~bzr-pqm/bzr/bzr.dev

# Copyright (C) 2008 Canonical Ltd

#

# This program is free software; you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation; either version 2 of the License, or

# (at your option) any later version.

#

# This program is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

# GNU General Public License for more details.

#

# You should have received a copy of the GNU General Public License

# along with this program; if not, write to the Free Software

# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

#

"""B+Tree indices"""

import array

import bisect

from bisect import bisect_right

from copy import deepcopy

import math

import struct

import tempfile

import zlib

from bzrlib import (

    chunk_writer,

    debug,

    errors,

    index,

    lru_cache,

    osutils,

    trace,

    )

from bzrlib.index import _OPTION_NODE_REFS, _OPTION_KEY_ELEMENTS, _OPTION_LEN

from bzrlib.transport import get_transport

_BTSIGNATURE = "B+Tree Graph Index 2\n"

_OPTION_ROW_LENGTHS = "row_lengths="

_LEAF_FLAG = "type=leaf\n"

_INTERNAL_FLAG = "type=internal\n"

_INTERNAL_OFFSET = "offset="

_RESERVED_HEADER_BYTES = 120

_PAGE_SIZE = 4096

# 4K per page: 4MB - 1000 entries

_NODE_CACHE_SIZE = 1000

class _BuilderRow(object):

    """The stored state accumulated while writing out a row in the index.

    :ivar spool: A temporary file used to accumulate nodes for this row

        in the tree.

    :ivar nodes: The count of nodes emitted so far.

    """

    def __init__(self):

        """Create a _BuilderRow."""

        self.nodes = 0

        self.spool = tempfile.TemporaryFile()

        self.writer = None

    def finish_node(self, pad=True):

        byte_lines, _, padding = self.writer.finish()

        if self.nodes == 0:

            # padded note:

            self.spool.write("\x00" * _RESERVED_HEADER_BYTES)

        skipped_bytes = 0

        if not pad and padding:

            del byte_lines[-1]

            skipped_bytes = padding

        self.spool.writelines(byte_lines)

        remainder = (self.spool.tell() + skipped_bytes) % _PAGE_SIZE

        if remainder != 0:

            raise AssertionError("incorrect node length: %d, %d"

                                 % (self.spool.tell(), remainder))

        self.nodes += 1

        self.writer = None

class _InternalBuilderRow(_BuilderRow):

    """The stored state accumulated while writing out internal rows."""

    def finish_node(self, pad=True):

        if not pad:

            raise AssertionError("Must pad internal nodes only.")

        _BuilderRow.finish_node(self)

class _LeafBuilderRow(_BuilderRow):

    """The stored state accumulated while writing out a leaf rows."""

class BTreeBuilder(index.GraphIndexBuilder):

    """A Builder for B+Tree based Graph indices.

    The resulting graph has the structure:

    _SIGNATURE OPTIONS NODES

    _SIGNATURE     := 'B+Tree Graph Index 1' NEWLINE

    OPTIONS        := REF_LISTS KEY_ELEMENTS LENGTH

    REF_LISTS      := 'node_ref_lists=' DIGITS NEWLINE

    KEY_ELEMENTS   := 'key_elements=' DIGITS NEWLINE

    LENGTH         := 'len=' DIGITS NEWLINE

    ROW_LENGTHS    := 'row_lengths' DIGITS (COMMA DIGITS)*

    NODES          := NODE_COMPRESSED*

    NODE_COMPRESSED:= COMPRESSED_BYTES{4096}

    NODE_RAW       := INTERNAL | LEAF

    INTERNAL       := INTERNAL_FLAG POINTERS

    LEAF           := LEAF_FLAG ROWS

    KEY_ELEMENT    := Not-whitespace-utf8

    KEY            := KEY_ELEMENT (NULL KEY_ELEMENT)*

    ROWS           := ROW*

    ROW            := KEY NULL ABSENT? NULL REFERENCES NULL VALUE NEWLINE

    ABSENT         := 'a'

    REFERENCES     := REFERENCE_LIST (TAB REFERENCE_LIST){node_ref_lists - 1}

    REFERENCE_LIST := (REFERENCE (CR REFERENCE)*)?

    REFERENCE      := KEY

    VALUE          := no-newline-no-null-bytes

    """

    def __init__(self, reference_lists=0, key_elements=1, spill_at=100000):

        """See GraphIndexBuilder.__init__.

