€•eM      Œsphinx.addnodes”Œdocument”“”)”}”(Œ	rawsource”Œ ”Œchildren”]”(Œtranslations”ŒLanguagesNode”“”)”}”(hhh]”(h Œpending_xref”“”)”}”(hhh]”Œdocutils.nodes”ŒText”“”ŒChinese (Simplified)”…””}”(hhŒparent”hubaŒ
attributes”}”(Œids”]”Œclasses”]”Œnames”]”Œdupnames”]”Œbackrefs”]”Œ	refdomain”Œstd”Œreftype”Œdoc”Œ	reftarget”Œ%/translations/zh_CN/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuŒtagname”hhhubh)”}”(hhh]”hŒChinese (Traditional)”…””}”(hhhh2ubah}”(h]”h ]”h"]”h$]”h&]”Œ	refdomain”h)Œreftype”h+Œ	reftarget”Œ%/translations/zh_TW/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuh1hhhubh)”}”(hhh]”hŒItalian”…””}”(hhhhFubah}”(h]”h ]”h"]”h$]”h&]”Œ	refdomain”h)Œreftype”h+Œ	reftarget”Œ%/translations/it_IT/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuh1hhhubh)”}”(hhh]”hŒJapanese”…””}”(hhhhZubah}”(h]”h ]”h"]”h$]”h&]”Œ	refdomain”h)Œreftype”h+Œ	reftarget”Œ%/translations/ja_JP/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuh1hhhubh)”}”(hhh]”hŒKorean”…””}”(hhhhnubah}”(h]”h ]”h"]”h$]”h&]”Œ	refdomain”h)Œreftype”h+Œ	reftarget”Œ%/translations/ko_KR/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuh1hhhubh)”}”(hhh]”hŒSpanish”…””}”(hhhh‚ubah}”(h]”h ]”h"]”h$]”h&]”Œ	refdomain”h)Œreftype”h+Œ	reftarget”Œ%/translations/sp_SP/RCU/rculist_nulls”Œmodname”NŒ	classname”NŒrefexplicit”ˆuh1hhhubeh}”(h]”h ]”h"]”h$]”h&]”Œcurrent_language”ŒEnglish”uh1h
hhŒ	_document”hŒsource”NŒline”NubhŒcomment”“”)”}”(hŒ SPDX-License-Identifier: GPL-2.0”h]”hŒ SPDX-License-Identifier: GPL-2.0”…””}”(hhhh£ubah}”(h]”h ]”h"]”h$]”h&]”Œ	xml:space”Œpreserve”uh1h¡hhhžhhŸŒ?/var/lib/git/docbuild/linux/Documentation/RCU/rculist_nulls.rst”h KubhŒsection”“”)”}”(hhh]”(hŒtitle”“”)”}”(hŒ1Using RCU hlist_nulls to protect list and objects”h]”hŒ1Using RCU hlist_nulls to protect list and objects”…””}”(hh½hh»hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hh¶hžhhŸh³h KubhŒ	paragraph”“”)”}”(hŒ…This section describes how to use hlist_nulls to
protect read-mostly linked lists and
objects using SLAB_TYPESAFE_BY_RCU allocations.”h]”hŒ…This section describes how to use hlist_nulls to
protect read-mostly linked lists and
objects using SLAB_TYPESAFE_BY_RCU allocations.”…””}”(hhÍhhËhžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h Khh¶hžhubhÊ)”}”(hŒ&Please read the basics in listRCU.rst.”h]”hŒ&Please read the basics in listRCU.rst.”…””}”(hhÛhhÙhžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h Khh¶hžhubhµ)”}”(hhh]”(hº)”}”(hŒUsing 'nulls'”h]”hŒUsing â€˜nullsâ€™”…””}”(hhìhhêhžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hhçhžhhŸh³h KubhÊ)”}”(hŒUUsing special makers (called 'nulls') is a convenient way
to solve following problem.”h]”hŒYUsing special makers (called â€˜nullsâ€™) is a convenient way
to solve following problem.”…””}”(hhúhhøhžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h KhhçhžhubhÊ)”}”(hŒñWithout 'nulls', a typical RCU linked list managing objects which are
allocated with SLAB_TYPESAFE_BY_RCU kmem_cache can use the following
algorithms.  Following examples assume 'obj' is a pointer to such
objects, which is having below type.”h]”hŒùWithout â€˜nullsâ€™, a typical RCU linked list managing objects which are
allocated with SLAB_TYPESAFE_BY_RCU kmem_cache can use the following
algorithms.  Following examples assume â€˜objâ€™ is a pointer to such
objects, which is having below type.”…””}”(hj  hj  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h KhhçhžhubhŒliteral_block”“”)”}”(hŒWstruct object {
  struct hlist_node obj_node;
