev_best) + len(ranges_part)
        best_assignments.append(copy.deepcopy(cur_best))

    assert len(best_assignments) == len(ranges_sorted)

    best = best_assignments[-1]

    return best


def get_updated_ranges(ranges, max_live=None):
    ''' Set LiveRange.defined = -1 if it is None
        Set LiveRange.used = max_live if it is None
        Set LiveRanee.size = 1 if it is None
    '''

    def _get_max_live(ranges):
        max_live = max(x[1].used for x in ranges if x[1].used) + 1
        return max_live

    def _update_range(x, max_live, size):
        cx = x
        if x[1].defined is None:
            cx = (cx[0], cx[1]._replace(defined=-1))
        if x[1].used is None:
            cx = (cx[0], cx[1]._replace(used=max_live))
        if x[1].size is None:
            cx = (cx[0], cx[1]._replace(size=size))
        return cx

    if max_live is None:
        max_live = _get_max_live(ranges)
    ranges = [_update_range(x, max_live, 1) for x in ranges]

    return ranges


def compute_assignments(ranges, static_blobs, algo):
    '''
    algo: Method used to find assignments (AssignmentAlgorithm.GREEDY or
          AssignmentAlgorithm.DYNAMIC_PROGRAMMING).
          AssignmentAlgorithm.DYNAMIC_PROGRAMMING gives optimal solution at the
          cost of more computation.
          AssignmentAlgorithm.GREEDY may be better in the case 'blob_sizes' is
          not provided.
    '''

    # Sort the ranges based on when they are last used.
    # If LiveRange.used is None, then the blob is never used and could
    # be consumed externally. Sort these to the end of the list as opposed
    # to the beginning so that they can be shared as well.
    ranges = sorted(
        ranges.items(),
        key=lambda p: (p[1].used is None, p[1].used),
    )
    # Update None values
    ranges = get_updated_ranges(ranges)

    # Sharable blobs
    ranges_sharable = [x for x in ranges if x[0] not in static_blobs]
    # Static blobs, not sharable
    ranges_static = [x for x in ranges if x[0] in static_blobs]

    log.info("Total sharable blobs {}".format(len(ranges_sharable)))

    best_assignment = []
    if algo == AssignmentAlgorithm.DYNAMIC_PROGRAMMING:
        best_assignment = compute_assignments_dp(ranges_sharable, [])
    elif algo == AssignmentAlgorithm.GREEDY:
        best_assignment = compute_assignments_greedy(ranges_sharable, [])
    else:
        assert "Invalid algo name {}".format(algo)
    best_assignment += [[x] for x in ranges_static]

    # verify_assignments(best_assignment)

    return best_assignment


def verify_assignments(assignments):
    for cur in assignments:
        for x, y in zip(cur[0:-1], cur[1:]):
            assert x[1].used < y[1].defined


def compute_interference_graph(ops):
    g = nx.DiGraph()
    for i, op in enumerate(ops):
        g.add_node(i, op=op)
    for i, parent_op in enumerate(ops):
        for j, child_op in enumerate(ops):
            if i >= j:
                continue
            if any(output in child_op.input for output in parent_op.output):
                deps = set(child_op.input).intersection(parent_op.output)
                g.add_edge(i, j, deps=deps)
                assert nx.is_directed_acyclic_graph(g), child_op
    return g


Optimization = collections.namedtuple(
    'Optimization', ['net', 'assignments', 'blob_assignments'])


def apply_assignments(net, blob_assignments):
    def canonical_name(blob):
        if blob not in blob_assignments:
            return blob
        return blob_assignments[blob]

    for op in net.op:
        # Descend into subnets of the recurrent network
        if op.type.startswith('RecurrentNetwork'):
            apply_recurrent_blob_assignments(op, blob_assignments, canonical_name)

        for i, input_ in enumerate(op.input):
            op.input[i] = canonical_name(input_)
        for i, output in enumerate(op.output):
            op.output[i] = canonical_name(output)


def apply_recurrent_blob_assignments(op, blob_assignments, canonical_name):
    log.debug("Applying assignments to recurrent op: {}".format(op.type))

    # Apply on alias_dst
    alias_dst_args = [a for a in op.arg if a.name.endswith("alias_dst")]
    for alias_dst in alias_dst_args:
        for i, blob in enumerate(alias_dst.strings):
            alias_dst.strings[i] = canonical_name(blob.decode()).encode()

    # Apply on link_external
    link_external_args = [a for a in op.arg if a.name.endswith("link_external")]
    for link_external in link_external_args:
        for i, blob in enumerate(link_external.strings):
            link_external.strings[i] = canonical_name(blob.decode()).encode()

    # Recurse into step nets
    step_args = [a for a in op.arg if a.name.endswith("step_net")]
    for step_arg in step_args:
        apply_assignments(step_arg.n, blob_assignments)
        for i, einp in enumerate(step_arg.n.external_input):
            if einp in blob_assignments:
                step_arg.n.external_input[i] = canonical_name(einp)