        :param spill_at: Optional parameter controlling the maximum number

            of nodes that BTreeBuilder will hold in memory.

        """

        index.GraphIndexBuilder.__init__(self, reference_lists=reference_lists,

            key_elements=key_elements)

        self._spill_at = spill_at

        self._backing_indices = []

        # A map of {key: (node_refs, value)}

        self._nodes = {}

        # Indicate it hasn't been built yet

        self._nodes_by_key = None

    def add_node(self, key, value, references=()):

        """Add a node to the index.

        If adding the node causes the builder to reach its spill_at threshold,

        disk spilling will be triggered.

        :param key: The key. keys are non-empty tuples containing

            as many whitespace-free utf8 bytestrings as the key length

            defined for this index.

        :param references: An iterable of iterables of keys. Each is a

            reference to another key.

        :param value: The value to associate with the key. It may be any

            bytes as long as it does not contain \0 or \n.

        """

        # we don't care about absent_references

        node_refs, _ = self._check_key_ref_value(key, references, value)

        if key in self._nodes:

            raise errors.BadIndexDuplicateKey(key, self)

        self._nodes[key] = (node_refs, value)

        self._keys.add(key)

        if self._nodes_by_key is not None and self._key_length > 1:

            self._update_nodes_by_key(key, value, node_refs)

        if len(self._keys) < self._spill_at:

            return

        self._spill_mem_keys_to_disk()

    def _spill_mem_keys_to_disk(self):

        """Write the in memory keys down to disk to cap memory consumption.

        If we already have some keys written to disk, we will combine them so

        as to preserve the sorted order.  The algorithm for combining uses

        powers of two.  So on the first spill, write all mem nodes into a

        single index. On the second spill, combine the mem nodes with the nodes

        on disk to create a 2x sized disk index and get rid of the first index.

        On the third spill, create a single new disk index, which will contain

        the mem nodes, and preserve the existing 2x sized index.  On the fourth,

        combine mem with the first and second indexes, creating a new one of

        size 4x. On the fifth create a single new one, etc.

        """

        iterators_to_combine = [self._iter_mem_nodes()]

        pos = -1

        for pos, backing in enumerate(self._backing_indices):

            if backing is None:

                pos -= 1

                break

            iterators_to_combine.append(backing.iter_all_entries())

        backing_pos = pos + 1

        new_backing_file, size = \

            self._write_nodes(self._iter_smallest(iterators_to_combine))

        dir_path, base_name = osutils.split(new_backing_file.name)

        # Note: The transport here isn't strictly needed, because we will use

        #       direct access to the new_backing._file object

        new_backing = BTreeGraphIndex(get_transport(dir_path),

                                      base_name, size)

        # GC will clean up the file

        new_backing._file = new_backing_file

        if len(self._backing_indices) == backing_pos:

            self._backing_indices.append(None)

        self._backing_indices[backing_pos] = new_backing

        for pos in range(backing_pos):

            self._backing_indices[pos] = None

        self._keys = set()

        self._nodes = {}

        self._nodes_by_key = None

    def add_nodes(self, nodes):

        """Add nodes to the index.

        :param nodes: An iterable of (key, node_refs, value) entries to add.

        """

        if self.reference_lists:

            for (key, value, node_refs) in nodes:

                self.add_node(key, value, node_refs)

        else:

            for (key, value) in nodes:

                self.add_node(key, value)

    def _iter_mem_nodes(self):

        """Iterate over the nodes held in memory."""

        nodes = self._nodes

        if self.reference_lists:

            for key in sorted(nodes):

                references, value = nodes[key]

                yield self, key, value, references

        else:

            for key in sorted(nodes):

                references, value = nodes[key]

                yield self, key, value

    def _iter_smallest(self, iterators_to_combine):

        if len(iterators_to_combine) == 1:

            for value in iterators_to_combine[0]:

                yield value

            return

        current_values = []

        for iterator in iterators_to_combine:

            try:

                current_values.append(iterator.next())

            except StopIteration:

                current_values.append(None)

        last = None

        while True:

            # Decorate candidates with the value to allow 2.4's min to be used.

            candidates = [(item[1][1], item) for item

                in enumerate(current_values) if item[1] is not None]

            if not len(candidates):

                return

            selected = min(candidates)

            # undecorate back to (pos, node)

            selected = selected[1]

            if last == selected[1][1]:

                raise errors.BadIndexDuplicateKey(last, self)

            last = selected[1][1]

            # Yield, with self as the index

            yield (self,) + selected[1][1:]

            pos = selected[0]

            try:

                current_values[pos] = iterators_to_combine[pos].next()

            except StopIteration:

                current_values[pos] = None

    def _add_key(self, string_key, line, rows):

        """Add a key to the current chunk.