  atomic_t refcnt;
  unsigned int key;
};”h]”hŒWstruct object {
  struct hlist_node obj_node;
  atomic_t refcnt;
  unsigned int key;
};”…””}”(hhhj  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h Khhçhžhubhµ)”}”(hhh]”(hº)”}”(hŒ1) Lookup algorithm”h]”hŒ1) Lookup algorithm”…””}”(hj)  hj'  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj$  hžhhŸh³h K!ubj  )”}”(hXã  begin:
rcu_read_lock();
obj = lockless_lookup(key);
if (obj) {
  if (!try_get_ref(obj)) { // might fail for free objects
    rcu_read_unlock();
    goto begin;
  }
  /*
  * Because a writer could delete object, and a writer could
  * reuse these object before the RCU grace period, we
  * must check key after getting the reference on object
  */
  if (obj->key != key) { // not the object we expected
    put_ref(obj);
    rcu_read_unlock();
    goto begin;
  }
}
rcu_read_unlock();”h]”hXã  begin:
rcu_read_lock();
obj = lockless_lookup(key);
if (obj) {
  if (!try_get_ref(obj)) { // might fail for free objects
    rcu_read_unlock();
    goto begin;
  }
  /*
  * Because a writer could delete object, and a writer could
  * reuse these object before the RCU grace period, we
  * must check key after getting the reference on object
  */
  if (obj->key != key) { // not the object we expected
    put_ref(obj);
    rcu_read_unlock();
    goto begin;
  }
}
rcu_read_unlock();”…””}”(hhhj5  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h K%hj$  hžhubhÊ)”}”(hŒŽBeware that lockless_lookup(key) cannot use traditional hlist_for_each_entry_rcu()
but a version with an additional memory barrier (smp_rmb())”h]”hŒŽBeware that lockless_lookup(key) cannot use traditional hlist_for_each_entry_rcu()
but a version with an additional memory barrier (smp_rmb())”…””}”(hjE  hjC  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h K:hj$  hžhubj  )”}”(hXM  lockless_lookup(key)
{
  struct hlist_node *node, *next;
  for (pos = rcu_dereference((head)->first);
       pos && ({ next = pos->next; smp_rmb(); prefetch(next); 1; }) &&
       ({ obj = hlist_entry(pos, typeof(*obj), obj_node); 1; });
       pos = rcu_dereference(next))
    if (obj->key == key)
      return obj;
  return NULL;
}”h]”hXM  lockless_lookup(key)
{
  struct hlist_node *node, *next;
  for (pos = rcu_dereference((head)->first);
       pos && ({ next = pos->next; smp_rmb(); prefetch(next); 1; }) &&
       ({ obj = hlist_entry(pos, typeof(*obj), obj_node); 1; });
       pos = rcu_dereference(next))
    if (obj->key == key)
      return obj;
  return NULL;
}”…””}”(hhhjQ  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h K?hj$  hžhubhÊ)”}”(hŒKAnd note the traditional hlist_for_each_entry_rcu() misses this smp_rmb()::”h]”hŒJAnd note the traditional hlist_for_each_entry_rcu() misses this smp_rmb():”…””}”(hŒJAnd note the traditional hlist_for_each_entry_rcu() misses this smp_rmb():”hj_  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h KKhj$  hžhubj  )”}”(hX
  struct hlist_node *node;
for (pos = rcu_dereference((head)->first);
     pos && ({ prefetch(pos->next); 1; }) &&
     ({ obj = hlist_entry(pos, typeof(*obj), obj_node); 1; });
     pos = rcu_dereference(pos->next))
  if (obj->key == key)
    return obj;
return NULL;”h]”hX
  struct hlist_node *node;
for (pos = rcu_dereference((head)->first);
     pos && ({ prefetch(pos->next); 1; }) &&
     ({ obj = hlist_entry(pos, typeof(*obj), obj_node); 1; });
     pos = rcu_dereference(pos->next))
  if (obj->key == key)
    return obj;