    # Store renamings
    for blob, renamed in blob_assignments.items():
        if blob in list(op.input) + list(op.output):
            a = caffe2_pb2.Argument()
            a.name = blob + ".rename"
            a.s = str(renamed).encode("ascii")
            op.arg.extend([a])


class AssignmentAlgorithm(enum.Enum):
    GREEDY = 0
    DYNAMIC_PROGRAMMING = 1


def optimize_inference_fast(net, static_blobs):
    optim = caffe2_pb2.NetDef()
    optim_str = C.memonger_optimize_inference_net(
        net.SerializeToString(),
        [str(s).encode('utf-8') for s in static_blobs]
    )
    optim.ParseFromString(optim_str)
    return optim


def optimize_interference(net, static_blobs,
                          ordering_function=topological_sort_traversal,
                          blob_sizes=None,
                          algo=AssignmentAlgorithm.GREEDY):
    """
    ordering_function: topological_sort_traversal or
                       topological_sort_traversal_longest_path.
                       topological_sort_traversal_longest_path gives better
                       results but needs a bit more computation.
    algo: Method used to find assignments (AssignmentAlgorithm.GREEDY or
          AssignmentAlgorithm.DYNAMIC_PROGRAMMING).
          AssignmentAlgorithm.DYNAMIC_PROGRAMMING gives optimal solution at the
          cost of more computation.
          AssignmentAlgorithm.GREEDY may be better in the case 'blob_sizes' is
          not provided.
    """

    """
    1) Use a BFS traversal of the execution graph to generate an
       ordering of the node executions.
    2) Generate use-def ranges for each `blob` in the BFS traversal
       order.
    3) Assign blobs to `canonical blobs`
    4) Rename blobs to canonical blobs
    """

    net = copy.deepcopy(net)
    g = compute_interference_graph(net.op)
    ordering = ordering_function(g)
    linearized_ops = [net.op[i] for i in ordering]

    # Reorder ops in net based on the computed linearlized order.
    # If the graph has multiple topological orderings and if the NetDef's
    # ordering differs from the order used to compute ranges, then the
    # runtime might end up overwriting blobs before they are used.
    del net.op[:]
    net.op.extend(linearized_ops)

    ranges = compute_ranges(linearized_ops, blob_sizes)
    assignments = compute_assignments(ranges, static_blobs, algo)
    blob_assignments = compute_blob_assignments(assignments)
    apply_assignments(net, blob_assignments)
    return Optimization(
        net=net,
        blob_assignments=blob_assignments,
        assignments=assignments)


def verify_inplace_blobs(net_a, net_b):
    """
    Verifies that net_a and net_b have the same in-place blob assignments.
    Particularly, that memonger did not add an in-place assignment when that
    did not exist before.
    """
    def get_inplaces(op):
        out = list(op.output)
        inplaces = []
        for j, inp in enumerate(op.input):
            if inp in out:
                inplaces.append([j, out.index(inp)])
        return inplaces

    for op_a, op_b in zip(net_a.op, net_b.op):
        if op_a.type != op_b.type:
            return False
        if get_inplaces(op_a) != get_inplaces(op_b):
            return False
    return True


def verify_graph_equality(net_a, net_b):
    """
    Determines if the execution of two graphs are identical.
    That is, all inputs blobs are mapped to the same output blobs
    for each operator in their respective positions.

    This is meant to check the output of memonger with the original graph.
    It assumes that the nets have same external input and output.

    O(E) runtime + O(1) amortized cost to hash for python dict
    """

    def parent_list(ops):
        parent_list = [[] for _ in ops]
        edge_owner = {}
        for i, op in enumerate(ops):
            for blob in op.input:
                parent_id = edge_owner.get(blob)
                if parent_id is not None:
                    parent_list[i].append(parent_id)
            for blob in op.output:
                edge_owner[blob] = i

        return parent_list

    # Operator wise equality checks
    if (len(net_a.op) != len(net_b.op)):
        return False
    for op_a, op_b in zip(net_a.op, net_b.op):
        if (op_a.type != op_b.type or
                op_a.device_option != op_b.device_option or
                op_a.engine != op_b.engine):
            return False

    # Print debug info
    parent_list_a = parent_list(net_a.op)
    parent_list_b = parent_list(net_b.op)
    if parent_list_a != parent_list_b:
        j = 0
        for a, b in zip(parent_list_a, parent_list_b):
            if a != b:
                print("Difference {} vs {} \n {}".format(
                    j, net_a.op[j], net_b.op[j]))
                print("Parents: {} vs {}".format(a, b))

            j += 1

    # Net wise equality check
    return parent_list_a == parent_list_b


Statistics = collections.namedtuple(
    'Statistics', ['baseline_nbytes', 'optimized_nbytes'])


def blob_nbytes(blob):
    sz = 0
    try:
        sz = workspace.FetchBlob(blob).nbytes
    except Exception:
        log.warning('Error when fetching blob {}'.format(blob))
    return sz


def compute_statistics(assignments):
    blob_bytes = {
        blob: blob_nbytes(blob) for assignment in assignments
        for (blob, _) in assignment}
    baseline_nbytes = sum(blob_bytes.values())
    optimized_nbytes = sum(
        max(blob_bytes[blob] for (blob, _) in assignment)
        for assignment in assignments)
    return Statistics(
        baseline_nbytes=baseline_nbytes,
        optimized_nbytes=optimized_nbytes)


def collect_blob_sizes(net):
    blobs = {}
    for op in net.op:
        for blob in op.input:
            blobs[blob] = blob_nbytes(blob)
        for blob in op.output:
            blobs[blob] = blob_nbytes(blob)

    return blobs