        :param string_key: The key to add.

        :param line: The fully serialised key and value.

        """

        if rows[-1].writer is None:

            # opening a new leaf chunk;

            for pos, internal_row in enumerate(rows[:-1]):

                # flesh out any internal nodes that are needed to

                # preserve the height of the tree

                if internal_row.writer is None:

                    length = _PAGE_SIZE

                    if internal_row.nodes == 0:

                        length -= _RESERVED_HEADER_BYTES # padded

                    internal_row.writer = chunk_writer.ChunkWriter(length, 0)

                    internal_row.writer.write(_INTERNAL_FLAG)

                    internal_row.writer.write(_INTERNAL_OFFSET +

                        str(rows[pos + 1].nodes) + "\n")

            # add a new leaf

            length = _PAGE_SIZE

            if rows[-1].nodes == 0:

                length -= _RESERVED_HEADER_BYTES # padded

            rows[-1].writer = chunk_writer.ChunkWriter(length)

            rows[-1].writer.write(_LEAF_FLAG)

        if rows[-1].writer.write(line):

            # this key did not fit in the node:

            rows[-1].finish_node()

            key_line = string_key + "\n"

            new_row = True

            for row in reversed(rows[:-1]):

                # Mark the start of the next node in the node above. If it

                # doesn't fit then propogate upwards until we find one that

                # it does fit into.

                if row.writer.write(key_line):

                    row.finish_node()

                else:

                    # We've found a node that can handle the pointer.

                    new_row = False

                    break

            # If we reached the current root without being able to mark the

            # division point, then we need a new root:

            if new_row:

                # We need a new row

                if 'index' in debug.debug_flags:

                    trace.mutter('Inserting new global row.')

                new_row = _InternalBuilderRow()

                reserved_bytes = 0

                rows.insert(0, new_row)

                # This will be padded, hence the -100

                new_row.writer = chunk_writer.ChunkWriter(

                    _PAGE_SIZE - _RESERVED_HEADER_BYTES,

                    reserved_bytes)

                new_row.writer.write(_INTERNAL_FLAG)

                new_row.writer.write(_INTERNAL_OFFSET +

                    str(rows[1].nodes - 1) + "\n")

                new_row.writer.write(key_line)

            self._add_key(string_key, line, rows)

    def _write_nodes(self, node_iterator):

        """Write node_iterator out as a B+Tree.

        :param node_iterator: An iterator of sorted nodes. Each node should

            match the output given by iter_all_entries.

        :return: A file handle for a temporary file containing a B+Tree for

            the nodes.

        """

        # The index rows - rows[0] is the root, rows[1] is the layer under it

        # etc.

        rows = []

        # forward sorted by key. In future we may consider topological sorting,

        # at the cost of table scans for direct lookup, or a second index for

        # direct lookup

        key_count = 0

        # A stack with the number of nodes of each size. 0 is the root node

        # and must always be 1 (if there are any nodes in the tree).

        self.row_lengths = []

        # Loop over all nodes adding them to the bottom row

        # (rows[-1]). When we finish a chunk in a row,

        # propogate the key that didn't fit (comes after the chunk) to the

        # row above, transitively.

        for node in node_iterator:

            if key_count == 0:

