~bzr-pqm/bzr/bzr.dev

# Copyright (C) 2008, 2009, 2010 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

#

"""B+Tree indices"""

import cStringIO

from bisect import bisect_right

import math

import tempfile

import zlib

from bzrlib import (

    chunk_writer,

    debug,

    errors,

    fifo_cache,

    index,

    lru_cache,

    osutils,

    static_tuple,

    trace,

    transport,

    )

from bzrlib.index import _OPTION_NODE_REFS, _OPTION_KEY_ELEMENTS, _OPTION_LEN

_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 = None# tempfile.TemporaryFile(prefix='bzr-index-row-')

        self.writer = None

    def finish_node(self, pad=True):

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

        if self.nodes == 0:

            self.spool = cStringIO.StringIO()

            # padded note:

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

        elif self.nodes == 1:

            # We got bigger than 1 node, switch to a temp file

            spool = tempfile.TemporaryFile(prefix='bzr-index-row-')

            spool.write(self.spool.getvalue())

            self.spool = spool

        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

        self._optimize_for_size = False

    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.

        """

        # Ensure that 'key' is a StaticTuple

        key = static_tuple.StaticTuple.from_sequence(key).intern()

        # 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] = static_tuple.StaticTuple(node_refs, value)

        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._nodes) < 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.

        """

        if self._combine_backing_indices:

            (new_backing_file, size,

             backing_pos) = self._spill_mem_keys_and_combine()

        else:

            new_backing_file, size = self._spill_mem_keys_without_combining()

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

        #       direct access to the new_backing._file object

        new_backing = BTreeGraphIndex(transport.get_transport('.'),

                                      '<temp>', size)

        # GC will clean up the file

        new_backing._file = new_backing_file

        if self._combine_backing_indices:

            if len(self._backing_indices) == backing_pos:

                self._backing_indices.append(None)

            self._backing_indices[backing_pos] = new_backing

            for backing_pos in range(backing_pos):

                self._backing_indices[backing_pos] = None

        else:

            self._backing_indices.append(new_backing)

        self._nodes = {}

        self._nodes_by_key = None

    def _spill_mem_keys_without_combining(self):

        return self._write_nodes(self._iter_mem_nodes(), allow_optimize=False)

    def _spill_mem_keys_and_combine(self):

        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),

                              allow_optimize=False)

        return new_backing_file, size, backing_pos

    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, allow_optimize=True):

        """Add a key to the current chunk.

        :param string_key: The key to add.

        :param line: The fully serialised key and value.

        :param allow_optimize: If set to False, prevent setting the optimize

            flag when writing out. This is used by the _spill_mem_keys_to_disk

            functionality.

        """

        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

                    if allow_optimize:

                        optimize_for_size = self._optimize_for_size

                    else:

                        optimize_for_size = False

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

                        optimize_for_size=optimize_for_size)

                    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,

                optimize_for_size=self._optimize_for_size)

            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 propagate 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,

                    optimize_for_size=self._optimize_for_size)

                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, allow_optimize=allow_optimize)

    def _write_nodes(self, node_iterator, allow_optimize=True):

        """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.

        :param allow_optimize: If set to False, prevent setting the optimize

            flag when writing out. This is used by the _spill_mem_keys_to_disk

            functionality.

        :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,

        # propagate 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

            string_key, line = _btree_serializer._flatten_node(node,

                                    self.reference_lists)

            self._add_key(string_key, line, rows, allow_optimize=allow_optimize)

        for row in reversed(rows):

            pad = (type(row) != _LeafBuilderRow)

            row.finish_node(pad=pad)

        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')

        if row_lengths and row_lengths[-1] > 1:

            result = tempfile.NamedTemporaryFile(prefix='bzr-index-')

        else:

            result = cStringIO.StringIO()

        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:])

            if len(node) == _PAGE_SIZE:

                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, value, reference_lists). 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)

        # Note: We don't use keys.intersection() here. If you read the C api,

        #       set.intersection(other) special cases when other is a set and

        #       will iterate the smaller of the two and lookup in the other.

        #       It does *not* do this for any other type (even dict, unlike

        #       some other set functions.) Since we expect keys is generally <<

        #       self._nodes, it is faster to iterate over it in a list

        #       comprehension

        nodes = self._nodes

        local_keys = [key for key in keys if key in nodes]

        if self.reference_lists:

            for key in local_keys:

                node = nodes[key]

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

        else:

            for key in local_keys:

                node = nodes[key]

                yield self, key, node[1]

        # Find things that are in backing indices that have not been handled

        # yet.

        if not self._backing_indices:

            return # We won't find anything there either

        # Remove all of the keys that we found locally

        keys.difference_update(local_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, ) + tuple(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._nodes) + 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(dict):

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

    __slots__ = ('min_key', 'max_key', '_keys')

    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.

        key_list = _btree_serializer._parse_leaf_lines(bytes,

            key_length, ref_list_length)

        if key_list:

            self.min_key = key_list[0][0]

            self.max_key = key_list[-1][0]

        else:

            self.min_key = self.max_key = None

        super(_LeafNode, self).__init__(key_list)

        self._keys = dict(self)

    def all_items(self):

        """Return a sorted list of (key, (value, refs)) items"""

        items = self.items()

        items.sort()

        return items

    def all_keys(self):

        """Return a sorted list of all keys."""

        keys = self.keys()

        keys.sort()

        return keys

class _InternalNode(object):

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

    __slots__ = ('keys', 'offset')

    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:])

        as_st = static_tuple.StaticTuple.from_sequence

        for line in lines[2:]:

            if line == '':

                break

            nodes.append(as_st(map(intern, line.split('\0'))).intern())

        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, unlimited_cache=False,

                 offset=0):

        """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.

        :param unlimited_cache: If set to True, then instead of using an

            LRUCache with size _NODE_CACHE_SIZE, we will use a dict and always

            cache all leaf nodes.

        :param offset: The start of the btree index data isn't byte 0 of the

            file. Instead it starts at some point later.

        """

        self._transport = transport

        self._name = name

        self._size = size

        self._file = None

        self._recommended_pages = self._compute_recommended_pages()

        self._root_node = None

        self._base_offset = offset

        self._leaf_factory = _LeafNode

        # Default max size is 100,000 leave values

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

        if unlimited_cache:

            self._leaf_node_cache = {}

            self._internal_node_cache = {}

        else:

            self._leaf_node_cache = lru_cache.LRUCache(_NODE_CACHE_SIZE)

            # We use a FIFO here just to prevent possible blowout. However, a

            # 300k record btree has only 3k leaf nodes, and only 20 internal

            # nodes. A value of 100 scales to ~100*100*100 = 1M records.

            self._internal_node_cache = fifo_cache.FIFOCache(100)

        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."""