return NULL;”…””}”(hhhjn  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h KMhj$  hžhubhÊ)”}”(hŒQuoting Corey Minyard::”h]”hŒQuoting Corey Minyard:”…””}”(hŒQuoting Corey Minyard:”hj|  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h KVhj$  hžhubj  )”}”(hXï  "If the object is moved from one list to another list in-between the
time the hash is calculated and the next field is accessed, and the
object has moved to the end of a new list, the traversal will not
complete properly on the list it should have, since the object will
be on the end of the new list and there's not a way to tell it's on a
new list and restart the list traversal. I think that this can be
solved by pre-fetching the "next" field (with proper barriers) before
checking the key."”h]”hXï  "If the object is moved from one list to another list in-between the
time the hash is calculated and the next field is accessed, and the
object has moved to the end of a new list, the traversal will not
complete properly on the list it should have, since the object will
be on the end of the new list and there's not a way to tell it's on a
new list and restart the list traversal. I think that this can be
solved by pre-fetching the "next" field (with proper barriers) before
checking the key."”…””}”(hhhj‹  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h KXhj$  hžhubeh}”(h]”Œlookup-algorithm”ah ]”h"]”h$]”Œ1) lookup algorithm”ah&]”uh1h´hhçhžhhŸh³h K!Œ
referenced”Kubhµ)”}”(hhh]”(hº)”}”(hŒ2) Insertion algorithm”h]”hŒ2) Insertion algorithm”…””}”(hj§  hj¥  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj¢  hžhhŸh³h KbubhÊ)”}”(hX_  We need to make sure a reader cannot read the new 'obj->obj_node.next' value
and previous value of 'obj->key'. Otherwise, an item could be deleted
from a chain, and inserted into another chain. If new chain was empty
before the move, 'next' pointer is NULL, and lockless reader can not
detect the fact that it missed following items in original chain.”h]”hXk  We need to make sure a reader cannot read the new â€˜obj->obj_node.nextâ€™ value
and previous value of â€˜obj->keyâ€™. Otherwise, an item could be deleted
from a chain, and inserted into another chain. If new chain was empty
before the move, â€˜nextâ€™ pointer is NULL, and lockless reader can not
detect the fact that it missed following items in original chain.”…””}”(hjµ  hj³  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h Kdhj¢  hžhubj  )”}”(hXH  /*
 * Please note that new inserts are done at the head of list,
 * not in the middle or end.
 */
obj = kmem_cache_alloc(...);
lock_chain(); // typically a spin_lock()
obj->key = key;
atomic_set_release(&obj->refcnt, 1); // key before refcnt
hlist_add_head_rcu(&obj->obj_node, list);
unlock_chain(); // typically a spin_unlock()”h]”hXH  /*
 * Please note that new inserts are done at the head of list,
 * not in the middle or end.
 */
obj = kmem_cache_alloc(...);
lock_chain(); // typically a spin_lock()
obj->key = key;
atomic_set_release(&obj->refcnt, 1); // key before refcnt
hlist_add_head_rcu(&obj->obj_node, list);
unlock_chain(); // typically a spin_unlock()”…””}”(hhhjÁ  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h Klhj¢  hžhubeh}”(h]”Œinsertion-algorithm”ah ]”h"]”Œ2) insertion algorithm”ah$]”h&]”uh1h´hhçhžhhŸh³h Kbubhµ)”}”(hhh]”(hº)”}”(hŒ3) Removal algorithm”h]”hŒ3) Removal algorithm”…””}”(hjÜ  hjÚ  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj×  hžhhŸh³h KyubhÊ)”}”(hŒ½Nothing special here, we can use a standard RCU hlist deletion.