                # First key triggers the first row

                rows.append(_LeafBuilderRow())

            key_count += 1

            # TODO: Flattening the node into a string key and a line should

            #       probably be put into a pyrex function. We can do a quick

            #       iter over all the entries to determine the final length,

            #       and then do a single malloc() rather than lots of

            #       intermediate mallocs as we build everything up.

            #       ATM 3 / 13s are spent flattening nodes (10s is compressing)

            string_key, line = _btree_serializer._flatten_node(node,

                                    self.reference_lists)

            self._add_key(string_key, line, rows)

        for row in reversed(rows):

            pad = (type(row) != _LeafBuilderRow)

            row.finish_node(pad=pad)

        result = tempfile.NamedTemporaryFile()

        lines = [_BTSIGNATURE]

        lines.append(_OPTION_NODE_REFS + str(self.reference_lists) + '\n')

        lines.append(_OPTION_KEY_ELEMENTS + str(self._key_length) + '\n')

        lines.append(_OPTION_LEN + str(key_count) + '\n')

        row_lengths = [row.nodes for row in rows]

        lines.append(_OPTION_ROW_LENGTHS + ','.join(map(str, row_lengths)) + '\n')

        result.writelines(lines)

        position = sum(map(len, lines))

        root_row = True

        if position > _RESERVED_HEADER_BYTES:

            raise AssertionError("Could not fit the header in the"

                                 " reserved space: %d > %d"

                                 % (position, _RESERVED_HEADER_BYTES))

        # write the rows out:

        for row in rows:

            reserved = _RESERVED_HEADER_BYTES # reserved space for first node

            row.spool.flush()

            row.spool.seek(0)

            # copy nodes to the finalised file.

            # Special case the first node as it may be prefixed

            node = row.spool.read(_PAGE_SIZE)

            result.write(node[reserved:])

            result.write("\x00" * (reserved - position))

            position = 0 # Only the root row actually has an offset

            copied_len = osutils.pumpfile(row.spool, result)

            if copied_len != (row.nodes - 1) * _PAGE_SIZE:

                if type(row) != _LeafBuilderRow:

                    raise AssertionError("Incorrect amount of data copied"

                        " expected: %d, got: %d"

                        % ((row.nodes - 1) * _PAGE_SIZE,

                           copied_len))

        result.flush()

        size = result.tell()

        result.seek(0)

        return result, size

    def finish(self):

        """Finalise the index.

        :return: A file handle for a temporary file containing the nodes added

            to the index.

        """

        return self._write_nodes(self.iter_all_entries())[0]

    def iter_all_entries(self):

        """Iterate over all keys within the index

        :return: An iterable of (index, key, reference_lists, value). There is no

            defined order for the result iteration - it will be in the most

            efficient order for the index (in this case dictionary hash order).

        """

        if 'evil' in debug.debug_flags:

            trace.mutter_callsite(3,

                "iter_all_entries scales with size of history.")

        # Doing serial rather than ordered would be faster; but this shouldn't

        # be getting called routinely anyway.

        iterators = [self._iter_mem_nodes()]

        for backing in self._backing_indices:

            if backing is not None:

                iterators.append(backing.iter_all_entries())

        if len(iterators) == 1:

            return iterators[0]

        return self._iter_smallest(iterators)

    def iter_entries(self, keys):

        """Iterate over keys within the index.

        :param keys: An iterable providing the keys to be retrieved.

        :return: An iterable of (index, key, value, reference_lists). There is no

            defined order for the result iteration - it will be in the most

            efficient order for the index (keys iteration order in this case).

        """

        keys = set(keys)

        if self.reference_lists:

            for key in keys.intersection(self._keys):

                node = self._nodes[key]

                yield self, key, node[1], node[0]

        else:

            for key in keys.intersection(self._keys):

                node = self._nodes[key]

                yield self, key, node[1]

        keys.difference_update(self._keys)

        for backing in self._backing_indices:

            if backing is None:

                continue

            if not keys:

                return

            for node in backing.iter_entries(keys):

                keys.remove(node[1])

                yield (self,) + node[1:]

    def iter_entries_prefix(self, keys):

        """Iterate over keys within the index using prefix matching.

        Prefix matching is applied within the tuple of a key, not to within

        the bytestring of each key element. e.g. if you have the keys ('foo',

        'bar'), ('foobar', 'gam') and do a prefix search for ('foo', None) then

        only the former key is returned.

        :param keys: An iterable providing the key prefixes to be retrieved.

            Each key prefix takes the form of a tuple the length of a key, but

            with the last N elements 'None' rather than a regular bytestring.

            The first element cannot be 'None'.

        :return: An iterable as per iter_all_entries, but restricted to the

            keys with a matching prefix to those supplied. No additional keys

            will be returned, and every match that is in the index will be

            returned.