But thanks to SLAB_TYPESAFE_BY_RCU, beware a deleted object can be reused
very very fast (before the end of RCU grace period)”h]”hŒ½Nothing special here, we can use a standard RCU hlist deletion.
But thanks to SLAB_TYPESAFE_BY_RCU, beware a deleted object can be reused
very very fast (before the end of RCU grace period)”…””}”(hjê  hjè  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h K{hj×  hžhubj  )”}”(hŒÂif (put_last_reference_on(obj) {
  lock_chain(); // typically a spin_lock()
  hlist_del_init_rcu(&obj->obj_node);
  unlock_chain(); // typically a spin_unlock()
  kmem_cache_free(cachep, obj);
}”h]”hŒÂif (put_last_reference_on(obj) {
  lock_chain(); // typically a spin_lock()
  hlist_del_init_rcu(&obj->obj_node);
  unlock_chain(); // typically a spin_unlock()
  kmem_cache_free(cachep, obj);
}”…””}”(hhhjö  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h Khj×  hžhubeh}”(h]”Œremoval-algorithm”ah ]”h"]”Œ3) removal algorithm”ah$]”h&]”uh1h´hhçhžhhŸh³h Kyubeh}”(h]”Œusing-nulls”ah ]”h"]”Œusing 'nulls'”ah$]”h&]”uh1h´hh¶hžhhŸh³h KubhŒ
transition”“”)”}”(hŒJ--------------------------------------------------------------------------”h]”h}”(h]”h ]”h"]”h$]”h&]”uh1j  hŸh³h KŠhh¶hžhubhµ)”}”(hhh]”(hº)”}”(hŒAvoiding extra smp_rmb()”h]”hŒAvoiding extra smp_rmb()”…””}”(hj%  hj#  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj   hžhhŸh³h KubhÊ)”}”(hŒCWith hlist_nulls we can avoid extra smp_rmb() in lockless_lookup().”h]”hŒCWith hlist_nulls we can avoid extra smp_rmb() in lockless_lookup().”…””}”(hj3  hj1  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h Khj   hžhubhÊ)”}”(hXø  For example, if we choose to store the slot number as the 'nulls'
end-of-list marker for each slot of the hash table, we can detect
a race (some writer did a delete and/or a move of an object
to another chain) checking the final 'nulls' value if
the lookup met the end of chain. If final 'nulls' value
is not the slot number, then we must restart the lookup at
the beginning. If the object was moved to the same chain,
then the reader doesn't care: It might occasionally
scan the list again without harm.”h]”hX  For example, if we choose to store the slot number as the â€˜nullsâ€™
end-of-list marker for each slot of the hash table, we can detect
a race (some writer did a delete and/or a move of an object
to another chain) checking the final â€˜nullsâ€™ value if
the lookup met the end of chain. If final â€˜nullsâ€™ value
is not the slot number, then we must restart the lookup at
the beginning. If the object was moved to the same chain,
then the reader doesnâ€™t care: It might occasionally
scan the list again without harm.”…””}”(hjA  hj?  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h K‘hj   hžhubhÊ)”}”(hŒtNote that using hlist_nulls means the type of 'obj_node' field of
'struct object' becomes 'struct hlist_nulls_node'.”h]”hŒ€Note that using hlist_nulls means the type of â€˜obj_nodeâ€™ field of
â€˜struct objectâ€™ becomes â€˜struct hlist_nulls_nodeâ€™.”…””}”(hjO  hjM  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h K›hj   hžhubhµ)”}”(hhh]”(hº)”}”(hŒ1) lookup algorithm”h]”hŒ1) lookup algorithm”…””}”(hj`  hj^  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj[  hžhhŸh³h K ubj  )”}”(hX§  head = &table[slot];
begin:
rcu_read_lock();
hlist_nulls_for_each_entry_rcu(obj, node, head, obj_node) {
  if (obj->key == key) {
    if (!try_get_ref(obj)) { // might fail for free objects
      rcu_read_unlock();
      goto begin;
    }
    if (obj->key != key) { // not the object we expected
      put_ref(obj);
      rcu_read_unlock();
      goto begin;
    }
    goto out;
  }
}

// If the nulls value we got at the end of this lookup is
// not the expected one, we must restart lookup.
// We probably met an item that was moved to another chain.
if (get_nulls_value(node) != slot) {
  put_ref(obj);
  rcu_read_unlock();
  goto begin;
}
obj = NULL;

out:
rcu_read_unlock();”h]”hX§  head = &table[slot];
begin:
rcu_read_lock();
hlist_nulls_for_each_entry_rcu(obj, node, head, obj_node) {
  if (obj->key == key) {
    if (!try_get_ref(obj)) { // might fail for free objects
      rcu_read_unlock();
      goto begin;
    }
    if (obj->key != key) { // not the object we expected
      put_ref(obj);
      rcu_read_unlock();
      goto begin;
    }
    goto out;
  }
}

// If the nulls value we got at the end of this lookup is
// not the expected one, we must restart lookup.
// We probably met an item that was moved to another chain.
if (get_nulls_value(node) != slot) {
  put_ref(obj);
  rcu_read_unlock();
  goto begin;
}
obj = NULL;

out:
rcu_read_unlock();”…””}”(hhhjl  ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h K¤hj[  hžhubeh}”(h]”Œid1”ah ]”h"]”h$]”jŸ  ah&]”uh1h´hj   hžhhŸh³h K j¡  Kubhµ)”}”(hhh]”(hº)”}”(hŒ2) Insert algorithm”h]”hŒ2) Insert algorithm”…””}”(hj†  hj„  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1h¹hj  hžhhŸh³h KÄubhÊ)”}”(hŒ[Same to the above one, but uses hlist_nulls_add_head_rcu() instead of
hlist_add_head_rcu().”h]”hŒ[Same to the above one, but uses hlist_nulls_add_head_rcu() instead of
hlist_add_head_rcu().”…””}”(hj”  hj’  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhŸh³h KÆhj  hžhubj  )”}”(hX•  /*
 * Please note that new inserts are done at the head of list,
 * not in the middle or end.
 */
obj = kmem_cache_alloc(cachep);
lock_chain(); // typically a spin_lock()
obj->key = key;
atomic_set_release(&obj->refcnt, 1); // key before refcnt
/*
 * insert obj in RCU way (readers might be traversing chain)
 */
hlist_nulls_add_head_rcu(&obj->obj_node, list);
unlock_chain(); // typically a spin_unlock()”h]”hX•  /*
 * Please note that new inserts are done at the head of list,
 * not in the middle or end.