        """

        # XXX: To much duplication with the GraphIndex class; consider finding

        # a good place to pull out the actual common logic.

        keys = set(keys)

        if not keys:

            return

        for backing in self._backing_indices:

            if backing is None:

                continue

            for node in backing.iter_entries_prefix(keys):

                yield (self,) + node[1:]

        if self._key_length == 1:

            for key in keys:

                # sanity check

                if key[0] is None:

                    raise errors.BadIndexKey(key)

                if len(key) != self._key_length:

                    raise errors.BadIndexKey(key)

                try:

                    node = self._nodes[key]

                except KeyError:

                    continue

                if self.reference_lists:

                    yield self, key, node[1], node[0]

                else:

                    yield self, key, node[1]

            return

        for key in keys:

            # sanity check

            if key[0] is None:

                raise errors.BadIndexKey(key)

            if len(key) != self._key_length:

                raise errors.BadIndexKey(key)

            # find what it refers to:

            key_dict = self._get_nodes_by_key()

            elements = list(key)

            # find the subdict to return

            try:

                while len(elements) and elements[0] is not None:

                    key_dict = key_dict[elements[0]]

                    elements.pop(0)

            except KeyError:

                # a non-existant lookup.

                continue

            if len(elements):

                dicts = [key_dict]

                while dicts:

                    key_dict = dicts.pop(-1)

                    # can't be empty or would not exist

                    item, value = key_dict.iteritems().next()

                    if type(value) == dict:

                        # push keys

                        dicts.extend(key_dict.itervalues())

                    else:

                        # yield keys

                        for value in key_dict.itervalues():

                            yield (self, ) + value

            else:

                yield (self, ) + key_dict

    def _get_nodes_by_key(self):

        if self._nodes_by_key is None:

            nodes_by_key = {}

            if self.reference_lists:

                for key, (references, value) in self._nodes.iteritems():

                    key_dict = nodes_by_key

                    for subkey in key[:-1]:

                        key_dict = key_dict.setdefault(subkey, {})

                    key_dict[key[-1]] = key, value, references

            else:

                for key, (references, value) in self._nodes.iteritems():

                    key_dict = nodes_by_key

                    for subkey in key[:-1]:

                        key_dict = key_dict.setdefault(subkey, {})

                    key_dict[key[-1]] = key, value

            self._nodes_by_key = nodes_by_key

        return self._nodes_by_key

    def key_count(self):

        """Return an estimate of the number of keys in this index.

        For InMemoryGraphIndex the estimate is exact.

        """

        return len(self._keys) + sum(backing.key_count() for backing in

            self._backing_indices if backing is not None)

    def validate(self):

        """In memory index's have no known corruption at the moment."""

class _LeafNode(object):

    """A leaf node for a serialised B+Tree index."""

    def __init__(self, bytes, key_length, ref_list_length):

        """Parse bytes to create a leaf node object."""

        # splitlines mangles the \r delimiters.. don't use it.

        self.keys = dict(_btree_serializer._parse_leaf_lines(bytes,

            key_length, ref_list_length))

class _InternalNode(object):

    """An internal node for a serialised B+Tree index."""

    def __init__(self, bytes):

        """Parse bytes to create an internal node object."""

        # splitlines mangles the \r delimiters.. don't use it.

        self.keys = self._parse_lines(bytes.split('\n'))

    def _parse_lines(self, lines):

        nodes = []

        self.offset = int(lines[1][7:])

        for line in lines[2:]:

            if line == '':

                break

            nodes.append(tuple(line.split('\0')))

        return nodes

class BTreeGraphIndex(object):

    """Access to nodes via the standard GraphIndex interface for B+Tree's.

    Individual nodes are held in a LRU cache. This holds the root node in

    memory except when very large walks are done.

    """

    def __init__(self, transport, name, size):

        """Create a B+Tree index object on the index name.

        :param transport: The transport to read data for the index from.

        :param name: The file name of the index on transport.

        :param size: Optional size of the index in bytes. This allows

            compatibility with the GraphIndex API, as well as ensuring that

            the initial read (to read the root node header) can be done

            without over-reading even on empty indices, and on small indices

            allows single-IO to read the entire index.