 */
obj = kmem_cache_alloc(cachep);
lock_chain(); // typically a spin_lock()
obj->key = key;
atomic_set_release(&obj->refcnt, 1); // key before refcnt
/*
 * insert obj in RCU way (readers might be traversing chain)
 */
hlist_nulls_add_head_rcu(&obj->obj_node, list);
unlock_chain(); // typically a spin_unlock()”…””}”(hhhj   ubah}”(h]”h ]”h"]”h$]”h&]”h±h²uh1j  hŸh³h KËhj  hžhubeh}”(h]”Œinsert-algorithm”ah ]”h"]”Œ2) insert algorithm”ah$]”h&]”uh1h´hj   hžhhŸh³h KÄubeh}”(h]”Œavoiding-extra-smp-rmb”ah ]”h"]”Œavoiding extra smp_rmb()”ah$]”h&]”uh1h´hh¶hžhhŸh³h Kubeh}”(h]”Œ1using-rcu-hlist-nulls-to-protect-list-and-objects”ah ]”h"]”Œ1using rcu hlist_nulls to protect list and objects”ah$]”h&]”uh1h´hhhžhhŸh³h Kubeh}”(h]”h ]”h"]”h$]”h&]”Œsource”h³uh1hŒcurrent_source”NŒcurrent_line”NŒsettings”Œdocutils.frontend”ŒValues”“”)”}”(h¹NŒ	generator”NŒ	datestamp”NŒsource_link”NŒ
source_url”NŒtoc_backlinks”Œentry”Œfootnote_backlinks”KŒsectnum_xform”KŒstrip_comments”NŒstrip_elements_with_classes”NŒstrip_classes”NŒreport_level”KŒ
halt_level”KŒexit_status_level”KŒdebug”NŒwarning_stream”NŒ	traceback”ˆŒinput_encoding”Œ	utf-8-sig”Œinput_encoding_error_handler”Œstrict”Œoutput_encoding”Œutf-8”Œoutput_encoding_error_handler”jé  Œerror_encoding”ŒUTF-8”Œerror_encoding_error_handler”Œbackslashreplace”Œlanguage_code”Œen”Œrecord_dependencies”NŒconfig”NŒ	id_prefix”hŒauto_id_prefix”Œid”Œdump_settings”NŒdump_internals”NŒdump_transforms”NŒdump_pseudo_xml”NŒexpose_internals”NŒstrict_visitor”NŒ_disable_config”NŒ_source”h³Œ_destination”NŒ_config_files”]”Œ7/var/lib/git/docbuild/linux/Documentation/docutils.conf”aŒpep_references”NŒpep_base_url”Œhttps://peps.python.org/”Œpep_file_url_template”Œpep-%04d”Œrfc_references”NŒrfc_base_url”Œ&https://datatracker.ietf.org/doc/html/”Œ	tab_width”KŒtrim_footnote_reference_space”‰Œfile_insertion_enabled”ˆŒraw_enabled”KŒline_length_limit”M'Œsyntax_highlight”Œlong”Œsmart_quotes”ˆŒsmartquotes_locales”]”Œcharacter_level_inline_markup”‰Œdoctitle_xform”‰Œdocinfo_xform”KŒsectsubtitle_xform”‰Œimage_loading”Œlink”Œembed_stylesheet”‰Œcloak_email_addresses”ˆŒsection_self_link”‰Œembed_images”‰Œenv”NubŒreporter”NŒindirect_targets”]”Œsubstitution_defs”}”Œsubstitution_names”}”Œrefnames”}”Œrefids”}”Œnameids”}”(jÃ  jÀ  j  j  Œ1) lookup algorithm”NjÔ  jÑ  j	  j  j»  j¸  j³  j°  uŒ	nametypes”}”(jÃ  Nj  Nj.  NjÔ  Nj	  Nj»  Nj³  Nuh}”(jÀ  h¶j  hçj›  j$  jÑ  j¢  j  j×  j¸  j   j|  j[  j°  j  uŒfootnote_refs”}”Œcitation_refs”}”Œautofootnotes”]”Œautofootnote_refs”]”Œsymbol_footnotes”]”Œsymbol_footnote_refs”]”Œ	footnotes”]”Œ	citations”]”Œautofootnote_start”KŒsymbol_footnote_start”K Œ
id_counter”Œcollections”ŒCounter”“”}”j÷  Ks…”R”Œparse_messages”]”hŒsystem_message”“”)”}”(hhh]”hÊ)”}”(hŒ6Duplicate implicit target name: "1) lookup algorithm".”h]”hŒ:Duplicate implicit target name: â€œ1) lookup algorithmâ€.”…””}”(hhhjR  hžhhŸNh Nubah}”(h]”h ]”h"]”h$]”h&]”uh1hÉhjO  ubah}”(h]”h ]”h"]”h$]”h&]”j|  aŒlevel”KŒtype”ŒINFO”Œsource”h³Œline”K uh1jM  hj[  hžhhŸh³h K ubaŒtransform_messages”]”Œtransformer”NŒinclude_log”]”Œ
decoration”Nhžhub.