        """

        self._transport = transport

        self._name = name

        self._size = size

        self._file = None

        self._page_size = transport.recommended_page_size()

        self._root_node = None

        # Default max size is 100,000 leave values

        self._leaf_value_cache = None # lru_cache.LRUCache(100*1000)

        self._leaf_node_cache = lru_cache.LRUCache(_NODE_CACHE_SIZE)

        self._internal_node_cache = lru_cache.LRUCache()

        self._key_count = None

        self._row_lengths = None

        self._row_offsets = None # Start of each row, [-1] is the end

    def __eq__(self, other):

        """Equal when self and other were created with the same parameters."""

        return (

            type(self) == type(other) and

            self._transport == other._transport and

            self._name == other._name and

            self._size == other._size)

    def __ne__(self, other):

        return not self.__eq__(other)

    def _get_root_node(self):

        if self._root_node is None:

            # We may not have a root node yet

            nodes = list(self._read_nodes([0]))

            if len(nodes):

                self._root_node = nodes[0][1]

        return self._root_node

    def _cache_nodes(self, nodes, cache):

        """Read nodes and cache them in the lru.

        The nodes list supplied is sorted and then read from disk, each node

        being inserted it into the _node_cache.

        Note: Asking for more nodes than the _node_cache can contain will

        result in some of the results being immediately discarded, to prevent

        this an assertion is raised if more nodes are asked for than are

        cachable.

        :return: A dict of {node_pos: node}

        """

        if len(nodes) > cache._max_cache:

            trace.mutter('Requesting %s > %s nodes, not all will be cached',

                         len(nodes), cache._max_cache)

        found = {}

        for node_pos, node in self._read_nodes(sorted(nodes)):

            if node_pos == 0: # Special case

                self._root_node = node

            else:

                cache.add(node_pos, node)

            found[node_pos] = node

        return found

    def _get_nodes(self, cache, node_indexes):

        found = {}

        needed = []

        for idx in node_indexes:

            if idx == 0 and self._root_node is not None:

                found[0] = self._root_node

                continue

            try:

                found[idx] = cache[idx]

            except KeyError:

                needed.append(idx)

        found.update(self._cache_nodes(needed, cache))

        return found

    def _get_internal_nodes(self, node_indexes):

        """Get a node, from cache or disk.

        After getting it, the node will be cached.

        """

        return self._get_nodes(self._internal_node_cache, node_indexes)

    def _get_leaf_nodes(self, node_indexes):

        """Get a bunch of nodes, from cache or disk."""

        found = self._get_nodes(self._leaf_node_cache, node_indexes)

        if self._leaf_value_cache is not None:

            for node in found.itervalues():

                for key, value in node.keys.iteritems():

                    if key in self._leaf_value_cache:

                        # Don't add the rest of the keys, we've seen this node

                        # before.

                        break

                    self._leaf_value_cache[key] = value

        return found

    def iter_all_entries(self):

        """Iterate over all keys within the index.

        :return: An iterable of (index, key, value) or (index, key, value, reference_lists).

            The former tuple is used when there are no reference lists in the

            index, making the API compatible with simple key:value index types.

            There is no defined order for the result iteration - it will be in

            the most efficient order for the index.

        """

        if 'evil' in debug.debug_flags:

            trace.mutter_callsite(3,

                "iter_all_entries scales with size of history.")

        if not self.key_count():

            return

        start_of_leaves = self._row_offsets[-2]

        end_of_leaves = self._row_offsets[-1]

        needed_nodes = range(start_of_leaves, end_of_leaves)

        # We iterate strictly in-order so that we can use this function

        # for spilling index builds to disk.

        if self.node_ref_lists:

            for _, node in self._read_nodes(needed_nodes):

                for key, (value, refs) in sorted(node.keys.items()):

                    yield (self, key, value, refs)

        else:

            for _, node in self._read_nodes(needed_nodes):

                for key, (value, refs) in sorted(node.keys.items()):

                    yield (self, key, value)

    @staticmethod

    def _multi_bisect_right(in_keys, fixed_keys):

        """Find the positions where each 'in_key' would fit in fixed_keys.

        This is equivalent to doing "bisect_right" on each in_key into

        fixed_keys

        :param in_keys: A sorted list of keys to match with fixed_keys

        :param fixed_keys: A sorted list of keys to match against

        :return: A list of (integer position, [key list]) tuples.

        """

        if not in_keys:

            return []

        if not fixed_keys:

            # no pointers in the fixed_keys list, which means everything must

            # fall to the left.

            return [(0, in_keys)]